Great question, Chris!
The twin "paradox" we discuss in several other answers to
questions on this web site deals with an effect which is easy to
explain with special relativity -- moving clocks run slow. A clock that
is taken away at high speed, accelerated to turn around, and brought
back, will read less time than an identical clock which doesn't go on
the trip.
As you correctly mention, there are additional effects Gravity has
on time. Clocks that are deep within gravitational fields run slower
than ones that are farther out. If the earth did not rotate, you could
put a clock at the bottom of a tower and a clock at the top of a tower
and the clock at the top of the tower would run faster than the one at
the bottom. The difference is quite small, however, and you have to be
very careful that other effects (the special relativistic time dilation
effect in particular) are not bigger than the gravitational effect. For
example, you could compare the clocks halfway up the tower and arrange
it so that each clock undergoes the same speed versus time journey from
the middle of the tower to the top and bottom, and do the same thing at
the end of the experiment when the clocks are brought together for
comparison.
As you even more correctly state, the fact that the Earth rotates
complicates the experiment -- the clock at the top of a tower is moving
faster (in the reference fram of the Earth) than the one at the bottom
and therefore the special-relativistic time dilation will make it run
slow relative to the one at the bottom of the tower. (Viewed from the
point of view of the clock's 'accelerating' frame, the same effect
seems like a General Relativistic effect. mbw) So if you did a real
experiment with a real earth and a real tower (the clocks would
probably be some maser or other atomic frequency standard, which
produces electromagnetic waves, which conveniently could be used to
interfere with a similar system at the bottom of the tower and the
change in constructive/destructive interference over time would be a
very sensitive measure), you would have to correct for the special
relativistic time dilation just due to the motion. (This correction,
however, is quite small compared to the gravitational effect. mbw)
Actually, the experiment done at Harvard used the Mossbauer effect,
a really amazing feature of solids whereby a material can absorb a
photon within a narrow absorption resonance which is not broadened by
the Doppler shift due to the recoil of an atom after the absorption. In
effect, the entire block of absorbing material picks up the recoil
momentum. So if the absorption resonance is very narrow and matched to
a narrow emission line, then the absorption rate is very very very
sensitive to slow motions of the absorber and the emitter via the
ordinary Doppler effect. By putting the emitter at the top of a tower
and the absorber at the bottom, and making one move slowly towards (or
away from) the other, the absorption rate can be scanned out versus the
doppler shift, and the time dilation effects can be measured with
extreme precision. You can exchange the emitter and the absorber for
cancellation of some systematic uncertainties.
Sources:
Pound and Rebka, "Apparent wieght of Photons"
Phys. Rev. Lett. 4 337 (1960)
Pound and Snider "Effect of gravity on nuclear resonance"
Phys. Rev. Lett. 13 539 (1964)
Pound and Snider "Effect of gravity on gamma radiation"
Phys. Rev. B 140, 788 (1965)
Well done!
Tom Junk
(published on 10/22/2007)
