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 on Bell inequalities and the de BroglieBohm pilot wave version of QM

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  In bell_bohm@yahoogroups.com, "Tom" <tkuntzle@u...> wrote:
> Hi
Tk, tunneling occurs when a particle is able to penetrate a region
>
> 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
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 twoslit 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   In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
wrote:
> So in my version of QFT BM, interference is due to time being multi
Hey Carl,
> 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.
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  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, singlevalued 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 spacelike 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
observerindependent objective existence and actually is the object.
For a nonrelativistic Nparticle system the wavefunction is a
complexvalued field in a 3N 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 "complexvalued field in a 3N
dimensional space." My interpretation is that this field is only
the result we get when we force the situation into an eitheror 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 3N
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 3dimensional (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
builtin 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 Nbody scenario, in standard quantum
mechanics, requires a 3N 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 Nbody 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 multiparticle 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 nonrelativistic
systems the Schrodinger wave equation is a good approximation to
reality. (See "Is manyworlds 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 > Dear David Strayhorn; From my point of view, the best argument for MWI
The idea that photons interfere with themselves on light paths that may be
> 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.
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 selfinterference conclusion is
implied no more than that light follows resonant paths.
>>From that effect, it's natural to conclude that there are different
That won't work if one path is five light years longer.
> 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.
I think it is clear there is no absolute time frame.
> That is, the MWI is based on the inherent assumption that time works
> in a linear, singlevalued 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.
>
Yes and no. You have established that everything is a clock in that it
> 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.
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
correlation does not imply influences
> time ordering is relative, that is, that there is no way of
> determining the time ordering of spacelike 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
exactly.
> propagate faster than light, and therefore that causality is
> preserved.
>
the wave function is only probabilities.
> 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.
>
Only the now exists fleetingly. It includes ordering in space and time
> 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.
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):
Objectivity must be defined with respect to all communicating
>
>
> 1) The metaphysical assumption: That the wavefunction does not
> merely encode the all the information about an object, but has an
> observerindependent objective existence and actually is the object.
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 nonrelativistic Nparticle system the wavefunction is a
This agrees with your assertion that every participant manifests a time
> complexvalued field in a 3N dimensional space.
ordering.>> I hold that the wave function does not encode all the possible
What time ordering operator? There is none. The evolution of the field?
> 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 "complexvalued field in a
> 3N dimensional space". My interpretation is that this
> field is only the result we get when we force the situation into an
> eitheror kind of linear sequence of operations (if you know QFT,
> think of the time ordering operator, especially in the rest of this
> explanation).
>
ok
>>From my point of view, the requirement that the base space be 3N
> 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
> 3dimensional (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
> builtin time ordering. (Note the assumption of a Bohmian view
> on particles in this argument.)
>
Renormalization formally removes all the infinities, it removes all self
> 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 Nbody scenario, in standard quantum
> mechanics, requires a 3N 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 Nbody 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.
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
Two dimensional signals across time can only paint 3 dimensions. That
> universe ends up with way too many dimensions.
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
You get discrete events but that's not where the time ordering comes from,
> 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.
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
This is not a renormalization effect. Mass/energy, time/space are imposed
> 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.
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
Perspectives grow exponentially with the number of participants.
> 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 multiparticle states. The usual linear
> superposition seen in standard quantum mechanics, in this view, is
> actually only a result of the result of renormalization.
Fortunately the number of participants does not increase too often.
> That is, the usual additive linear superposition is the result of the
The many world theory attempts to account for the failure of QM to predict
> 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 nonrelativistic
> systems the Schrodinger wave equation is a good approximation to
> reality. (See "Is manyworlds 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 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
>
>
>
>
>
>
>
>
>
>
> Yahoo! Groups Links
>
> To visit your group on the web, go
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> to:bell_bohmunsubscribe@yahoogroups.com Your use of Yahoo!
> Groups is subject to the Yahoo! Terms of Service. Dear Jim Whitescarver:
> The idea that photons interfere with
This is a thought experiment only, and is an interference between a
> 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.
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
I'm not sure what you're getting at here, so I'm going to more fully
> 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).
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 spacelike 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
Yes, this is the standard objective of renormalization, and is in
> all the infinities, it removes all self
> reference, and removes all time.
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
My view on the gauge theories is that they're due to all the forces
> where the time ordering comes from,
> I don't think. You get time ordering
> because Gauge theories impose a time
> perspective in their formulation.
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 spacetime. 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
I agree, at the very least from a philosophical point of view. But
> account for the failure of QM to predict
> the wave collapse by asserting that
> there is none. This is contrary to
> experience. Shit happens.
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
When I was in grad school I never had time to think about elementary
> 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?
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 KaluzaKlein
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/KleinGordon.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  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 'spacetime' 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, singlevalued 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 spacelike 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
observerindependent objective existence and actually is the object.
For a nonrelativistic Nparticle system the wavefunction is a
complexvalued field in a 3N 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 "complexvalued field in a 3N
dimensional space." My interpretation is that this field is only
the result we get when we force the situation into an eitheror 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 3N
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 3dimensional (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
builtin 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 Nbody scenario, in standard quantum
mechanics, requires a 3N 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 Nbody 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 multiparticle 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 nonrelativistic
systems the Schrodinger wave equation is a good approximation to
reality. (See "Is manyworlds 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
Do you Yahoo!?
Yahoo! Finance: Get your refund fast by filing online  Thanks for a thoughtful response CAB. Comments below.
brannenworks wrote:
> Dear Jim Whitescarver:
Here you are talking about correlated actions and aggregate non
>
> > 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.
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.
>
Photon direction of travel is time independent. In the microcosm
>
> > 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 spacelike 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.
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.
>
I think your intuition about the renormalization process is dead on
>
> > 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.
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.
>
I don't think it is proper to associate any relative physical property
>
> > 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.
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 spacetime. 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 KaluzaKlein
> 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/KleinGordon.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  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
It seems to me that you could implement at least a simplistic version of th=
> 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.
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 prequantum 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 multipleworlds 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
I understand your idea that "time is linear and single valued" <==> "the
> 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, singlevalued 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.
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
IOW, the time ordering of events for one observer (particle) may be (probab=
> 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.
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 Â– see below.
> It's a pretty good place to start, but it isn't proof,
Exactly: if you want to timeorder events, it is first necessary to specify=
> 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 spacelike separated events.
a frame
of reference, and no frame is priveleged over any other.
> A good percentage
Very true. My take is that, if people are going to have a meaningful
> 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.
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 Â– it is, in fact, instantane=
ous.
Nevertheless Â– as you also mention Â– 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,
I agree.
> 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
Hmm. I would think that you can put a time ordering on it, provided that yo=
> ordering on it, but only to the extent that creation precedes
> annihilation.
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 nonmultiply connected ones.)
> This is at least subtly different from MWI.
What else is there to know?
>
> 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
> observerindependent objective existence and actually is the object.
> For a nonrelativistic Nparticle system the wavefunction is a
> complexvalued field in a 3N 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
I share your inherent unease with the heavy reliance on complex numbers in =
> differ from MWI (and maybe Bohmian too) in the assumption that the
> objective existence is formed of a "complexvalued field in a 3N
> dimensional space."
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 =
complexvalued 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
I'm familiar with the basics of path integrals, not so familiar with QFT.
> the result we get when we force the situation into an eitheror 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 3N
I'm getting lost here.
> 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 3dimensional (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
> builtin time ordering. (Note the assumption of a Bohmian view on
> particles in this argument.)
> The single particle propagators in QFT correspond in quantum theory
I don't follow the connection between timeordering and the number of
> 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 Nbody scenario, in standard quantum
> mechanics, requires a 3N dimensional space, at least in my opinion.
dimensions needed.
> But if you look at the problem from the point of view of the bare
I understand the notion that 3 dimensions is preferable to 3N dimensions
> 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 Nbody 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.
from an ontological PoV.
> Let me try and explain this another way. If you take a bath and
Â… and they're not, hence the need for 3N dimensions? Â…
> 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
!? interesting..
> 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
Speaking of spinors Â– are you aware that there is a way to model the
> with geometrical algebra and spinors)
rotational properties of a spin1/2 object using ordinary euclidean space =
(without using quaternions)? It's in MTW, the "cube within a cube" model Â– =
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
Yup Â– this wouldn't bother me, except for the fact that the probabilities
> 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 multiparticle 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?
combine via addition of complexvalued amplitudes Â– which is, of course, ve=
ry
"weird."
> This is awfully suspicious, as
I am **very** interested in what you just said. Do you have a reference for=
> 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.
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 ^( Â–i S/ h)
[where S is the classical action],
I have:
Probability ~ sum over paths of logarithm of [(1/4)(1  e ^( Â–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,
I've never understood the notion that in the MWI, "there is no collapse of =
> 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.
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 spinup 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'estce pas?
> For nonrelativistic
I read that section Â– didn't quite follow it. My simplistic notion is that:=
> systems the Schrodinger wave equation is a good approximation to
> reality. (See "Is manyworlds a relativistic theory?" for how the
> more general case is handled with quantum field theory or third
> quantisation.
"MWI and
standard QM are equally compatible (or not) with relativity."
> >>>
Would this be along the same lines of an Objectivist proving that Existence=
>
> 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.
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  Thanks for the interesting comments, Jim;
> Here you are talking about correlated
It's obvious we're talking past each other on this point. We
> 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.
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
For any one Feynman diagram, it is not only possible for a photon to
> are time dependent. there is no
> way to see them backwards. Experience
> suggests that such is the law of
> the universe.
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  brannenworks wrote:
> Thanks for the interesting comments, Jim;
Yes. But we may be getting to the point and I believe we agree. At
>
> > 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.
least you are confirming me objections to the standard interpretations
of photon selfinterference. To be clear the interpretation of resonant
channels (in space) as a superior interpretation of selfinteraction
which gets removed may be rather novel.
> We
The point is that the photons travel for billions of years crossing
> probably differ on what "interference" means. Distant galaxies are
> seen clearly because telescopes use optics and shields to eliminate
> unwanted interference.
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
I disagree. Interactions with the atmosphere are NOT photon
> stars in daylight.
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
This is simple a power discrepancy. If you remove the larger signal,
> broadcasting on the same frequency.
the smaller signal will still be there.
>
Suppose there is a resonant channel structure in every reference
>
> 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.
frame. (The binary nature of discrimination also suggests this may be
true). Instead of possibilities evolving over time, these resonate
channels evolve.
>
But only on the photon with respect to itself, not with other photons.
>
> 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.
>
The photon going back in time is always superficial or because another
>
> > 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.
observer sees the photon going the other direction.
> That is, the
Right, it is artificial, no faster than light signaling is involved.
> 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.
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
I already got the point... but thanks for making it.
> 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
Jim
>
>
> CAB  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
I'm working on some more papers, but they're in Latex, so they can't
> website  I'm halfway through your first
> paper. I think it helps me understand
> your PoV at least a little bit.
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
In the face of incomplete knowledge, even the classical world is
> 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 prequantum 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 multipleworlds 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.
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
I think you've described what I think better than I did.
> 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?
> IOW, the time ordering of events for one
It is not my understanding of the MWI either. What I'm trying to
> 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 Â– see below.
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 Â– as you also mention Â– no
Maybe the MOND gravitational anomaly, if it continues to survive,
> one has ever demonstrated a strict
> conflict with GTR, and I have no reason
> to believe that anyone ever will.
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
Yes, you are exactly correct. It might be just a weird coincidence
> 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.
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
If you've been reading my website, you'll see that I think that
> function, prior to running an experiment]?
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
Yes, that was a really short explanation for a subject that I feel
> timeordering and the number of
> dimensions needed.
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 3N dimensional wave domains.
(b) Quantum statistics require time ordering operators.
(c) Renormalization imposes a time sequence on creation and
annihilation operators.
> Speaking of spinors Â– are you aware
Yes, I've seen it. My problem is that I don't know how to turn it
> that there is a way to model the
> rotational properties of a spin1/2
> object using ordinary euclidean space
> (without using quaternions)? It's in
> MTW, the "cube within a cube" model Â–
> 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.)
into a mathematical theory. That's the big reason I'm starting with
QFT, it's something that already gives the right answer.
> Yup Â– this wouldn't bother me, except for
This was something that bothered me for a long time as well. I'm
> the fact that the probabilities
> combine via addition of complexvalued
> amplitudes Â– which is, of course, very
> "weird."
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 spacetime. 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
Maybe I have overstated my case. Let me try and restate exactly
> 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?
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 3N 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 /hbar) Psi(x,0).
Take the log:
phi(x,t) =  i H t /hbar + 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/hepph/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 "spacetime" to a random position,
except that the time coordinate is multiplied by i.
> I have attempted my own rederivation of the path
Maybe I should try and give a reason for why complicated (not
> integral formalism where probabilities of individual
> paths combine as real numbers in an intuitive fashion,
> not as complex amplitudes in the usual "weird" fashion.
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 3N. 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,
I agree.
> which means we collapsed onto the spinup
> 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'estce pas?
CAB ok, I won't say the P word ever again...
The following definitions come from the sewlexicon glossary
http://www.sewlexicon.com/glossary.htm
this is the Q page
http://www.sewlexicon.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 NANOMETERscale device in which each dot stores a single electron. [10:2993] NOTE: A quantumdot 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 fasterthanlight 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]
QUANTUMWELL INFRARED PHOTODETECTOR (QWIP)  A sensor which can be arrayed and tailored to absorb radiation in the longwavelength infrared (IR) region from 3 to 20 micrometers. [10:2808] NOTE: QWIP technology is based on phototransitions between electron energy states in socalled quantum wells, the energy level between an electron's valance and conduction band. By using different thickness and compositions of quantumwell materials, wavelength response can be customized and accurately specified. The quantumwell materials can be stacked to increase IR absorption or to yield a sensor with several specific absorption bands.
QUANTUM WIRE  See BUCKY TUBE.
Do you Yahoo!?
Yahoo! Mail SpamGuard  Read only the mail you want.  In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
wrote:
> In the face of incomplete knowledge, even the classical world is
True, although I think it is instructive to note that there is no reason th=
> 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.
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 prequantum 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 prequantum 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
yup: as Feynman said, the 2slit exp contains "_the_" mystery of QM!
> classical wave theory), but instead, like Feynman said, the oddest
> thing about quantum mechanics is the two slit experiment.
>
[...]
> It is not my understanding of the MWI either. What I'm trying to
So the question comes up: what criteria do we use to judge a theory? You
> 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.
>
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 personspecific!
>
I question whether science can ever, in principle, reveal what is "behind t=
> > Nevertheless Â– as you also mention Â– 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.
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
Yes, that's the way I see it: each different branch will have a different t=
> 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.
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 Â– are you aware
Doesn't Hadley's idea of 4geons do this  turn the cube within a cube mod=
> > that there is a way to model the
> > rotational properties of a spin1/2
> > object using ordinary euclidean space
> > (without using quaternions)? It's in
> > MTW, the "cube within a cube" model Â–
> > 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.
el
into a mathematical theory?
DS
PS I am still working through your website.  Dear David Strayhorn;
> How do you determine the "ontological correctness"
We can never determine that a theory is ontologically correct. All
> of a theory (or interpretation of a theory)?
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
The history of physics (and science) is one of curtains being
> 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.
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,
Quantum statistics is odd enough that physicists call the EPR
> > 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.
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 4geons do this
I'd call it more of a philosophical theory, a guess. What he needs
>  turn the cube within a cube model
> into a mathematical theory?
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 KaluzaKlein theory). Once
you've got the resulting 3d 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 spacetime 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 electroweak and strong forces.
CAB   In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
wrote:>... if a
I would submit the idea that there is no such thing as a theory that does not
> 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.
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 reallife theory that has one and only one
possible ontology?
> This is a very basic problem with any theory
I'm not following the difference between the sort of symmetry that you think is
> 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.
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
Slightly off topic  that makes me think of Feynman's discussion in his
> symmetries.
_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 suppose that we are begging the question of what we mean when we talk
> > 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.
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 humanlikeish 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
It would seem that there is a "conservation of weirdness." If you squish the
> time.
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
In your derivation, do you assume Einstein's equation (in whatever form it
> 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. [...]
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
How's it goin'?
> find out later tonite, maybe. When I get that far, I'll publish it,
> as I will have unified the electroweak and strong forces.
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 realvalued nonnegative
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  Dear David Strayhorn;
> ... God has a big collection of tapes that he
I can't make any sense out of your argument. If what you're saying,
> watches ... holodeck ... little green leprechauns ...
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 reallife
If classical mechanics worked, that would be an example.
> theory that has one and only one possible ontology?
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
As an example, consider the vibrations in a circular drum membrane.
> sort of symmetry that you think is
> allowed, and the gauge symmetry that is forbidden.
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//0201539292/1022597904
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
The probability density for a ground state electron in a hydrogen
> mind) that the HUP produces a "force"
> (!?) that keeps the electron a certain
> distance away from the nucleus.
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
My use of the term is to describe something that is not yet
> the curtain," my understanding is that we
> are talking about something that
> cannot, in principle, be tested by experimentation.
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
Well, I'm convinced that there is an ether, but I'm also convinced
> 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.
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//0674854330/1022597904
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 sunearth 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
Yes, my hope is to cancel some of the weirdness of quantum mechanics
> of weirdness." If you squish the
> weirdness here, it pops up there. Each
> interpretation of QM has the weirdness
> in a different place.
against some of the weirdness of relativity.
> In your derivation, do you assume
No, as far as the Dirac equation goes, I'm working in an entirely
> 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.
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  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 (s1)/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 1u is also
unipotent:
(1u)(1u) = 12u+u^2 = 12u+u = (1u).
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 (1s)
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 (xiy)(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
(1s)/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  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
The book I bought is "Nature Loves to Hide" by Shimon Malin. I
> 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 'spacetime' 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.
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 spacetime) 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 spacetime 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 spacetime 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 spacetime, 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 timelike 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   In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
wrote:> Dear David Strayhorn;
Nope, that's not what I think at all. I was sorta doing a "demonstrating
>
> > ... 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,
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
I agree  and I would say that that especially applies to *physical* problems.
> in solving any mathematics problem is to assume that it is possible
> to solve.
>
In my above example, I was trying to argue that not even classical mechanics
> > Can you give me an example of a reallife
> > theory that has one and only one possible ontology?
>
> If classical mechanics worked, that would be an example.
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,
Hmm. What is the justification for the statement: since there are waves, there
> each with specific values at any given time. Since there are waves,
> there must be an ether,
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
What makes you say momentum is not "real" in relativity? In general, for X to
> 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.
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
It seems like what you are doing is to describe what sort of things guide your
> 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.
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
Maybe the wave function is not a "real/true" thing, but is just a mathematical
> 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//0201539292/1022597904
> 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.
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
True  what Feynman derived (Lectures, Vol III, page 26) was not the peak
> 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.
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.
>
This is where we were using terms differently.
> > 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
Once again, it comes down to the definition of ontology. I have a Gene
> > 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.
Roddenberryesque 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
Interesting. I know nothing about that.
> 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//0674854330/1022597904
> 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
I've always considered that to be one specific example (out of many) of the
> center of the universe.
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
And the view of GR is that what rotates around what depends on your frame
> 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.
>
of reference, and no frame of reference is preferred over any other ...
> So was Galileo's search for an ontological understanding of the
Me too, in a way.
> 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 sunearth 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
I suppose the reason to generalize would be if the "weirdness of relativity" that
> > 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.
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 GRweirdness basically comes from closed timelike curves, which are
GR but not SRentities.
> There is a similar version of relativity that has a few people
One more than me ;)
> 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'?
It's funny  I've noticed that things that seem soooo obvious to me (a chain of
>
> 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.
>
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
  In bell_bohm@yahoogroups.com, "brannenworks" <brannenworks@y...>
wrote:
> When I was a graduate student, I had two problems with QM. ... the
There's a discussion that is sorta brewing in the group, qm2, on the topic of
> 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.
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 modifiedpath
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  Dear David Strayhorn;
> What is the justification for the
The "ether" is supposed to be the medium which allows light to
> statement: since there are waves,
> there must be an ether? GR has waves but no ether.
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
QM uses a "momentum cutoff" (among other things) to make QED
> that there had to be an ether?
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"
Momentum in GR is not "real" because it cannot be defined except
> 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"?
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
It's not beauty that distinguishes between a phenomenological and an
> 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?
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 welldefined 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
To be ontologically correct, a theory need only have its most basic
> 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).
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