If one believes Einstein's principle of equivalence it may be
appropriate to look at what gravity does to electrons. I'm going
to set this one up a bit before explaining what it's all about.
Back in the fifties a virtuoso experimentalist at Stanford, Bill
Fairbank, proposed measuring the ratio* of the magnetic moment of
the electron (in units of the Bohr magneton) to its spin angular
momentum (in units of h-bar) by doing magnetic spin resonance in
freely falling electrons - effectively in a free electron gas.
This is very difficult because the speed of the particles which
make up a gas is proportional to the square root of the ratio of
the gas temperature and the particle mass. For equivalent
temperatures electrons move at speeds about 240 times greater
than the speeds with which air molecules move. At room
temperature the electrons in a dilute gas would have speeds
averaging around 80 km/s!
In order to measure the magnetic moment of an electron with the
accuracy Fairbank required it is necessary to have the electron
remain within the measuring apparatus for a "long" time. Thus it
was necessary to do the experiment at the lowest attainable
tremperature and with the largest attainable volume for the
experimental apparatus. Even then only the tiniest fraction of
the electrons in a gas could be used, those with the smallest
speeds in the distribution. Fairbank was brilliant, however, and
together with a small group of grad students and encouragement
from colleagues he set out on his quest.
The idea was to produce a pulse of upwardly directed electrons
inside a vertical copper tube. The lowest speed electrons would
then fall back down into the tube at a later time. They would be
the electrons to be measured. The copper tube was necessary to
shield the electrons from any stray electric fields and it was
also kept at the low temperature of the experiment.
The grad student who was to produce the pulse and demonstrate
the falling electrons completed his work and got his PhD. At
some subsequent point a theoretician at Stanford, Leonard Schiff,
pointed out that what Fairbank had intended to do couldn't be
done! Schiff's reason was simple: The electrons in the vertical
copper tube feeel the Earth's gravitational field. Like the air
molecules in the atmosphere they slump to the bottom producing
a net negative charge there and a net positive charge at the
upper end. The electric field which results is one which exactly
cancels the effect of the gravitational field, so the electrons
within the copper tube are in equilibrium. Their electric field,
however, extends into the space around the copper, into the tube
itself. It is just sufficient to guarantee that even the slowest
upwardly moving electron won't fall back down. (The apparently
successful experiment was soon shown to be one which looked at
negative helium ions, not electrons.)
Thus there is a steady electrical potential difference between
the upper and lower ends of a vertical copper wire at any
temperature, and you now have enough information to calculate it.
By the principle of equivalence this is the same potential one
would have on a vertical copper wire accelerating at one gee in
zero gravity.
Leigh
*This is called the "gyromagnetic ratio" (hence its conventional
symbol, g. As you see it might be more properly termed the
magnetomechanical ratio, since that is the order in the quotient.
Fairbank's trick was to be able to measure the small difference
between g and its platonic (read: "simpleminded") value of 2 and
its real value by measuring g-2 directly for electrons orbiting
in a uniform magnetic field.