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Re: multiple versions of the particle

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  • 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 1 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 2 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 3 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 4 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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