>I just read a fascinating article that was pointed out to me by a
>young-earth creationist. It is Tom Van Flandern, "How fast is Gravity--what
>the Experiments say Physics Letters A 250(1998):1-11
>
>The article was cited in an article by Tom Bethell as an example of how
>modern physics is about to be overthrown. Bethell's article can be found at
>
>http://www.spectator.org/499TAS/bethell.htm
<snip excerpts from papers>
>What I am interested in is what is your take on this David? Please keep it
>at a Jr. High level for us.
I'm sorry to have taken so long in responding but our email server here
has been up and down intermittently for over a week, and then the crush
of a new semester beginning had taken away my extra time once I had
finally read Glenn's message. I finally got a chance to read both
Bethell's American Spectator article and Van Flandern's Phys. Lett. A
paper. BTW, there is also an internet version of Van Flandern's Phys.
Lett. A paper posted at
<http://www.ldolphin.org/vanFlandern/gravityspeed.html> which, besides
containing everything in the journal article, also has some extra
material of lower quality which, apparently, was edited out to get the
paper past the Phys. Lett. A reviewers.
Contrary to the hype that the Bethell article gave for it, the Van
Flandern paper does not provide any evidence against either the special
or general theories of relativity. Rather, it provides evidence which
*confirms* their predictions. What the Van Flandern paper actually shows
is that a naive (but understandably mistaken) understanding of relavity
and gravitation could easily lead an unsuspecting person to conclude that
the experimental evidence is against relativity. The Van Flandern
article is entirely directed against a *straw man version* of the
predictions of relativity, against which he *does* marshall persuasive
evidence. But, AFAIK, none of his evidence is anything new to workers in
the field, and they are not upset by it. If the evidence was anything
different, *then* they would have cause to worry about the standard
paradigm. Presumably, the only reason why the paper was published was
that it was somewhat useful in that it *did* further confirm the evidence
against a popular but mistaken caricature of relativity, which in the
absense of such evidence, might also be considered as a viable
interpretation.
For instance, in the slow speed limit of relativity the gravitational
force on an orbiting planet *should* be toward the instantaneous location
of the Sun (at least up to terms of order 1/c^2) rather than toward the
apparent direction toward it as seen by the aberrated image caused by the
time delay in the light propagating to the planet from the Sun, which is
merely a 1/c effect.
Actually, in the first sentence of his paper Van Flandern really gives
the game away.
He says:
"The most amazing thing I was taught as a graduate student of celestial
mechanics at Yale in the 1960s was that all gravitational interactions
between bodies in all dynamical systems had to be taken as
instantaneous. This seemed unacceptable ...."
Here is comes out and admits that the proper way, i.e. the way he was
taught, was to use instantaneous positions in calculating celestial
orbits. The relativistic corrections to this approximation go as 1/c^2
(or maybe even 1/c^3--I'm not sure which for gravity) which is too small
to show up in the data for our solar system--even in the data that Van
Flandern presents in his paper. Since this is counterintuitive (and
contradicts a naive understanding of relativity), he says that this
situation is "amazing". *If* the Sun's gravitational force *had* been
observed to align with the optical abberated image of the Sun, then the
result *would* contradict relativity, rather than its *straw man*
version. Actually, even if there was no gravity (or GR) at all, and the
Earth, instead, was held in orbit around the Sun by an electrostatic
force because of an opposite charge between the Earth and the Sun the
direction of the electrostatic force would *also* point to the
instantaneous position (up to terms of 1/c^2) of the Sun even though the
Sun's optical image would suffer aberration (which differs from the
instantaneous direction by terms of order 1/c). In this later case
*both* the light from the Sun *and* the binding electrostatic force
satisfies Maxwell's equations and are subject to *all* the strictures of
SR.
It is simply not true that relativity predicts that gravitational or
electrostatic forces should point towards the time retarded positions of
the sources. But it *is* true that changes in the dynamical behavior
of a source from its cuurrent motion will not have its effect show up
at the point of observation until the appropriate time delay (traveling
at speed c). The reason for this is that the direction that the forces
(electrostatic forces for charges and gravitational forces for masses)
between the sources point toward each other is automatically toward a
future-projected location based on the source's retarded location and
velocity (and in the case of gravitation, the acceleration as well).
For example, suppose we have two oppositely charged objects A and B in
relative motion w.r.t. each other. Suppose that at some time t they
are separated by a distance L such that it takes L/c amount of time
for them to communicate via the EM force. For now assume a frame which
has object B at rest and object A moving. The direction that the force
on B points is not at the location of A at the time t - L/c. Rather, it
is at the location that object A *would be* at time t *if* at time
t - L/c object A continued along the tangent trajectory it had at t - L/c
with the *same* velocity. IOW, the force leads the motion just like a
hunter leads his target when he is trying to shoot a running deer. As
long as the deer doesn't change course during the time it takes the
hunter to re-aim plus the time it takes for the bullets to arrive at the
deer, then the deer is liable to be hit if the hunter is a good shot and
knows how to predict the location of the deer at the time the bullets
arrive. In the case of electromagnetism the electric force leads the
motion of the charges in a similar way in that it gets the direction
correct as long as the charges are in uniform constant velocity motion.
If the charges accelerate in complicated ways than this 'leading' effect
breaks down and the force is in the wrong direction (i.e. doesn't
match the instantaneous direction).
But in the case of general relativity at low speeds, (AFAIK since I'm
not an expert) the behavior is similar *except* that the 'leading' action
effect is even more sophisticated. In this case if mass A is moving by
mass B then the gravitational force on mass B at time t points in the
direction mass A would be then *if* at time t - L/c it kept the same
velocity *and acceleration* it had then right up until time t.
Part of the reason for the difference between these two cases is that
uniformly moving constant velocity charges do not radiate EM radiation
and the amount radiation produced by a moving source is, to lowest
order, proportional to the square of the source's acceleration (or
second time derivative of its electric dipole moment and proportional to
1/c^3). Whereas for gravitation there is no gravitational radiation from
uniformly *accelerating* masses, and the amount of radiation produced by
a moving source is, to lowest order, proportional to the square of the
source's *jerk rate*, i.e. time derivative of acceleration, (or third
time derivative of its mass quadrupole moment and proportional to
1/c^5).
I suppose that the reason the Van Flandern was so coy about all of this
in his paper is that he had ulterior motives in publishing it. He heads
a fringe science (maybe pseudoscience) organization called Metaresearch
that advocates a bunch of wierd non-mainstream theories. One of them is
the "exploding planet" theory for the formation of many features of the
solar system. Another is a different theory of space and time (other
than standard relativity theory) that has an "absolute time" and requires
instantaneous interactions between objects like Newtonian theory
requires.
David Bowman
dbowman@georgetowncollege.edu