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starship-design: The "So-called" Twin Paradox, cont'd
Steve VanDevender says, on 1/27 at 04:07 EST:
>Note that Einstein says "to a first approximation". ...
Precisely the point I make in my Relativity Paper.
>The difference in trip time is ultimately the result of different
>paths through spacetime.
The difference in trip time could also be attributed to different
paths through *space*, but relativists don't like absolutes. (I
see the idea of an absolute frame of reference in Timothy's
comment, in his email of 1/26 at 10:12 EST, "So to find the
symmetry breaking factor in the Twin Paradox you *need* to look at
a global (non-homogeneous) environment.") But, one relativist,
Einstein himself (on p. 56 of his "The Meaning of Relativity,"
Fifth Edition, Princeton, 1956), raises the possibility of an
absolute frame by citing "Mach's Principle," which postulates that
"a material particle [moves] relatively to the centre of mass of
the universe." [See also Holstein and Swift, Amer. J. Phys. 40,
p. 749 (1972).]
>Paul's path relative to an inertial observer will clearly show
>that he is accelerating in a spaceship, as it will travel far
>away and come back.
--Through space (with respect to a "fixed" frame).
Then the difference in trip time between Peter's time (delta-t)
and Paul's time (delta-t') can be attributed to Paul having
traversed space (delta-x) in a frame "fixed" with respect to
Peter, according to the "interval" relation (for each one-way
trip), which is *independent of velocity*,
(delta-t)^2 = (delta-t')^2 + (delta-x/c)^2 .
Steve adds, on 1/27 at 04:19 EST, (responding to Timothy):
>Unfortunately it's because both Rex and I were oversimplifying a
>bit. I think we actually still agree...
I'll buy that. I think Steve's elaboration of his 11/29/96
remarks has brought us considerably closer together.
>Unfortunately relativity does not recognize any sort of global
Except for Einstein's comment cited above.
>In a sense, Rex's formulation only puts blinders on Peter and
>Paul, preventing them from making the observations that they
>could make entirely between themselves to determine who should
>age less. If we remove these unreasonable restrictions then they
>could easily determine between themselves who should have aged
>least when they meet again.
However, if the "observations...entirely between themselves" are
composed of Doppler-shift measurements by each of light from the
other, they both measure exactly the same shift (as the Special
Theory stipulates) and can't tell which one is "moving." But they
*can* determine which one is moving by looking at the Doppler
shift of light from the "fixed stars." That was my point that I
may have oversimplified a bit in my 11/29/96 response to Nick.