Re: the basis of relativity

Bilge wrote:
Baugh: >Bilge wrote:
>> >
>> >For the quantity to be meaningful it *must* be independent of
>> >those choices we make in the description which are not physical,
>> >i.e. choice of basis, choice of zero phase, etc.
>> >> Once again, I said nothing to the contrary. You seem to missing
>> the point, entirely.
>
>Very well what then do you mean by "we are perfectly free to ...
>not gauge invariant." above.
I mean exacty that. If one can develop a theory which isn't gauge
invariant, but explains the phenomena correctly, one is free to do
so. I have no idea what such a theory would be, but I know I haven't
seen one (that works). 

What do you mean by "explains the pheonomena correctly".  A theory
*predicts* phenomeona it does not explain it.  Again my original point
that gauge invariance is more necessary than you imply.  Predictions
which depend on the units you use are not meaningful.  Before they
can be considered correct vs incorrect we must first ask if they
are meaningful and they are not if the predictions depend on choices
of convention.  Possibly you are considering the distinction between
"implicit" and "manifest" gauge covariance/invariance.

In being formulated the theory may not be expressly or manifestly founded on gauge invariance. The gauge may be fixed implicitly.
The predictions nonetheless must be independent of choices of gauge.

>> >Otherwise we "change reality" by doing a little math. You are
>> >correct in that we needn't do physics. One can create theories
>> >which are not self consistent or unambiguously interpreted.
>> >> If you believe that, then why are you having so much difficulty
>> attributing physical significance to the mathematical quantities
>> that make the theory consistent?
>
>Because the physical significance is relative to two artificial
>constructs, in this case space-time and the potential fields.
You seem to be talking at two different levels at the same time
and treating one as ``artificial'' and the other as a more fundamental
description and implying that one is ``real'' or at least more real.

Possibly, I take observables as fundamental. I'm not concerned with "reality" but rather what is observable.

But that never was the issue and in any case, I don't dicount a rock
as being real just because I know it's composed of more fundamental
things.


This is not my view.  I'm not concerned with models be they constructive
or derivative.  I'm concerned with the theory which is only and always
the predictive elements.


 >Let x be a physical quantity, make up quantities y and z = x+y.
 >y and z are not physically significant alone but their relation
 >to each  other is.

That's a strawman. 

Wasn't ment to prove anything, but to exemplify the relationship.
The electromagnetic potential has no direct physical meaning until
you fix a gauge.

>Given a theory derived using quantities y and z as elementary then of
>course you cannot simply drop one.
>This is what occurs when we insist on the canonical formalism
>and its underlying fixed symplectic structure to derive quantum
>gauge theories.
Find a superfluous degree of freedom in the qed lagrangian. The
j.A term exists precisely because it's necessary. 

But of course.  You seem to be implying I would remove A from
the lagrangian formulation.  Again I am not arguing that A
should be excised from the current formulation. However...

The lagrangian is method of theory formulation it is
not a mathematical representation of some "reality out there".
I'm not arguing that the A term is not necessary in a Lagrangian

Since the Lagrangian formulation builds into its workings, a base manifold of space-time then there will of necessity be a
connection for the fields or groups between distinct points.

I'm saying that A is a relationship between elements of a model.
Said model corresponds to the physical theory in its definition
of E and B and charged particle paths.  The rest is background
model elements.  Alter A in some ways and nothing physically
changes.  Alter A in other ways and indeed some physical differences
occur.  The A field itself is a composite of physical and non-physical
components.

When I speak of alternative formulations I am refering to formulations
alternative to Lagrangian mechanics over a manifold (and its quantization). All your arguments have been within this context.

[...]
>> >Gauge invariance "under a particular group structure".
>> >> The point being what? Try to find a different group structure that
>> corresponds to physical measurements. If it were that simple, minimal
>> SU(5) would have been guaranteed to work, since the standard model
>> _is_ a _particular_ decomposition of SU(5). However, it did not
>> work.
>
>Your point being what? I assert that the standard model and various
>extensions makes a major unfounded assumption, that the generators of
>one the distinct gauge sub-groups, U(1), SU(2) and SU(3) all commute
>with the the generators of another of these groups and with the Poincare
>group. 

  Since calculations based on those assumptions (whatever those are - your
statement is rather vague) reproduce the experimental data, those
assumptions can't be too bad. Regardless of what theory lies beyond the
standard model, that theory will have to reduce to the standard model.


Yes, but only at the level of physical observations, not in the choice
of undelying model structure.

 >            There are more ways to vary the total gauge group than just
 >tacking on more generators.

  Say what? That's rather vague. What is ``tacked on?'' Are you
referring to the quantum numbers for c,b,t? Those exist because
one cannot write the quarks as an SU(6) multiplet


No, I'm refering to say embedding SU(2)xSU(3) in e.g. SU(5) perserving
the ad hoc commutation relations between weak-isospin transformations
and color transformations.

The "tacking on" of additional generators refers to the fact that
the eleven SU(2)xSU(3) generators are still there in SU(5) as a subgroup. You simply add additional thirteen generators to fill
out the SU(5)'s Lie algebra.

As an alternative (not likely viable but as an example) consider instead SU(2) and SU(3) subgroups of an SU(4) group. In effect color symmetry manifests only when weak symmetry is broken et vis versa. Again this is an example of a distinct class of unifications ignored in standard GUT's.

Note then that you have both vector and adjoint representations of SU(3)
within the adjoint representation of SU(4).  Likewise with the SU(2)
subgroup.  There are only four additional generators in the SU(4)'s
Lie algebra which are a sum of the SU(3)'s scalar and vector reps.
And depending on how SU(2) is embedded may be a pair of doublets
or a doublet and two singlets.

 > And there is no specific reason to assume that weak isospin is
 >independent of color and hyper-charge or say spin and momentum.

  Since those are hypotheses, they are justified by the fact that
they lead to experimentally verified results.

The question I'm raising is to what extent the experimentally verified results rely on the specific assumptions. On top of the group structure
assumed in the Standard Model are a whole set of ad hoc conditions which
we get directly from observation. Why are there no E-M neutral colored particles? Why are there not both left and right handed weak-isospin
singlets and doublets?

The conventional answer is to impose additional conditions on the
SU(2)xSU(3) or SU(2) x O(3,1) symmetries.  These possibly may
be answered more directly without invoking Higgs or other mechanisms
by reconsidering the full symmetry group where in different sectors
distinct subgroups emerge as residual symmetry groups.

Thus for example, instead of U(2)xSU(3)xISO(3,1) everywhere we
may see a larger unified symmetry group but one for which the above
is *not* a subgroup, e.g. SO(6,2) (and its spin group) with SO(6)=SU(4)
subgroup defining U(4) EM-lepto-color interior to the nuclii, and a distinct U(1)xISO(3) spatial spin, momentum and E-M phase outside.

In such a formulation quark confinement would be a matter of necessarily
breaking SU(3) symmetry inside to restore translational symmetry outside. SU(3) and ISO(3,1) are sub-symmetries but not independent ones.

>To the contrary there is obviously serious interplay there since the
>various gauge charges for the fundamental particles do indeed have
>strong correlations.
In what conext do you find, say, \alpha_strong mixed with the fermi
coupling, G_f? I think you are confusing gauge couplings with eigenstates. 

Not quite what I'm doing.  The eigen-states of the Hamiltonian i.e.
time translation operator defines the physical particle modes.
There is an a priori assumption that space-time translations commute
with color transformations and weak-isospin transformations.
Remove that assumption and you can define a much smaller unified
group in which SU(3) is a symmetry commuting with time translation
alone (and thus the color group is dependent on the inertial frame).
Also that the weak-isospin fails to commute with time translation
hence weak isospinor bosons can only exist intermittently.
They decay due to the effect of time translation on the weak isopsin
eigen-states which is reflected in the fact that [del_t,I_2] \= 0.

Note that couplings are something we add in by hand to alter the
commutivity of gauge transformations and translations of space-time.
I'm suggesting we consider smaller groups where they do not
commute to begin with but wherein the value of their commutator
becomes very small due to factors of scale.

Weak and strong interactions are simultaneously diagnolizable, but that
is just simple quantum mechanics. 

They are simultaneously diagonalizable *by assumption*.  Explain
how this assumption is necessary to explain the observed particle
spectrum.


However, there are no couplings like, 

             /gluon
            /
photon-----x
            \
             \gluon

[...] 

Which translates to the fact that E-M phase generator and the color
generators commute and thus are simultaneously diagonalizable.
However explain to me the experiment where this failure to couple
is observed?  In what experiment do you verify that gluons do not have
electro-magnetic charge?  Or are even eigen-modes of the charge
operator?

>> >> Nonsense. SU(3) color is believed to be an exact symmetry. You can
>> ``observe'' the color degrees of freedom as directly as most anything
>> else observed (I've never ``seen'' an electron either, beyond the
>> predicted behavior of a signal in counter.) The color degrees of freedom
>> can be observed in deep inelastic scattering and electron positron
>> scattering. For example, the branching ratio for e+ + e- -> hadrons
>> vs. e+ e- -> \mu+\mu- differs for a model with and without color
>> degrees of freedom. By a factor of 3. >
>Yes but observing that one model fits data better than another is
>not the same thing as observing the component of that model.

  But, that was not how it played out. The branching ratio for
e+ + e- -> hadrons and e+ + e- -> \mu+ \mu- can be calculated
and under SU(3) color, you get a factor of 2 at barycentric energies
(u,d,s quarks predominate) from the color degrees of freedom.  For
three quarks without color, you have a sum over thw quarks, i = u,d,s
with charges q of,

    \sum (q_i)^2  = (2/3)^2 + (1/3)^2 + (1/3)^2 = 2/3

With three color degrees of freedom, you have a sum over three colors
as well giving a factor of 3 x 2/3 = 2. The experimental scattering
cross section fits the latter. It's not merely a choice between which
fits ``best.'' It's a specific prediction based on two criteria,
quarks with and without color.

>You cannot directly measure the color of a particle it is not a physical
>observable in the theory although it is treated as one in the model.
You're playing with words. It's quite obvious that one can measure
the degrees of freedom associated with the color charge. You can call
it something else, but that doesn't make it different. Electron/positron
scattering measures the number of quark interactions of the form:
q _
\ / Where the propagator is the photon. It produces qq \ / pairs electromagnetically. Count the quark colors.
/~~~~\ Obtain the cross section relative to -> \mu+\mu-.
/ \ _ It's obvious that with r,g,b colored quarks, there
q are three times the number of final states available.

[...]
>> So what? Everything is ``ad hoc'' until it's either shown to be
>> incorrect or explained by something less ``ad hoc.'' >
>But my point is that we introduce "ad hoc" assumptions to explain
>phenomena which are not directly observed but rather are components
>of the model. It is like asking what is the mechanism by which the
>aether shrinks measuring rods in the pre-Einsteinian interpretation
>of the M-M experiment.
That's another strawman, since that is not the type of question
I would ask. 
Pardon, then ignore the example.

I have some rather more fundamental questions, like,
how does one derive the weak interaction based on only the assumptions
and principles of the theory?




>> The standard model and general relativity explain a great deal
>> more with a great many fewer ad hoc assumptions. By an yardstick
>> ever used in any physical theory, the quantities in the standard
>> model are justifiably considered physical.
>> >Possibly you are correct. I may be drawing a line between "physical"
>and "conceptual" which must be drawn somewhere and I may simply be
>drawing it too conservatively for your tastes.
I'd say, too metaphysically, for my tastes. I don't think reality is
all that deep. 

Not metaphysical, rather meta-scientific.  The point is to excise
the meta-physics as much as possible.  The point is to look closely
at which constructs are tied to some ontological model and which
are tied to the empirical observables.  If we must include model
elements (and I don't say we should necessarily eliminate them)
then we should be careful to distinguish them as such.  That's
all.  As to why it is important, I believe that failure to do
so interfers with research into improved better predicting theories.

I think rocks are real, even though I don't have a
description for one using a theory of quantum gravity.
What you think is immaterial, what you can predict is the question.
When doing masonary one need not invoke quantum gravity to predict
the behavior of rocks. The predictions based on a "rocks are real"
model are fine. When you begin considering the "state of reality
of an electron" however you get into a little trouble with
the quantum theory. You do better to abandon any issue of
state and reality. Stick instead to the experimental interpretation
of the electron's wave-function. It is a representation of how
you expect the electron to behave (or assume the electron has behaved) with respect to various experimental acts of determination.

It's sufficient to quantify its properties.

Exactly, its empirical properties (or specifically the values of said properties). This, if you listen carefully is central to my whole point. When we construct models we throw in a lot which is not
directly tied to empirical properties. Arguments over the charge
of a quark or a gluon can be irresolvable until you distinguish
that the quark is an element of a model and *defined* to have a specific
charge. But as to the reality of it, we do not observe quarks
directly, we cannot quite raise their status from elements of
a model to physical objects. We certainly cannot measure their
mass to charge ratio by measuring their deflection in a strong
B field, nor can we directly execute a photon-gluon scattering
experiment.

We can at best adjust free parameters in a model to better fit
empirical data.  We cannot observe directly many of those parameters.

Conversely, something which can never
be quantified, even in principle, doesn't exist. I tend to take the
information theoretic point of view, that reality is only deep as the
information that can be obtained.


As do I.  But I simply drop the "reality" part and all it's metaphysical
baggage.

[...]
>which we may directly observe hadrons and leptons. When we then
>consider quarks, is it meaningful to assume the operator defining
>momentum commutes with the projection operators which distinguishes a
>red top quark?
Surem but now you are imposing some classical bias into things
which are intrinsically quantum mechanical.

How so? Either there is an experiment where you translate quarks
and so the meaning is in the empirical determination up to an error bar,
or the value of the commutator is a free parameter in a model which
can be adjusted to zero by perturbing other definitions. In the
first case the meaning is in "zero = small" and that is not
the structure of the standard model. In the latter case I'm
considering alternative "adjustments" which might yield better predictive theories.

 >Certainly with confinement we cannot readily translate
 >them.

[...]
>> I mean, look, this is about the aharanov-bohm effect. If you
>> can demonstrate how to obtain the shift in the interference
>> pattern using just the E and B field, please do.
>
>I am by no means arguing that you can ignore the A field in the
>field theory. (classical or quantum). But in the case of the
>A-B effect we do not observe phase, we rather observe the shift of
>interference which we interpret in terms of relative phase shifts for
I never suggested that we observe phases. That would contradict
the very assumption of gauge invariance and require non-conservation
of charge.

Yes. But you assert slightly more physical meaning to the A field than I base on their effect on phases. The A-B effect does not yield measurement of A. It yields a phenomenon which requires the inclusion
of A in conventional formulations of QED.

As the phase is not an empirical observable of an electron we needn't
assume that a shift in phase represents a local physical action
on the electron.  Rather the A keeps track of the change in
relationships between acts on electrons as expressed in different
frames at different points of space-time.

>paths. So saying the A field affects phase doesn't quite mean we
>observe the A field indirectly in the A-B experiment. It is two levels
>of abstraction deep rather than the one level deep for E and B
>which we observe by observing forces on charged particles.
It's more than that. The aharanov-bohm effect does not exert a force
on the charges. It's purely quantum mechanical interference. 

It does not exert a transverse force on the charges.  However in
the four-vector formulation you may consider the momentum of the
electron for the two paths to be distinct by exactly the difference
in the A fields.  It is not a "local force" but rather a difference
in the phase-rates for the two paths.  If you scale the experiment
up by building a clock out of particles all of which have charge
-e then you will note that the clock traveling along one of the
two paths will run slower than the other.

Effectively the A field expressed the fact that the geometry
of the paths is different for charged vs neutral particles.
Or more precisely the geometry is charge dependent with
neutrality defined as revertion to the default geometry.

>By the same token, the necessity of including ghost particles in the
>successful quantum field theories is not an argument for their
>physicality. The success of the theory argues that they must be
>included in the mathematical calculations but not that we should
>take their "reality" seriously and go looking for ghosts.
That's a red herring. Ghosts appear as the result of a specific quan-
tization procedure (e.g., brst), in which the ghosts are explicitly
removed by the procedure itself. But, since the procedure itself requires
choosing a gauge in which to quantize a theory which is manifestly gauge
invariant, it's not surprising that there appear bookkepping artifacts
tied to the procedure, which in the end, gives a result that is also
gauge invariant with no ghost states. 

Very nicely stated.  Now consider the A field in the same light.
My assertion is that the A field is also a "book keeping artifact"
tied to the procedure of quantizing fields over a base manifold.
You have to keep the A field in there, it is physically significant
in keeping track of relations between empirical and model based
components.


  An analogous (and much less mysterious) situation occrs in calculating
shell model states in nuclei. Since the nucleons are moving within their
own mean field, there is no obvious way to fix the center of mass, so one
fixes a point and attaches the nucleus to this point with an harmonic
oscillator potential. One then calculates the levels, but due to the
artifice used to fix the system, one ends up with spurious states which
are unphysical and must be removed from the spectrum. Ghosts are just
spurious states created by gauge-fixing.


Totally aside from this discussion, thanks for this analogy!  Nice.

 >> [...]

>> I beg to differ. Allow me to quote a line from the first volume of
>> ``Quantum Fields and Strings: A Course for Mathematicians'', Witten, E.,
>> et al, Chapter 1, Classical Field Theory:
>> >> ``Rather, we can couple [a relativistic particle] to fields,
>> specifically to an electromagnetic field (abelian connection)
>> and to a gravitational field (variable lorentz metric).''
>> >> The electromagnetic field here is A_u. By ``potential function,''
>> they refer to the type of potential one would write in a galilean
>> invariant theory, e.g., U(r) = e^2/r. >
>In the modern treatment one works with propagators and Feynman diagrams.
You should pass that on to freed and deligne who wrote that chapter.
The two-volume set was published in 1999, so they might want to modernize
it.

[...]
>every point of a space-time manifold. Rather the notation for
>creation and annihilation operators, a(x) a*(x) is reinterpreted
>as a parameterization of the acts of creation and annihilation
>of quanta. Space-time becomes a *parameter manifold* instead of
>a physical one.
I have no idea where you are going with this, since (1) quantization
is completely irrelevant to anything being discussed, (2) the effect
in question just requires simple quantum mechanics, (3) quantizing the
world, doesn't make the effect go away.

My apologies, are we talking about "Modern" Field Theory or quantum mechanics? The critical distinction is in the interpretation of the
space-time manifold. That same issue however arises in this discussion
of the A-B effect. The A field is an artifact of the fixture of the
geometry between the two cases in the A-B experiment. This fixture
is a model dependent artifact. When you go to measure the geometry
i.e. distance traveled by a particle you use exactly the phase relationships which are affected in the experiment. You can
rewrite the field equations without A but instead with charge
dependent metric and space-time connection. I know this sounds
like shuffling of labels but my point is that this shuffling
points out that the ontological interpretation of those labeled
objects is relative.

>> [...]
>> >gravitation you then have in the gauge transformations of standard EM
>> >a variation of the geometry of the 5 dimensional K-K manifold.
>> >> Sure. So what?
>
>The point again is the comparison of interpretation for the same
>quantity in two distinct models of the same theory.
Again, so what? It's _a_ quantity and regardless of what name you give
it, it's the _same_ quantity.

But only if it is defined by something other than the model, specifically, only if the quantity is a physical observable.
"_same_" here has a necessary context. If on the other hand
you are comparing two models and identifying quantities of each
which are not direct physical observables then you are demonstrating
that the "same" quantity has distinct ontological interpretations
in the distinct models.

[...]
>> >Essentially one re parametrizes the this 5-d manifold so that the
>> >x_mu in one case is x'_\mu, a mixture of x_mu and theta in the other.
>> >> In which case, it can't ``project'' out at ``zero phase.'' The
>> phase transforms. It's unobservable. That's not the same as being zero.
>
>Yes but the "vacuum" case defines the zero phase modulo choices of
>gauge. Fixing the gauge is precisely the choice of coordinates on
>this 5-d manifold. The constraint $(x,y,z,t,phi) = (x,y,z,t,0)$
>defined the projection to which I referred.

  Huh? Who said anything about gauge fixing? Choosing a gauge is
irrelvant. The phase shift is \integral dx.A and independent of what gauge
you choose.

But your integral defining the phase shift is *not* the same calculation
if you where to do a Kaluza-Klein type formulation of the same A-B effect. This goes again back to the fact you've dismissed. You are
arguing the physicality of A because it affects another non-observable
in a specific class of models.

Asserting the physical significance of including the A field in a specific choice of model/formulation (something we agree on) is not the same as asserting the physical significance of the A field itself apart
from the choice of models/formulations.

Choosing a convenient gauge only affords you the opportunity
to not calculate terms that have to vanish. The result can't depend on the
choice of gauge.

>> >I'm suggesting that the equivalence principle is not fully
>> >integrated into such theories.
>> >> Sure they are. The standard model treats all mass as inertial mass.
>
>That alone is not the E.P. 

  I didn't say that it was. I started with the standard model, because the
standard model performs the first step in identifying weak, electromagnetic
and strong mass as simply inertial mass. The rest was in the rest of the
paragraph.

[...]

>Let me further state that elimination of the A field is not my goal.
>I'm not trying to "explain the A-B effect using just the F field."
>I'm not trying to explain anything. I'm specifically trying to
>quantize gravitation. I don't specifically recall how we got on to
>this topic.
I do. You initially responded to tom roberts regarding whether the
connection coeficients or the metric should be treated as the field.
Tom identified the fundamental field with the connection, whereas you
identified it with the metric. I pointed out that the field A was
considered the fundamental field in E&M and pointed out the aharanov-
bohm effect which is dependent on A, not F and the possibility that
such an effect could exist gravitationally. Since then, you've been
attempting to find some way to not give any physical meaning to the
gauge fields throughout the standard model and I've been providing
the experimental data that contradicts that assertion. However,
you don't have to believe me regarding the connection coefficients
in general relativity. There appears to be a lot of literature on
the subject. 

Thanks for the review.  Hmmm...  we have digressed quite far off
this point.  I don't recall identifying the metric as fundamental.
To the contrary I I did, I would consider that a mistake.  I did
however at times in our digression point out that the A field appears
as additional terms in the metric when we invoke Kaluza-Klein
type unifications.  (at least I implied this).  It is in fact
where it wasa included in the original work.  A_\mu = g_{\mu 5}.

The difficulty is and part of what I've been trying to argue is
that the choice of "where" to "stick" the A field in such cases
is dependent on how you compare the theories.  Given neither GR
and Kaluza-Klein are in the format of a field theory over a fixed
geometry then there is an additional freedom in matching these
up with standard emag.

I've been arguing that the A field is not "fundamental" in the
sense of the empirical interpretation of the theory but rather
in terms of being the quantity from which others are derived
based on a specific class of formulations.

Consider it this way. Assert that the covariant derivative D_\mu
is "fundamental" in whatever context you choose. Now consider
that the separation of D_\mu into components D_\mu = del_\mu + eA_\mu(x)
is dependent on how we separate parameters into "space-time-coordinates" and "phase". It is in this sense that the A_\mu defines a relationship
between a "fundamental" action, translating via D_\mu and an
action in the formal language, translating the parameter x via del_\mu.

To counter some of your arguments which depend on a specific class of
formulation I've tried to point out alternative formulations.

If you want to consider "fundamental" elements start with those
which are operationally fundamental, the actions (and relative actions)
you can perform on physical objects, and the observables you can
measure.  These are the exponentials of covariant derivatives
T(x) = exp(x^\mu D_\mu), and the other group elements involving
boosts, rotations, and phase-shifts.  The fundamental observables
of an object can be put into correspondence with these, namely
"linear" and angular momenta and charge.  We then construct
a model with fixed group geometry in that certain structure constants
for the group are assumed which define the action of the group elements
on the charges.  We see empirically deviations from the assumed
structure so we break up the elements into the "idealized" component
plus the field terms such as A_\mu.

This splitting up is dependent on our choice of idealization.
In the case of standard E-M theory we idealize a flat space-time manifold and consider diffeomorphisms of that manifold which
can be expressed via operators of the form U^\mu(x)del_\mu.

We compare the group structure of these operators with the actual
acts of translation which we express via U^\mu(x) D_\mu.

The "connection fields" of both GR and E-M are there to relate
the idealization with the empirical.

All of your points and arguments presuppose a particular choice
of this idealization.  I point out the dependence on that choice.


[...]
>> I think you should compare theory to experiment a bit more.
>> A four-vector has four degrees of freedom. The photon has two.
>> How does one account for the two missing degrees of freedom?
>
>By noting that the photon in actuality has a huge number of degrees
>of freedom which we call infinite for want of an exact number.
Now, you're just being silly. 

How so?   How many parameters must you specify to pin down a unique
actual photon?  Specifically how do you distinguish between a photon
localized at Greenwich England, 1:30 AM GMT 2001, from a photon
with left circular polarization in a cavity in the optics lab of
Georgia Tech, last thursday between 1:00 and 3:00 pm ?

My point is that in separating location-momentum from polarization you are assuming some pretty specific things about the structure of the
space-time-phase group. This assumption is not simply a matter of
choosing subgroups, i.e. a choice of basis in the Lie algebra, i.e.
a choice of labeling for physical actions. It is in the structure
which in the standard case is highly singular and unstable under
perturbation. It is a highly singular assumption.

I am suggesting that by more careful treatment of the group structure
you account for the two missing degrees of freedom by recognizing
that they shouldn't have been included in the first place. A photon
is not a four vector field sitting on a space-time substrate.
A photon is a chargeless, massless quantum of linear+angular momentum.
How we construct its group representation from independent components
and then eliminate all but one irreducible case need not be accounted
for unless you take the independence of those components as some physical axiom. I am stating that this need not be the case and
trying to point out to you how one might formulate an alternative.

But I seem to be having no success so I'll drop that and you
may read the papers if/when I ever succeed and publish it.
Pointing out the ideas seems not to be enough but I hesitate
to venture that you'd be willing to be dragged through the
bloody details of such a theory.


--
Regards,
James Baugh
.

Relevant Pages

  • Re: the basis of relativity
    ... >> to create theories which are not gauge invariant. ... physicality. ... The very distinction between "classic" QFT and "modern" QFT is exactly the abandonment of this picture of field values at every point of a space-time manifold. ...
    (sci.physics.relativity)
  • Re: How many plots are there? (Re: Public whine)
    ... Any suggestions from other people here on anything else worth saying, ... aside from quoting Heinlein? ... Does anybody write gaget stories anymore? ... Pat Lundrigan ...
    (rec.arts.sf.composition)
  • Re: Physics is simple...we complicate it
    ... affects the ability of a theory to make predictions it is obviously semantic ... Show me the physicality of EM fields? ... affects the ability of theories that use it to make predictions. ... To believe semantic quibbling about if an adjective in front of a concept is ...
    (sci.physics.relativity)