Re: Lorentz transformations are not universal and not exact
From: Androcles (androc1es_at_nospamblueyonder.co.uk)
Date: 08/03/04
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Date: Tue, 03 Aug 2004 08:13:29 GMT
"Eugene" <eugenev@synopsys.com> wrote in message
news:410DF034.20203@synopsys.com...
|
|
| 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?
Short for "As Far As (Bull Hobba) Can See", which isn't very far at all.
Androcles
| 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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