43: file eq43.gif
or with sufficient accuracy by
eq. 44: file eq44.gif
This expression may also be stated in the following form:
eq. 45: file eq45.gif
If we represent the difference of potential of the centrifugal force
between the position of the clock and the centre of the disc by f,
i.e. the work, considered negatively, which must be performed on the
unit of mass against the centrifugal force in order to transport it
from the position of the clock on the rotating disc to the centre of
the disc, then we have
eq. 46: file eq46.gif
From this it follows that
eq. 47: file eq47.gif
In the first place, we see from this expression that two clocks of
identical construction will go at different rates when situated at
different distances from the centre of the disc. This result is aiso
valid from the standpoint of an observer who is rotating with the
disc.
Now, as judged from the disc, the latter is in a gravititional field
of potential f, hence the result we have obtained will hold quite
generally for gravitational fields. Furthermore, we can regard an atom
which is emitting spectral lines as a clock, so that the following
statement will hold:
An atom absorbs or emits light of a frequency which is dependent on
the potential of the gravitational field in which it is situated.
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