As far as I understood, the generalized clock postulate says that there is no difference between the measurements of a non-inertial observer (NIO) and those of his co-moving inertial observer (CMIO) who instantsneously shares his time and position (of course the CMIO will change after an infinitesimal time interval).

However: let's suppose that in this time interval both the NIO and the CMIO measure the acceleration of a particle that is passing near them. Basing on classical mechanics, I would expect the two measurments to be different, since NIO's also depends on the fictitious force caused by its own acceleration, while the CMIO's does not. Where am i going wrong?

  • $\begingroup$ I don’t recognize this as a statement of the clock postulate. Do you have a reference? It might help me and others understand the context of the statement. $\endgroup$ – Dale Sep 1 at 20:13

My understanding of the clock postulate is that observations of (not by) the two clocks reveals no difference between the clock of the NIO and the one of the CMIO.

The NIOs acceleration affects how he sees other clocks. His own clock is unaffected. Clocks in the direction of his acceleration appear to him to be running faster, those in the opposite direction appear to be running slower.

The effect is linear and proportional to their distance.

That is why the leading and trailing observers with two accelerating clocks agree which clock seems to be running faster than the other.

The CMIO does not see this effect. Looking at any series of events in the direction of his acceleration, The NIO will see them proceeding at a faster rate than the CMIO sees them. The accelerating third particle will seem to the NIO to be accelerating at a greater rate if it is in this direction.

If the acceleration of the NIO is away from the third particle he will see it accelerating more slowly than the CMIO sees it.

  • $\begingroup$ I'm not following. Please explain why NIO & CMIO see distant clocks differently? Moreover, how your speech relates to measuring force and acceleration? $\endgroup$ – Mohammad Javanshiry Sep 28 at 20:04
  • $\begingroup$ Does this extension help? The effect of acceleration is derived from the Lorenz transformation by comparing observed time as a function of position before and after a speed change. I make no comment on measuring force or acceleration, only on observing the motion. $\endgroup$ – DrC Sep 28 at 22:40

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