Re: Tensor Physics & WMD
From: ZZBunker (zzbunker_at_netscape.net)
Date: 11/08/04
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Date: 7 Nov 2004 19:55:28 -0800
Jack Sarfatti <sarfatti@pacbell.net> wrote in message news:<ke9jd.18644$6q2.8390@newssvr14.news.prodigy.com>...
> On Nov 6, 2004, at 10:02 AM, Saul-Paul & Mary-Minn Sirag wrote:
>
>
> [Saul-Paul Sirag] The issue of coordinate dependence of tensors is very
> tricky. Perhaps the following statements (by Arthur Eddington, 1920)
> will clarify the issue.
Since that's obviously the same Eddington that proved that
the fine structure constant equals 137, you should
actually say that he tought geodesics were tricky.
Since Tensors are so simple you can computerize them,
since they have no coordinate dependence.
Which is really Einstone used elevators in addition
to trains in his gedankers, to show that geodesics
are tensor-free algebras rather than calculus'.
> 1. "A tensor does not express explicitly the measure of an intrinsic
> quality of the world, for some kind of mesh-system is essential to the
> idea of measurement of a property, except in certain very special cases
> where the property is expressed by a single number termed an invariant,
> e.b. the interval, or the total curvature."
Tensors are now and always been, the fairly simple calculus
of transformations. Which is really why they were
first used by Maxwell in EM theory to show that
magnetic fields are coordinate invariant, and not by
Einstone and astrologers.
> 2."But to state that a tensor vanishes, or that it is equal to another
> tensor in the same region, is a statement of intrinsic property, quite
> independent of the mesh-system chosen."
>
> Saul-Paul
>
> Yes, a good start. Let's continue.
>
> A tensor (or spinor or twistor) transformation is a multi-linear
> homogeneous transformation on "objects".
>
> A spinor is a complex double-valued representation of some continuous
> groups like SU(2) that covers O(1,3) of special relativity.
>
> The objects are N-dimensional hyper-matrix arrays of elements of an
> algebraic field.
>
> Let X be the basic linear transformation.
>
> For example, using summation convention on repeated pairs of identical
> upper and lower indices, ^ denotes upper index
>
> Au --> Au' = Xu'^uAu
>
> is a simple linear transformation.
>
> S ---> S' = S is a scalar invariant.
>
> For example S = AuA^u
>
> The simplest multi-linear transformation is
>
> Fuv ---> Fu'v' = Xu'^uXv'^vFuv
>
> X in general is a homomorphic image or representation of some GROUP
> (maybe semi-group and maybe even up to a CATEGORY?)
>
> Therefore we really have X(G) where G is some group.
>
> All laws of physics must be covariant under the physical symmetry groups G.
>
> This means that the laws of physics must be tensor equations in this
> general sense.
>
> What applies to the laws of physics DOES NOT APPLY to the fundamental
> VACUUM SOLUTIONS of those laws! Or to any solution.
>
> There is a lot of confusion on this issue.
>
> In the SPECIAL CASE of Einstein's 1916 theory of gravity
>
> G = GCT AKA DIFF(4), i.e. generally NONLINEAR LOCAL coordinate
> transformations AT A FIXED POINT EVENT P.
But in the special case of Einstein's 1919 theory
of gravity, that is not true. Since by that
time *he* had already disregarded the cosmological
constant, in favor of a dynamic model of gravity.
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