[Physics] Physics Digest, Vol 1, Issue 25

[Ilja Schmelzer]

2016-10-23 19:26 GMT+02:00, Doug Marett <dm88dm at gmail.com>:
> From my reckoning, the two observers, because
> they are on a solid body and on a vertical line passing through the center
> of the earth, have no choice but to count exactly the same "rate" of time,
> so after some very long period of time, they will always agree on how many
> days have passed.

But this is some global synchronization, it is not a local clock.  The
clock which measures proper time is a local clock.  In the ideal, it
has the size of a point.  Of course, every real clock will be greater,
but a clock of point size would be the ideal clock necessary to
measure proper time.

> After some long period of time, the atomic
> clocks will disagree, but the rotational clocks will agree on what time it
> is. How can this be?

The atomic clocks measure (approximately) proper time, the big
rotational clock not.  The rotational clock measures some variant of
coordinate time - the time which does not depend on the path of the
clock but simply on the position of the Earth and some synchronization
(say, they look at the position of some star, but if we take into
account the finite speed of light, it slightly depends on which star
they look at).

> If gravitational time dilation means that "real" time
> is passing into the future faster at A than at B, then it should not be
> possible to design a clock that is immune to time dilation, but we just
> did. Further, it would soon be clear that the atomic clock at observer A
> has counted more rotations of the earth than has actually occurred. So it
> is clearly in error. Further, if atomic clock A on top of the building was
> actually in the future compared to the atomic clock at the base, then if I
> walk up the building to clock B and read the time, it implies I am now in
> the future.

The proper time of relativity is clock time - the time shown measured
by point-like local clocks.  Some "real time" does not exist.  This is
positivism.  Only what can be exactly measured exists.  So, if we
cannot measure time, it does not exist.  And once different clocks
measure different proper time between the same events, once they
travel differently between them,  we cannot measure real time with
such a clock time.  So, that real time simply does not exist.  Point.
Stupid philosophy, but positivism is stupid, such is life.

One can take a different position, an accept that some real time
exists.  But then GR has the problem that it cannot be measured. Real
time would have to be some time coordinate, but which? Proper time
measures something different.  Your procedure would define some  time
coordinate.  But there would be a lot of freedom of choice of
appropriate time coordinates.  Which is the true time?