Re: Lorentz transformations are not universal and not exact

From: Eugene (eugenev_at_synopsys.com)
Date: 08/02/04 

Date: Mon, 02 Aug 2004 00:41:40 -0700

Bill Hobba wrote:

>
>
>>I do have a relativistic quantum theory of charged particles which
>>does not assume the universality of Lorents transformations
>>(one postulate less!).
>>It predicts exacly the same S-matrix as QED. So, the fantastic
>>10^{-9} % QED accuracy is still there. However, my theory is better than
>>QED for two reasons:
>>
>>1. It does not have ultraviolet divergences
>>2. It describes the time-dependent dynamics of particles.
>
>
> How does it handle the electroweak region? Because QED is an approximation
> to a more fundamental theory it is in fact quite reasonable we need to
> impose a cutoff to get sensible answers. If your theory does not need to
> impose a cutoff then I believe that is a point against it. As Weinberg
> showed we know that at low energies any theory will look like a QFT - the
> divergences of QED follow from the Lagrangeian AFAICS and are unavoidable.

No, I don't have any electroweak stuff yet, just straight QED.
What is AFAICS?
Sorry, I couldn't wait for this "more fundamental theory" to
materialize. I just went ahead and cleaned up some mess still left
in QED. This mess included the divergences and, what is even more
important, the absence of the Hamiltonian and the lack of proper
description of the time evolution.

>>
>>My theory is published in three papers
>>
>>E. V. Stefanovich, ``Quantum Effects in Relativistic Decays''
>>Int. J. Theor. Phys. 35 (1996), 2539-2554.
>>
>>E. V. Stefanovich, `` Quantum Field Theory without Infinities''
>>Ann. Phys. (NY) 292 (2001), 139-156.
>>
>>E. V. Stefanovich, ``Is Minkowski Space-Time Compatible with
>>Quantum Mechanics?'' Found. Phys. 32 (2002), 673-703.
>
>
> Yea had a peek at the above paper. It said similar things to what you have
> been posting eg removing the requirement allows you to get around the no
> interaction theorems. I think it is rather deceitful for you not to give
> the full detail of what is happening either in the paper or your postings.
> These 'no go' theorems have been known for some time - as well as their
> resolution - which does not require the abandonment of lorentz invariance eg
> the introduction of a field or other measures such as that taken by Feynman
> and Wheeler.
>
>

In my opinion, introduction of fields did not solve the problem raised
by the 'no go' theorem. The
fields have no physical interpretation. They cannot be measured.
They are just some abstract operator functions of 4 variables. Their
only role in QFT is to provide some convenient
building blocks for constructing the interacting Hamiltonian satisfying
relativistic constraints and cluster separability. (This idea is
expressed so well in Weinberg's book. Of course, Weinberg did not go as
far as I do in reducing fields to merely convenient combinations of
creation and annihilation operators, but the idea is there in his book,
and even in earlier writings in the beginning of 1960's) As soon as we
constructed the
Hamiltonian as a function of particle creation and annihilation
operators we can forget about fields. The fields can be discarded.

If thus obtained QFT Hamiltonian were finite we would be able to obtain
all desired dynamical information, such as time dependence of particle
observables. The problem of QFT is that this Hamiltonian turns out to be
  infinite
(as a result of renormalization). We can still work with this infinite
  Hamiltonian, but we are
limited to calculations of the S-matrix and energies of bound states.
These quantities obey the universal linear Lorentz transformations,
I agree. But the 'no go' theorem is not about them. The Currie-Jordan-
Sudarshan theorem is about the time evolution of particle observables
(trajectories in the classical limit). QFT has nothing to say about
such trajectories. Simply, QFT is not designed to study the time
evolution, because there is no finite Hamiltonian.

In my modification of QED (see paper in Ann. Phys. referenced above),
I found the way how to make the Hamiltonian finite while preserving
the amazingly accurate S-matrix of the usual renormalized theory.
In my approach, one CAN calculate particle trajectories, and then
the problem raised by the 'no go' theorem becomes apparent: The
trajectories do not transform according to universal linear Lorentz
transformations. But the Poincare invariance of the theory is preserved,
and there is no violation of the principle of relativity.

Eugene.

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