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From: weemba@brahms.BERKELEY.EDU (Matthew P. Wiener)
Newsgroups: net.origins,net.physics
Subject: Re: So Much For Absolute Rotation
Message-ID: <12477@ucbvax.BERKELEY.EDU>
Date: Tue, 18-Mar-86 08:23:37 EST
Article-I.D.: ucbvax.12477
Posted: Tue Mar 18 08:23:37 1986
Date-Received: Fri, 21-Mar-86 02:59:19 EST
References: <388@ihnet.UUCP>
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Reply-To: weemba@brahms.UUCP (Matthew P. Wiener)
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I am directing all follow ups to net.physics.  This discussion has gone
on long enough in net.origins.

In article <388@ihnet.UUCP> eklhad@ihnet.UUCP (K. A. Dahlke) writes:
>1.	In an article I posted about 27 years ago (it seems like it),
>I made the statement:
>> Motion is relative *only* when considering inertial reference frames.
>> It is not a matter of mathematical complexity,
>> the earth really does rotate.
>
>Was the statement correct?  The answer seems to be a resounding *no*.

The statement above about when is motion relative is obviously false from
the meaning of the word 'relative', not from any knowledge of physics.

The question of does the earth really rotate is that YES, the earth
really DOES rotate.  "Rotate" in today's modern physics language means
that the local space-time geometry has approximately an exterior Kerr
metric.  (A Kerr metric is just the the mathematical way of describing
rotation about a mass in general relativity.  I am being circular here,
but the abstract description of a Kerr metric makes no reference to
rotation.  Exterior means I am not considering black holes.)  This
property is something intrinsic to the very space-time geometry we live
in, not to any particular reference frames.  Of course, sometimes the
easiest way to understand an intrinsic fact is to take a frame-particular
point of view.  Passing to a frame with the earth at rest does NOT mean
the earth has suddenly stopped rotating!

(One can of course adopt the meaning that rotation means rotation in
your current reference frame.  Some people did that in various postings,
but the current view thinks that is a pretty useless definition.  One
wants to study the physics of the situation, not of the frame.)

The real beauty of Einstein's theory of general relativity is his vision
of intrinsic geometry of space-time as being the essence of gravitation.
Passing to coordinate frames is usually required for doing calculations,
but from the theoretical point of view, coordinate frames are a blemish.
From a practical point of view, coordinate frames are the number one
source of confusion about relativity.

Rotation seems to be the current winner in the confusion game.  How easy
it is to view the earth as not moving and concluding that as measured in
that frame stars and galaxies are moving megadistances in one day, whizzing
at speeds ready to tear the universe apart.  And the speed of light is only
one light-day per day!  This thinking is very tempting, but if one returns
to the intrinsic geometric view, one knows that moving slower/faster than
light is an intrinsic property of objects under consideration, and so the
tachyonic vision can be dismissed as absurd.  The paradox can only be seen
by insisting on a coordinate frame point of view, and then by pulling a
fast one on yourself: the number one gets for the velocity of light in one
frame need not have any relation to the number one gets for the velocity
of light in another frame.  Indeed, in a rotating frame, the number one
gets for the velocity of light depends on where the light your timing is
located!  The further away you measure, the larger the number you get.

This sort of confusion is easy to do, and has caught people who should
know better before.  Even Einstein nodded.

As a further example, I consider the very phrase "Lorentz contraction" to
mean ouch, nothing more and nothing less.  The contraction refers to the
difference between two numbers obtained in different reference frames, and
is at first a source of astonishment, but from the intrinsic point of view,
somebody's measurement of somebody else's space ship is a piece of trivia,
not of physics.  The physics lies in the what and where and when of the
space ship, not in the frame measurements.

An even more notorious example is the "twin paradox", which also means ouch
in modern day physics.  The notion of proper time is well-defined in special
relativity, namely as the integral of ds = sqrt(c^2*dt^2-dx^2-dy^2-dz^2)
along the path in question.  Given a particular path, accelerated or not,
one sticks in the induced relations between t,x,y,z into the ds equation,
and integrates.  Numerically, of all the paths connecting (0,0,0,0) to
(T,0,0,0) one gets the largest value for the straight line path x=y=z=0
for all time t.  Anyone who wants to drag in general relativity as an
explanation here doesn't know what he is talking about: the space-time is
flat == uncurved, so if some gullible space traveller wants to believe the
travel brochures about earth gravity all the way, that's his problem.  Whee!
Curvature == gravitation shows up when it is impossible to find ANY frame
where ds has the above simple formula, not just the frame one happens to be
looking at.  Part of the beauty of differential geometry is its ability to
detect and measure this phenomena directly.

Before I finish, let me point out that I keep referring to the geometry and
curvature of space-time, not of space.  There's a big difference between the
two notions, which is almost never made in the popular literature.

For an undergraduate level text on relativity, the beautiful little book
by W Rindler _Essential Relativity_ is highly recommended.  A little
physics, a little calculus, and you're ready to go.  (Also recommended
to the experts.)

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