Re: Lorentz transformations are not universal and not exact
From: Bill Hobba (bhobba_at_rubbish.net.au)
Date: 07/31/04
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Date: Sat, 31 Jul 2004 02:48:38 GMT
"Eugene" <eugenev@synopsys.com> wrote in message
news:410AA7E9.5000304@synopsys.com...
>
>
> Perfectly Innocent wrote:
> > Eugene <eugenev@synopsys.com> wrote in message
news:<4109D313.6040800@synopsys.com>...
> >
> >
> >>A theorem was proven by Currie, Jordan, and Sudarshan (Rev. Mod.
> >>Phys. 35 (1963), 350) that trajectories of two interacting particles
simply
> >>cannot transform according to Lorentz.
And the same Sudarshan (Fields and Quanta 2 1973) showed that the easiest
way around the problem is to introduce the concept of a fields - in fact
other ways of doing it is really the field concept in disguise. Even more
directly the same conclusion was reached by Van-Dam and Wigner in 1966 and
well known before then. Its proof, and its resolution, can be found on page
113 - Gravitation and Space-time under the heading of Local Fields vs Action
at a Distance and is based on the violation of assumed conservation laws.
It is however possible to formulate EM is such a way that only action at a
distance is required (Reviews of Modern Physics - Volume 21 no 3 - July
1947 - Feynaman and Wheeler - Classical Electrodynamics in Terms of Direct
Interparticle Action) - the out being 'the energy tensor can only be
regarded as a provisional means of representing matter - In reality matter
consists of electrically charges particles '. In other words they
demonstrated if your are willing to put up with the consequences of these
'no go theorems' (ie total momentum etc in the usual sense is not
necessarily being conserved - you need a non intuitive many-times
formulation of things like energy and momentum derived directly from their
lagrangian) then no problems really arise. It may be mathematically, or
even conceptually, less appealing but it does not have the problems of a
particles field acting on itself.
> >
> >
> > There are many exceptions to this theorem in the literature:
> >
> > http://www.lns.cornell.edu/spr/2002-08/msg0043518.html
> >
> > Take a look in google for the two-body problem in relativistic
> > action-at-a-distance theories.
> >
> > Eugene Shubert
> > http://www.everythingimportant.org
>
> You are probably talking about "constraint dynamics" in which CJS
> theorem does not hold. My statement should be more specific:
> "In Hamiltonian dynamics, trajectories of interacting particles
> cannot transform according to Lorentz".
What a load of bollocks. The Langrangian formulation (which is strongly
related to the Hamiltonian formulation) is easily extended to relativity and
is Lorentz invariant - for example see the lagrangian in Feynmans paper
referenced above. Also see the introductory chapters of Landau - Classical
Theory of Fields. Both the Lagrangeian and Hamiltonian of the EM
interaction is Lorentz invariant - however the PLA applies directly to
Lagrangians not Hamiltonians.
> My view is that Hamiltonian
> dynamics is a better way to describe interactions.
The Lagrangian formulation is the usual method. But it is well known they
are related.
> Quantum field theory
> is based on the Hamiltonian dynamics.
It is based on langrangians just as much as Hamiltonians - the exact
relation between them can be found on page 22 - Weinberg - Quantum Theory of
Fields. Weinberg prefers Hamiltonians because it directly appears in the
Schrodenger equation whereas the rational for introducing langrangians is it
makes it easy 'to choose interaction Hamiltonians for which the S matrix
satisfies various symmetries'. Other books however take a different view
and introduce Lagrangians right from the start. Indeed the modern view is
to concentrate on the symmetries and lagrangians (via Noethers theorem)
would seem to make it the more natural choice - but Weinberg is not a man to
be dismissed lightly.
> I haven't heard if
> "constraint dynamics" can be used for many-body quantum problems
> where particle creation and annihilation is permitted. Maybe I missed
> something.
>
> My point is that violation of Lorentz transformations by the
> interacting Hamiltonian dynamics is not a problem.
My point is it is not violated - the concept of a field or a willingness to
introduce concepts like advanced and retarded potentials rescues it.
> Lorentz
> transformations in their usual form are valid only for
> non-interacting particles. In the presence of interactions
> they should be modified.
Bollocks
Bill
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