Re: Lorentz invariance beyond the S-matrix?
From: Ken S. Tucker (dynamics_at_vianet.on.ca)
Date: 02/09/05
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Date: Wed, 9 Feb 2005 06:49:19 +0000 (UTC)
"But just riding two horses simultaneously, as you do now,
will not, but will cause you to fall down once the horses move apart"
says Arnold Neumaier .
I'm likely under-qualified, but I can share my apprehension.
The tensor analysis is performed prior to specializing a CS,
that is once a CS is selected one cannot use the laws of
calculus that relate general CS's.
Consider this, if a CS group is bounded by spacetime (4D),
with a fixed dimensionality, can we really say the tensor logic
applies in an unrestrictred fashion?
I say no, for this reason...the imagination of 4D we share
should not define the laws of nature, indeed, I will be so
bold as to suggest the laws of nature should be independant
of any preconcieved dimensionality.
An example is the thinking underwriting the Lagrange,
where there is no fixed number of dimensions necessary.
IOW's I think we should recall that spacetime itself is a
specialization of a CS (group), and then take care how to
apply the very general tensor analysis to that specialized
CS.
The point I'd like to stress is, certain laws like the
conservation of momentum and energy do not
depend upon aprior fixing dimensionality, hence
such a law may be *invariant* wrt dimensionality.
I wonder if the laws of physics may be defined
independantly of dimensionality, but then apply
to spacetime for our measurement.
Regards
Ken S. Tucker
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