From: Hal Finney (hal@finney.org)
Date: Wed Jul 23 2003 - 00:24:17 MDT
Lee Corbin writes:
> When I was a teen, I used to tell my friends that the
> sun wasn't really where they thought it was. When they
> evinced surprise, I proudly announced that it really was
> two degrees to the west of where it looked like it was,
> or about four sun-diameters.
>
> I explained that this was (of course) because the light
> took eight minutes to reach us, and so the sun's real
> position was two degrees to the right (looking from the
> Northern hemisphere).
>
> None of them spotted the flaw in my logic :-) and it may
> take a few on this list a moment or two to see where I was
> going wrong.
That's a good puzzle; it fooled me for a few minutes. If the sun were
actually "rising" and "setting", travelling around the earth every 24
hours and drawn by Apollo's chariot, then what you say would be right,
its apparent position would lag its actual position. But since the sun is
stationary, and the earth is rotating and moving slowly enough to mostly
neglect aberration, then when the earth turns so that you are closest
to the sun, the sun really is directly over your head at that instant.
> Anyway, it seems that Laplace *did* correctly determine
> that where the sun is as measured by a sensitive gravimeter
> is not the same place that it looks like it is. There is a
> very nice exercise in "Problem Book in Relativity and
> Gravitation", Lightman, Press, Price, and Teukolsky:
>
> "The position of the sun in the sky can in principle be
> measured by a sensitive tidal gravimeter. What is the
> angular difference between this position and its position
> as measured optically? If the actual position of the sun
> were at its optical position, there would be a force in
> the direction of the Earth's motion. If this were the case
> find the radius of the Earth's orbit as a function of time."
It's interesting that in this passage it seems to go without saying
that the position measured by the gravimeter is in fact the "actual"
position of the sun. That is certainly non-obvious and in fact it is
something that can stand considerable discussion, as this and related
threads have shown.
> The answer has something to do with the aberration of light,
> as I understand it. If the Earth is going 66,000 miles per
> hour (30 km/sec) past the sun, then the sun appears slightly
> shifted towards the forward direction. That makes sense.
Often an analogy is used to vertically-falling raindrops, where if you
are moving forward the raindrops appear to fall slanted, from in front
of you, in your frame of reference.
> So what I infer from this problem is that *gravitationally*
> it isn't so! The gravity waves don't lie! There must not
> be anything like "aberration of gravitons". (This thought
> is also what lent me credence in my earlier post that perhaps
> the frame of reference of the space-bending (i.e. gravitating)
> object is the correct frame of reference to use. Mostly?
It's not that gravitons are immune to aberration. Presumably if you could
emit and detect a graviton beam, they would be subject to aberration
just like any other particles. (Let's not forget that gravitons are
very hypothetical at this point.)
Rather, the action of gravitons as mediators of gravitational force is
quite different from simple emission and absorption. Instead, gravitons
are to gravititational force as photons are to electrical force.
If you bring two oppositely charged particles together, they attract.
In quantum theory, this is expressed by the action of "virtual" photons
whose shadowy existence produces indirect effects that lead to the
measured force. These virtual photons don't have well-defined paths
and can even travel at speeds other than c. In some ways it is better
to think of them as mathematical terms in a series expansion than as
real particles.
This is why electric fields, like gravitational ones, are not subject to
aberration. If the sun were charged and you could measure its position
with a sensitive electrometer, it would show up at the same spot as
shown by the gravitational meter.
In principle, gravitons would play the same role for gravity as
photons play for electromagnetism, but in practice the theories are
not so similar. Attempts to come up with a consistent quantum field
theory for gravity have failed; the tricks that worked for the photons
fail for gravitons. As I have heard it, the problem is that gravitons,
having mass and energy, exert gravity; while photons, being uncharged,
do not generate electromagnetic fields. This extra complication with
the gravitons produces infinities in the theory that have not been
successfully eliminated.
If you want to know more about virtual particles, a good next step is
the discussion in the sci.physics FAQ,
http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html.
Hal
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