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Re: [Phys-L] another DIY relativity experiment

On 05/20/2016 11:45 AM, Bob Sciamanda wrote:

the rate of some changes are, by their physics, already dependent on
the strength of local gravity. For instance, a clock whose period is
determined by a pendulum would not even work on the ship which is in
gravity free space! So the above statement opens the question of how
it applies to phenomena whose physics of time evolution includes a
dependence on gravity apart from any relativistic effects?

The short answer is that metrologists stopped depending on
pendulum clocks a long time ago, circa 1736.

Harrison's chronometers were built with high symmetry, to
make them immune from accelerations of all kinds, including
the local gravitational field as well as the tossing and
heaving of the ship. Even more impressively, they were
insensitive to angular velocity and angular acceleration
in the yaw, pitch, and roll directions.

Bismarck said politics is the art of the possible. In some
sense, the same applies to physics: If you have a clock that
doesn't do what you want, get a better clock. This becomes
a well-defined notion when you find that there is a verrry
wide class of clocks that all give the same answer.

At the next level of conceptual sophistication, the local
gravitational acceleration is of minimal interest in general
relativity. That's because you can always get rid of it,
locally, by switching to a different reference frame.

For example, the mass of the earth means there is a /difference/
in the local g-vector from one side of the earth to the other.
This difference is more interesting than either g-value separately.
The difference cannot be canceled by any straight-line acceleration
of the reference frame. (You can cancel either one separately,
but not both, and not the difference.)

==========

In a uniformly accelerating frame, any formula proportional to
"g h" is clearly incorrect. For starters, any correct formula
would exhibit gauge invariance with respect to h.