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From: gwyn@brl-smoke.ARPA (Doug Gwyn )
Newsgroups: net.physics
Subject: Re: Mach's principle
Message-ID: <1949@brl-smoke.ARPA>
Date: Thu, 20-Mar-86 01:48:02 EST
Article-I.D.: brl-smok.1949
Posted: Thu Mar 20 01:48:02 1986
Date-Received: Mon, 31-Mar-86 06:27:57 EST
References: <368@ihnet.UUCP> <2057@jhunix.UUCP> <2874@sjuvax.UUCP> <446@3comvax.UUCP> <1825@brl-smoke.ARPA> <12430@ucbvax.BERKELEY.EDU>
Reply-To: gwyn@brl.ARPA
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In article <12430@ucbvax.BERKELEY.EDU> desj@brahms.UUCP (David desJardins) writes:
>In article <1825@brl-smoke.ARPA> gwyn@brl.ARPA writes:
>>The idea that centrifugal force can be explained by the inductive
>>effect of all matter in the universe is known as Mach's principle.
>>This principle appears to be necessary for any theory that claims
>>that there is no absolute motion.
>
>   Am I stupid?  I have reread the first sentence above many many times
>and can't make any sense out of it.  In an empty (flat) universe some
>frames are accelerated and some are not.  This is in the absence of any
>matter.  What does "the inductive effect of all matter in the universe"
>have to do with centrifugal force??

No, David, there are some subtle issues involved here.  The nonlinear
system of PDEs that constitutes Einstein's general relativistic field
law can be expected to have different solutions for different
"boundary conditions".  For instance, the original 1915 theory with
asymptotically "flat" (Rijkl -> 0) spacetime might be a cosmological
model; this particular model happens not to support Mach's principle.
For another example, suppose the universe were to have some positive
average density of matter; then spinning it around an axis would mean
that a humongous amount of mass is being moved, most of it at great
distances from the axis.  If Mach was right, this would have an effect
on local physics, indistinguishable from rotating the local frame
in the opposite direction in a static universe.  The "inductive effect"
appears to actually exist for laboratory-scale mass motions, although
it is hard to detect experimentally.

Einstein was very much aware of the importance of boundary
conditions.  Since he (originally) strongly believed in Mach's
principle, he looked for ways to make sure it was obeyed.  One
such attempt was the introduction of the "cosmological term"
into the field law; another (not entirely unrelated) was to
avoid boundary conditions altogether by imposing topological
constraints on the space-time manifold (e.g. closed universe).

In my favorite unified field theory, there is no such thing as
an empty universe, which nullifies your objection.  (This is a
prediction of the theory, not an assumption.)  Indeed, that
theory produces the interesting effect that its universe is
locally self-gauging, which has all sorts of ramifications,
Mach's principle probably included.

P.S. In conventional general relativity, flat => empty but
not conversely.

P.P.S. A fairly good discussion of Mach's principle from the
conventional point of view can be found in Chapter 10 of
"Principles of Relativity Physics" by James L. Anderson
(Academic Press, 1967).