From: Hal Finney (hal@finney.org)
Date: Sun Jun 08 2003 - 21:25:20 MDT
I used to argue quite a bit with Tom van Flandern 20 years ago on
the old Compuserve Science and Math Forum. He had many of the same
incorrect ideas back then that he is pushing now. Yet somehow he had
managed to maintain the image of a respectable mainstream scientist,
and even was giving public speeches and leading science-based tours as
an expert astronomer.
The speed of gravity is perhaps worth talking about. What does that
mean, the speed of gravity? When we speak of the speed of light, or
the speed of sound, that has a pretty well defined meaning. We can send
a pulse of sound or light and see how long it takes to get from A to B.
But gravity is different, it is more pervasive. It's always there,
between A and B. It's like asking for the speed of temperature, or
pressure, or density.
This ambiguity seemed to be the foundation for many of TvF's mistakes.
Here is an example he used. Imagine we have two masses orbiting around
their common center of gravity, like a binary star system. In Newtonian
physics, this is a stable system. And for it to be stable, each star
must be gravitationally attracted to where the other star is precisely at
that moment. That is, the acceleration vector has to point directly at
the other star. If the vector is off, then the star system will speed
up or slow down and the orbits are unstable.
Then TvF argued, if we modify this Newtonian picture to incorporate
relativity, then the stars should not be attracted to the current
position of the other star. Instead, they should be attracted to where
the other star was in the past. If the two stars are a light-day apart,
then they should be attracted to where the other star was one day ago.
That's because of the "speed of gravity", it should take that long for
information about the other star's position to get to this star.
However, if star systems worked like this, binary star systems would be
highly unstable and their orbits would quickly be destroyed. Since this
does not happen, TvF concluded that the speed of gravity must be infinite,
or at least a lot faster than c, to explain why stars are attracted to
the current position of the other star.
Now, as described, this is a pretty good relativity paradox. It does
have a certain plausibility. It would be a good problem to teach a
student of special and general relativity, to help explain the concepts.
However, it is nothing more than that. There is no difficulty in
accounting for the stability of orbits in relativity theory, and this
is done without invoking a speed greater than c for gravity.
The simplest way to explain it is to consider a single, linearly moving
star and to consider its gravitational field. The field surrounds the
star and moves with it. Imagine the field as a physical object built of
wood, a gigantic framework that surrounds the star. As the star moves,
the framework moves too.
As the star passes by an observer, the field points to the current
position of the star. That's because the field is moving uniformly with
the star. In the case of a wooden framework, the beams would point
directly at where the star is right now, because that is how the frame is
built.
It turns out that gravity is not unique in this respect. Electric fields
work the same way. If the star carried an electric charge, and you had
an instrument to detect it, the instrument would be attracted towards
the current position of the star, not to where the star was in the past.
It's for the same reason, that the electric field moves along with
the star.
The orbital example is a little more complex, because each star is moving
in an ellipse. The details of the curved motion affect the star slightly
differently than the remote parts of the field, so the field does not
point exactly at the star. But it's very close. The discrepancy does
cause orbits to decay, but at an extremely slow rate.
The truth is, orbits are unstable in GR, but the degree is insignificant
for all but the heaviest objects in the smallest orbits. This orbital
decay predicted by general relativity can be explained by the creation of
gravitational waves as the stars orbit, a new phenomenon not predicted
by Newtonian physics. This orbital instability can also be seen as
a manifestation of gravity not being directed exactly at the current
position of the attracting object.
So the bottom line is that TvF's example does not show that gravity moves
faster than c; in fact, the phenomenon actually illustrates how accurate
relativity theory is at explaining the details of orbital mechanics.
And of course there is no need for anything to move faster than light
in relativity.
Despite the attempts by me and others to explain these details, TvF was
unconvinced, and apparently the same thing is true today. I can't help
noticing that he gets a lot more attention this way than he would if he
were the ordinary NASA Astronomer that he claims to be.
Hal
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