From: mcirvin@husc10.harvard.edu (Mcirvin)
Newsgroups: alt.sci.physics.new-theories
Subject: Re: Elapsed Time near c
Date: 29 Jul 92 20:57:45 GMT

silverstein@vxdesy.desy.de writes:

>In article <7696@lee.SEAS.UCLA.EDU>, mitch@seashell.seas.ucla.edu (Robert R. Mitchell (SEAS admin)) writes:
>> Does the influence of gravity act instantaneously?  Suppose you had
>> a mass detector of some sort, and you were detecting mass X at
>> a distance of say, 1 LY.  If that mass were moved suddenly, wouldn't
>> your mass detector note the movement instantly?  What glaring blunder
>> have I committed?

Essentially, using the Newtonian formula for gravity, when in fact
general relativity must be used to analyze such situations.  It's
not that glaring a blunder, but it does illustrate an important initial
motivation for general relativity:  Newtonian gravity is fundamentally
incompatible with special relativity.

>Gravity wave detectors have been built to detect such events as supernovae
>over long distances, but as far as I am aware, no positive measurements have
>been made yet (none of them were turned on when SN1987A was observed).
>However, it is believed that the gravitational force is transmitted at light
>speed, and not instantaneously.

...though the situation is actually kind of complicated, as was pointed
out in initially paradoxical-seeming language by Tom van Flandern in sci.
physics some time ago.  It turned out, after some disbelief, that his GR 
facts were correct; he had described a rather cute phenomenon.

To wit:

General relativity is a causal theory; events cannot affect other events
outside their forward light cones via gravitation, at least not
in the case where fields are weak and topology is simple.  However, in the
solar system the sun follows a trajectory of small oscillations as it 
is perturbed gravitationally by the planets, and superficially the
effect of these oscillations seems "instantaneous."  The point
toward which planets are attracted in the solar system is the *current*
position of the sun in the solar system's rest frame, or is at least
much closer to that point than to, say, the position of the sun d/c
ago where d is the distance, or *even* that position extrapolated along
the sun's straight-line motion. 

To figure out how this can be so, consider electromagnetism.  The
electrostatic field of a charge moving in a straight line always
points toward the current position of the charge.  This is so
even in special relativity, where the electromagnetic field can
only transmit information at a finite speed.  But this "instantaneous"
effect *doesn't* transmit any information that couldn't be figured
out by someone plotting the charge's straight-line course at a
distance.  If the charge is suddenly accelerated, points a
distance d away won't see the effects until a time d/c later.

But the sun seems to be transmitting the effects of acceleration
instantaneously!  Why?  Well, in a very real sense the sun *isn't*
accelerating; it's just following a geodesic in free fall, and as
the sun falls, its gravitational field "falls" as well.  It's
the general-relativistic equivalent of straight-line motion.  The
gravitational attraction is toward a point that always moves along
a geodesic; this doesn't transmit any information that someone
with a large enough computer couldn't predict at a distant point.

If you were to somehow shake the sun via some nongravitational
force, or introduce a perturbing mass into the solar system with
enormous rocket engines, the gravitational effect of this
disturbance would still travel at c.

Van Flandern, an astronomer with lots of idiosyncratic ideas,
ran computer models demonstrating that, in fact, the attraction
of planets to the sun couldn't possess any obvious kind of
delay, since this would make the solar system wildly unstable.
He was led by this to differ with the statement that gravitational
effects are transmitted at finite speed.  However, since this
"instantaneous" effect can no more be used to transmit messages
than can EPR effects (a point with which he agreed), I think it's 
fairly safe to say that gravitational effects are transmitted
at the speed of light.  

Like most Net discussions, the whole thing turned into
a battle over semantics and imploded under its own weight.
It was fun while it lasted.

-- 
Matt McIrvin  mcirvin@husc.harvard.edu