From: scerir (scerir@libero.it)
Date: Fri Aug 23 2002 - 14:45:01 MDT
Charles Hixson
Lets set one of them in motion such that on inertia it will
eventually complete a circuit of the universe (i.e., I'm assuming
that there does exist a closed path that orbits the universe), and
such that at some point along it's trajectory it will come sufficiently
close to the other clock, which is balanced at an essentially stable
point (say at a stable Lagrange point around a galaxy at the edge
of a small stable cluster). As they pass the first time, synchronize
the clocks. When they pass the second time, will the times be
different?
[from Pais' "Subtle is the Lord" (p. 145)]
Einstein rather casually mentioned that if two
synchronous clocks C_1 and C_2 are at the
same initial position and if C_2 leaves A and moves
along a closed orbit, then upon return to A, C_2
will run slow relative to C_1, as often observed
since in the laboratory. He called this result
a theorem and cannot be held responsible for
the misnomer "clock paradox", which is of later
vintage. Indeed, as Einstein himself noted
later, "no contradiction in the foundations
of the theory can be constructed from this
result" since C_2 but not C_1 has experienced
acceleration.
But for modern experts, like this one, the situation is rather messy ...
"I have, so far, collected 54 different so-called 'explanations' (up to Summer
1999), published in mainstream physics journals (all suitably peer reviewed!)
and textbooks, and each implies that most of the others are wrong!!! These
so-called explanations are broken down as follows: 8 say it is inexplicable, and
causes a huge problem for Relativity (among these is Essen the inventor of the
cesium clock); 4 say the differential aging is all caused solely during the
acceleration & deceleration phases (this includes Langevin, Bondi, Rindler and a
standard 1990's textbook); 9 say the acceleration has nothing whatever to do
with the explanation; 3 say that General Relativity has nothing to do with the
explanation; 4 say that General Relativity gives the sole explanation; 2 say
jumping from one Inertial Frame to another explains the paradox. Other more
exotic and bizarre explanations make up the rest. So, it as all very simple, and
the correct explanation is to be seen in every standard text? Like hell it is!
Møller's widely used text "The Theory of Relativity" had to admit that its
original explanation was not correct. In later editions it concocts a mass that
suddenly goes from + to - for a twin! That must be an interesting experience!
OBizarre¹ is the word for that. Umberto Bartocci has yet another explanation (if
this has been published, it can be counted as number 55) viz: that the path of
one of the clocks is 'geodesic, the other definitively not". He claims that "the
'postulate of relativity' either special or general, never asserts that supposed
complete symmetry between the two clocks". I claim that Einstein said just that
in his 1922 book (see above). Also, in relation to this paradox why not also
quote another simple objection; if the twins never met again, and just start by
passing each other at high speed and exchange photographs, and after 30 years of
each others own recorded 'time' take another photograph and post that to the
other twin?. This is the simple set-up that is very carefully avoided in the
debate. Or what of the "Peter would be dead and Paul alive on the one hand,
while Paul would be dead and Peter alive on the other hand" problem set by
Lovejoy in 1931. We have Peter both dead and alive, and also Paul both dead and
alive! Why, oh why, do so many adherents of S.R. adopt a lofty condescending
attitude on this problem, as if everyone else was stupid, and 'dead from the
neck up'?
Something more? Look at what Percival writes:
http://www.dipmat.unipg.it/~bartocci/percadd'.html
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