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[Phys-L] Re: "moving clock runs slower" (yes)



Bob Sciamanda wrote:
John Denker wrote:
| . . . 2b) The simplest and IMHO most satisfactory explanation is that
elapsed
| time is path-dependent for the same reason that path-length is
| path-dependent.

I like this description

:-)

It looks like we are converging toward a consensus.

(it is not, however, a physical "explanation").

I'm not sure why not. In particular cases, it sure looks physical
to me; I can draw it on a space-time diagram.

Just a comment:

It seems obvious that we are talking about a *comparison* of two clock
readings and not some absolute or intrinsic time dependence upon path. If
the traveler left (and returned to) an uninhabited (and un-instrumented)
earth, he would not notice this effect. While traveling, his passengers are
oblivious to their space-time trajectory - they merely read their clocks.
Even if they knew that their clock-time is path-dependent, how do they
correct it - to agree with what standard?

I agree Moe (the traveller) could be obvlivious if he wanted to be.

However, he need not be oblivious. If we confine ourselves to
special (not general) relativity, Moe could easily keep track of the
details of his world line, using an INS (inertial navigation system).
The INS contains accelerometers and gyroscopes, and keeps track
of the "current" position by integrating (time-stepping) the
equations of motion. Using the INS data, Moe can know how to draw
the _chord_ (i.e. the most-direct path) from his initial position
to his current position. He could then calculate the elapsed time
along the direct path, and compare it to the observed time along
his actual path.

Moe is by no means required to do this calculation and comparison,
but he could do it if he desired.

The path-dependence has utility only with respect to the path of a second
(standard?) clock.

We agree that the notion of "younger" versus "older" has meaning only
w.r.t some other clock.

But more generally, path-dependence is useful even if you don't have
any sort of "standard" clock to compare against. In particular,
Fermat's principle of least time depends on comparing each path to
other nearby paths, none of which come to us pre-labelled as
"standard".

When the second clock stays fixed on earth it seems
natural to consider its proper time as the really useful variable
(standard?).

The whole idea of a "standard" frame is contrary to the spirit of
relativity.

Besides, what makes Earthlings so special? As the bumper sticker says:
The meek shall inherit the earth. The rest of us will go to the stars.

What do we say when the departure and re-uniting space points are different?
Suppose Joe and Moe leave Earth and meet on Io, taking very different
space-time trajectories. Can we choose a clock? Why do we need to? Each
generates its own time base variable for doing physics from its proper
frame - including an analysis of events on the other's world line.

I agree with the concluding sentence. I assume the preceding questions
were merely rhetorical. Moe can choose whatever clock he prefers, and
Joe can choose whatever clock he prefers. We can choose a third clock
if we prefer. Nobody needs to meddle in anybody else's choice.
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