Re: the basis of relativity
- From: dubious@xxxxxxxxxxxxxxxxxxxxxxxxxxxx (Bilge)
- Date: Fri, 03 Jun 2005 06:38:08 GMT
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).
>> >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.
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.
>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.
>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.
[...]
>> >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.
> 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
> 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.
>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.
Weak and strong interactions are simultaneously diagnolizable, but that
is just simple quantum mechanics. However, there are no couplings like,
/gluon
/
photon-----x
\
\gluon
[...]
>>
>> 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. 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. I think rocks are real, even though I don't have a
description for one using a theory of quantum gravity. It's sufficient
to quantify its properties. 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.
[...]
>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.
>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.
>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.
>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.
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.
>> [...]
>> 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.
>> [...]
>> >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.
[...]
>> >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. 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.
[...]
>> 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.
.
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