On Feb 9, 2:05 pm, (Dushan Mitrovich) wrote:
"Sue..." wrote:
On Feb 6, 3:23 am, "Rich L." wrote:
In QM energy is related to frequency by h_bar. In Relativity mass is
related to energy. A particle at rest can be represented by a wave
function exp(-i*w_0*t) where w_0 is the frequency corresponding to the
rest mass of the particle. GR predicts a gravitational red shift. I
assume that this red shift applies to this rest mass frequency as
well. Therefore, if I'm thinking about this correctly, the rest mass
of a particle deep in a gravitational well (wrt the observer) is
reduced. Is this correct, or am I missing a key concept?

If this is correct, then by the time such a particle reaches the event
horizon it's apparent mass (as seen by the observer higher in the
well) will be reduced to zero (since g_00 goes to zero at that
point). If the particle was allowed to fall freely to this point, I
assume all the rest mass energy has been converted to kinetic energy.
Of course in the frame comoving with the particle it would always have
the original rest mass.

I'm also not quite sure what it means to the observer that the rest
mass of the particle has been reduced. How would he measure this,
since by definition he can't be with the particle. Would this be
observable, or is this "mass reduction" meaningless in terms of
observations?

This is observed in the Pound-Snider experiment. There is
more inertial coupling to the subatomic constituants of an
iron-salt near the earth's surface than a similar structure
at the top of a tower. The proximity to the earth's surface

?? Why should 'proximity to the earth's surface' be relevant? 'Deeper
in the earth's gravitational field' I would understand.


Gravity is maxmum at the surface and that is how the experiment
was performed. That is a good question tho. I am not aware
of anyone repeating the experiment down a well or mine shaft.

It is well known that pendulum clocks speed up whether moved
above or below the surface but that isn't quite a fair comparison.

GR (or Schwartzchild geometry) gets pretty vague without
a free-space path, making singularities event horizions and
other spooky stuff. I would think a mine shaft expeiment
might clear some of that up.

The concept is: "gravity there, makes the inerta here", and
you test the concept by moving an inertial oscillator closer to the
a gravitational source. Sure enough, GPS clocks are slower
down here.

A bullet follows a curved trajectory on the surface of the earth
and a straight trajectory at the earths center or in deep space
so my guess is that an atomic clock would speed up with with
either altitude or depth.

Whether the clock's oscillator exploits a ridgid frame or
an eliptical path to conserve momentum would also seem
an important factor.

I still would like to see a mine-shaft experiment
if you know of one.

Sue...

lowers the nuclear resonant frequency enough that atomic
absorption of light emitted from the tower-top is inhibited.

http://en.wikipedia.org/wiki/Mossbauer_spectroscopy
http://link.aps.org/abstract/PRL/v13/p539

--L.B.Okun
http://arxiv.org/abs/physics/9907017

- Dushan Mitrovich-