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  • brannenworks
    ... Tk, tunneling occurs when a particle is able to penetrate a region where it does not have enough classical energy to be present in. Bohmian mechanics
    Message 1 of 23 , Feb 13, 2004
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      --- In bell_bohm@yahoogroups.com, "Tom" <tkuntzle@u...> wrote:
      > Hi
      >
      > I am an amatuer who would like to know, qualitatively, how Bohmian
      > mechanics describes tunneling. Further, what is the mechanism of
      > radioactive decay as described by Bohm's theory?
      >
      > tk

      Tk, tunneling occurs when a particle is able to penetrate a region
      where it does not have enough classical energy to be present in.
      Bohmian mechanics differs from the usual quantum mechanics in that
      it includes the addition of a "quantum potential". The quantum
      potential accounts for the odd trajectories of particles.

      The Bohmian point of view holds that particles follow connected
      trajectories, so there must be a trajectory that starts at one side
      of the potential barrier and ends up on the other. On the other
      hand, most particles do not make it over the barrier, instead they
      are reflected.

      So what happens, from a Bohmian point of view, is that if you send a
      stream of particles towards the barrier, some of them make it
      through and some are reflected. As with the two-slit experiment,
      which stream the particle ends up in is determined by which part of
      the stream it started in.

      Effectively, in the Bohmian viewpoint, the theoretically solid
      potential barrier has to be replaced with a barrier that has heights
      that differ over time. In other words, it's impossible to make a
      barrier that always has exactly the same height. You can look at
      this as just a consequence of the Heisenberg uncertainty principle
      for the product of energy and time.

      From the Bohmian point of view, it would be possible to predict
      whether a particular particle was going to make it over the barrier
      or not, if you happened to know ALL the details about its position
      and its wave function (or quantum potential, more or less). That we
      can't do this is due to the fact that our fingers are clumsy, and
      whenever we try to measure precisely something small we modify its
      motion or position.

      I hope that this is explanation is accurate and satisfying. My own
      view is that Bohmian mechanics is the right direction, but I differ
      with it on the interpretation of wave particle duality. From my
      point of view, the wave function and the particle itself do not
      appear at the same time. Before the particle makes its flight, its
      future trajectory choices are defined by the wave function. But the
      particle itself eventually chooses only one of those trajectories.

      If you hang around waiting for an electron to be emitted in a
      radioactive decay, at first the wave function is spherical. That
      is, the electron can go any direction with equal probability.
      Eventually the neutron starts decaying, and the electron appears.
      As the electron chooses a direction to go in, the wave function
      collapses and concentrates towards that direction. As the electron
      continues to move in that direction, the wave function continues to
      collapse. Eventually the electron passes your detector, and by that
      time its wave function has fully collapsed.

      By contrast, the Bohmian interpretation is that the wave function
      never collapses, it exists through all time, but only as a guide for
      the electron. I reject this for ontological reasons.

      The problem with my version is that if you make my assumptions, you
      have to conclude that time is very complicated. I should explain.
      According to the version of wave function and particle I've
      described above, it's surprising that the electron is able to
      interfere with itself. Self interference suggests that the electron
      wave function has to have lost track of exactly which of the
      possible interfering paths the particle really will choose to get to
      a particular spot. My conclusion is that time is not an arrow, but
      is instead more like a shower of arrows.

      A better explanation for my version of Bohmian mechanics is to cast
      the problem as a quantum field theory problem. This is probably
      beyond the scope of this discussion:

      If you look at the quantum field theory (QFT) description of the
      movement of an electon from a Bohmian point of view, the creation
      and annihilation operators (in the coordinate representation)
      correspond to points where the particle momentarily exists, while
      the wave functions (i.e. propagators) correspond to possible
      movements of the electron to its next existence point. The particle
      only exists for instants of time. So its path, instead of being a
      smooth trajectory as in standard Bohmian mechanics, becomes a
      sequence of points. (It turns out that at each of these points the
      particle must be described by a mathematical object that defines a
      velocity and rotation, but that's way beyond this discussion.)

      So in my version of QFT BM, interference is due to time being multi
      valued. That is, in this version, the particle exists in multiple
      versions that interfere with each other. Any one particular version
      of the electron moves (propagates) from its creation vertex to its
      annihilation vertex. In standard QFT, vertices correspond to where
      an electron might emit or absorb a photon, but the same mathematical
      treatment also allows vertices where the electron is annihilated,
      while another electron is created in its place.

      The creation corresponds to the creation of a wave function, the
      annihilation corresponds to the collapse of a wave function. But
      this is not to say that the annihilation operators in QFT are the
      wave function collapse of standard quantum mechanics. This would be
      impossible because it would correspond to wave function collapse at
      way too high a rate. Instead, I suppose that as time goes by, the
      collection of different copies of the same electron is reduced,
      eventually leaving just one wave function collapse as the true one
      (i.e. the one that becomes a part of the history of the world).

      CAB
    • David Strayhorn
      ... Hey Carl, It sounds like what you are describing here is akin to multiple worlds -- that is, when you say that time is multi valued , this could be
      Message 2 of 23 , Feb 14, 2004
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        --- In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
        wrote:

        > So in my version of QFT BM, interference is due to time being multi
        > valued. That is, in this version, the particle exists in multiple
        > versions that interfere with each other. Any one particular version
        > of the electron moves (propagates) from its creation vertex to its
        > annihilation vertex.

        Hey Carl,

        It sounds like what you are describing here is akin to multiple worlds -- that is,
        when you say that time is "multi valued", this could be interpreted such that
        there are multiple worlds, and each individual world has its own time variable,
        and that is why you call time "multi valued" .... does this make sense from your
        PoV? ie, can you translate your "multiple versions" of the particle into the
        multiple worlds framework [1]?

        straycat

        [1] FAQ on the multiple worlds interpretation (aka the Everett interpretation):
        http://www.hedweb.com/manworld.htm
      • brannenworks
        Dear David Strayhorn; From my point of view, the best argument for MWI is to note that photons do (as far as I know) exhibit interference even between paths
        Message 3 of 23 , Feb 15, 2004
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          Dear David Strayhorn; From my point of view, the best argument for
          MWI is to note that photons do (as far as I know) exhibit
          interference even between paths that are separated by millions of
          light years, as when a distant galaxy is multiply imaged due to
          galactic lensing.

          From that effect, it's natural to conclude that there are different
          worlds, one where the photon went through the lens one way, another
          where it went through the other (and infinite other choices).

          But the conclusion is due to an assumption of how time works. That
          is, the MWI is based on the inherent assumption that time works in a
          linear, single-valued fashion. Another way of putting it is to say
          that the inherent assumption is to believe that the universe can be
          described in the form of a motion picture. That is, if you believe
          that the full state of the universe exists from moment to moment,
          you naturally also have to believe that there are multiple worlds to
          allow the interference to work.

          Where I take issue with this is in what I think is its observer
          centered notion of how time works. From my point of view, what we
          really know about time is that for any given particle, things happen
          in order. That is, time defines an ordering for the sequence of
          things that happen to a particle. This is also compatible with what
          we see as beings contemplating the universe, which is why I
          say "observer centered". But just because the universe appears to
          have a time ordering for any given particle (if you assume a
          particular reference frame), or for any given observer, this does
          not prove that the universe as a whole also possesses a time
          ordering. It's a pretty good place to start, but it isn't proof,
          and there are indications that time is more complicated than that.
          For example, the interpretation of positrons as electrons travelling
          backwards in time is contrary to the naive notion of how time works.

          Let me try and argue it this way: Einstein already proved that time
          ordering is relative, that is, that there is no way of determining
          the time ordering of space-like separated events. A good percentage
          of your typical QFT textbook is devoted to proving that QFT, despite
          having influences that exceed the speed of light, nevertheless is
          compatible with relativity in that no signal can propagate faster
          than light, and therefore that causality is preserved.

          But if you carefully examine these proofs, you will notice that what
          is proved is that causality is not violated for the results
          of "observations". That is, after the wave function has collapsed
          (or whatever you want to call a measurement), the result will
          satisfy causality. They do not show that the wave function itself
          satisfies causality because wave functions themselves very
          explicitly do not.

          My conclusion is that the universe is a collection of particles,
          each one of which has an ordered time sequence (created, then
          annihilated), but the universe itself does not have any such ordered
          time sequence. For multiple particle situations, you can put a time
          ordering on it, but only to the extent that creation precedes
          annihilation. This is at least subtly different from MWI.

          Here's my critique of their tenets (from your link):

          <<<
          1) The metaphysical assumption: That the wavefunction does not
          merely encode the all the information about an object, but has an
          observer-independent objective existence and actually is the object.
          For a non-relativistic N-particle system the wavefunction is a
          complex-valued field in a 3-N dimensional space.
          >>>

          I hold that the wave function does not encode all the possible
          information about an object, just what we can tell prior to running
          the experiment. In this I agree with Bohmian mechanics. I also
          differ from MWI (and maybe Bohmian too) in the assumption that the
          objective existence is formed of a "complex-valued field in a 3-N
          dimensional space." My interpretation is that this field is only
          the result we get when we force the situation into an either-or kind
          of linear sequence of operations (if you know QFT, think of the time
          ordering operator, especially in the rest of this explanation).

          From my point of view, the requirement that the base space be 3-N
          dimensional only appears when the theory has been made into what the
          QFT theorists call an "effective" theory. In other words, I believe
          that there is an underlying theory which is only 3-dimensional (at
          least as far as x, y, and z are concerned, but that's another
          story). When that underlying theory is renormalized, you get the
          standard QFT, which then requires time ordering.

          As an illustration of this effect of renormalization, look at the
          simple renormalization that takes a bare single particle propagator,
          and absorbs all the self energy terms into it, to create the
          observed single particle propagator (sometimes called "exact"
          propagator). Any single Feynmann diagram that goes into the
          observed single particle propagator implies a sequence of specific
          actions to the particle, that is, a history or time ordering. This
          fact implies that the observed single particle propagators have a
          built-in time ordering. (Note the assumption of a Bohmian view on
          particles in this argument.)

          The single particle propagators in QFT correspond in quantum theory
          to the Dirac equation (or KG or whatever), they're just the Green's
          functions for the given wave function. So from QFT, it is clear
          that quantum mechanics must be careful about time ordering. This is
          why the description of an N-body scenario, in standard quantum
          mechanics, requires a 3-N dimensional space, at least in my opinion.

          But if you look at the problem from the point of view of the bare
          QFT theory, that is one which is not an effective field theory for
          some other, underlying field, then I believe that there will be no
          need for time ordering, so an N-body scenario can be described in
          terms of a field on the usual 3 dimensions (more or less). What I'm
          saying here is that renormalization automatically causes a necessity
          for time ordering. This is a clue that the unrenormalized bare
          field theory will not have that requirement. And I think that is
          more natural from an ontological point of view. Otherwise the
          universe ends up with way too many dimensions.

          Let me try and explain this another way. If you take a bath and
          make waves in your (classical) bathtub, you can describe the
          situation at any given time with a field on 3 dimensions only.
          Where wave mechanics becomes complicated is when it is
          renormalized. The action of renormalization is to hide a bunch of
          wave function collapses into an overall wave effect. But those wave
          function collapses (i.e. the annihilators of QFT) have to be
          correctly time ordered.

          Another way of explaining this. In Quantum mechanics, we do two
          distinct operations when combining two wave functions. If we are
          creating a new wave function for a single particle we use addition
          (i.e. the law of linear superposition). If we are creating a two
          particle wave function, we use multiplication, with symmetrization.
          It would appear that these two operations are so distinct that they
          cannot be reconciled. Here's a simple technique for reconciling
          these differences:

          Since mass appears to be a renormalization effect, take a good look
          at the massless Dirac equation (i.e. the Weyl equation). Note that
          weak forces apparently couple to this version, so it's a pretty good
          bet that the fundamental base field theory is massless (and chiral,
          but that's another story). Suppose that Psi(x,t) is a solution to
          this massless equation. Then exp(Psi(x,t)) is also a solution. Try
          this if you don't believe it, it's very easy.

          Because of this fact, (along with some other reasoning having to do
          with geometrical algebra and spinors) I believe that the base field
          theory is connected to the standard QFT through an exponential
          mapping. Under this assumption, the true linear superposition for
          waves corresponds not to the usual linear (additive) superposition
          of quantum mechanics, but instead corresponds to the multiplicative
          techniques for multi-particle states. The usual linear
          superposition seen in standard quantum mechanics, in this view, is
          actually only a result of the result of renormalization.

          That is, the usual additive linear superposition is the result of
          the fact that the Feynmann path integral formalism uses addition
          over the paths. Ever notice that the Feynmann path formalism puts
          equal weight to all paths? This is awfully suspicious, as
          statistical mechanics generally weights things according to an
          exponential map of the energy. (Anyone reading this who finds this
          unfamiliar should pick up a statistical mechanics book and look in
          the index for "canonical ensemble"). This means that if you
          rederive the Feynmann path integral formalism with an assumption
          that the Dirac equation gives logarithms of probabilities instead of
          square roots of probabilities, you will get to use the usual
          exponential weighting already familiar to us in statistical
          mechanics. But if you look at the FPI from the usual point of view,
          the wave functions have already been scaled according to
          probability, so you naturally do it with an assumption of equal
          weight.


          <<<
          2) The physical assumption: The wavefunction obeys the empirically
          derived standard linear deterministic wave equations at all times.
          The observer plays no special role in the theory and, consequently,
          there is no collapse of the wavefunction. For non-relativistic
          systems the Schrodinger wave equation is a good approximation to
          reality. (See "Is many-worlds a relativistic theory?" for how the
          more general case is handled with quantum field theory or third
          quantisation.)
          >>>

          I, for one, know that I am an observer. For anyone who doubts that
          they are an observer, and who believes that they are just an
          unimportant collection of atoms, I can provide them with an
          unpleasant experience that will convince them otherwise. And of
          course everyone agrees that the Schroedinger wave equation is pretty
          accurate.

          CAB
        • Jim Whitescarver
          ... The idea that photons interfere with themselves on light paths that may be light years different in length is contradicted by the simple fact that photons
          Message 4 of 23 , Feb 15, 2004
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            > Dear David Strayhorn; From my point of view, the best argument for MWI
            > is to note that photons do (as far as I know) exhibit
            > interference even between paths that are separated by millions of
            > light years, as when a distant galaxy is multiply imaged due to
            > galactic lensing.


            The idea that photons interfere with themselves on light paths that may be
            light years different in length is contradicted by the simple fact that
            photons do not interfere with one another and the light speed violation
            involved.

            Quantum theory tells us about probabilistic behavior. If it is proven
            that single electrons will exhibit such interference it would suggest that
            the paths contribute to a space time path structure which constrain
            propagation through spacetime. The self-interference conclusion is
            implied no more than that light follows resonant paths.

            >>From that effect, it's natural to conclude that there are different
            > worlds, one where the photon went through the lens one way, another
            > where it went through the other (and infinite other choices).


            That won't work if one path is five light years longer.



            > But the conclusion is due to an assumption of how time works.
            > That is, the MWI is based on the inherent assumption that time works
            > in a linear, single-valued fashion.& Another way of putting it is
            > to say that the inherent assumption is to believe that the universe
            > can be described in the form of a motion picture. That is, if
            > you believe that the full state of the universe exists from moment to
            > moment, you naturally also have to believe that there are multiple
            > worlds to allow the interference to work.

            I think it is clear there is no absolute time frame.
            >
            > Where I take issue with this is in what I think is its observer
            > centered notion of how time works. From my point of view, what we
            > really know about time is that for any given particle, things happen
            > in order. That is, time defines an ordering for the sequence of
            > things that happen to a particle. This is also compatible with
            > what we see as beings contemplating the universe, which is why I
            > say "observer centered";. But just because the universe
            > appears to have a time ordering for any given particle (if you assume
            > a > particular reference frame), or for any given observer, this does not
            > prove that the universe as a whole also possesses a time
            > ordering. It's a pretty good place to start, but it isn't proof,
            > and there are indications that time is more complicated than
            > that. For example, the interpretation of positrons as electrons
            > travelling backwards in time is contrary to the naive notion of how
            > time works.

            Yes and no. You have established that everything is a clock in that it
            manifests a dimension or ordering in time. But an energy exchange lacks
            an absolute direction in time. Relatively speaking each participant sees
            the energy going from higher relative energy to lower relative energy such
            that the future cones of two participants can disagree on which way the
            photon went. But these disagreements or disorderings of time are limited
            to light speed. They are the manifestation of space like orderings rather
            than time like orderings. Absolute time orderings are experienced by each
            participant and no observer can witness any clocks going backwards since
            the preceding event is gone by the time the succeeding event is manifest
            {a delay would involve another event). The reversible of events stops
            when an event is perceived by a participant manifesting a tick of the
            cosmic event clock.

            Exactly two independent perspectives on the event are propagated to the
            exclusion of all others. It is possible both participants see a gain or
            loss of energy or agree on the transfer direction.

            > Let me try and argue it this way: Einstein already proved that
            > time ordering is relative, that is, that there is no way of
            > determining the time ordering of space-like separated events. A
            > good percentage of your typical QFT textbook is devoted to proving
            > that QFT, despite having influences that exceed the speed of light,
            correlation does not imply influences
            > nevertheless is compatible with relativity in that no signal can
            > propagate faster than light, and therefore that causality is
            > preserved.
            exactly.
            >
            > But if you carefully examine these proofs, you will notice that what
            > is proved is that causality is not violated for the results
            > of "observations". That is, after the wave function has
            > collapsed (or whatever you want to call a measurement), the result
            > will
            > satisfy causality. They do not show that the wave function itself
            > satisfies causality because wave functions themselves very
            > explicitly do not.
            the wave function is only probabilities.
            >
            > My conclusion is that the universe is a collection of particles,
            > each one of which has an ordered time sequence (created, then
            > annihilated), but the universe itself does not have any such ordered
            > time sequence. For multiple particle situations, you can put a
            > time ordering on it, but only to the extent that creation precedes
            > annihilation. This is at least subtly different from MWI.


            Only the now exists fleetingly. It includes ordering in space and time
            depending on time independence (distance) and relative motion, but events
            involve exactly two participants advancing both their time in exactly one
            direction by one event. Events have no preexistence or post existence.

            > Here's my critique of their tenets (from your link):
            >
            >
            > 1) The metaphysical assumption: That the wavefunction does not
            > merely encode the all the information about an object, but has an
            > observer-independent objective existence and actually is the object.


            Objectivity must be defined with respect to all communicating
            participants. Perspectives that have no participant making that
            particular measurement are not manifest while those perspective having a
            participant which manifests that perspective may. Each perception
            precludes all alternate perceptions.

            > For a non-relativistic N-particle system the wavefunction is a
            > complex-valued field in a 3-N dimensional space.


            This agrees with your assertion that every participant manifests a time
            ordering.>
            > I hold that the wave function does not encode all the possible
            > information about an object, just what we can tell prior to running
            > the experiment. In this I agree with Bohmian mechanics. I
            > also differ from MWI (and maybe Bohmian too) in the assumption that
            > the objective existence is formed of a "complex-valued field in a
            > 3-N dimensional space". My interpretation is that this
            > field is only the result we get when we force the situation into an
            > either-or kind of linear sequence of operations (if you know QFT,
            > think of the time ordering operator, especially in the rest of this
            > explanation).
            What time ordering operator? There is none. The evolution of the field?
            >
            >>From my point of view, the requirement that the base space be 3-N
            > dimensional only appears when the theory has been made into what the
            > QFT theorists call an "effective" theory. In other
            > words, I believe that there is an underlying theory which is only
            > 3-dimensional (at least as far as x, y, and z are concerned, but
            > that's another
            > story). When that underlying theory is renormalized, you get the
            > standard QFT, which then requires time ordering.
            ok
            >
            > As an illustration of this effect of renormalization, look at the
            > simple renormalization that takes a bare single particle propagator,
            > and absorbs all the self energy terms into it, to create the
            > observed single particle propagator (sometimes called "exact"
            > propagator). Any single Feynmann diagram that goes into the
            > observed single particle propagator implies a sequence of specific
            > actions to the particle, that is, a history or time ordering.
            > This fact implies that the observed single particle propagators have a
            > built-in time ordering. (Note the assumption of a Bohmian view
            > on particles in this argument.)
            ok
            >
            > The single particle propagators in QFT correspond in quantum theory to
            > the Dirac equation (or KG or whatever), they're just the Green's
            > functions for the given wave function.  So from QFT, it is clear
            > that quantum mechanics must be careful about time ordering. This
            > is why the description of an N-body scenario, in standard quantum
            > mechanics, requires a 3-N dimensional space, at least in my opinion.
            >
            > But if you look at the problem from the point of view of the bare QFT
            > theory, that is one which is not an effective field theory for some
            > other, underlying field, then I believe that there will be no need for
            > time ordering, so an N-body scenario can be described in terms of a
            > field on the usual 3 dimensions (more or less). What I'm saying
            > here is that renormalization automatically causes a necessity for time
            > ordering. This is a clue that the unrenormalized bare field
            > theory will not have that requirement. And I think that is more
            > natural from an ontological point of view.


            Renormalization formally removes all the infinities, it removes all self
            reference, and removes all time. Existence is by indirect self reference
            in a participatory universe. Nothing can be said to have existed unless
            it is propagated through time. Time only emerges from incomplete
            renormalization in participatory existence.

            > Otherwise the
            > universe ends up with way too many dimensions.


            Two dimensional signals across time can only paint 3 dimensions. That
            each participant manifests an independent time ordering or dimension can
            be the root of all the dimensions we perceive. Rather than needing extra
            dimensions of differing nature, the independent time dimensions are
            sufficient to account for experience.

            > Let me try and explain this another way. If you take a bath and
            > make waves in your (classical) bathtub, you can describe the
            > situation at any given time with a field on 3 dimensions only. 
            > Where wave mechanics becomes complicated is when it is
            > renormalized. The action of renormalization is to hide a bunch of
            > wave function collapses into an overall wave effect. But those
            > wave function collapses (i.e. the annihilators of QFT) have to be
            > correctly time ordered.


            You get discrete events but that's not where the time ordering comes from,
            I don't think. You get time ordering because Gauge theories impose a time
            perspective in their formulation.

            > Another way of explaining this. In Quantum mechanics, we do two
            > distinct operations when combining two wave functions. If we are
            > creating a new wave function for a single particle we use addition
            > (i.e. the law of linear superposition). If we are creating a two
            > particle wave function, we use multiplication, with
            > symmetrization. It would appear that these two operations are so
            > distinct that they cannot be reconciled. Here's a simple
            > technique for reconciling these differences:
            >
            > Since mass appears to be a renormalization effect, take a good look at
            > the massless Dirac equation (i.e. the Weyl equation).  Note that
            > weak forces apparently couple to this version, so it's a pretty good
            > bet that the fundamental base field theory is massless (and chiral,
            > but that's another story). Suppose that Psi(x,t) is a solution to
            > this massless equation.  Then exp(Psi(x,t)) is also a
            > solution. Try this if you don't believe it, it's very easy.


            This is not a renormalization effect. Mass/energy, time/space are imposed
            by perspective. They are inherent in the gage theory not due to
            renormalization.

            > Because of this fact, (along with some other reasoning having to do
            > with geometrical algebra and spinors) I believe that the base field
            > theory is connected to the standard QFT through an exponential
            > mapping. Under this assumption, the true linear superposition for
            > waves corresponds not to the usual linear (additive) superposition of
            > quantum mechanics, but instead corresponds to the multiplicative
            > techniques for multi-particle states.  The usual linear
            > superposition seen in standard quantum mechanics, in this view, is
            > actually only a result of the result of renormalization.


            Perspectives grow exponentially with the number of participants.
            Fortunately the number of participants does not increase too often.

            > That is, the usual additive linear superposition is the result of the
            > fact that the Feynmann path integral formalism uses addition
            > over the paths. Ever notice that the Feynmann path formalism puts
            > equal weight to all paths? This is awfully suspicious, as
            > statistical mechanics generally weights things according to an
            > exponential map of the energy.  (Anyone reading this who finds
            > this unfamiliar should pick up a statistical mechanics book and look
            > in the index for "canonical ensemble"). This means
            > that if you rederive the Feynmann path integral formalism with an
            > assumption
            > that the Dirac equation gives logarithms of probabilities instead of
            > square roots of probabilities, you will get to use the usual
            > exponential weighting already familiar to us in statistical
            > mechanics, But if you look at the FPI from the usual point of
            > view, the wave functions have already been scaled according to
            > probability, so you naturally do it with an assumption of equal
            > weight.
            >
            >
            >
            > 2) The physical assumption: The wavefunction obeys the empirically
            > derived standard linear deterministic wave equations at all times. The
            > observer plays no special role in the theory and, consequently, there
            > is no collapse of the wavefunction. For non-relativistic
            > systems the Schrodinger wave equation is a good approximation to
            > reality. (See "Is many-worlds a relativistic theory?" for how
            > the more general case is handled with quantum field theory or third
            > quantisation.)
            >
            >
            > I, for one, know that I am an observer. For anyone who doubts
            > that they are an observer, and who believes that they are just an
            > unimportant collection of atoms, I can provide them with an
            > unpleasant experience that will convince them otherwise. And of
            > course everyone agrees that the Schroedinger wave equation is pretty
            > accurate.


            The many world theory attempts to account for the failure of QM to predict
            the wave collapse by asserting that there is none. This is contrary to
            experience. Shit happens.

            Your view of renormalization is not unlike some others I have heard
            suggesting that it somehow imposes perspective in time or whatever. This
            is very different from what I learned in school and the interpretations I
            have read by the masters. Am I missing something?

            Jim
            >
            > CAB
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          • brannenworks
            ... This is a thought experiment only, and is an interference between a single photon and itself. To make it work in the real world, you d have to have the
            Message 5 of 23 , Feb 15, 2004
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              Dear Jim Whitescarver:

              > The idea that photons interfere with
              > themselves on light paths that may be
              > light years different in length is
              > contradicted by the simple fact that
              > photons do not interfere with one
              > another and the light speed violation
              > involved.

              This is a thought experiment only, and is an interference between a
              single photon and itself. To make it work in the real world, you'd
              have to have the two interfering legs very close to equal in
              length. But under that assumption, the standard view of physics is
              that there will be interference. Also, different photons do
              interfere. Normally one can't see the effect because there is no
              correlation between two photons. To get the interference effect
              between two completely different photons, you can use two similar
              lasers to produce the photons. Unless you control the phase
              relationship between the two lasers you will be unable to predict
              the particular interference pattern, but it is there.

              > Absolute time orderings are experienced
              > by each participant and no observer can
              > witness any clocks going backwards since
              > the preceding event is gone by the time
              > the succeeding event is manifest
              > {a delay would involve another event).

              I'm not sure what you're getting at here, so I'm going to more fully
              describe the problem with time ordering in electrons and positrons.
              In the case of QED, it is possible for an electron to propagate over
              a space-like interval. (The probability is small, but it can
              happen. Similarly, light can travel faster or slower than c. This
              happens when the particles are not on their mass shell.) In such a
              case, there are some reference frames where the situation will be
              seen as an electron traveling, for example, East, and other
              reference frames where the same situation will be interpreted as a
              positron travelling West. The important note here is that observers
              cannot always agree on the time ordering of events that correspond
              to consecutive positions of the same particle.

              > Renormalization formally removes
              > all the infinities, it removes all self
              > reference, and removes all time.

              Yes, this is the standard objective of renormalization, and is in
              all the textbooks. What I am studying, instead, are the accidental
              side effects of renormalization. A trivial example is that you can
              use renormalize a massless theory to get one with mass (see the
              paper on this later in this post). I'm working on showing that the
              color force is correlated to the usual spatial coordinates, but that
              this correlation disappears essentially as a result of a
              renormalization. This has applications in explaining the anomalous
              cosmic ray "Centauro" events. I guess I should mention that there
              is a QFT theorem that says that if you mix the internal quantum
              states with spatial coordinates (as I've suggested above), then
              Lorentz symmetry cannot be perfect.

              > You get discrete events but that's not
              > where the time ordering comes from,
              > I don't think. You get time ordering
              > because Gauge theories impose a time
              > perspective in their formulation.

              My view on the gauge theories is that they're due to all the forces
              of nature being associated, at the bare level, with a single force
              that is not internal, but is instead correlated to the usual spatial
              dimensions in a manner similar to spin. As support for this, I
              should note that spin is pretty much the only observable of quantum
              mechanics that is not adjusted by renormalization. This suggests
              that spin allows us to peek beneath the renormalization haze and see
              the bare nature of a particle. And since spin is correlated with
              spatial coordinates, the natural conclusion is that the other
              particle interactions are also spatial in nature, at least before
              renormalization.

              Let me explain how spin comes from the gauge principle, since I've
              not seen the obvious argument anywhere else. The universe is
              symmetric with respect to Lorentz transformations, at least to some
              high degree of accuracy. This is a global symmetry. Following the
              gauge prescription, one wishes to promote this global symmetry to a
              local symmetry. This means that we will have to define a Lorentz
              transformation at each point of space-time. But a spinor is a
              Lorentz transformation, and so a wave function is nothing more than
              a field of Lorentz transformations, or the result of the usual gauge
              principle applied to the Lorentz symmetry. So if all particle
              interactions are modeled after the spin interaction, it's only
              natural that the gauge principle works.

              > The many world theory attempts to
              > account for the failure of QM to predict
              > the wave collapse by asserting that
              > there is none. This is contrary to
              > experience. Shit happens.

              I agree, at the very least from a philosophical point of view. But
              there is a place where wave function collapse is supposed to be
              visible. It's called the quantum zeno effect (QZE), and it's one of
              the most interesting effects in physics.

              > Your view of renormalization is not
              > unlike some others I have heard
              > suggesting that it somehow imposes
              > perspective in time or whatever. This
              > is very different from what I learned
              > in school and the interpretations I
              > have read by the masters. Am I missing
              > something?

              When I was in grad school I never had time to think about elementary
              particle physics from a theoretical point of view. The primary
              thing we were taught was how to crank out predictions of particle
              experiments. No one ever mentioned anything about the Bohmian
              interpretation, or the QZE, but they did talk about the Aharanov
              Bohm effect. I can't recall any mention of the Lorentzian
              interpretation of special and general relativity (which I don't
              believe is mentioned in Misner, Thorne and Wheeler, but that wasn't
              the text we used), but there was mention of the Kaluza-Klein
              derivation of E&M. We were very busy, the big thing was to pass the
              qualifier exam. After that, you concentrated on a dissertation. So
              there was never any chance of learning alternative perspectives on
              particle theory.

              As far as how I am interpreting things, I believe it is unusual, but
              I'm not completely lost out in the woods. For example, I've never
              seen anyone look at the creation and annihilation operators as
              examples of a sort of wave function collapse, but I really can't see
              how they can be seen otherwise. All I'm doing is giving a literal
              interpretation to the mathematics. Probably the reason for the
              hesitancy is the fact that the creation and annihilation operators
              can be described in different representations (like coordinate or
              momentum). Like the boy who finds a ton of BS under the christmas
              tree, the fact that there are lots of different representations
              doesn't worry me, so long as one of them is the ontological truth.
              The Galilean preferred reference frame had the same problem, as does
              the Lorentzian interpretation of relativity.

              I first saw the topological effects of renormalization on mass
              hinted at in a book for the popular audience by Feynman, not in grad
              school. The calculation is shown on pages 4 and 5 of this paper,
              which references the Feynman book:
              http://www.oberlin.edu/physics/dstyer/StrangeQM/Klein-Gordon.pdf

              That light (and electrons) can travel faster than light is mentioned
              in many QFT textbooks, for example Peskin & Schroeder, and I think
              it's also mentioned in the above Feynman book. As soon as you have
              faster than light propagation there is a problem in interpretation
              of causality, so the textbooks then go to great lengths to show that
              the problem doesn't leak into the observables.

              CAB
            • lady ganesha
              What this theory of time points to is Plato s notion of the numinous world that preceeds the phenomenal (measurable, three dimensional, sensate, tactile)
              Message 6 of 23 , Feb 16, 2004
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                What this theory of time points to is Plato's notion of the numinous world that preceeds the phenomenal (measurable, three dimensional, sensate, tactile) world. In other words, if consciousness is the root of all matter, then time is the ordering of consciousness and time itself carries with it fundamental characteristics (called archetypes). Therefore, if you look at quantum fields, they are 'intelligent' in that they have 'primary' qualities that tend to manifest themselves, by virtue of the creative nature of consciousness itself, as 'space-time' units. Plato called this the numinous world which gives rise to the myriad diversity of the phenomenold world.
                 
                As earnest as science is to keep philosphy out of its house, I think we are seeing an inevitable collision if science wants to go on to the next level of evolution.
                LG

                brannenworks <brannenworks@...> wrote:
                Dear David Strayhorn; From my point of view, the best argument for
                MWI is to note that photons do (as far as I know) exhibit
                interference even between paths that are separated by millions of
                light years, as when a distant galaxy is multiply imaged due to
                galactic lensing.

                From that effect, it's natural to conclude that there are different
                worlds, one where the photon went through the lens one way, another
                where it went through the other (and infinite other choices).

                But the conclusion is due to an assumption of how time works.  That
                is, the MWI is based on the inherent assumption that time works in a
                linear, single-valued fashion.  Another way of putting it is to say
                that the inherent assumption is to believe that the universe can be
                described in the form of a motion picture.  That is, if you believe
                that the full state of the universe exists from moment to moment,
                you naturally also have to believe that there are multiple worlds to
                allow the interference to work.

                Where I take issue with this is in what I think is its observer
                centered notion of how time works.  From my point of view, what we
                really know about time is that for any given particle, things happen
                in order.  That is, time defines an ordering for the sequence of
                things that happen to a particle.  This is also compatible with what
                we see as beings contemplating the universe, which is why I
                say "observer centered".  But just because the universe appears to
                have a time ordering for any given particle (if you assume a
                particular reference frame), or for any given observer, this does
                not prove that the universe as a whole also possesses a time
                ordering.  It's a pretty good place to start, but it isn't proof,
                and there are indications that time is more complicated than that. 
                For example, the interpretation of positrons as electrons travelling
                backwards in time is contrary to the naive notion of how time works.

                Let me try and argue it this way:  Einstein already proved that time
                ordering is relative, that is, that there is no way of determining
                the time ordering of space-like separated events.  A good percentage
                of your typical QFT textbook is devoted to proving that QFT, despite
                having influences that exceed the speed of light, nevertheless is
                compatible with relativity in that no signal can propagate faster
                than light, and therefore that causality is preserved.

                But if you carefully examine these proofs, you will notice that what
                is proved is that causality is not violated for the results
                of "observations".  That is, after the wave function has collapsed
                (or whatever you want to call a measurement), the result will
                satisfy causality.  They do not show that the wave function itself
                satisfies causality because wave functions themselves very
                explicitly do not.

                My conclusion is that the universe is a collection of particles,
                each one of which has an ordered time sequence (created, then
                annihilated), but the universe itself does not have any such ordered
                time sequence.  For multiple particle situations, you can put a time
                ordering on it, but only to the extent that creation precedes
                annihilation.  This is at least subtly different from MWI.

                Here's my critique of their tenets (from your link):

                <<<
                1) The metaphysical assumption: That the wavefunction does not
                merely encode the all the information about an object, but has an
                observer-independent objective existence and actually is the object.
                For a non-relativistic N-particle system the wavefunction is a
                complex-valued field in a 3-N dimensional space.
                >>>

                I hold that the wave function does not encode all the possible
                information about an object, just what we can tell prior to running
                the experiment.  In this I agree with Bohmian mechanics.  I also
                differ from MWI (and maybe Bohmian too) in the assumption that the
                objective existence is formed of a "complex-valued field in a 3-N
                dimensional space."  My interpretation is that this field is only
                the result we get when we force the situation into an either-or kind
                of linear sequence of operations (if you know QFT, think of the time
                ordering operator, especially in the rest of this explanation).

                From my point of view, the requirement that the base space be 3-N
                dimensional only appears when the theory has been made into what the
                QFT theorists call an "effective" theory.  In other words, I believe
                that there is an underlying theory which is only 3-dimensional (at
                least as far as x, y, and z are concerned, but that's another
                story).  When that underlying theory is renormalized, you get the
                standard QFT, which then requires time ordering.

                As an illustration of this effect of renormalization, look at the
                simple renormalization that takes a bare single particle propagator,
                and absorbs all the self energy terms into it, to create the
                observed single particle propagator (sometimes called "exact"
                propagator).  Any single Feynmann diagram that goes into the
                observed single particle propagator implies a sequence of specific
                actions to the particle, that is, a history or time ordering.  This
                fact implies that the observed single particle propagators have a
                built-in time ordering.  (Note the assumption of a Bohmian view on
                particles in this argument.)

                The single particle propagators in QFT correspond in quantum theory
                to the Dirac equation (or KG or whatever), they're just the Green's
                functions for the given wave function.  So from QFT, it is clear
                that quantum mechanics must be careful about time ordering.  This is
                why the description of an N-body scenario, in standard quantum
                mechanics, requires a 3-N dimensional space, at least in my opinion.

                But if you look at the problem from the point of view of the bare
                QFT theory, that is one which is not an effective field theory for
                some other, underlying field, then I believe that there will be no
                need for time ordering, so an N-body scenario can be described in
                terms of a field on the usual 3 dimensions (more or less).  What I'm
                saying here is that renormalization automatically causes a necessity
                for time ordering.  This is a clue that the unrenormalized bare
                field theory will not have that requirement.  And I think that is
                more natural from an ontological point of view.  Otherwise the
                universe ends up with way too many dimensions.

                Let me try and explain this another way.  If you take a bath and
                make waves in your (classical) bathtub, you can describe the
                situation at any given time with a field on 3 dimensions only. 
                Where wave mechanics becomes complicated is when it is
                renormalized.  The action of renormalization is to hide a bunch of
                wave function collapses into an overall wave effect.  But those wave
                function collapses (i.e. the annihilators of QFT) have to be
                correctly time ordered.

                Another way of explaining this.  In Quantum mechanics, we do two
                distinct operations when combining two wave functions.  If we are
                creating a new wave function for a single particle we use addition
                (i.e. the law of linear superposition).  If we are creating a two
                particle wave function, we use multiplication, with symmetrization. 
                It would appear that these two operations are so distinct that they
                cannot be reconciled.  Here's a simple technique for reconciling
                these differences:

                Since mass appears to be a renormalization effect, take a good look
                at the massless Dirac equation (i.e. the Weyl equation).  Note that
                weak forces apparently couple to this version, so it's a pretty good
                bet that the fundamental base field theory is massless (and chiral,
                but that's another story).  Suppose that Psi(x,t) is a solution to
                this massless equation.  Then exp(Psi(x,t)) is also a solution.  Try
                this if you don't believe it, it's very easy.

                Because of this fact, (along with some other reasoning having to do
                with geometrical algebra and spinors) I believe that the base field
                theory is connected to the standard QFT through an exponential
                mapping.  Under this assumption, the true linear superposition for
                waves corresponds not to the usual linear (additive) superposition
                of quantum mechanics, but instead corresponds to the multiplicative
                techniques for multi-particle states.  The usual linear
                superposition seen in standard quantum mechanics, in this view, is
                actually only a result of the result of renormalization.

                That is, the usual additive linear superposition is the result of
                the fact that the Feynmann path integral formalism uses addition
                over the paths.  Ever notice that the Feynmann path formalism puts
                equal weight to all paths?  This is awfully suspicious, as
                statistical mechanics generally weights things according to an
                exponential map of the energy.  (Anyone reading this who finds this
                unfamiliar should pick up a statistical mechanics book and look in
                the index for "canonical ensemble").  This means that if you
                rederive the Feynmann path integral formalism with an assumption
                that the Dirac equation gives logarithms of probabilities instead of
                square roots of probabilities, you will get to use the usual
                exponential weighting already familiar to us in statistical
                mechanics.  But if you look at the FPI from the usual point of view,
                the wave functions have already been scaled according to
                probability, so you naturally do it with an assumption of equal
                weight.


                <<<
                2) The physical assumption: The wavefunction obeys the empirically
                derived standard linear deterministic wave equations at all times.
                The observer plays no special role in the theory and, consequently,
                there is no collapse of the wavefunction. For non-relativistic
                systems the Schrodinger wave equation is a good approximation to
                reality. (See "Is many-worlds a relativistic theory?" for how the
                more general case is handled with quantum field theory or third
                quantisation.)
                >>>

                I, for one, know that I am an observer.  For anyone who doubts that
                they are an observer, and who believes that they are just an
                unimportant collection of atoms, I can provide them with an
                unpleasant experience that will convince them otherwise.  And of
                course everyone agrees that the Schroedinger wave equation is pretty
                accurate.

                CAB


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              • Jim Whitescarver
                Thanks for a thoughtful response CAB. Comments below. ... Here you are talking about correlated actions and aggregate non resonance not interference between
                Message 7 of 23 , Feb 17, 2004
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                  Thanks for a thoughtful response CAB. Comments below.
                  brannenworks wrote:

                  > Dear Jim Whitescarver:
                  >
                  > > The idea that photons interfere with
                  > > themselves on light paths that may be
                  > > light years different in length is
                  > > contradicted by the simple fact that
                  > > photons do not interfere with one
                  > > another and the light speed violation
                  > > involved.
                  >
                  > This is a thought experiment only, and is an interference between a
                  > single photon and itself. To make it work in the real world, you'd
                  > have to have the two interfering legs very close to equal in
                  > length. But under that assumption, the standard view of physics is
                  > that there will be interference. Also, different photons do
                  > interfere. Normally one can't see the effect because there is no
                  > correlation between two photons. To get the interference effect
                  > between two completely different photons, you can use two similar
                  > lasers to produce the photons. Unless you control the phase
                  > relationship between the two lasers you will be unable to predict
                  > the particular interference pattern, but it is there.

                  Here you are talking about correlated actions and aggregate non
                  resonance not interference between individual photons. Photon
                  interference is contradicted by QED and the simple facts that the
                  planets and distant galaxies are seen clearly.

                  >
                  >
                  > > Absolute time orderings are experienced
                  > > by each participant and no observer can
                  > > witness any clocks going backwards since
                  > > the preceding event is gone by the time
                  > > the succeeding event is manifest
                  > > {a delay would involve another event).
                  >
                  > I'm not sure what you're getting at here, so I'm going to more fully
                  > describe the problem with time ordering in electrons and positrons.
                  > In the case of QED, it is possible for an electron to propagate over
                  > a space-like interval. (The probability is small, but it can
                  > happen. Similarly, light can travel faster or slower than c. This
                  > happens when the particles are not on their mass shell.) In such a
                  > case, there are some reference frames where the situation will be
                  > seen as an electron traveling, for example, East, and other
                  > reference frames where the same situation will be interpreted as a
                  > positron traveling West. The important note here is that observers
                  > cannot always agree on the time ordering of events that correspond
                  > to consecutive positions of the same particle.

                  Photon direction of travel is time independent. In the microcosm
                  participants disagree on which way the photon went. Disagreement in
                  time ordering manifests space like ordering. The clocks of the
                  participants are independent according to the distance x, t=x/c. there
                  is no time ordering (locality) defined by a single event. only multiple
                  events exhibit time independence when they share a participant. Events
                  that do not share a participant manifest space independence.

                  My point is that time dependent events are time dependent. there is no
                  way to see them backwards. Experience suggests that such is the law of
                  the universe.

                  >
                  >
                  > > Renormalization formally removes
                  > > all the infinities, it removes all self
                  > > reference, and removes all time.
                  >
                  > Yes, this is the standard objective of renormalization, and is in
                  > all the textbooks. What I am studying, instead, are the accidental
                  > side effects of renormalization. A trivial example is that you can
                  > use renormalize a massless theory to get one with mass (see the
                  > paper on this later in this post). I'm working on showing that the
                  > color force is correlated to the usual spatial coordinates, but that
                  > this correlation disappears essentially as a result of a
                  > renormalization. This has applications in explaining the anomalous
                  > cosmic ray "Centauro" events. I guess I should mention that there
                  > is a QFT theorem that says that if you mix the internal quantum
                  > states with spatial coordinates (as I've suggested above), then
                  > Lorentz symmetry cannot be perfect.

                  I think your intuition about the renormalization process is dead on
                  correct, but a viseversalation of the process. In the process of
                  renormalization you get the actual discrete results of the perspective
                  modeled in your gauge theory. You can use there results, as in the
                  paper sighted, to deduce the renormalized measurebles of near by related
                  gauge theories manifesting other measurables. But these other solutions
                  are in the process of being removed in remormalization to reviel the
                  single perspective of the gauge theory. In the end, by removing all
                  self reference time itself is sacrificed, as well as existence in our
                  participatory existence. In effect, the baby is thrown out with the
                  bath water in the arbitrary process of renormalization.

                  >
                  >
                  > > You get discrete events but that's not
                  > > where the time ordering comes from,
                  > > I don't think. You get time ordering
                  > > because Gauge theories impose a time
                  > > perspective in their formulation.
                  >
                  > My view on the gauge theories is that they're due to all the forces
                  > of nature being associated, at the bare level, with a single force
                  > that is not internal, but is instead correlated to the usual spatial
                  > dimensions in a manner similar to spin. As support for this, I
                  > should note that spin is pretty much the only observable of quantum
                  > mechanics that is not adjusted by renormalization. This suggests
                  > that spin allows us to peek beneath the renormalization haze and see
                  > the bare nature of a particle. And since spin is correlated with
                  > spatial coordinates, the natural conclusion is that the other
                  > particle interactions are also spatial in nature, at least before
                  > renormalization.

                  I don't think it is proper to associate any relative physical property
                  with differences before renormalization. There is a separate gauge
                  theory for each independent perspective. The number of gauge theories
                  can grow exponentially by the number of participants or perspectives
                  that exist. This is consistent with an independent time dimension for
                  each participant.

                  Although I've addressed some of your points below, they contain
                  interesting speculations which are worth further delving into more
                  deeply and perhaps applied to relative state spaces.

                  Time to get some some real world work done. Thanks again.

                  Jim

                  >
                  > Let me explain how spin comes from the gauge principle, since I've
                  > not seen the obvious argument anywhere else. The universe is
                  > symmetric with respect to Lorentz transformations, at least to some
                  > high degree of accuracy. This is a global symmetry. Following the
                  > gauge prescription, one wishes to promote this global symmetry to a
                  > local symmetry. This means that we will have to define a Lorentz
                  > transformation at each point of space-time. But a spinor is a
                  > Lorentz transformation, and so a wave function is nothing more than
                  > a field of Lorentz transformations, or the result of the usual gauge
                  > principle applied to the Lorentz symmetry. So if all particle
                  > interactions are modeled after the spin interaction, it's only
                  > natural that the gauge principle works.
                  >
                  > > The many world theory attempts to
                  > > account for the failure of QM to predict
                  > > the wave collapse by asserting that
                  > > there is none. This is contrary to
                  > > experience. Shit happens.
                  >
                  > I agree, at the very least from a philosophical point of view. But
                  > there is a place where wave function collapse is supposed to be
                  > visible. It's called the quantum zeno effect (QZE), and it's one of
                  > the most interesting effects in physics.
                  >
                  > > Your view of renormalization is not
                  > > unlike some others I have heard
                  > > suggesting that it somehow imposes
                  > > perspective in time or whatever. This
                  > > is very different from what I learned
                  > > in school and the interpretations I
                  > > have read by the masters. Am I missing
                  > > something?
                  >
                  > When I was in grad school I never had time to think about elementary
                  > particle physics from a theoretical point of view. The primary
                  > thing we were taught was how to crank out predictions of particle
                  > experiments. No one ever mentioned anything about the Bohmian
                  > interpretation, or the QZE, but they did talk about the Aharanov
                  > Bohm effect. I can't recall any mention of the Lorentzian
                  > interpretation of special and general relativity (which I don't
                  > believe is mentioned in Misner, Thorne and Wheeler, but that wasn't
                  > the text we used), but there was mention of the Kaluza-Klein
                  > derivation of E&M. We were very busy, the big thing was to pass the
                  > qualifier exam. After that, you concentrated on a dissertation. So
                  > there was never any chance of learning alternative perspectives on
                  > particle theory.
                  >
                  > As far as how I am interpreting things, I believe it is unusual, but
                  > I'm not completely lost out in the woods. For example, I've never
                  > seen anyone look at the creation and annihilation operators as
                  > examples of a sort of wave function collapse, but I really can't see
                  > how they can be seen otherwise. All I'm doing is giving a literal
                  > interpretation to the mathematics. Probably the reason for the
                  > hesitancy is the fact that the creation and annihilation operators
                  > can be described in different representations (like coordinate or
                  > momentum). Like the boy who finds a ton of BS under the christmas
                  > tree, the fact that there are lots of different representations
                  > doesn't worry me, so long as one of them is the ontological truth.
                  > The Galilean preferred reference frame had the same problem, as does
                  > the Lorentzian interpretation of relativity.
                  >
                  > I first saw the topological effects of renormalization on mass
                  > hinted at in a book for the popular audience by Feynman, not in grad
                  > school. The calculation is shown on pages 4 and 5 of this paper,
                  > which references the Feynman book:
                  > http://www.oberlin.edu/physics/dstyer/StrangeQM/Klein-Gordon.pdf
                  >
                  > That light (and electrons) can travel faster than light is mentioned
                  > in many QFT textbooks, for example Peskin & Schroeder, and I think
                  > it's also mentioned in the above Feynman book. As soon as you have
                  > faster than light propagation there is a problem in interpretation
                  > of causality, so the textbooks then go to great lengths to show that
                  > the problem doesn't leak into the observables.
                  >
                  > CAB
                • David Strayhorn
                  Hey CAB,I ve been slowly going through your website -- I m halfway through your fir= st paper. I think it helps me understand your PoV at least a little
                  Message 8 of 23 , Feb 17, 2004
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                    Hey CAB,

                    I've been slowly going through your website -- I'm halfway through your fir=
                    st
                    paper. I think it helps me understand your PoV at least a little bit.

                    --- In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
                    wrote:
                    > Dear David Strayhorn; From my point of view, the best argument for
                    > MWI is to note that photons do (as far as I know) exhibit
                    > interference even between paths that are separated by millions of
                    > light years, as when a distant galaxy is multiply imaged due to
                    > galactic lensing.

                    It seems to me that you could implement at least a simplistic version of th=
                    e
                    MWI even if the world did *not* display all the weirdness of QM (quantum
                    statistics, interference, etc), but *was* nondeterministic. For example -- =
                    go
                    back to the pre-quantum era, when people thought the world was
                    deterministic and obeyed "normal" (intuitive) statistics. If someone
                    (hypothetically) came along and showed that the world was fundamentally
                    nondeterministic -- so the best physicists could do was to calculate
                    probabilities -- but quantum statistics had not been discovered (so that in=
                    this
                    hypothetical theory of the world, there is no "weirdness" -- statistics is =
                    entirely
                    normal/intuitive), then they might still come up with a multiple-worlds typ=
                    e of
                    interpretation. It would be very uncomplicated and trivial; basically, it w=
                    ould be
                    the idea that every possible outcome happens in a "parallel universe," and =

                    nothing more than that.

                    > From that effect, it's natural to conclude that there are different
                    > worlds, one where the photon went through the lens one way, another
                    > where it went through the other (and infinite other choices).
                    >
                    > But the conclusion is due to an assumption of how time works. That
                    > is, the MWI is based on the inherent assumption that time works in a
                    > linear, single-valued fashion. Another way of putting it is to say
                    > that the inherent assumption is to believe that the universe can be
                    > described in the form of a motion picture.

                    I understand your idea that "time is linear and single valued" <==> "the
                    universe can be described in the form of a motion picture." But I don't act=
                    ually
                    see the relation between the "motion picture"assumption, and the multiple-
                    worlds assumption. For example, if I believed in a "one world" interpretati=
                    on
                    (not the MWI), I might still imagine that I could describe the evolution of=
                    the
                    state of the universe in the form of a motion picture. If we switch to the =
                    MWI,
                    then I would say that each individual world would be associated with its ow=
                    n
                    video tape. (Or, perhaps it would be better to say that when a world branch=
                    es,
                    there is one tape that corresponds to the world before the split, but after=
                    the
                    split, you have to use a separate tape for each separate branch.) Have I
                    understood your position correctly?

                    >That is, if you believe
                    > that the full state of the universe exists from moment to moment,
                    > you naturally also have to believe that there are multiple worlds to
                    > allow the interference to work.
                    >
                    > Where I take issue with this is in what I think is its observer
                    > centered notion of how time works. From my point of view, what we
                    > really know about time is that for any given particle, things happen
                    > in order. That is, time defines an ordering for the sequence of
                    > things that happen to a particle. This is also compatible with what
                    > we see as beings contemplating the universe, which is why I
                    > say "observer centered". But just because the universe appears to
                    > have a time ordering for any given particle (if you assume a
                    > particular reference frame), or for any given observer, this does
                    > not prove that the universe as a whole also possesses a time
                    > ordering.

                    IOW, the time ordering of events for one observer (particle) may be (probab=
                    ly
                    is) different than the time ordering for another observer. This is certainl=
                    y true
                    according to the standard theory of relativity (as you mention below). My
                    understanding is that it is also true for the MWI. However, it appears to m=
                    e
                    (correct me if I'm wrong) that you are assuming that according to the MWI: =
                    "the
                    universe as a whole also possesses a time ordering." This is not my
                    understanding of the MWI – see below.

                    > It's a pretty good place to start, but it isn't proof,
                    > and there are indications that time is more complicated than that.
                    > For example, the interpretation of positrons as electrons travelling
                    > backwards in time is contrary to the naive notion of how time works.
                    >
                    > Let me try and argue it this way: Einstein already proved that time
                    > ordering is relative, that is, that there is no way of determining
                    > the time ordering of space-like separated events.

                    Exactly: if you want to time-order events, it is first necessary to specify=
                    a frame
                    of reference, and no frame is priveleged over any other.

                    > A good percentage
                    > of your typical QFT textbook is devoted to proving that QFT, despite
                    > having influences that exceed the speed of light, nevertheless is
                    > compatible with relativity in that no signal can propagate faster
                    > than light, and therefore that causality is preserved.
                    >
                    > But if you carefully examine these proofs, you will notice that what
                    > is proved is that causality is not violated for the results
                    > of "observations". That is, after the wave function has collapsed
                    > (or whatever you want to call a measurement), the result will
                    > satisfy causality. They do not show that the wave function itself
                    > satisfies causality because wave functions themselves very
                    > explicitly do not.

                    Very true. My take is that, if people are going to have a meaningful
                    conversation about "causality," we need to recognize that there are differe=
                    nt
                    ways to define it. As you mention, wavefunction collapse does not at first =

                    glance satisfy the normal concept of causality – it is, in fact, instantane=
                    ous.
                    Nevertheless – as you also mention – no one has ever demonstrated a strict =

                    conflict with GTR, and I have no reason to believe that anyone ever will.

                    > My conclusion is that the universe is a collection of particles,
                    > each one of which has an ordered time sequence (created, then
                    > annihilated), but the universe itself does not have any such ordered
                    > time sequence.

                    I agree.

                    > For multiple particle situations, you can put a time
                    > ordering on it, but only to the extent that creation precedes
                    > annihilation.

                    Hmm. I would think that you can put a time ordering on it, provided that yo=
                    u
                    first specify the observer. This is in analogy to the situation in GR: if y=
                    ou
                    specifiy the frame of reference, then you can time order events, but the ti=
                    me
                    ordering will differ between observers. (In fact, with a suitable change of=

                    reference frame, you could even reverse time ordering, so that "annihilatio=
                    n"
                    would preceed "creation" -- I think this is true for multiply connected
                    manifolds; I'm not sure if it's true for non-multiply connected ones.)

                    > This is at least subtly different from MWI.
                    >
                    > Here's my critique of their tenets (from your link):
                    >
                    > <<<
                    > 1) The metaphysical assumption: That the wavefunction does not
                    > merely encode the all the information about an object, but has an
                    > observer-independent objective existence and actually is the object.
                    > For a non-relativistic N-particle system the wavefunction is a
                    > complex-valued field in a 3-N dimensional space.
                    > >>>
                    >
                    > I hold that the wave function does not encode all the possible
                    > information about an object, just what we can tell prior to running
                    > the experiment.

                    What else is there to know?

                    > In this I agree with Bohmian mechanics. I also
                    > differ from MWI (and maybe Bohmian too) in the assumption that the
                    > objective existence is formed of a "complex-valued field in a 3-N
                    > dimensional space."

                    I share your inherent unease with the heavy reliance on complex numbers in =

                    QM, which you discuss in your website. (eg, GR does not need complex
                    numbers.) Although I suppose I am not quite so uneasy; my take is that the =

                    complex-valued wavefunction is an ABSTRACT representation of reality. At a =

                    minimum, it is an accurate represention of reality. If we could find a
                    representation that is not so abstract, nonintuitive, "weird," but neverthe=
                    less
                    accurate, then that would be an improvement.

                    > My interpretation is that this field is only
                    > the result we get when we force the situation into an either-or kind
                    > of linear sequence of operations (if you know QFT, think of the time
                    > ordering operator, especially in the rest of this explanation).

                    I'm familiar with the basics of path integrals, not so familiar with QFT.

                    > From my point of view, the requirement that the base space be 3-N
                    > dimensional only appears when the theory has been made into what the
                    > QFT theorists call an "effective" theory. In other words, I believe
                    > that there is an underlying theory which is only 3-dimensional (at
                    > least as far as x, y, and z are concerned, but that's another
                    > story). When that underlying theory is renormalized, you get the
                    > standard QFT, which then requires time ordering.
                    >
                    > As an illustration of this effect of renormalization, look at the
                    > simple renormalization that takes a bare single particle propagator,
                    > and absorbs all the self energy terms into it, to create the
                    > observed single particle propagator (sometimes called "exact"
                    > propagator). Any single Feynmann diagram that goes into the
                    > observed single particle propagator implies a sequence of specific
                    > actions to the particle, that is, a history or time ordering. This
                    > fact implies that the observed single particle propagators have a
                    > built-in time ordering. (Note the assumption of a Bohmian view on
                    > particles in this argument.)

                    I'm getting lost here.

                    > The single particle propagators in QFT correspond in quantum theory
                    > to the Dirac equation (or KG or whatever), they're just the Green's
                    > functions for the given wave function. So from QFT, it is clear
                    > that quantum mechanics must be careful about time ordering. This is
                    > why the description of an N-body scenario, in standard quantum
                    > mechanics, requires a 3-N dimensional space, at least in my opinion.

                    I don't follow the connection between time-ordering and the number of
                    dimensions needed.

                    > But if you look at the problem from the point of view of the bare
                    > QFT theory, that is one which is not an effective field theory for
                    > some other, underlying field, then I believe that there will be no
                    > need for time ordering, so an N-body scenario can be described in
                    > terms of a field on the usual 3 dimensions (more or less). What I'm
                    > saying here is that renormalization automatically causes a necessity
                    > for time ordering. This is a clue that the unrenormalized bare
                    > field theory will not have that requirement. And I think that is
                    > more natural from an ontological point of view. Otherwise the
                    > universe ends up with way too many dimensions.

                    I understand the notion that 3 dimensions is preferable to 3-N dimensions
                    from an ontological PoV.

                    > Let me try and explain this another way. If you take a bath and
                    > make waves in your (classical) bathtub, you can describe the
                    > situation at any given time with a field on 3 dimensions only.
                    > Where wave mechanics becomes complicated is when it is
                    > renormalized. The action of renormalization is to hide a bunch of
                    > wave function collapses into an overall wave effect. But those wave
                    > function collapses (i.e. the annihilators of QFT) have to be
                    > correctly time ordered.

                    … and they're not, hence the need for 3-N dimensions? …

                    > Another way of explaining this. In Quantum mechanics, we do two
                    > distinct operations when combining two wave functions. If we are
                    > creating a new wave function for a single particle we use addition
                    > (i.e. the law of linear superposition). If we are creating a two
                    > particle wave function, we use multiplication, with symmetrization.
                    > It would appear that these two operations are so distinct that they
                    > cannot be reconciled. Here's a simple technique for reconciling
                    > these differences:
                    >
                    > Since mass appears to be a renormalization effect, take a good look
                    > at the massless Dirac equation (i.e. the Weyl equation). Note that
                    > weak forces apparently couple to this version, so it's a pretty good
                    > bet that the fundamental base field theory is massless (and chiral,
                    > but that's another story). Suppose that Psi(x,t) is a solution to
                    > this massless equation. Then exp(Psi(x,t)) is also a solution. Try
                    > this if you don't believe it, it's very easy.

                    !? interesting..

                    > Because of this fact, (along with some other reasoning having to do
                    > with geometrical algebra and spinors)

                    Speaking of spinors – are you aware that there is a way to model the
                    rotational properties of a spin-1/2 object using ordinary euclidean space =

                    (without using quaternions)? It's in MTW, the "cube within a cube" model – =

                    look up spinors (or spin?) in the index and turn to that page. (I don't ha=
                    ve
                    MTW here with me, otherwise I'd give you the page.)

                    > I believe that the base field
                    > theory is connected to the standard QFT through an exponential
                    > mapping. Under this assumption, the true linear superposition for
                    > waves corresponds not to the usual linear (additive) superposition
                    > of quantum mechanics, but instead corresponds to the multiplicative
                    > techniques for multi-particle states. The usual linear
                    > superposition seen in standard quantum mechanics, in this view, is
                    > actually only a result of the result of renormalization.
                    >
                    > That is, the usual additive linear superposition is the result of
                    > the fact that the Feynmann path integral formalism uses addition
                    > over the paths. Ever notice that the Feynmann path formalism puts
                    > equal weight to all paths?

                    Yup – this wouldn't bother me, except for the fact that the probabilities
                    combine via addition of complex-valued amplitudes – which is, of course, ve=
                    ry
                    "weird."

                    > This is awfully suspicious, as
                    > statistical mechanics generally weights things according to an
                    > exponential map of the energy. (Anyone reading this who finds this
                    > unfamiliar should pick up a statistical mechanics book and look in
                    > the index for "canonical ensemble"). This means that if you
                    > rederive the Feynmann path integral formalism with an assumption
                    > that the Dirac equation gives logarithms of probabilities instead of
                    > square roots of probabilities, you will get to use the usual
                    > exponential weighting already familiar to us in statistical
                    > mechanics.

                    I am **very** interested in what you just said. Do you have a reference for=
                    this
                    sort of presentation of the Dirac equation? I have attempted my own
                    rederivation of the path integral formalism where probabilities of individu=
                    al
                    paths combine as real numbers in an intuitive fashion, not as complex
                    amplitudes in the usual "weird" fashion. The final solution for the probabi=
                    lity
                    looks similar to Feynman's solution for the amplitude, except that where th=
                    e
                    FPI has:

                    amplitude ~ sum over paths of e ^( –i S/ h)

                    [where S is the classical action],

                    I have:

                    Probability ~ sum over paths of logarithm of [(1/4)(1 - e ^( –i S'/ h))]

                    So you see, the form I derived has a big fat logarithm thrown in. [Also, in=
                    my
                    equation, instead of S my equation uses S', which is the change in the acti=
                    on
                    as the path is varied. ]


                    > But if you look at the FPI from the usual point of view,
                    > the wave functions have already been scaled according to
                    > probability, so you naturally do it with an assumption of equal
                    > weight.
                    >
                    >
                    > <<<
                    > 2) The physical assumption: The wavefunction obeys the empirically
                    > derived standard linear deterministic wave equations at all times.
                    > The observer plays no special role in the theory and, consequently,
                    > there is no collapse of the wavefunction.

                    I've never understood the notion that in the MWI, "there is no collapse of =
                    the
                    wavefunction." When a world splits into N worlds (let's say N=2, one for sp=
                    in
                    up, one for spin down), then when standard QM says: "we measure spin up,
                    which means we collapsed onto the spin-up state" the MWI would say: "we
                    measure spin up, which means we picked branch #1 instead of branch #2."
                    So MWI does have collapse, n'est-ce pas?

                    > For non-relativistic
                    > systems the Schrodinger wave equation is a good approximation to
                    > reality. (See "Is many-worlds a relativistic theory?" for how the
                    > more general case is handled with quantum field theory or third
                    > quantisation.

                    I read that section – didn't quite follow it. My simplistic notion is that:=
                    "MWI and
                    standard QM are equally compatible (or not) with relativity."

                    > >>>
                    >
                    > I, for one, know that I am an observer. For anyone who doubts that
                    > they are an observer, and who believes that they are just an
                    > unimportant collection of atoms, I can provide them with an
                    > unpleasant experience that will convince them otherwise.

                    Would this be along the same lines of an Objectivist proving that Existence=

                    Exists? [some variation of "take a long walk off a short pier ..." ;) ]

                    straycat


                    > And of
                    > course everyone agrees that the Schroedinger wave equation is pretty
                    > accurate.
                    >
                    > CAB
                  • sudellwood@aol.com
                    My optical bench is casting no shadows on the cave wall. Sutherland
                    Message 9 of 23 , Feb 17, 2004
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                      My optical bench is casting no shadows on the cave wall.
                       
                      Sutherland
                    • brannenworks
                      Thanks for the interesting comments, Jim; ... It s obvious we re talking past each other on this point. We probably differ on what interference means.
                      Message 10 of 23 , Feb 17, 2004
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                        Thanks for the interesting comments, Jim;

                        > Here you are talking about correlated
                        > actions and aggregate non
                        > resonance not interference between
                        > individual photons. Photon
                        > interference is contradicted by QED
                        > and the simple facts that the
                        > planets and distant galaxies are seen
                        > clearly.

                        It's obvious we're talking past each other on this point. We
                        probably differ on what "interference" means. Distant galaxies are
                        seen clearly because telescopes use optics and shields to eliminate
                        unwanted interference. Photon interference is why you can't see the
                        stars in daylight. It's also why you can't hear WKRP when WKRQ is
                        broadcasting on the same frequency.

                        Two photons will interfere even when they are absorbed by the object
                        they impinge on (as in a film exposure). Since the photons are
                        absorbed, there can be no resonance. The same thing applies to two
                        lasers. The laser resonance is only inside the laser cavity, it
                        does not exist at the place where the lasers interfere.

                        The usual QED model for particle interactions implies that the final
                        particles are free. This means that to model photon interference,
                        you have to have the photons be on interior lines, rather than
                        exterior (output) lines. That is, to model photon interference with
                        QED you have to include the film as part of the system. In this
                        case, the interference takes the form of a subtraction between two
                        Feynman diagrams, one with the photons swapped. If you work the
                        problem in the position representation, the interference is
                        identical to the usual calculation for any other kind of
                        interference between waves.

                        > My point is that time dependent events
                        > are time dependent. there is no
                        > way to see them backwards. Experience
                        > suggests that such is the law of
                        > the universe.

                        For any one Feynman diagram, it is not only possible for a photon to
                        propagate faster than light, it goes on all the time. That is, the
                        photon movement is spacelike and therefore both time orderings are
                        possible, depending on which frame of reference you look at it
                        from. This effect doesn't do any good for signalling faster than
                        light, but it is an important part of QED. Here's a reference, look
                        at the section titled "Do they go faster than light? Do virtual
                        particles contradict relativity or causality?"

                        http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

                        CAB
                      • Jim Whitescarver
                        ... Yes. But we may be getting to the point and I believe we agree. At least you are confirming me objections to the standard interpretations of photon
                        Message 11 of 23 , Feb 17, 2004
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                          brannenworks wrote:

                          > Thanks for the interesting comments, Jim;
                          >
                          > > Here you are talking about correlated
                          > > actions and aggregate non
                          > > resonance not interference between
                          > > individual photons. Photon
                          > > interference is contradicted by QED
                          > > and the simple facts that the
                          > > planets and distant galaxies are seen
                          > > clearly.
                          >
                          > It's obvious we're talking past each other on this point.

                          Yes. But we may be getting to the point and I believe we agree. At
                          least you are confirming me objections to the standard interpretations
                          of photon self-interference. To be clear the interpretation of resonant
                          channels (in space) as a superior interpretation of self-interaction
                          which gets removed may be rather novel.

                          > We
                          > probably differ on what "interference" means. Distant galaxies are
                          > seen clearly because telescopes use optics and shields to eliminate
                          > unwanted interference.

                          The point is that the photons travel for billions of years crossing
                          photons of all frequencies and arrive here without the slightest
                          distortion besides the gravitational lensing effects if present.

                          > Photon interference is why you can't see the
                          > stars in daylight.

                          I disagree. Interactions with the atmosphere are NOT photon
                          interference. The main reason your can't see the stars it they are not
                          bright enough. When the moon is visible, it is perfectly clear except
                          for the distortions due to varying atmospheric temperature and pressure.

                          > It's also why you can't hear WKRP when WKRQ is
                          > broadcasting on the same frequency.

                          This is simple a power discrepancy. If you remove the larger signal,
                          the smaller signal will still be there.

                          >
                          >
                          > Two photons will interfere even when they are absorbed by the object
                          > they impinge on (as in a film exposure). Since the photons are
                          > absorbed, there can be no resonance. The same thing applies to two
                          > lasers. The laser resonance is only inside the laser cavity, it
                          > does not exist at the place where the lasers interfere.

                          Suppose there is a resonant channel structure in every reference
                          frame. (The binary nature of discrimination also suggests this may be
                          true). Instead of possibilities evolving over time, these resonate
                          channels evolve.

                          >
                          >
                          > The usual QED model for particle interactions implies that the final
                          > particles are free. This means that to model photon interference,
                          > you have to have the photons be on interior lines, rather than
                          > exterior (output) lines. That is, to model photon interference with
                          > QED you have to include the film as part of the system. In this
                          > case, the interference takes the form of a subtraction between two
                          > Feynman diagrams, one with the photons swapped. If you work the
                          > problem in the position representation, the interference is
                          > identical to the usual calculation for any other kind of
                          > interference between waves.

                          But only on the photon with respect to itself, not with other photons.

                          >
                          >
                          > > My point is that time dependent events
                          > > are time dependent. there is no
                          > > way to see them backwards. Experience
                          > > suggests that such is the law of
                          > > the universe.
                          >
                          > For any one Feynman diagram, it is not only possible for a photon to
                          > propagate faster than light, it goes on all the time.

                          The photon going back in time is always superficial or because another
                          observer sees the photon going the other direction.

                          > That is, the
                          > photon movement is spacelike and therefore both time orderings are
                          > possible, depending on which frame of reference you look at it
                          > from. This effect doesn't do any good for signalling faster than
                          > light, but it is an important part of QED.

                          Right, it is artificial, no faster than light signaling is involved.
                          The only this this suggest is that clocks are independent, there is no
                          absolute time frame, but we knew that already, didn't we?

                          > Here's a reference, look
                          > at the section titled "Do they go faster than light? Do virtual
                          > particles contradict relativity or causality?"
                          >
                          > http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

                          I already got the point... but thanks for making it.

                          Jim

                          >
                          >
                          > CAB
                        • brannenworks
                          Dear David Strayhorn; Thanks for going to the trouble to read all that stuff. The easiest way to sharpen an idea is to talk it over with someone who has a
                          Message 12 of 23 , Feb 17, 2004
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                            Dear David Strayhorn; Thanks for going to the trouble to read all
                            that stuff. The easiest way to sharpen an idea is to talk it over
                            with someone who has a critical eye.

                            > I've been slowly going through your
                            > website -- I'm halfway through your first
                            > paper. I think it helps me understand
                            > your PoV at least a little bit.

                            I'm working on some more papers, but they're in Latex, so they can't
                            be put on the web as easily. When I get ready to release them for
                            publication, I will copy them to .pdf and put them up on my
                            website. They're a lot more mathematical and less intuitive, since
                            the objective is to get them published in the physics literature.

                            > It seems to me that you could implement
                            > at least a simplistic version of the
                            > MWI even if the world did *not* display
                            > all the weirdness of QM (quantum
                            > statistics, interference, etc), but *was*
                            > nondeterministic. For example -- go
                            > back to the pre-quantum era, when people
                            > thought the world was
                            > deterministic and obeyed "normal"
                            > (intuitive) statistics. If someone
                            > (hypothetically) came along and showed
                            > that the world was fundamentally
                            > nondeterministic -- so the best physicists
                            > could do was to calculate
                            > probabilities -- but quantum statistics
                            > had not been discovered (so that inthis
                            > hypothetical theory of the world, there
                            > is no "weirdness" -- statistics is entirely
                            > normal/intuitive), then they might still
                            > come up with a multiple-worlds type of
                            > interpretation. It would be very uncomplicated
                            > and trivial; basically, it would be
                            > the idea that every possible outcome
                            > happens in a "parallel universe," and
                            > nothing more than that.

                            In the face of incomplete knowledge, even the classical world is
                            inherently statistical. Physicists probably wouldn't have any
                            reason to come up with the multiple world hypothesis because the
                            things that didn't happen wouldn't have any effect on the things
                            that did. What's odd about quantum mechanics is not the statistical
                            nature of it, nor simply the quantization (which can happen also in
                            classical wave theory), but instead, like Feynman said, the oddest
                            thing about quantum mechanics is the two slit experiment.


                            > I understand your idea that "time is
                            > linear and single valued" <==> "the
                            > universe can be described in the form
                            > of a motion picture." But I don't actually
                            > see the relation between the "motion
                            > picture" assumption, and the multiple-
                            > worlds assumption. For example, if I
                            > believed in a "one world" interpretation
                            > (not the MWI), I might still imagine
                            > that I could describe the evolution ofthe
                            > state of the universe in the form of
                            > a motion picture. If we switch to the MWI,
                            > then I would say that each individual
                            > world would be associated with its own
                            > video tape. (Or, perhaps it would be
                            > better to say that when a world branches,
                            > there is one tape that corresponds to
                            > the world before the split, but afterthe
                            > split, you have to use a separate tape
                            > for each separate branch.) Have I
                            > understood your position correctly?

                            I think you've described what I think better than I did.

                            > IOW, the time ordering of events for one
                            > observer (particle) may be (probably
                            > is) different than the time ordering for
                            > another observer. This is certainly true
                            > according to the standard theory of
                            > relativity (as you mention below). My
                            > understanding is that it is also true
                            > for the MWI. However, it appears to me
                            > (correct me if I'm wrong) that you are
                            > assuming that according to the MWI: "the
                            > universe as a whole also possesses a
                            > time ordering." This is not my
                            > understanding of the MWI – see below.

                            It is not my understanding of the MWI either. What I'm trying to
                            say is that the MWI is an alternative to the classical motion
                            picture theory, where they end up with a huge collection of motion
                            pictures. Obviously a single motion picture doesn't work. Standard
                            quantum mechanics works, but it requires assumptions about existence
                            that are not acceptable from an ontological (i.e. reality based)
                            point of view. What it boils down to is that quantum mechanics
                            (like relativity) is a phenomenological theory. It's based on the
                            simplest mathematics that can explain complicated observations. But
                            neither theory is ontologically correct in that you could construct
                            a universe based on them (and you were God). In both cases, the
                            problem is that there are multiple ways of describing the same
                            physical situation, and those multiple ways are ontologically
                            incompatible. The MWI theory is also an ontological attempt to
                            explain quantum mechanics (that is, to get beyond the mathematics to
                            the reality), but I think that it is unnecessarily bulky.


                            > Nevertheless – as you also mention – no
                            > one has ever demonstrated a strict
                            > conflict with GTR, and I have no reason
                            > to believe that anyone ever will.

                            Maybe the MOND gravitational anomaly, if it continues to survive,
                            will be a counterexample to exact GTR. But my main problem with
                            relativity is that it is lacking from an ontological point of view.
                            It's a phenomenological theory based on observations about the speed
                            of light and acceleration. No one could construct a physical model
                            of a world that operated according to the principle of relativity,
                            not even God. Like QM, it works great for predicting results, but
                            it doesn't say anything about what is hiding behind the curtain,
                            because we do not know how to create physical structures that would
                            support waves even remotely similar to matter waves. This is a
                            complaint similar to the one that the MWI people voice about QM.

                            > Hmm. I would think that you can put a
                            > time ordering on it, provided that you
                            > first specify the observer. This is in
                            > analogy to the situation in GR: if you
                            > specifiy the frame of reference, then you
                            > can time order events, but the time
                            > ordering will differ between observers.

                            Yes, you are exactly correct. It might be just a weird coincidence
                            that anti particles act like particles travelling backwards in
                            time. But where I get suspicious is that since we can, after the
                            fact, always assign a full time ordering, then why can't we assign
                            the time ordering as we go along? The problem with doing that is
                            that in order to provide a time ordering we would have to know which
                            branches were taken. That is, you can't order time without knowing
                            which events to order, and therefore know which events are in
                            existence. But quantum interference doesn't allow us to do this,
                            all possibilities contribute to the probability. So while I agree
                            that the past is fully time ordered (which is why Bohmian mechanics
                            works), I think that the present does not have a general time
                            ordering.

                            > What else is there to know [about a wave
                            > function, prior to running an experiment]?

                            If you've been reading my website, you'll see that I think that
                            there is a hidden dimension available for movement, similar to the
                            Kaluza Klein or string theory. In either case, physics has only, at
                            best, statistical information about the particle in that hidden
                            dimension.

                            > I don't follow the connection between
                            > time-ordering and the number of
                            > dimensions needed.

                            Yes, that was a really short explanation for a subject that I feel
                            intuitive about but haven't written down before. Trying to explain
                            things helps flesh out arguments.

                            In QFT, time ordering is only important because fermions do not
                            commute. The "time ordering operator" is just the rule that you
                            multiply a product of annihilation and creation operators by -1 if
                            there are an odd number of fermion swaps required to put the
                            annihilation and creation operators in time order. This is a lot
                            simpler than it sounds:

                            T(0 1 2 3) = (0 1 2 3)
                            T(1 0 2 3) = -(0 1 2 3)
                            T(3 2 1 0) = (0 1 2 3)
                            T(0 3 2 1) = -(0 1 2 3)

                            The minus sign has the effect of enforcing Fermi statistics, it is
                            the Pauli exclusion principle as seen in QFT. (I.e., if you swap
                            two identical fermions, you're going to screw up the time ordering,
                            so to put it back you're going to get a minus sign.) Now since the
                            ordering of the operators does have an overall sign effect, we are
                            forced to keep track of time ordering. This is in contrast to the
                            case of bosons, which commute. I don't think that this can be
                            understood, in terms of the connection with a base field theory,
                            without a careful comparison to the boson case.

                            For bosons, the time ordering operator always give +1. And for
                            bosons, we do have full linear superposition, sort of, after taking
                            into account the fact that the wave functions have to be squared to
                            convert them into probability densities. For example, photons are
                            bosons and so these rules apply, with the photon density being
                            proportional to E^2 + B^2. Another way of saying the same thing is
                            that if a bunch of photons all have the same energy, then their
                            total energy is proportional to the number of them, but we know that
                            the energy in a EM wave is proportional to E^2 + B^2, therefore this
                            must be proportional to the photon number.

                            Now we normally keep track of large numbers of photons with just the
                            E and B fields, which are defined on only 3 dimensions. This is
                            only true if all we care about is the photon density at single
                            points, rather than photon correlations, but photon correlation
                            effects are again due to quantum statistics which is what explicitly
                            requires the need to keep track of time ordering for fermions in QFT.

                            So I know that many may not find this a very convincing connection,
                            but there you have the clues:
                            (a) Quantum statistics require 3-N dimensional wave domains.
                            (b) Quantum statistics require time ordering operators.
                            (c) Renormalization imposes a time sequence on creation and
                            annihilation operators.

                            > Speaking of spinors – are you aware
                            > that there is a way to model the
                            > rotational properties of a spin-1/2
                            > object using ordinary euclidean space
                            > (without using quaternions)? It's in
                            > MTW, the "cube within a cube" model –
                            > look up spinors (or spin?) in the index
                            > and turn to that page. (I don't have
                            > MTW here with me, otherwise I'd give
                            > you the page.)

                            Yes, I've seen it. My problem is that I don't know how to turn it
                            into a mathematical theory. That's the big reason I'm starting with
                            QFT, it's something that already gives the right answer.


                            > Yup – this wouldn't bother me, except for
                            > the fact that the probabilities
                            > combine via addition of complex-valued
                            > amplitudes – which is, of course, very
                            > "weird."

                            This was something that bothered me for a long time as well. I'm
                            convinced I've found the solution. It starts with Hestene's work in
                            the Geometric Algebra. Here's a link to a good introductory
                            (undergraduate level) paper on this:
                            http://modelingnts.la.asu.edu/html/GAinQM.html

                            I now have a much sweeter derivation of the Dirac equation than
                            Hestenes', but I'm using the geometric algebra on the 4 dimensional
                            space you saw mentioned on my website. Hestenes, by contrast, is
                            using a 4 dimensional space-time. The essential difference is that
                            I'm using time as an independent variable, while Hestenes follows
                            the nearly universal modern custom of enforcing Lorentz symmetry by
                            promoting time to a part of the metric. Since I doubt that Lorentz
                            symmetry is an exact symmetry of nature, I don't think it's a good
                            idea to base a theory on it. From an ontological point of view,
                            Lorentz symmetry requires matter waves to do some mighty funky
                            things.

                            > I am **very** interested in what
                            > you just said: "if you
                            > rederive the Feynmann path integral
                            > formalism with an assumption
                            > that the Dirac equation gives
                            > logarithms of probabilities instead of
                            > square roots of probabilities,
                            > you will get to use the usual
                            > exponential weighting already
                            > familiar to us in statistical
                            > mechanics." Do you have a
                            > reference for this sort
                            > of presentation of the
                            > Dirac equation?

                            Maybe I have overstated my case. Let me try and restate exactly
                            what is known. First, it's obvious that QM is unchanged if you make
                            the following substitution:

                            Psi(x,t) <= exp( phi(x,t)), where phi(x,t) = ln(Psi(x,t))

                            Having made this substitution, one wonders what is the nature of the
                            wave function phi(x). You know that the nature of the wave function
                            Psi is that it is a square root of a probability density multiplied
                            by a complicated thing. Like I mentioned before, if you are
                            considering the massless Dirac equation, if Psi is a solution, then
                            so is phi. So, in particular, linear superposition applies to phi,
                            but the linear superposition of phi corresponds to multiplicative
                            superposition of Psi, which gets back to my point about the
                            relationship between linear superposition, quantum statistics, and
                            the need for 3-N dimensional wave function domains.

                            Now in order to interpret phi in a traditional statistical
                            mechanical fashion, you will first have to wade through Hestenes'
                            paper on the geometric algebra. What Hestenes does is to factor the
                            Dirac wave equation. The factorization that he gives is as follows
                            (he has a lot of papers, some use this factorization, some slightly
                            different):

                            Psi(x,t) = sqrt(rho(x,t)) R(x,t).

                            Here, rho is the probability density that is the subject of
                            statistical mechanics. R is a field in the Geometric Algebra (which
                            he calls "Spacetime Algebra"), and has the nature of being a
                            description of a Lorentz transformation.

                            But when you rewrite the above factorization into phi = ln(Psi), you
                            separate the statistical part from the Lorentz transformation part:

                            phi(x,t) = ln(rho(x,t))/2 + ln(R(x,t)).

                            Now the Dirac equation is unchanged when you convert from Psi to phi
                            because of the fact that it is linear and first order, (the
                            exponential cancels out, if you tried it). But while the equation
                            has the same terms and everything, by splitting it out this way
                            you've changed the interpretation of its parts. Now, instead, you
                            have a mysterious Lorentz transform part, and a statistical
                            mechanical part. We should ignore the Lorentz transform part
                            because it requires familiarity with the Geometric Algebra (which is
                            a type of Clifford algebra), and that is not understood, at this
                            time, by very many people. It's not that I don't want to talk about
                            GA, it has beauty in its equations that is unsurpassed. It makes
                            tensors look ugly, difficult, and useless by comparison. It's just
                            that I can't imagine easily convincing anyone to learn enough about
                            it to carry on a conversation.

                            Psi(x,t) = exp(- i H t /h-bar) Psi(x,0).

                            Take the log:

                            phi(x,t) = - i H t /h-bar + phi(x,0).

                            Now in the geometric algebra, "i" is interpreted as a geometrical
                            quantity, rather than as sqrt(-1). It is therefore part of the
                            equation that we will ignore. The remainder of the equation looks
                            pretty much like what you'd expect from statistical mechanics, if
                            you make a analytic continuation of the time coordinate to imaginary
                            time, which is pretty much nothing more than replacing t with i t.
                            For more on the subject, read section 2.3 of this paper:
                            http://arxiv.org/PS_cache/hep-ph/pdf/9504/9504271.pdf

                            Of course the literature is rife with comparisons between
                            statistical mechanics and quantum mechanics. The usual technique is
                            to rotate the time axis from the real axis to the imaginary axis.
                            This corresponds to a conversion from a signature of (+++-) as in
                            Minkowski space, to a signature of (++++) as in Euclidian space.
                            Since my topology already has a signature of (++++), I don't have to
                            assume imaginary time. It's a bit bizarre, but the paper I am
                            writing up uses the lattice gauge calculations from QCD (as in the
                            above paper) as support for my version of QCD on the "Proper Time
                            Topology". Basically, you don't need the analytic continuation
                            because I already have a Euclidian time coordinate.

                            This change transforms lattice QCD calculations from being
                            fundamentally different than the usual statistical mechanical
                            calculations to being identical in form. That is, when making
                            lattice calculations in statistical mechanics it is usual to move
                            the system to a new random position and to make measurements. With
                            lattice QCD, one instead moves "space-time" to a random position,
                            except that the time coordinate is multiplied by i.

                            > I have attempted my own rederivation of the path
                            > integral formalism where probabilities of individual
                            > paths combine as real numbers in an intuitive fashion,
                            > not as complex amplitudes in the usual "weird" fashion.

                            Maybe I should try and give a reason for why complicated (not
                            necessarily complex) fields might be needed to describe a
                            probability density. Now I believe in a bare field, and I believe
                            that it lives on 3 dimensions, rather than 3-N. But in addition, I
                            believe that the field corresponds to perturbations or waves in some
                            firmament or ether. As such, one would wonder how one should
                            describe such a wave.

                            Well we can't use single real numbers to describe classical waves,
                            so why should we believe that waves in the ether should possess real
                            representations? I do not believe in the existence of
                            a "probability wave" per se. I think the statistical part of the
                            quantum wave function only shows up because of statistical
                            principles. That is, it's a bunch of things all added up. But what
                            is the things that should be added up? For simplicity, let's work
                            with simple water waves in 2 dimensions.

                            I'd like to have a wave that travels North be able to cancel a wave
                            that travels South with the same strength. And the same for East
                            and West. So it's going to be natural for me to associate a 2
                            dimensional vector with each wave. Since a complex number has two
                            real components, that's just perfect for describing water waves in
                            two dimensions. Of course the fact that it is complex wouldn't
                            enter into the calculation because there is no need to multiply the
                            waves. But if you read the papers on the GA you will get clues as
                            to why complex numbers rear their fair head.

                            Of course the ether of the universe will have more dimensions, and
                            it may have more complexity in what kinds of waves it can
                            propagate. It's my view that the GA is just a short form
                            description for something that could be described at an even lower
                            level, but until I work out the details of QED and QCD, I'm just not
                            going to worry about it.

                            > when standard QM says: "we measure spin up,
                            > which means we collapsed onto the spin-up
                            > state" the MWI would say: "we measure spin up,
                            > which means we picked branch #1 instead of branch
                            > #2." So MWI does have collapse, n'est-ce pas?

                            I agree.

                            CAB
                          • lady ganesha
                            ok, I won t say the P word ever again... The following definitions come from the sew-lexicon glossary http://www.sew-lexicon.com/glossary.htm this is the Q
                            Message 13 of 23 , Feb 18, 2004
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                              ok, I won't say the P word ever again...

                              The following definitions come from the sew-lexicon glossary

                              http://www.sew-lexicon.com/glossary.htm

                              this is the Q page

                              http://www.sew-lexicon.com/gloss_qr.htm#QQ

                              This definition of Qubit seems to be a proof of G. Spencer Browns LAWS OF FORM ????

                              QUANTUM BIT (QUBIT) -  The fundamental unit of quantum information.  Qubits are remarkable in that they can be in two states simultaneously (i.e., be in a zero and one state at the same time).   Consequently, qubits have the potential to greatly increase the speed of computing.   [10:2872]

                              HERE ARE OTHER INTERESTING MILITARY DEFINITIONS FOR QUANTUM WORDS:

                              QUANTUM COMPUTER - A computer that controls the actions among QUANTUM BITs (QUBITs) to perform certain types of calculations. [10:2925]

                              QUANTUM CRYPTOGRAPHY - A technique for encoding and sending data along unsecured public fiber optic lines that exploits the fact that small particles of matter (e.g., photons) are both intertwined and yet completely isolated.  Any attempt by an outside party to analyze the (intercepted) coded material changes the atoms' characteristics, rendering the transmission useless.   [10:2851]

                              QUANTUM DOT - A NANOMETER-scale device in which each dot stores a single electron.  [10:2993NOTE: A quantum-dot array could require only a few thousand atoms to store one bit, whereas now ( circa 2000 ), the densest dynamic random access memory (DRAM) requires tens of millions of atoms to record a single bit of data.

                              QUANTUM IMAGING - IMAGING that employs "entanglement," a key principle of quantum physics.  In the entangled state, two particles exhibit identical properties ( e.g., charge and frequency ) even though they are located in separate points in space.  Quantum imaging begins with a source device that generates two laser beams.  Each beam consists of a stream of single photons, and the twin photons in the second beam are identical in frequency, direction and polarization.  Thus, if one beam illuminates an object, the other beam can generate its image.  [10:2976]

                              QUANTUM POLARIZATION SHIFT COMMUNICATIONS - A concept which has potential for faster-than-light communications at any distance, and is jam proof.  It is based on the fact that when two photons are emitted by a particular light source and given a unique and identical polarization, they always share the same orientation.  If the polarity of one photon is changed, the other's polarity is changed instantaneously.  [10:2751]

                              QUANTUM-WELL INFRARED PHOTODETECTOR (QWIP) - A sensor which can be arrayed and tailored to absorb radiation in the long-wavelength infrared (IR) region from 3 to 20 micrometers.  [10:2808]   NOTE:  QWIP technology is based on phototransitions between electron energy states in so-called quantum wells, the energy level between an electron's valance and conduction band.  By using different thickness and compositions of quantum-well materials, wavelength response can be customized and accurately specified.  The quantum-well materials can be stacked to increase IR absorption or to yield a sensor with several specific absorption bands.

                              QUANTUM WIRE - See BUCKY TUBE.

                               


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                            • David Strayhorn
                              ... at the MWI would not work in the classical world, eg to thermodynamics, brownian motion, etc. As you point out, it would have no bearing on the equations
                              Message 14 of 23 , Feb 21, 2004
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                                --- In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
                                wrote:

                                > In the face of incomplete knowledge, even the classical world is
                                > inherently statistical. Physicists probably wouldn't have any
                                > reason to come up with the multiple world hypothesis because the
                                > things that didn't happen wouldn't have any effect on the things
                                > that did.

                                True, although I think it is instructive to note that there is no reason th=
                                at the
                                MWI would not work in the classical world, eg to thermodynamics, brownian
                                motion, etc. As you point out, it would have no bearing on the equations --=
                                it
                                would be entirely "philosophical." Of course, the issue would come up that =
                                in
                                the pre-quantum era, physics was thought to be entirely deterministic, desp=
                                ite
                                the fact that statistical mechanics makes explicit use of probabilities -- =
                                I'm sure
                                you know the ins and outs of that discussion.

                                Hmm. That makes me wonder: If I lived in the pre-quantum era, and I thought=

                                that the world was entirely deterministic, might I object to statistical me=
                                chanics
                                on "philosophical" grounds? Perhaps I would. Which serves to illustrate the=

                                dangers of objecting to something on "philosophical" grounds.

                                What's odd about quantum mechanics is not the statistical
                                > nature of it, nor simply the quantization (which can happen also in
                                > classical wave theory), but instead, like Feynman said, the oddest
                                > thing about quantum mechanics is the two slit experiment.
                                >

                                yup: as Feynman said, the 2-slit exp contains "_the_" mystery of QM!

                                [...]

                                > It is not my understanding of the MWI either. What I'm trying to
                                > say is that the MWI is an alternative to the classical motion
                                > picture theory, where they end up with a huge collection of motion
                                > pictures. Obviously a single motion picture doesn't work. Standard
                                > quantum mechanics works, but it requires assumptions about existence
                                > that are not acceptable from an ontological (i.e. reality based)
                                > point of view. What it boils down to is that quantum mechanics
                                > (like relativity) is a phenomenological theory. It's based on the
                                > simplest mathematics that can explain complicated observations. But
                                > neither theory is ontologically correct in that you could construct
                                > a universe based on them (and you were God). In both cases, the
                                > problem is that there are multiple ways of describing the same
                                > physical situation, and those multiple ways are ontologically
                                > incompatible. The MWI theory is also an ontological attempt to
                                > explain quantum mechanics (that is, to get beyond the mathematics to
                                > the reality), but I think that it is unnecessarily bulky.
                                >

                                So the question comes up: what criteria do we use to judge a theory? You
                                might say that there are 2 ways:
                                1. Does the theory make the right predictions?
                                2. Is it "ontologically" correct?

                                Criterion #1 is something we can all agree on, when we sit down and crank
                                out the numbers and do the experiments. But criterion #2 is troublesome. Ho=
                                w
                                do you determine the "ontological correctness" of a theory (or interpretati=
                                on of
                                a theory)? In practice, it seems to me that people can be pretty damn arbit=
                                rary
                                about whether a theory makes sense ontologically.

                                In my own mind, in place of criterion 2, I have a different criterion: is i=
                                t easy or
                                difficult to understand and / or implement the theory / interpretation? Is =
                                this
                                something that I could explain (in outline form) to a 10 year old? Or does =
                                it
                                make my head swim? When I actually implement the theory, do I need a huge
                                supercomputer, or can I do it one one page of paper?

                                IOW, I am basically asking whether a theory is "useful in principle to us m=
                                ere
                                mortals." this criterion is incapable of saying a particular interpretation=
                                is
                                "correct" or "incorrect." nevertheless, it is a very important criterion! A=
                                corollary
                                to my criterion #2 would be: does a particular interpretation help me to co=
                                me
                                up with creative new ideas that might lead to a better theory? These are
                                worthwhile questions, and can in principle be person-specific!

                                >
                                > > Nevertheless – as you also mention – no
                                > > one has ever demonstrated a strict
                                > > conflict with GTR, and I have no reason
                                > > to believe that anyone ever will.
                                >
                                > Maybe the MOND gravitational anomaly, if it continues to survive,
                                > will be a counterexample to exact GTR. But my main problem with
                                > relativity is that it is lacking from an ontological point of view.
                                > It's a phenomenological theory based on observations about the speed
                                > of light and acceleration. No one could construct a physical model
                                > of a world that operated according to the principle of relativity,
                                > not even God. Like QM, it works great for predicting results, but
                                > it doesn't say anything about what is hiding behind the curtain,
                                > because we do not know how to create physical structures that would
                                > support waves even remotely similar to matter waves. This is a
                                > complaint similar to the one that the MWI people voice about QM.

                                I question whether science can ever, in principle, reveal what is "behind t=
                                he
                                curtain." Instead of thinking in terms of the "reality behind the curtain,"=
                                I prefer
                                to think in terms of the criterion #2 above -- which I realize would be
                                philosophically offensive to some people ;), but o well, you can't please
                                everyone.

                                [...]

                                > Yes, you are exactly correct. It might be just a weird coincidence
                                > that anti particles act like particles travelling backwards in
                                > time. But where I get suspicious is that since we can, after the
                                > fact, always assign a full time ordering, then why can't we assign
                                > the time ordering as we go along? The problem with doing that is
                                > that in order to provide a time ordering we would have to know which
                                > branches were taken. That is, you can't order time without knowing
                                > which events to order, and therefore know which events are in
                                > existence.

                                Yes, that's the way I see it: each different branch will have a different t=
                                ime
                                ordering for any given event. In fact, some branches may not even have the =

                                event in question at all! So the reason we can assign a time ordering "afte=
                                r the
                                fact" is that before the fact, we don't know which branch we have taken, bu=
                                t
                                after the fact, we do.


                                But quantum interference doesn't allow us to do this,
                                > all possibilities contribute to the probability.

                                I don't understand the point here. I agree that quantum interference is dam=
                                n
                                weird. But let's go back to the classical world, with statistical mechanics=
                                , and
                                apply the MWI to it. Let's say that we have a particle that is moving rando=
                                mly
                                (eg some sort of Brownian motion), and at a particular time t, it has the o=
                                ption
                                of going in one of N directions. Each option has probability 1/N. We could =

                                imagine that there are N different potential worlds, but only one will actu=
                                ally
                                be realized. It is plain to see that the probability of arriving at world n=
                                is
                                influenced by the total number N of worlds, which means that all possibilit=
                                ies
                                contribute to the probability. And we are using classical statistics, not
                                quantum.

                                > > Speaking of spinors – are you aware
                                > > that there is a way to model the
                                > > rotational properties of a spin-1/2
                                > > object using ordinary euclidean space
                                > > (without using quaternions)? It's in
                                > > MTW, the "cube within a cube" model –
                                > > look up spinors (or spin?) in the index
                                > > and turn to that page. (I don't have
                                > > MTW here with me, otherwise I'd give
                                > > you the page.)
                                >
                                > Yes, I've seen it. My problem is that I don't know how to turn it
                                > into a mathematical theory. That's the big reason I'm starting with
                                > QFT, it's something that already gives the right answer.

                                Doesn't Hadley's idea of 4-geons do this -- turn the cube within a cube mod=
                                el
                                into a mathematical theory?

                                DS

                                PS I am still working through your website.
                              • brannenworks
                                Dear David Strayhorn; ... We can never determine that a theory is ontologically correct. All we can do is determine that it is not. There can only be one
                                Message 15 of 23 , Feb 21, 2004
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                                  Dear David Strayhorn;

                                  > How do you determine the "ontological correctness"
                                  > of a theory (or interpretation of a theory)?

                                  We can never determine that a theory is ontologically correct. All
                                  we can do is determine that it is not. There can only be one
                                  ontologically correct description of a situation. Therefore, if a
                                  theory provides a plethora of mutually incompatible descriptions of
                                  the same situation (even though all those descriptions give the same
                                  observables), then it is clear that the theory cannot possibly be
                                  ontologically correct. This is a very basic problem with any theory
                                  that has a non trivial gauge symmetry such as standard quantum
                                  mechanics or relativity.

                                  I should clarify. It's okay if a theory needs to define a somewhat
                                  arbitrary coordinate system in order to describe a physical
                                  situation. That sort of symmetry (that the situation remains the
                                  same when the coordinates change) is not forbidden on ontological
                                  grounds. Where gauge symmetries get into trouble is that they allow
                                  different descriptions of the same situation where the difference is
                                  (at least apparently) more than just a transformation of the
                                  coordinate system. The natural conclusion is that the success of
                                  gauge theory is due to forces being consequences of coordinate
                                  symmetries.


                                  > I question whether science can ever, in
                                  > principle, reveal what is "behind the
                                  > curtain." Instead of thinking in terms
                                  > of the "reality behind the curtain,"I prefer
                                  > to think in terms of the criterion #2
                                  > above -- which I realize would be
                                  > philosophically offensive to some people
                                  > ;), but o well, you can't please everyone.

                                  The history of physics (and science) is one of curtains being
                                  raised. Always we find another curtain behind the curtain just
                                  raised. I don't know if there are a finite number of curtains or
                                  not, but my suspicion is that there are only a few more to go. For
                                  example, the number of forces that remain to be unified is quite
                                  small.


                                  > > But quantum interference doesn't allow us to do this,
                                  > > all possibilities contribute to the probability.

                                  > I don't understand the point here. I
                                  > agree that quantum interference is damn
                                  > weird. But let's go back to the classical
                                  > world, with statistical mechanics, and
                                  > apply the MWI to it. Let's say that we
                                  > have a particle that is moving randomly
                                  > (eg some sort of Brownian motion), and at
                                  > a particular time t, it has the option
                                  > of going in one of N directions. Each
                                  > option has probability 1/N. We could
                                  > imagine that there are N different potential
                                  > worlds, but only one will actually
                                  > be realized. It is plain to see that the
                                  > probability of arriving at world N is
                                  > influenced by the total number N of worlds,
                                  > which means that all possibilities
                                  > contribute to the probability. And we are
                                  > using classical statistics, not quantum.

                                  Quantum statistics is odd enough that physicists call the EPR
                                  paradox "spooky" for good reason. Statistical mechanics is
                                  generally called "boring" (by physics grad students, but not when
                                  the professors are around), also for good reason. You just can't
                                  get the EPR result from classical statistical mechanics, even if you
                                  include combination wave / particles, until you give up locality.
                                  My point of view is to keep locality, but to give up the unity of
                                  time.

                                  > Doesn't Hadley's idea of 4-geons do this
                                  > -- turn the cube within a cube model
                                  > into a mathematical theory?

                                  I'd call it more of a philosophical theory, a guess. What he needs
                                  to do is to solve those equations. Without the solutions there
                                  isn't much there.

                                  Along this line, I finally completed a pretty derivation of the
                                  Dirac equation in that "Proper time topology" I've been working on.
                                  The assumptions are simpler than any assumptions I've ever seen for
                                  such a derivation. I begin with an equation which is the most
                                  natural Geometric Algebraic equation that can be written down for
                                  the Proper Time Topology (i.e. d Psi/dt = Del Psi, where Psi is an
                                  arbitrary GA multivector and Del is, to within a multiple of the
                                  scalar + psuedoscalar factor, the standard differential GA operator)
                                  and then solve it. No need to postulate 4x4 matrices or what have
                                  you, you just simply solve the equation. Once you've solved it in
                                  the PTT, you then define a mapping of your solutions into the usual
                                  3 dimensions. That is, you eliminate the s coordinate by taking a
                                  complex Fourier transform (as is done in Kaluza-Klein theory). Once
                                  you've got the resulting 3-d equation, you can then go backwards and
                                  figure out the differential equation that it is a solution to. That
                                  equation is the Dirac equation. That is, the Dirac equation is the
                                  complicated equation that you get when you are unaware of the simple
                                  equation using one more dimension.

                                  Probably the reason that the Geometric Algebra experts (like the
                                  Hestenes paper I linked to the other day) didn't find this
                                  derivation (assuming they haven't, it may be out there, the physics
                                  literature is vast) is that the mapping involves i = sqrt(-1).
                                  Among the GA types, it is believed that whenever a physics equation
                                  has an i, that i must be interpreted as an element of the GA that,
                                  when squared, gives -1. They are so sure of this that Hestens
                                  redefines "i" and uses it as the "unit psuedoscalar". This makes it
                                  difficult to make theories that use the GA as a vector space over
                                  the complexes instead of the (normal for GA) reals. That is, their
                                  notation makes it difficult to consider imaginary multiples of
                                  multivectors. While it is true that the simple equation in the PTT
                                  satisfies this prejudice against sqrt(-1) (which I heartily agree
                                  with), the mapping from PTT to standard space-time is only a
                                  mathematical relation, a trick to convert from the PTT to an
                                  approximation topology, so the sqrt(-1) is not in the physical part
                                  of the theory.

                                  The Dirac equation may have been the more difficult half of my
                                  goal. From symmetry principles, I believe that it will be easier to
                                  derive the corresponding solution and mapping for quarks, that is,
                                  the QCD equation of motion. This is because the natural symmetry
                                  group for the color force is simply R^4, and that's exactly the
                                  local topology that the PTT possesses. So how hard can it be? I'll
                                  find out later tonite, maybe. When I get that far, I'll publish it,
                                  as I will have unified the electro-weak and strong forces.

                                  CAB
                                • David Strayhorn
                                  ... I would submit the idea that there is no such thing as a theory that does not have mutually exclusive interpretations / ontologies. Let s say that someone
                                  Message 16 of 23 , Feb 22, 2004
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                                    --- In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
                                    wrote:
                                    >... if a
                                    > theory provides a plethora of mutually incompatible descriptions of
                                    > the same situation (even though all those descriptions give the same
                                    > observables), then it is clear that the theory cannot possibly be
                                    > ontologically correct.

                                    I would submit the idea that there is no such thing as a theory that does not
                                    have mutually exclusive interpretations / ontologies.

                                    Let's say that someone comes up with a TOE, that says that the ultimate
                                    equation of the universe is Equation X.

                                    Interpretation #1: The "movie" interpretation, like what we talked about
                                    earlier. God has a big collection of tapes that he watches over and over; our
                                    universe is what's on the tapes.

                                    Interpretation #2: The "holodeck" interpretation. The *real* universe ("behind
                                    the curtain") actually is governed by Equation Y. But Lt Commander Data
                                    thought it would be fun to program Equation X into the Holodeck just to see
                                    what would happen, and we are the result.

                                    Interpretation #3: The reason that Equation X works is that lots of little green
                                    leprechauns implement it / make it work at the molecular level.

                                    I can be a little more specific. For any theory that is not deterministic (<==> the
                                    best the theory can do is calculate probabilities), we have two mutually
                                    exclusive ontologies: (1) multiple worlds / parallel worlds, which all exist "in
                                    reality;" (2) there's only one "real" world, *our* world. Thus, according to what
                                    you said above, it is impossible for any theory that, at best, calculates
                                    probabilities (that can be less than 1 and greater than 0), to be ontologically
                                    acceptable.

                                    Can you give me an example of a real-life theory that has one and only one
                                    possible ontology?

                                    > This is a very basic problem with any theory
                                    > that has a non trivial gauge symmetry such as standard quantum
                                    > mechanics or relativity.
                                    >
                                    > I should clarify. It's okay if a theory needs to define a somewhat
                                    > arbitrary coordinate system in order to describe a physical
                                    > situation. That sort of symmetry (that the situation remains the
                                    > same when the coordinates change) is not forbidden on ontological
                                    > grounds. Where gauge symmetries get into trouble is that they allow
                                    > different descriptions of the same situation where the difference is
                                    > (at least apparently) more than just a transformation of the
                                    > coordinate system.

                                    I'm not following the difference between the sort of symmetry that you think is
                                    allowed, and the gauge symmetry that is forbidden. You say that GR should
                                    be forbidden on ontological grounds -- I suppose because it says that the
                                    "real" length of an object, for example, depends on your frame of reference.
                                    What about classical Newtonian mechanics? This says that the "real" velocity
                                    of an object depends on the frame of reference. On ontological grounds,
                                    would you allow Newtonian physics but forbid GR, and (if so) why?

                                    The natural conclusion is that the success of
                                    > gauge theory is due to forces being consequences of coordinate
                                    > symmetries.

                                    Slightly off topic -- that makes me think of Feynman's discussion in his
                                    _Lectures_ about how QM explains that the electron does not spiral into the
                                    nucleus. Basically, it's the HUP. Which leads to the natural conclusion (in my
                                    mind) that the HUP produces a "force" (!?) that keeps the electron a certain
                                    distance away from the nucleus. Strange that HUP => force.

                                    >
                                    > > I question whether science can ever, in
                                    > > principle, reveal what is "behind the
                                    > > curtain." Instead of thinking in terms
                                    > > of the "reality behind the curtain,"I prefer
                                    > > to think in terms of the criterion #2
                                    > > above -- which I realize would be
                                    > > philosophically offensive to some people
                                    > > ;), but o well, you can't please everyone.
                                    >
                                    > The history of physics (and science) is one of curtains being
                                    > raised. Always we find another curtain behind the curtain just
                                    > raised.

                                    I suppose that we are begging the question of what we mean when we talk
                                    about "behind the curtain."

                                    In my mind, I find it useful to draw a sharp distinction between a *theory* and
                                    an *interpretation* of a theory. eg, there is only one theory of QM, which is
                                    wildly successful when tested in the lab, but there are many interpretations of
                                    this one theory; these cannot in principle be tested against each other. If
                                    someone manipulates / massages in interpretaion so that it makes predictions
                                    that differ from the other interpretations, then we say that we have a
                                    competing theory, not a competing interpretation.

                                    Now I agree with you that the history of physics is one of replacing one theory
                                    with another theory, which is more accurate than the preceeding one. But
                                    science progresses because we never lose sight of the importance of
                                    experimentation / observation. When we talk about something that is "behind
                                    the curtain," my understanding is that we are talking about something that
                                    cannot, in principle, be tested by experimentation. IOW, my understanding is
                                    that an ontological issue is one that, *by definition*, cannot be settled by an
                                    appeal to experimentation. If it can be settled by an experiment, then it's not
                                    an "ontological" issue. And in the context of the current discussion, the thing
                                    that lay "behind the curtain" is the one and only one correct ontology, which
                                    we can not in principle test vs competing ontologies via experiment.

                                    BTW, I'd say that the history of physics could be graphed as a steady
                                    realization that the laws of physics do not have *us* as a variable. First we
                                    learned that the earth was not flat (my plot of ground is not special); then that
                                    it's not the center of the universe (earth is not special); then the sun's not the
                                    center (sun not special). Then we learned (Newton) that our velocity (the
                                    earth's velocity) does not define "zero velocity," ie it's not special in any way.
                                    Then we learned (Einstein) that our frame of reference is not a special in any
                                    way, there is no ether. In every step that I mention where we learn that
                                    something is "not special," I mean that the theory makes no special mention of
                                    it. At every step, we are always free to assert, without experimental
                                    verification: my own (plot of land, planet, star, velocity, frame, etc) is
                                    ontololgically special, even if we can't prove it. I know it and God knows it.

                                    At every step in this progression, there are people who resist. As a modern
                                    example, I would present the somewhat prevalent notion that QM makes
                                    special mention of a human-like-ish thing called "consciousness". People
                                    don't want to give up the idea that their own thoughts are somehow situated at
                                    the center of the universe.

                                    > My point of view is to keep locality, but to give up the unity of
                                    > time.

                                    It would seem that there is a "conservation of weirdness." If you squish the
                                    weirdness here, it pops up there. Each interpretation of QM has the weirdness
                                    in a different place.

                                    > Along this line, I finally completed a pretty derivation of the
                                    > Dirac equation in that "Proper time topology" I've been working on.
                                    > The assumptions are simpler than any assumptions I've ever seen for
                                    > such a derivation. [...]

                                    In your derivation, do you assume Einstein's equation (in whatever form it
                                    takes in GA ...?) ? I'm wondering whether you have, in some manner of
                                    speaking, derived the Dirac eqn from the Einstein eqn.

                                    > ... So how hard can it be? I'll
                                    > find out later tonite, maybe. When I get that far, I'll publish it,
                                    > as I will have unified the electro-weak and strong forces.

                                    How's it goin'?

                                    A week or two ago, I thought that I had found a way to reformulate the path
                                    integral technique in a way that assigns a real-valued non-negative
                                    probability measure to each individual path -- none of this "complex
                                    amplitude" weirdness. A week or so later, I decided that I hadn't quite done it.
                                    Actually, that's not fair: I think I *have* done it. But I think my solution applies
                                    only to a special class of problems, and I need to do more work to generalize
                                    it to all problems. Sort of like figuring out SR, and using it as a stepping stone
                                    to GR.

                                    DS
                                  • brannenworks
                                    Dear David Strayhorn; ... I can t make any sense out of your argument. If what you re saying, is that you believe that the physical world is inherently
                                    Message 17 of 23 , Feb 22, 2004
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                                      Dear David Strayhorn;

                                      > ... God has a big collection of tapes that he
                                      > watches ... holodeck ... little green leprechauns ...

                                      I can't make any sense out of your argument. If what you're saying,
                                      is that you believe that the physical world is inherently
                                      mysterious, then you are fully entitled to your opinion, but I doubt
                                      that I would make much progress in understanding what can be
                                      understood with that as my starting point. The most important step
                                      in solving any mathematics problem is to assume that it is possible
                                      to solve.

                                      > Can you give me an example of a real-life
                                      > theory that has one and only one possible ontology?

                                      If classical mechanics worked, that would be an example.
                                      Ontologically, the world would be composed of particles and waves,
                                      each with specific values at any given time. Since there are waves,
                                      there must be an ether, so there are no problems assigning definite
                                      values of momentum to the particles, unlike the case with relativity
                                      where there is no "real" momentum, just the momentum as it would be
                                      measured by different observers. Similarly, without quantum
                                      mechanics there is no Heisenberg uncertainty problem in assigning
                                      specific positions to particles. This was the state of physics
                                      circa 1904.

                                      Outside of physics, every field is filled with valid ontological
                                      theories. For example, biology believes in chromosomes and genes.
                                      Chemistry has atoms and all that.

                                      > I'm not following the difference between the
                                      > sort of symmetry that you think is
                                      > allowed, and the gauge symmetry that is forbidden.

                                      As an example, consider the vibrations in a circular drum membrane.
                                      One can use cartesian coordinates, but the problem may be simpler in
                                      cylindrical coordinates. Either solution gives the position of the
                                      drumhead as a function of time. Ontologically, the two sets of
                                      equations correspond to the same movement of the membrane. It's
                                      just a redefinition of the position coordinates. This kind of
                                      symmetry is not only allowed, it is required. It's not a
                                      consequence of there existing multiple versions of the same
                                      situation, it's just an artifact of how we choose to use mathematics
                                      to describe that situation. In all cases, it's just a drum head,
                                      and it has a particular position at any given time. The
                                      transformation between coordinates is an example of a trivial gauge
                                      transform.

                                      I don't say that gauge symmetry is "forbidden", what I am saying is
                                      that anytime you have a nontrivial gauge transform, that is an
                                      indication that your theory is not yet complete. The simplest
                                      example of a gauge transform that is mentioned in the physics books
                                      is that of the energy as used in standard quantum mechanics. If you
                                      transform a quantum state by changing all energies (i.e. energy
                                      potentials and the state of the particle) by the same (i.e. "global"
                                      in the vernacular of the gauge theorists) change del_E, the result
                                      will be that the wave state of your particle will be multiplied by a
                                      factor exp( i del_E t). This will mean that at any given position,
                                      the wave state will oscillate faster or slower by this factor. But
                                      there will be no change to the dynamics of the particle, because
                                      this change is a symmetry of Schroedinger's wave equation and it has
                                      no effect on any observable. By the way, if you're interested in
                                      this wonderfully simple example of a gauge transform, it is
                                      described at length in Sakurai's excellent book on Quantum mechanics
                                      (now in common use as a text for introductory graduate level quantum
                                      mechanics):
                                      http://www.amazon.com/exec/obidos/tg/detail/-/0201539292/102-2597904-
                                      4590519?v=glance

                                      Now my point is that when one takes the above gauge transform, one
                                      changes the rate at which the wave function oscillates. That is
                                      ontologically impossible. There can only be one "true" rate at
                                      which the "true" wave function is oscillating. This is much more
                                      than the trivial transforms associated with changes to coordinate
                                      systems. Also, note that this is only a nonrelativistic QM gauge
                                      transform, it is not a QED or QCD gauge transform, so it is not
                                      obvious that it has any real significance. But it makes a great
                                      example of a gauge transform.

                                      > Which leads to the natural conclusion (in my
                                      > mind) that the HUP produces a "force"
                                      > (!?) that keeps the electron a certain
                                      > distance away from the nucleus.

                                      The probability density for a ground state electron in a hydrogen
                                      atom has its maximum at the nucleus. So I'm not sure what you're
                                      saying here.

                                      > When we talk about something that is "behind
                                      > the curtain," my understanding is that we
                                      > are talking about something that
                                      > cannot, in principle, be tested by experimentation.

                                      My use of the term is to describe something that is not yet
                                      understood, but may or may not be understood in the future. For
                                      example, radioactivity was behind the curtain back in the 19th
                                      century. I see the history of physics as one of curtains being
                                      raised. Maybe there's a better way of putting this.

                                      > At every step, we are always free
                                      > to assert, without experimental
                                      > verification: my own (plot of land,
                                      > planet, star, velocity, frame, etc) is
                                      > ontololgically special, even if we can't
                                      > prove it. I know it and God knows it.

                                      Well, I'm convinced that there is an ether, but I'm also convinced
                                      that it has nothing to do with me, or my plot of land or whatever.
                                      If I had to make a guess as to the relative velocity of the ether,
                                      I'd say that it probably is about the same velocity as the cosmic
                                      microwave background, that is, about 390km/sec towards the
                                      constellation Leo.

                                      This gets back to the basic question of whether or not the universe
                                      has an ontology. If you assume that it does not, my guess is that
                                      you will miss any evidence that it does. And most of the advances
                                      of science (rather than physics, which is only a small part of
                                      science), have been due to improvements in ontological understanding
                                      of situations.

                                      There was recently a fascinating book (and well worth the low price)
                                      on the subject of the use of cathedrals in the Middle Ages to make
                                      solar observations:
                                      http://www.amazon.com/exec/obidos/tg/detail/-/0674854330/102-2597904-
                                      4590519?v=glance

                                      It includes a history of the relations between Galileo and the
                                      Church, but is mostly about how and why churches were used as solar
                                      observatories. Anyway, Galileo was ordered by the church to not
                                      make ontological arguments about whether or not the Earth was the
                                      center of the universe. He was allowed to make statements along the
                                      line of "thus it is possible to accurately predict the heavenly
                                      positions of Mars and Venus using the useful assumption that the
                                      motion is made relative to the sun, rather than the earth", but not
                                      to make statements along the line of "the earth, therefore, moves
                                      around the sun rather than vice versa".

                                      Now that 400+ years have gone by, it's frequently said that the
                                      church was wrong and Galileo was right, but, in fact, in 2004 we do
                                      not believe that the sun is the center of the universe. All Galileo
                                      had was his equations, he did not have the truth about the sun and
                                      earth in terms of how later physics understood it.

                                      So was Galileo's search for an ontological understanding of the
                                      motion of the sun and planets a waste of time? He was wrong, but
                                      was his effort wasted? You could have reproduced his results, as a
                                      mathematical fact, by simply subtracting out the sun-earth vector so
                                      as to convert sun centered calculations into earth centered
                                      calculations. This would have kept him from being excommunicated
                                      (or banned or whatever they did), but still, despite all the efforts
                                      of the authorities of the time, he stuck to his guns and paid the
                                      price.


                                      > It would seem that there is a "conservation
                                      > of weirdness." If you squish the
                                      > weirdness here, it pops up there. Each
                                      > interpretation of QM has the weirdness
                                      > in a different place.

                                      Yes, my hope is to cancel some of the weirdness of quantum mechanics
                                      against some of the weirdness of relativity.

                                      > In your derivation, do you assume
                                      > Einstein's equation (in whatever form it
                                      > takes in GA ...?) ? I'm wondering whether
                                      > you have, in some manner of
                                      > speaking, derived the Dirac eqn from
                                      > the Einstein eqn.

                                      No, as far as the Dirac equation goes, I'm working in an entirely
                                      flat metric, that is, in a metric that is equivalent to the flat
                                      metric of special relativity only. The theory can be generalized to
                                      GR, but since there are no experiments that cover QM in GR, there's
                                      little reason to make the (very large) effort to so generalize.
                                      There is a similar version of relativity that has a few people
                                      working on it. It's called "5D relativity", and they are mostly
                                      relativists so their efforts are in that direction. I only took one
                                      graduate class in relativity.

                                      > How's it goin'?

                                      I started working on QCD last night. It quickly became obvious that
                                      there is no differnce in wave equations for quarks and electrons.
                                      They both use the Dirac equation, it's just that there are
                                      differences in the number of degrees of freedom. This makes the
                                      whole thing smell like a difference in the vertices only, so I'm
                                      going back to make a derivation of the photon propagator.
                                      Hopefully, the photon propagator can be derived by computing dot
                                      products between appropriate electron wave function values. If this
                                      is the case, I should be able to generalize to QCD without a lot of
                                      trouble.

                                      I should explain more completely about why I think there is a
                                      relation between wave function values and vertices, but it's a long
                                      and complicated chain of calculations and reasoning (and won't fit
                                      in the margins of this text). Part of it has to do with that simple
                                      gauge transform (the one having to do with energy) that I mentioned
                                      early in this post.

                                      CAB
                                    • brannenworks
                                      Dear David Strayhorn; It appears to me that I ve figured out how to map both quarks and leptons into the same propagator. The solution is to use the PTT with
                                      Message 18 of 23 , Feb 23, 2004
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                                        Dear David Strayhorn;

                                        It appears to me that I've figured out how to map both quarks and
                                        leptons into the same propagator. The solution is to use the PTT
                                        with the simple wave equation on it. This is 16 coupled
                                        differential equations. You can partially uncouple them by using
                                        a "projection operator" that commutes with the differential
                                        equation. Such a projection operator will divide the 16 coupled
                                        differential equations into two uncoupled pairs of 8 differential
                                        equations each, where the relationship with the 16 equations is
                                        linear. So you take linear combinations.

                                        Now to get the Dirac Equation for the electron, I used the
                                        projection operator (s+/-1)/2, where "s" is the unit vector in the s
                                        dimension, and the operator is defined as "multiplication on the
                                        right". That is, Op(Psi) = Psi (s+1)/2 or = Psi (s-1)/2.

                                        That (s+1)/2 is a projection operator, in this context, is shown by
                                        the fact that (s+1)/2 (s+1)/2 = (s+1)/2. That is, (s+1)/2 is
                                        unipotent. When you have a unipotent operator u, then 1-u is also
                                        unipotent:
                                        (1-u)(1-u) = 1-2u+u^2 = 1-2u+u = (1-u).

                                        So your pair of unipotent operators give projection operators. That
                                        this particular pair commute with the differential equation is
                                        clear. The derivative operator is equivalent to a multiplication on
                                        the left, while the above projection operators multiply on the
                                        right. Therefore, any solution to the full equation can be written
                                        as the sum of two solutions, one in the subalgebra defined by the
                                        (1+s) operator, the other in the subalgebra defined by the (1-s)
                                        operator.

                                        The two subalgebras, which one might write as "GA(R^4) MOD (s+/-1)",
                                        each have eight degrees of freedom. Their eight elements are
                                        equivalent to the eight elements of the even subalgebra of GA(R^4).
                                        Of course the even subalgebras of a Geometric Algebra are equivalent
                                        to a spinor field, so it's hardly surprising that these two
                                        collections of eight real equations are each equivalent to the Dirac
                                        equation.

                                        It's easy to show that the wave equation, when demoted down to the
                                        subalgebra defined by either of the two projection operators, is
                                        equivalent to the Dirac equation. The easiest way to do this (or at
                                        least the first I saw), is to use the Dirac matrices as shown in
                                        Bjorken and Drell:
                                        http://www.amazon.com/exec/obidos/tg/detail/-/0070054940
                                        Since the Dirac equation has four complex functions, you need to
                                        define a set of four linear maps from the algebra to the complex
                                        numbers. Make a guess along the line of (x-iy)(1+s)/2 for use in
                                        one of those four complex functions (where x,y, and s are the unit
                                        vectors in the GA), and then simply follow through the consequences
                                        of that selection to determine the choices for the other 3
                                        functions. When you're done, if you made the lucky choice, you'll
                                        have a set of four linear maps, where each map takes a simple
                                        combination of four distinct elements of the GA. If you didn't get
                                        lucky, then try again with a different element, or just use your
                                        intuition to adjust the guess.

                                        Now all this gets you the Dirac equation for the electron from the
                                        simplest possible wave equation in the PTT. But it gives you a
                                        little more than that, in that you actually have two copies of the
                                        Dirac equation. The other solution, the one that was projected by
                                        (1-s)/2, you can use for the Dirac equation for the neutrino. Or
                                        better, you should use a linear combination of these two projections
                                        to define the electron and neutrino wave functions.

                                        But that's not all you get. In addition to breaking the equations
                                        up by projecting with (1+/-s)/2, you can also project along (1+/-
                                        x)/2, and the same with y and z.

                                        Now the nice thing about the projections in the s direction is that
                                        the funny business of the field was not coupled to the usual three
                                        dimensions. That's not the case with the projections along the x,
                                        y, and z directions. First, you've got exactly three of these,
                                        which is the same number of colors that quarks can come in. Second,
                                        just as with the electron/neutrino, you have two flavors for each of
                                        these projections. As with the electron / neutrino, you will
                                        probably have to make linear combinations to get the right electric
                                        charge, spin, and all that.

                                        Therefore, you have exactly the right number of Dirac equations as
                                        you need to supply two leptons and six quarks (six, that is,
                                        counting color).

                                        Now in the transformation from the PTT to R^3, we had to take a
                                        Fourier transform exp(i n s / R), where n is an integer, s is the
                                        coordinate, and R is the radius of the hidden dimension. The above
                                        calculations apply no matter what n is. So it's natural to
                                        associate n with the lepton/quark family. That is, n=1 gives e-
                                        neutrinos, electrons, and the u and d quarks. N=2 gives the u-
                                        neutrinos, muons, and s and c quarks. N=3 gives the tau leptons and
                                        the t and b quarks.

                                        This means that I have exactly the correct number of degrees of
                                        freedom I need to map the solutions in the PTT on to the standard
                                        quantum mechanical model of elementary fermions. My next task is to
                                        figure out what those linear combinations have to be, and from that
                                        derive the various Cabibo angles.

                                        Oh, and there's one other thing. The universe is clearly handed.
                                        You can insert that into that simple wave equation by replacing the
                                        Del operator with b(alpha) Del, where b is a linear combination of
                                        the scalar and psuedoscalar in the form:
                                        b(alpha) = cosh(alpha) + sinh(alpha) xyzs,
                                        where "xyzs" is the unit psuedoscalar. When you make this change,
                                        the new Del' = b Del operator is still a factorization of the Klein
                                        Gordon equation. The factorization works, by the way, because any
                                        vector v anticommutes with xyzs. That implies that:
                                        Del b(alpha) = b(-alpha) Del,
                                        so computing the square of the wave equation (and using the fact
                                        that b(-alpha) is the multiplicative inverse of b(alpha):

                                        b(alpha) Del b(alpha) Del = b(alpha) b(-alpha) Del Del = Del^2.

                                        Now when you include that b(alpha) factor, what you've done is to
                                        give the universe a handedness. Without that factor, the wave
                                        equation is symmetric under mirror images, but with it, b(alpha) has
                                        to go to b(-alpha). What this means is that instead of having to
                                        get handed particles by making rather arbitrary assumptions about
                                        the form of the Lagrangian for each type of particle, you can
                                        instead do it by making a single assumption about the nature of the
                                        space that all particles travel in.

                                        So things are going well, and I think I'll get the rest of the loose
                                        ends tied down towards the end of the month.

                                        Carl Brannen
                                      • brannenworks
                                        Dear Lady Ganesha; I just bought a book that gives me sort of an idea of what ... The book I bought is Nature Loves to Hide by Shimon Malin. I picked it up
                                        Message 19 of 23 , Mar 3, 2004
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                                          Dear Lady Ganesha;

                                          I just bought a book that gives me sort of an idea of what
                                          the "numinous world" is, and so I can now answer your comments:

                                          > What this theory of time points to is Plato's
                                          > notion of the numinous world that preceeds the
                                          > phenomenal (measurable, three dimensional, sensate,
                                          > tactile) world. In other words, if consciousness is
                                          > the root of all matter, then time is the ordering of
                                          > consciousness and time itself carries with it fundamental
                                          > characteristics (called archetypes). Therefore, if you
                                          > look at quantum fields, they are 'intelligent' in that
                                          > they have 'primary' qualities that tend to manifest
                                          > themselves, by virtue of the creative nature of
                                          > consciousness itself, as 'space-time' units. Plato
                                          > called this the numinous world which gives rise
                                          > to the myriad diversity of the phenomenold world.
                                          >
                                          > As earnest as science is to keep philosphy out of its
                                          > house, I think we are seeing an inevitable collision if
                                          > science wants to go on to the next level of evolution.

                                          The book I bought is "Nature Loves to Hide" by Shimon Malin. I
                                          picked it up at 1/2 price books which had it for under $10. He has
                                          a good introduction to the EPR effect. Let me quote from the book
                                          on the subject of the "noumenal" [p195]:

                                          <<<
                                          The cave allegory presents a vision of reality that consists of
                                          three major levels of being: first, "the Good," the highest and most
                                          real, the source of the being of the next level; next, the
                                          Intelligible realm of the many Forms (other than the Good) which
                                          eternally are; and last, the sensible world of transient phenomena
                                          in space and time, phenomena that are shadows of the other Forms.
                                          These transient phenomena are "shadows" because they do not have an
                                          independent existence; the source of their existence is the being of
                                          the Forms. We, who are conditioned by our senses, mistakenly
                                          consider the sensible world to independently existing and the only
                                          reality there is. We are in this respect like the prisoners in the
                                          cave, who mistake the shadows for the objects that cast the shadows.
                                          >>>

                                          In this venacular, what I would like to do is to derive properties
                                          of the objects that cast shadows from a careful analysis of the
                                          shadows. My complaint with the standard representation of these
                                          objects (other than the usual complaint that the forces of nature
                                          are not yet unified), is that the modes of vibration and movement in
                                          the purported objects (i.e. quantum states in space-time) do not
                                          correspond to what we have observed as the modes of vibration and
                                          movement in the "shadows" that we deal with on a day to day basis
                                          (such as drum heads or blocks of steel). Instead, QM and relativity
                                          imply that the objects must be multiply defined in ways that are
                                          mutually inconsistent.

                                          When I was a graduate student, I had two problems with QM. The
                                          first was an absence of an explicit role for the soul, and the
                                          second was that the theory uses complex numbers.

                                          Sure, E&M (and many other physics theories) can be (and are) written
                                          with complex numbers, but they can also be written without them --
                                          the complex numbers are only there to ease calculations. Quantum
                                          mechanics, in contrast, has complex numbers at its core, with no
                                          explanation. To get an idea of the depth of this distinction, look
                                          through the bible of relativity, "Gravitation" by Misner, Wheeler
                                          and Thorne, and try to find a single complex number. In relativity,
                                          there are no uses of complex numbers, for example, as with stresses
                                          and strains in a block of steel, all gravitational stresses are real.

                                          My guess on the "soul" problem was that the observer in QM
                                          corresponded, in some way, to the action of the soul. But I was
                                          unable to make any progress with this idea, and as I looked deeper
                                          into field theory, I became less sure of my guess. Right now I
                                          still feel that the soul can be modeled as a sort of particle, one
                                          that makes some sort of choices among the many available to a
                                          quantum object, but the connection is pretty vague. I still have no
                                          idea what the noumenal world would be like.

                                          So instead of working at this deep philosophical level, I began
                                          working at the problem from the other end, from the point of view of
                                          trying to remove the complex numbers from QM. I began by spending a
                                          few years trying to put the Dirac equation into a real form, rather
                                          than a complex form, because I do not believe that complex numbers
                                          make an ontologically correct description of reality. It turns out
                                          that there are many ways that you can do this, but none of them tell
                                          you much, at least as such. I ended up becoming very proficient at
                                          manipulating the Dirac equation, but I made no progress at putting
                                          it into a form which would match the stresses in a believable space.

                                          So I began looking instead at the underlying assumptions of reality,
                                          and tried to figure out which ones I was sure of, and which could be
                                          in need of being redone. It was clear that all the concepts that
                                          are renormalized in field theory cannot be trusted. That would
                                          include anything with a mass (such as momentum, mass or energy) or a
                                          coupling strength. What is left to trust is space-time or space and
                                          time. I figured that these concepts were simple enough that they
                                          would survive in any theory that derived the mass associated objects
                                          from a deeper theory.

                                          A subject I've always been fascinated with is symmetry. It turns
                                          out that the symmetry that an object appears to contain when looked
                                          at from a distance (as when one ignores its very small individual
                                          parts), can be, and usually is, quite different from the symmetry it
                                          possesses from a very short distance. Literally everything around
                                          us is an example of this. And when one moves from the small to the
                                          large symmetry can be either or gained either way. For example,
                                          balls that are perfectly spherically symmetric will naturally stack
                                          into crystalline structures that are hexagonal (think cannon ball
                                          stacks). For another example, molecules that are so assymetric as
                                          to be handed can crystallize into crystals that have no handedness
                                          (and vice versa).

                                          So I began to suspect that the symmetry of space-time did not relate
                                          to the actual symmetry of the underlying reality. (Note that is not
                                          the noumenal reality, it is still in the phenomenological realm.
                                          All I'm talking about here is math equations, not the real thing.)
                                          Of these two, it is time that is the more mysterious, so I began to
                                          think about time.

                                          Relativity is mostly about how movement affects the perceived
                                          passage of time. All observers can agree on the "proper time"
                                          experienced by an object, but not on anything else (other than the
                                          things that depend on mass, and therefore are known to be confused
                                          by renormalization). But proper time is not really part of
                                          Einstein's description of space-time, instead it's a derived
                                          quantity. Soon after that I realized that one could reinterpret the
                                          metric used in relativity so as to make proper time a coordinate,
                                          which is where I was just a year ago. This is sort of like what the
                                          string theorists were doing, but is different in that they
                                          interpreted the compact hidden dimensions as space dimensions, while
                                          I have a more time-like interpretation. Since then I've been busily
                                          rederiving QM from this point of view.

                                          But no, I still have no idea what is going on in the numinous
                                          world. I agree that it exists, but I do not have any idea what it
                                          is about. Still no room for consciousness, but I do feel that I am
                                          just a little closer to the goal of including it. I hope to get the
                                          first paper done this month.

                                          Carl Brannen
                                        • David Strayhorn
                                          ... Nope, that s not what I think at all. I was sorta doing a demonstrating absurdity by being absurd argument, but since it didn t seem to make sense to
                                          Message 20 of 23 , Mar 4, 2004
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                                            --- In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
                                            wrote:
                                            > Dear David Strayhorn;
                                            >
                                            > > ... God has a big collection of tapes that he
                                            > > watches ... holodeck ... little green leprechauns ...
                                            >
                                            > I can't make any sense out of your argument. If what you're saying,
                                            > is that you believe that the physical world is inherently
                                            > mysterious, then you are fully entitled to your opinion,

                                            Nope, that's not what I think at all. I was sorta doing a "demonstrating
                                            absurdity by being absurd" argument, but since it didn't seem to make sense
                                            to you, I'll assume I may have misunderstood your earlier position.



                                            > .. The most important step
                                            > in solving any mathematics problem is to assume that it is possible
                                            > to solve.

                                            I agree -- and I would say that that especially applies to *physical* problems.

                                            >
                                            > > Can you give me an example of a real-life
                                            > > theory that has one and only one possible ontology?
                                            >
                                            > If classical mechanics worked, that would be an example.

                                            In my above example, I was trying to argue that not even classical mechanics
                                            has one and only one possible ontology. But we may not be agreeing on what
                                            "ontology" means.

                                            > Ontologically, the world would be composed of particles and waves,
                                            > each with specific values at any given time. Since there are waves,
                                            > there must be an ether,

                                            Hmm. What is the justification for the statement: since there are waves, there
                                            must be an ether? GR has waves but no ether. In classical mechanics, we
                                            could certainly assume that there is an ether, but what would *require* us to
                                            assume it? ie, what experiment could tell us that there had to be an ether?

                                            > ...so there are no problems assigning definite
                                            > values of momentum to the particles, unlike the case with relativity
                                            > where there is no "real" momentum, just the momentum as it would be
                                            > measured by different observers.

                                            What makes you say momentum is not "real" in relativity? In general, for X to
                                            be a "real" thing (according to the way you define real), does X have to be
                                            invariant? In your mind, is GR tainted/tarnished because things that
                                            classically seem "real" are viewed in GR as not "real"?

                                            > ... Similarly, without quantum
                                            > mechanics there is no Heisenberg uncertainty problem in assigning
                                            > specific positions to particles. This was the state of physics
                                            > circa 1904.
                                            >
                                            > Outside of physics, every field is filled with valid ontological
                                            > theories. For example, biology believes in chromosomes and genes.
                                            > Chemistry has atoms and all that.
                                            >
                                            > > I'm not following the difference between the
                                            > > sort of symmetry that you think is
                                            > > allowed, and the gauge symmetry that is forbidden.
                                            >
                                            > As an example, consider the vibrations in a circular drum membrane.
                                            > One can use cartesian coordinates, but the problem may be simpler in
                                            > cylindrical coordinates. Either solution gives the position of the
                                            > drumhead as a function of time. Ontologically, the two sets of
                                            > equations correspond to the same movement of the membrane. It's
                                            > just a redefinition of the position coordinates. This kind of
                                            > symmetry is not only allowed, it is required. It's not a
                                            > consequence of there existing multiple versions of the same
                                            > situation, it's just an artifact of how we choose to use mathematics
                                            > to describe that situation. In all cases, it's just a drum head,
                                            > and it has a particular position at any given time. The
                                            > transformation between coordinates is an example of a trivial gauge
                                            > transform.
                                            >
                                            > I don't say that gauge symmetry is "forbidden", what I am saying is
                                            > that anytime you have a nontrivial gauge transform, that is an
                                            > indication that your theory is not yet complete.

                                            It seems like what you are doing is to describe what sort of things guide your
                                            intuition on your search for something new. ie, certain things are not strictly
                                            forbidden, but they are "not beautiful" (?) to you, and thus an indication that
                                            some sort of new ideas are needed. IOW, the aspects of a theory that cause
                                            you "ontological angst" are the aspects that you seek to replace. These are
                                            the rocks that you turn over. Would that be fair?

                                            > .. The simplest
                                            > example of a gauge transform that is mentioned in the physics books
                                            > is that of the energy as used in standard quantum mechanics. If you
                                            > transform a quantum state by changing all energies (i.e. energy
                                            > potentials and the state of the particle) by the same (i.e. "global"
                                            > in the vernacular of the gauge theorists) change del_E, the result
                                            > will be that the wave state of your particle will be multiplied by a
                                            > factor exp( i del_E t). This will mean that at any given position,
                                            > the wave state will oscillate faster or slower by this factor. But
                                            > there will be no change to the dynamics of the particle, because
                                            > this change is a symmetry of Schroedinger's wave equation and it has
                                            > no effect on any observable. By the way, if you're interested in
                                            > this wonderfully simple example of a gauge transform, it is
                                            > described at length in Sakurai's excellent book on Quantum mechanics
                                            > (now in common use as a text for introductory graduate level quantum
                                            > mechanics):
                                            > http://www.amazon.com/exec/obidos/tg/detail/-/0201539292/102-2597904-
                                            > 4590519?v=glance
                                            >
                                            > Now my point is that when one takes the above gauge transform, one
                                            > changes the rate at which the wave function oscillates. That is
                                            > ontologically impossible. There can only be one "true" rate at
                                            > which the "true" wave function is oscillating.

                                            Maybe the wave function is not a "real/true" thing, but is just a mathematical
                                            intermediary that we use to calculate probabilities. Given a mathematical
                                            formalism of a theory, do you think that it is necessary (or required, or perhaps
                                            merely preferred) that every term of every equation correspond to something
                                            that we can "point our finger to"? (ie, to be ontologically palatable).

                                            > This is much more
                                            > than the trivial transforms associated with changes to coordinate
                                            > systems. Also, note that this is only a nonrelativistic QM gauge
                                            > transform, it is not a QED or QCD gauge transform, so it is not
                                            > obvious that it has any real significance. But it makes a great
                                            > example of a gauge transform.
                                            >
                                            > > Which leads to the natural conclusion (in my
                                            > > mind) that the HUP produces a "force"
                                            > > (!?) that keeps the electron a certain
                                            > > distance away from the nucleus.
                                            >
                                            > The probability density for a ground state electron in a hydrogen
                                            > atom has its maximum at the nucleus. So I'm not sure what you're
                                            > saying here.

                                            True -- what Feynman derived (Lectures, Vol III, page 2-6) was not the peak
                                            of the probability density (which as you point out is at the nucleus), but the
                                            spread in its position. As he says: "Atoms are completely impossible from the
                                            classical point of view, since the electrons would spiral into the nucleus." But
                                            from the HUP, we have pa=h, where a is uncertainty in position. With only the
                                            HUP as a starting point, Feynman does one of those tricks where you
                                            somehow manage to seemingly derive an actual quantity out of thin air -- in
                                            this case, the Bohr radius: 0.528 angstroms. Amazing, imho. It just seemed to
                                            me like the HUP was a "force" that kept the electron out of the nucleus; I've
                                            never heard anyone *describe* the HUP as a force, but it sure looked like one
                                            to me in Feynman's derivation.

                                            >
                                            > > When we talk about something that is "behind
                                            > > the curtain," my understanding is that we
                                            > > are talking about something that
                                            > > cannot, in principle, be tested by experimentation.
                                            >
                                            > My use of the term is to describe something that is not yet
                                            > understood, but may or may not be understood in the future. For
                                            > example, radioactivity was behind the curtain back in the 19th
                                            > century. I see the history of physics as one of curtains being
                                            > raised. Maybe there's a better way of putting this.

                                            This is where we were using terms differently.

                                            > > At every step, we are always free
                                            > > to assert, without experimental
                                            > > verification: my own (plot of land,
                                            > > planet, star, velocity, frame, etc) is
                                            > > ontololgically special, even if we can't
                                            > > prove it. I know it and God knows it.
                                            >
                                            > Well, I'm convinced that there is an ether, but I'm also convinced
                                            > that it has nothing to do with me, or my plot of land or whatever.
                                            > If I had to make a guess as to the relative velocity of the ether,
                                            > I'd say that it probably is about the same velocity as the cosmic
                                            > microwave background, that is, about 390km/sec towards the
                                            > constellation Leo.
                                            >
                                            > This gets back to the basic question of whether or not the universe
                                            > has an ontology. If you assume that it does not, my guess is that
                                            > you will miss any evidence that it does.

                                            Once again, it comes down to the definition of ontology. I have a Gene
                                            Roddenberry-esque faith in the ability of the human spirit to conquer the
                                            universe, which means (in the context of our current discussion) that there is
                                            no Law of Nature that is beyond our ability to understand.

                                            > ... And most of the advances
                                            > of science (rather than physics, which is only a small part of
                                            > science), have been due to improvements in ontological understanding
                                            > of situations.
                                            >
                                            > There was recently a fascinating book (and well worth the low price)
                                            > on the subject of the use of cathedrals in the Middle Ages to make
                                            > solar observations:
                                            > http://www.amazon.com/exec/obidos/tg/detail/-/0674854330/102-2597904-
                                            > 4590519?v=glance
                                            >
                                            > It includes a history of the relations between Galileo and the
                                            > Church, but is mostly about how and why churches were used as solar
                                            > observatories.

                                            Interesting. I know nothing about that.

                                            Anyway, Galileo was ordered by the church to not
                                            > make ontological arguments about whether or not the Earth was the
                                            > center of the universe.

                                            I've always considered that to be one specific example (out of many) of the
                                            tendency of most people to believe certain things (1) that we want to believe
                                            (for whatever reason), despite (2) the fact that they contradict evidence that is
                                            available to us. (and that we are capable of reasoning through).

                                            > He was allowed to make statements along the
                                            > line of "thus it is possible to accurately predict the heavenly
                                            > positions of Mars and Venus using the useful assumption that the
                                            > motion is made relative to the sun, rather than the earth", but not
                                            > to make statements along the line of "the earth, therefore, moves
                                            > around the sun rather than vice versa".
                                            >
                                            > Now that 400+ years have gone by, it's frequently said that the
                                            > church was wrong and Galileo was right, but, in fact, in 2004 we do
                                            > not believe that the sun is the center of the universe. All Galileo
                                            > had was his equations, he did not have the truth about the sun and
                                            > earth in terms of how later physics understood it.
                                            >

                                            And the view of GR is that what rotates around what depends on your frame
                                            of reference, and no frame of reference is preferred over any other ...

                                            > So was Galileo's search for an ontological understanding of the
                                            > motion of the sun and planets a waste of time? He was wrong, but
                                            > was his effort wasted? You could have reproduced his results, as a
                                            > mathematical fact, by simply subtracting out the sun-earth vector so
                                            > as to convert sun centered calculations into earth centered
                                            > calculations. This would have kept him from being excommunicated
                                            > (or banned or whatever they did), but still, despite all the efforts
                                            > of the authorities of the time, he stuck to his guns and paid the
                                            > price.
                                            >
                                            >
                                            > > It would seem that there is a "conservation
                                            > > of weirdness." If you squish the
                                            > > weirdness here, it pops up there. Each
                                            > > interpretation of QM has the weirdness
                                            > > in a different place.
                                            >
                                            > Yes, my hope is to cancel some of the weirdness of quantum mechanics
                                            > against some of the weirdness of relativity.
                                            >

                                            Me too, in a way.


                                            > > In your derivation, do you assume
                                            > > Einstein's equation (in whatever form it
                                            > > takes in GA ...?) ? I'm wondering whether
                                            > > you have, in some manner of
                                            > > speaking, derived the Dirac eqn from
                                            > > the Einstein eqn.
                                            >
                                            > No, as far as the Dirac equation goes, I'm working in an entirely
                                            > flat metric, that is, in a metric that is equivalent to the flat
                                            > metric of special relativity only. The theory can be generalized to
                                            > GR, but since there are no experiments that cover QM in GR, there's
                                            > little reason to make the (very large) effort to so generalize.

                                            I suppose the reason to generalize would be if the "weirdness of relativity" that
                                            is needed to cancel (or give rise to) the weirdness of QM is present in GR but
                                            not special relativity. That's true in my conceptual framework -- a large part of
                                            the GR-weirdness basically comes from closed timelike curves, which are
                                            GR- but not SR-entities.

                                            > There is a similar version of relativity that has a few people
                                            > working on it. It's called "5D relativity", and they are mostly
                                            > relativists so their efforts are in that direction. I only took one
                                            > graduate class in relativity.

                                            One more than me ;)

                                            > > How's it goin'?
                                            >
                                            > I started working on QCD last night. It quickly became obvious that
                                            > there is no differnce in wave equations for quarks and electrons.
                                            > They both use the Dirac equation, it's just that there are
                                            > differences in the number of degrees of freedom. This makes the
                                            > whole thing smell like a difference in the vertices only, so I'm
                                            > going back to make a derivation of the photon propagator.
                                            > Hopefully, the photon propagator can be derived by computing dot
                                            > products between appropriate electron wave function values. If this
                                            > is the case, I should be able to generalize to QCD without a lot of
                                            > trouble.
                                            >
                                            > I should explain more completely about why I think there is a
                                            > relation between wave function values and vertices, but it's a long
                                            > and complicated chain of calculations and reasoning (and won't fit
                                            > in the margins of this text). Part of it has to do with that simple
                                            > gauge transform (the one having to do with energy) that I mentioned
                                            > early in this post.
                                            >

                                            It's funny -- I've noticed that things that seem soooo obvious to me (a chain of
                                            reasoning, an intuitive connection between one thing and another) are about
                                            as clear as mud to other people. Sometimes people object to a particular idea
                                            for reasons that seem arbitrary to me. But I suppose the reverse is also true.
                                            Different people have different intuitions.

                                            DS

                                            > CAB
                                          • David Strayhorn
                                            ... There s a discussion that is sorta brewing in the group, qm2, on the topic of complex numbers in QM. Maybe worth looking at if you re interested. I ve been
                                            Message 21 of 23 , Mar 4, 2004
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                                              --- In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
                                              wrote:

                                              > When I was a graduate student, I had two problems with QM. ... the
                                              > second was that the theory uses complex numbers.
                                              >
                                              > Sure, E&M (and many other physics theories) can be (and are) written
                                              > with complex numbers, but they can also be written without them --
                                              > the complex numbers are only there to ease calculations. Quantum
                                              > mechanics, in contrast, has complex numbers at its core, with no
                                              > explanation. ...

                                              > So instead of working at this deep philosophical level, I began
                                              > working at the problem from the other end, from the point of view of
                                              > trying to remove the complex numbers from QM. I began by spending a
                                              > few years trying to put the Dirac equation into a real form, rather
                                              > than a complex form, because I do not believe that complex numbers
                                              > make an ontologically correct description of reality. It turns out
                                              > that there are many ways that you can do this, but none of them tell
                                              > you much, at least as such. I ended up becoming very proficient at
                                              > manipulating the Dirac equation, but I made no progress at putting
                                              > it into a form which would match the stresses in a believable space.

                                              There's a discussion that is sorta brewing in the group, qm2, on the topic of
                                              complex numbers in QM. Maybe worth looking at if you're interested.

                                              I've been fiddling around lately with the path integral approach, and one of the
                                              manipulations that I did with it was to rework the basic approach in a way that
                                              makes no use of complex numbers. The fundamental problem of the path
                                              integral approach is to calculate the probability that a particle that starts at x1,
                                              t1 will end up at x2, t2. There are several steps that involve enumerating all
                                              paths, calculating the action for each path, calculating the phase for each path
                                              (which is a complex number), adding all the phases to get the "kernel", and
                                              then taking the square of the absolute value of the kernel to get the
                                              (differential) probability. This whole procedure can be summed up by one
                                              equation for the differential probability of ending up at x2, t2, ie:

                                              P = | sum (over all paths) e ^ (- i S / h) | ^ 2

                                              where S is the action. And this technique is general enough that, in principle,
                                              any QM problem can be solved by this method, iiuc.

                                              It took me only a few steps to put the above equation into a form so that you
                                              can calculate the probability without even knowing what complex numbers
                                              are. The implication (I think) is that, in principle, you should be able to do all of
                                              QM without ever using complex numbers. (it would be computationally more
                                              difficult, but possible, in theory.) If you're interested, I uploaded a draft of a
                                              paper I'm working on in the files of this group, called modified-path-
                                              integral.pdf -- look at page 5 (which is section 6), equations (41) through
                                              about (48) or so. I made it with LaTeX, which I recently learned :), so it should
                                              is easy to read the equations. (btw, much of the rest of the paper is still in draft
                                              form.)

                                              DS
                                            • brannenworks
                                              Dear David Strayhorn; ... The ether is supposed to be the medium which allows light to propagate. GR doesn t have much to say about light. For example,
                                              Message 22 of 23 , Mar 5, 2004
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                                                Dear David Strayhorn;

                                                > What is the justification for the
                                                > statement: since there are waves,
                                                > there must be an ether? GR has waves but no ether.

                                                The "ether" is supposed to be the medium which allows light to
                                                propagate. GR doesn't have much to say about light. For example,
                                                even something as basic as the polaroid filters in sunglasses cannot
                                                be described in GR alone. The waves that do occur in GR are gravity
                                                waves, but they've not yet been observed (as far as I know). I'm
                                                not a GR type, and I don't have any guesses as to whether or not
                                                those gravity waves will be seen or not.

                                                > ie, what experiment could tell us
                                                > that there had to be an ether?

                                                QM uses a "momentum cutoff" (among other things) to make QED
                                                calculations work right. If nature has a momentum cutoff, then
                                                there is a maximum momentum. That says that any object (an
                                                electron, for example) has a maximum possible momentum. A test for
                                                this is to accelerate an object to very high momenta. If the
                                                momentum cutoff is there, then you will eventually reach a limit
                                                where it is impossible to accelerate any further. Note that this
                                                would be a violation of Newton's (or Galileo's, I forget which) as
                                                well as Einstein's relativity.

                                                To find the ether, repeat the experiment twice, once in the +x
                                                direction, and once in the -x direction. You are rest with respect
                                                to the ether when the results from those two experiments match.

                                                > What makes you say momentum is not "real"
                                                > in relativity? In general, for X to
                                                > be a "real" thing (according to the way
                                                > you define real), does X have to be
                                                > invariant? In your mind, is GR tainted
                                                > /tarnished because things that
                                                > classically seem "real" are viewed in
                                                > GR as not "real"?

                                                Momentum in GR is not "real" because it cannot be defined except
                                                with respect to a particular rest frame. That means that it cannot
                                                be a fundamental part of a universe made up of "real" things. By
                                                contrast, if one considers the universe to be a mathematical
                                                construct, rather than a "real" thing, then there is no problem with
                                                defining momentum that way.

                                                I am in no way saying that GR is inconsistent with itself, or
                                                incompatible with observations. What I'm saying is that its
                                                consistency is limited to that of a mathematical construct. It does
                                                not possess the consistency that a description of an object in the
                                                world possesses. It's an "as if" theory.

                                                Rather than "tainted or tarnished", I would use the
                                                word "incomplete". It's somewhat ironic that this is the same
                                                complaint that Einstein had of quantum mechanics.

                                                > It seems like what you are doing is to
                                                > describe what sort of things guide your
                                                > intuition on your search for something new.
                                                > ie, certain things are not strictly
                                                > forbidden, but they are "not beautiful" (?)
                                                > to you, and thus an indication that
                                                > some sort of new ideas are needed. IOW, the
                                                > aspects of a theory that cause
                                                > you "ontological angst" are the aspects
                                                > that you seek to replace. These are
                                                > the rocks that you turn over. Would that
                                                > be fair?

                                                It's not beauty that distinguishes between a phenomenological and an
                                                ontological theory. My movement in this direction is not due to an
                                                appreciation of beauty. There is nothing more beautiful than SR and
                                                GR. In fact, I think it is this beauty that has bedazzled the eyes
                                                of physicists for so many years. We'd all like nature to be a
                                                beautiful thing, and we all have a strong tendency to believe
                                                theories that are more beautiful than not. For example, for
                                                centuries astronomers believed that planets moved on circles, rather
                                                than ellipses, because circles are more beautiful (or symmetric).
                                                This is human nature. And it is this human nature that has misled
                                                us. Instead of more beautiful mathematical constructs, I believe
                                                that what we need in physics now is more realistic descriptions.

                                                About a century ago, there was an influential physicist named Ernst
                                                Mach. He believed in "empiriocentrism", which is pretty much the
                                                opposite of my point of view. Let me quote from the book "Nature
                                                Loves to Hide":

                                                <<
                                                Science, according to Mach, is nothing more than a description of
                                                facts. And "facts" involve nothing more than sensations and the
                                                relations among them. Sensations are the only real elements. All
                                                the other concepts are extra; they are merely imputed on the real,
                                                i.e., on the sensations, by us. Concepts like "matter" and "atom"
                                                are merely shorthand for collections of sensations; they do not
                                                denote anything that exists.
                                                >>

                                                What it all boils down to is this: "A good theory is no more than a
                                                condensation of observations in accordance with the principle of
                                                thought economy." If you believe this, then there is no reason to
                                                suppose that relativity is explained by a hidden dimension. But
                                                here it is 2004 and the strong and weak forces are still not unified.

                                                Physics has followed Mach's philosophy for 100 years, and now we're
                                                stuck. What I'm saying is that we may need to ditch the philosophy,
                                                and go back and rederive physics without it. And that implies that
                                                we need to have a physics that is more than just logically or
                                                mathematically consistent.

                                                For example, QED is obviously a mathematical construction, not a
                                                real description of what goes on with electrons and photons. This
                                                is clear from the way that infinities have to be cancelled out of
                                                the theory. The great physicists like Feynmann recognize this, as
                                                he notes in his book on QED. Here's what Landau and Lifshitz says
                                                about QED:

                                                <<
                                                There is as yet no logically consistent and complete relativistic
                                                quantum theory. We shall see that the existing theory introduces
                                                new physical features into the nature of the description of particle
                                                states, which acquires some of the features of field theory (see
                                                chapter 10). The theory is, however, largely constructed on the
                                                pattern of ordinary quantum mechanics. This structure of the theory
                                                has yielded good results in quantum electrodynamics. The lack of
                                                complete logical consistency in this theory is shown by the
                                                occurrence of divergent expressions when the mathematical formalism
                                                is directly applied, although there are quite well-defined ways of
                                                eliminating these divergences. Nevertheless, such methods remain,
                                                to a considerable extent, semiempirical rules, and our confidence in
                                                the correctness of the results is ultimately based only on their
                                                excellent agreement with experiment, not on the internal consistency
                                                or logical ordering of the fundamental principles of the theory.
                                                >>

                                                The original reason I started delving into these matters was to
                                                repair the above inconsistency. I felt that it had something to do
                                                with the appearance of complex numbers in the theory. But as I
                                                continued to work on it, I was unable to make progress until I gave
                                                up perfect Lorentz symmetry. And by "gave up", I mean exactly
                                                that. Relativity was torn from me only by years of failing efforts
                                                to make QM logically consistent under the assumptions of perfect
                                                relativity. I couldn't do it. Neither could the rest of the
                                                physics community.

                                                The most recent response to these consistency problems in QM are
                                                called "string theories", and these were what got me interested in
                                                physics once again. But when I picked up a few books, it rapidly
                                                became obvious that they had more infinities getting cancelled than
                                                anything dreamed of in QED. So I began working on physics.

                                                > Given a mathematical
                                                > formalism of a theory, do you think that
                                                > it is necessary (or required, or perhaps
                                                > merely preferred) that every term of
                                                > every equation correspond to something
                                                > that we can "point our finger to"? (ie,
                                                > to be ontologically palatable).

                                                To be ontologically correct, a theory need only have its most basic
                                                units be "real", not every term of every equation. Also, I suppose
                                                I should mention that if someone did have a unified field theory,
                                                even one that was only a mathematical construct, I wouldn't be
                                                searching for an ontologically correct unified field theory.

                                                Carl Brannen
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