Re: Comparisons between SR and LET.

Ilja Schmelzer:
>Bilge:
>
[...]
>Nonetheless, in the classical special-relativistic limit LET vs. SR
>the mathematics and the physical predictions are identical, and the
>difference is purely interpretational.

Not even in the classical limit. For example, the energy-momentum
relations are derived by examining the lagrangian under an infinitesimal
spacetime displacement and insisting the lagrangian be invariant.
The energy-momentum relations are then the conserved current. LET is
_not_ invariant under spacetime displacements, so you cannot simply
assert tht L[q,qdot] - L[q',qdot'] = 0.

> >> >>
> >> >> Yes, I disagree.

>Other theories (like GR, GLET) may be the result of further theoretical
>work which has been started with SR or LET, but the math of these other
>theories is IMHO nothing _established_ by SR or LET.

Sure it is. To derive E^2 = p^2 + m^2 from special relativity,
I need the same first postulate from which I derive the lorentz
transforms. The same argument based on the first postulate carries
over to gauge invariance.

[...]
>> The equivalence principle establishes only the equivalence of
>> gravitational mass and _inertial_ mass. It does not establish any
>> relationship between the effective masses due to forces and inertial mass.
>
>The effective mass differences because of binding energy? Ok.

No. The mass in lorentz' theory was electromagnetic mass. There is
no principle on lorentz' theory which provides automatic equivalence
between the mass of the electron measured with the electromagnetic
interaction and the mass measured with the weak interaction.

[...]
>> The equivalence of electromagnetic mass and say, strong mass, comes about
>> in special relativity for the following reasons. (1) Noether's theorem
>> establishes a mass-energy-momentum relation as a conserved current which
>> does not depend on the introduction of a force at all. The invariant mass
>> is then an inertial mass.
>
>Ok, Noether is not specific to SR. LET as well as GLET have
>a Lagrange formalism too.

Noether's theorem is _specifically_ a theorem based on invariance.
You have to have the symmetry before noether's theorem can be used to
obtain conservation laws. In addition, you can't simply assert the
conservation laws and work backwards. Nother's theorem only works
one way, i.e., symmetry -> conservation law.

[...]
>> mass defines the wave equation, not the interpretation of light as
>> a wave in a medium. Light has no significance for relativistic theories.
>
>"Everything constructed from the same geometry" is IMHO equivalent
>to the universality of the ether in GLET. Mathematically it is the
>axiom that the Noether conservation laws are continuity and
>Euler equations of some material which does not interact
>with anything else.
>
>The velocity of light is not important for GLET too.

You are missing the entire point here. I also don't think it's
possible to explain it because you just take these things for
granted.

[...]
>> The ``massless'' phonons in different media propagate at velocities that
>> depend upon the interaction strength between the constituents of the
>> media.
>
>I agree that in certain directions relativity is more restrictive. But in
>other directions ether theory is more restrictive (like topology of
>spacetime).

That ought to be sufficient to agree with my original point that
special relativity and LET are _not_ the same theory. They share
some rather trivial transformations, but the same transformations
apply to galilean invariance in the limit c -> \infty, so the fact
that they share those coordinate transforms is largely irrelevant
to the point.

>> On what basis is gauge invariance justified in LET?
>
>It is well-known that gauge fields may be used to describe
>lattice defects in crystals.

That didn't answer my question. You start with a model which is
fundamentally _not_ invariant. You haven't explained how you
arrive at any invariance whatsoever.

[...]
>> LET posits
>> an absolute frame, and therefore the absolute phase of a wave
>> is a physically meaningful quantity in LET.
>
>Yep. But it does not follow that they are observable for
>internal observers.

If it isn't observable, then it isn't meaningful.

[...]
>> I know how to answer the questions using relativity.
>> What I can't seem to do is get either of the two people who posted
>> earlier to even understand the questions, much less answer them.
>
>In this case, the failure is IMHO at least partially yours, because

It's not incumbent upon me to know how to derive a result
using a model from which I don't the results can be derived.
It's up to the claimant.

>you do not distinguish in a sufficiently clear way the given theories
>(LET, SR, as classical theories about EM and charged matter

I was perfectly clear. I even specified precisely what equations
I wanted to see derived and interpreted using LET, neither of which
were required the introduction of E&M from the standpoint of relativity.
It's simple. Use LET to derive and interpret the mass-energy-momentum
relations and the dirac equations and prove that the mathematical
path to these equations is identical to that of special relativity.
Just don't use invariance anywhere as an argument. Use the ether,
which is the basis for LET.

[...]
>
>The identity of the \gamma^i follows from the assumption of isotropy
>of space, which is quite natural in an ether theory. A similar assumption

Why is that natural in ether theory? If it's ``natural,'' then you
assume a metric, otherwise there's nothing natural about it. You might
call the metric a 3-d metric, but it's a metric just the same. If your
goal is to provide some additional metaphysics to explain geometry,
then don't you think it ought to address space, too?

>of symmetry between space and time is not natural.

Why not? It's just geometry, so I can't see any basis for that
statement.

[...]
>> So, I don't consider
>> bohmian mechanics to be a point in favor of any theory. Second,
>> there is experimental evidence against such a theory with a preferred
>> frame, done with moving beam splitters. For example, Physical Review. A,
>> volume 67, 042115. Also, quant-ph/0311004 and references therein.
>
>I don't believe in experimental evidence against BM which
>is not experimental evidence against QM because the

Nevertheless, you have the references. It goes beyond just bohmian
mechanics, however. It applies to any pilot wave model that requires an
absolute frame.

You also adopt several features of quantum theory which aren't
consistent with bohmian mechanics and then ignore the incon- sistency.
First the only thing that bohm's theory has in common with standard
quantum theory is the schroedinger equation. Period. The quantum
mechanical interpretation of identical particles is blatantly incompatible
with the idea of a well-defined trajectory in bohmian mechanics. If you
have independent single particle trajectories, then your schroedinger
equation uses single particle wave functions, not the symmeterized
wavefunctions.

>equivalence of the physical predictions of BM and QM
>is a simple proven theorem.

It's not a proven theorem. All that's a ``proven theorem'' is that
if you assume randomness for no particular reason, you'll have that
randomness in the result. That has nothing to do with identical particles.

.

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