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From: weemba@brahms.BERKELEY.EDU (Matthew P. Wiener)
Newsgroups: net.physics
Subject: The death of bogus physics
Message-ID: <12603@ucbvax.BERKELEY.EDU>
Date: Sun, 23-Mar-86 18:19:06 EST
Article-I.D.: ucbvax.12603
Posted: Sun Mar 23 18:19:06 1986
Date-Received: Tue, 25-Mar-86 03:42:48 EST
Sender: usenet@ucbvax.BERKELEY.EDU
Reply-To: weemba@brahms.BERKELEY.EDU (Matthew P. Wiener)
Organization: University of California, Berkeley
Lines: 90

I'd like to apologize to Jim Giles for getting nasty with him.  I guess
I just wasn't making myself clear at first.  Also, I ended up bringing
my copy of MTW in from home to the office, which for me is a two mile
walk these days.

Strange and inaccurate versions of general relativity seem to be rather
common: once it got its myth of incomprehensibility, comprehension was
no longer a requirement for speaking about it.

A good way to clear out the educational system's brainwashing efforts here
is to read Albert Einstein's original works on the subject.  They shine
with a crystal clearness with no one's muddy simplifications to hide the
true beauty of general relativity.  (And Pais _Subtle is the Lord_ is a
fine guidebook to these originals.)

From "Die Grundlage der allgemeinen Relativitaetstheorie", _Annalen der
Physik_, 49, 1916 (from the Dover paperback translation):

Of all imaginable spaces ... in any kind of motion relatively to one
another, there is none which we may look upon as privileged a priori....
THE LAWS OF PHYSICS MUST BE OF SUCH A NATURE THAT THEY APPLY TO SYSTEMS
OF REFERENCE IN ANY KIND OF MOTION.        [p 113]

This view of space and time [that space and time coordinates have
intrinsic physical meaning] has alway been in the minds of physicists....
But we shall now show that we must put it aside and replace it by a more
general view, in order to be able to carry through the postulate of
general relativity....
In a space which is free of gravitational fields we introduce a Galilean
system of reference K(x,y,z,t) and also a system of co-ordinates
K'(x',y',z',t') in uniform rotation relatively to K.  Let the origins of
both systems, as well as their axes of Z, permanently coincide.  We
shall show that for a space-time measurement in the system K' the above
definition of the physical meaning of length and times cannot be maintained.
[Because of special relativity, the circumference is measured by contracted
rods and so seems longer, so the spatial geometry is not Euclidean.  Clocks
too are our position dependent in K'.
[Editorial comment here: I earlier posted a remark that fake gravity induced
by accelerations cannot change the geometry.  The point is that while only
mass-energy can alter the space-time geometry, different coordinate choices
CAN alter your spatial geometry.  It is the frame chooser's responsibility
to make sure he knows what he is doing, not Einstein's.]
We therefore reach this result:--In the general theory of relativity,
space and time cannot be defined in such a way that differences of the
spatial co-ordinates can be directly measured by the unit measuring-rod,
or differences in the time co-ordinate by a standard clock.
The method hitherto employed for laying co-ordinates ... breaks down....
So there is nothing for it but to regard all imaginable systems of
co-ordinates, on principle, as equally suitable for the description of
nature.  This comes to requiring that:--
THE GENERAL LAWS OF NATURE ARE TO BE EXPRESSED BY EQUATIONS WHICH HOLD
GOOD FOR ALL SYSTEMS OF CO-ORDINATES, THAT IS, ARE CO-VARIANT WITH RESPECT
TO ANY SUBSTITUTIONS WHATEVER (GENERALLY CO-VARIANT).    [pp 115-117]

[In choosing among co-ordinate systems], there is no immediate reason for
preferring certain systems of co-ordinates to others.   [p 117]

From _The Meaning of Relativity_, fifth edition:

The case that we have been considering [K and K' in relative rotation] is
analogous to that which is presented in the two-dimensional treatment of
surfaces.  It is impossible in the latter case also, to introduce co-ord-
inates on a surface (eg the surface of an ellipsoid) which have a simple
metrical significance, while on a plane the Cartesion co-ordinates, x1, x2,
signify directly lengths measured by a unit measuring rod.  Gauss overcame
this difficulty, in his theory of surfaces, by introducing curvilinear
co-ordinates which, apart from satisfying conditions of continuity, were
wholly arbitrary, and only afterwards these co-ordinates were related to
the metrical properties of the surface.  In an analogous way we shall
introduce int he general theory of relativity arbitrary co-ordinates,
x1, x2, x3, x4, which shall number uniquely the space-time points, so that
neighbouring events are associated with neighbouring values of the co-ord-
inates; otherwise the choice of co-ordinates is arbitrary.  We shall be
true to the principle of relativity in its broadest sense if we give such
a form to the laws that they are valid in every such four-dimensional system
of co-ordinates, that is, if the equations expressing the laws are co-variant
with respect to arbitrary transformations.    [p 61]
-----------------------------------------------------------------------
As a final point, the assertion that most frames in general relativity
are local Lorentz frames is just plain false.  Off the top of my head there
are Schwarzschild, Reissner-Nordstrom, Kerr, Boyer-Linquist, Kruskal-Szekeres,
Taub-NUT, plane wave, de Sitter, anti-de Sitter, Roberston-Walker, Godel,
and mixmaster coordinate systems, and not one of them is a local Lorentz
frame!

It is true that the theoretical justification of certain points is easier
to do with calculations in a local Lorentz frame.  So keep reading MTW Jim,
you'll get to the good stuff eventually.

ucbvax!brahms!weemba	Matthew P Wiener/UCB Math Dept/Berkeley CA 94720