On 5/31/22 2:54 AM, Luigi Fortunati wrote:
> In accelerated reference frames, the clocks do not stay synchronized
> with each other.
Hmmm. Clocks that are at the same "altitude" relative to the
acceleration do remain synchronized.
Note also that "accelerated frame" is an oxymoron -- "frame" implies a
set of four mutually-orthogonal coordinate axes, which can occur ONLY
for inertial coordinates.
> Yet on Earth, which is an accelerated reference frame,
No, it is not. On the surface of the earth, a "small" region of
spacetime can be considered to be equivalent to an accelerated system in
flat spacetime, but larger regions on the surface are nowhere close to
an accelerated system in flat spacetime. Here "small" depends on one's
> all the clocks that are at the same altitude remain perfectly
> synchronized with each other wherever they are, why?
Because in weak gravity, "gravitational time dilation" depends on the
gravitational potential, which primarily depends on altitude (as in an
accelerated system in flat spacetime). This is only approximate: when
measured very accurately, the potential at a given altitude depends on
the density of the material below, and on the positions of sun, moon,
and planets above -- at 15,000 feet above earth's geoid, the potential
over Pike's Peak is measurably different from that over Death Valley.