Re: Download a new book on quantum mechanics and relativity.

From: Eugene Stefanovich (eugenev_at_synopsys.com)
Date: 10/07/04 

Date: Thu, 07 Oct 2004 10:50:33 -0700

Bilge wrote:
> Eugene Stefanovich:
> >Bilge wrote:
>
> >> Physics doesn't depend upon a representation.
> >
> >I remember we discussed this point already. There are different
> > "representations" in physics. For example, I agree that nothing
> >depends on whether you choose to write your wavefunction in the
> >position representation or momentum representation.
>
> For someone who is trying to explain the difference between a
> group and a representation, you certainly seem confused about
> what that difference is. Physics does not depend upon the
> representation. What matters are the structure constants of
> the group.

That's wrong. Two different representations of the Poincare group
are physically inequivalent. See subsection 8.2.3

>
> [...]
> >> >2. If you introduce interaction in the Hamiltonian (generator of time
> >> > translations) and want to preseve commutators of the Poincare Lie
> >> > algebra (= relativistic invariance) you MUST introduce interaction
> >> > terms either in generators of boosts or other generators (translations
> >> > and/or rotations).
> >>
> >> You've just done it incorrectly. What you ar claiming is that
> >> p_u x^u != p_u'x^u'.
> >
> >Are you talking to me? Where did I write these symbols?
>
> You didn't write them. The problem is that you don't preserve
> that as an invariant.

Could you please explain how you come to this conclusion,
and what's the big deal in preserving these combinations as invariants?

[...]
>
> You're like the other crackpots, eugene. Despite the fact that the
> validity of your theory could easily be addressed by existing data, you
> simply deny that your theory has consequences that are amenable to more
> than the most naive, brute force experiment.

You are right, I will concede that my theory is wrong only if there is
clear contradiction to experiment or a hole in my logic is demonstrated.
  Handwavings about fields and gauges will not do much damage to my
approach.

> Whether that is due to you
> knowing nothing about how to connect your theory to reeality or just lack
> of ever having to compare theory to experiment, I can't say. What makes
> you a crackpot is your refusal to believe anything but the most naive,
> brute force experiment is capable of addressing your theory. If the rest
> of the physicists in the world operated that way, we'd still be in the
> dark ages. But, anazingly enough, those who are really interested in
> testing theories manage to find a way. If physicists would have taken your
> approach to testing minimal SU(5), we'd have to wait for a 10^14 GeV
> accelerator to come on line (in case that doesn't mean anything to you,
> the highest energy accelerators now online, have energies in the ballpark
> of 10^3 GeV). You have no interest in any experiment but those that
> haven't been done, and I believe that regardless of what experiment
> would be done to suit you, you'd reject the results. You already
> reject charge conservation as an argument.

That's not true. I told you three times, at least, that charge is
conserved in my approach.

>
>
> >> > rotations are kinematical: they do not depend on interactions,
> >>
> >> Boosts and rotations are the same algebra. [K_i, K_j] = -e_ijk S_k
> >> [S_i, S_j] = e_ijk S_k => [S_i,S_j] = [K_j,K_i]
> >
> >You are exactly right, these are commutation relations of rotation
> >and boost generators in the Poincare Lie algebra. These commutation
> > relations do not depend on interaction, that's right. However
> >the Hermitian operators which represent generators of boosts in the
> >Hilbert space DO depend on interaction.
>
> Wrong. You've simply ended up with them there because your hamiltonian
> wasn't invariant in the first place and you treated it as if it were.

Then you are saying that Hamiltonians used by Weinberg and Bjorken &
Drell are not invariant either. Then you must show me an error in my
proof of the relativistic invariance of the theory in subsection
11.1.3. You just throw the same unsubstantiated allegations time
after time and ignore my replies supported by facts, proofs, or
references.

>
> >You are probably not denying that Hamiltonian (the generator of time
> >translations) has interaction-dependent terms.
>
> No, what I'm denying is the validity of what you did.
>
> >Why you oppose the presence of interaction terms in the (Hermitian
> >representative of the) boost generator?
>
> (1) You've obtained that result by ignoring relativity in
> constructing your theory,

Wrong. My theory is relativistically invariant because Poincare
commutation relations are satisfied. Your insistance on manifestly
covariant tensorial transformations of quantities has nothing to do
with the principle of relativity. These are artificial requirements.

>
> (2) It contradicts the principle of equivalence, which is known
> to be correct to great precision.

What the principle of equivalence (between inertial and gravitational
masses I presume) has to do with all this? Didn't we agree to
ignore gravity?

>
> (3) It obviously confuses the spacetime manifold with a U(1)
> bundle.

Neither one of these things is present in my approach. You confuse
my theory with something else.

[...]

>
> [...]
> >suspicion (at least from my point of view). I do not consider this
> >"geometry" as something self-evident.
>
> I'm not asking you to consider it self-evident. However, no geometry
> is any more self-evident than another, so if you expect a justification
> for relativity, then I expect a justication for what your bias has
> led you to believe is self-evident.

I do not assume any geometry in my aproach (except self-evident 3D
  geometry). I assume the principle of relativity, the Poincare group
properties, quantum mechanics etc. The relationships between time and
position of different events (what you probably call geometry)
come out as a result of my approach, not as an axiom.

>
> >I need proofs that representation of boost in the Hilbert space is
> >interaction independent.
>
> I've done that.

No, you haven't. I gave you rebuttals to each of your points.
You just ignored them.

Eugene.

>
>

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