Dingle’s Argument And
Question About Special Relativity
Professor
Herbert Dingle was one of the most respected relativists of his era – at least
until he started asking questions that no one could answer. As discussed on the
Report page, Dingle became involved in a much publicized debate about the Twin
Paradox and his name became intimately linked with that paradox. However,
Dingle soon took the essence of the Twin Paradox and created a very simple
question about Special Relativity. He was to pursue his questioning of Special
Relativity for decades. Many relativists heaped scorn and ridicule on Dingle
and his question, but no answer was received.
In his book,
"Science At The Crossroads", Dingle, on page 7, gave the
simple, basic question – see below:
THE QUESTION
“According to
the theory, if you have two exactly similar clocks, A and B, and one is
moving with respect to the other, they must work at different rates (a more
detailed, but equally simple, statement is given on pp. 456, but this gives
the full essence of the matter), i.e. one works more slowly than the other.
But the theory also requires that you cannot distinguish which clock is the
'moving' one; it is equally true to say that A rests while B moves and that B
rests while A moves. The question therefore arises: how does one determine,
consistently with the theory, which clock works the more slowly?
Unless this question is answerable, the theory unavoidably requires that A
works more slowly than B and B more slowly than A which it requires no
superintelligence to see is impossible. Now, clearly, a theory that requires
an impossibility cannot be true, and scientific
integrity requires, therefore, either that the question just posed shall be
answered, or else that the theory shall be acknowledged to be false. But, as
I have said, more than 13 years of continuous effort have failed to produce
either response.”

Dingle saw that
if one could not explain the net proper time difference using Special
Relativity’s time dilation equation, then Special Relativity could not be
directly describing actual clock slowing, i.e., it could not be directly
describing proper time. In time, most of the mainstream quietly came to agree
with Dingle regarding his view on the Twin Paradox, but they either did not see
or publicize the corollary that, therefore, Special Relativity could not be
directly describing proper time.
Further Interpretation
If one contends
that a clock cannot accumulate proper time both faster and slower than another
clock, then one cannot interpret Special Relativity’s time dilation equation as
describing proper time and, hence, cannot interpret it as directly describing
what’s occurring physically. Since Special Relativity’s length contraction
equation was derived using the same basic logic as for the time dilation
equation, an analogous conclusion holds for that equation. It then follows that
Special Relativity’s equations for kinetic energy and momentum cannot be
directly describing what’s occurring physically. Putting it succinctly, Special
Relativity cannot directly describe what’s occurring physically and that
includes, given its definition of clock synchronization, its postulate on the
speed of light in inertial frames.
Einstein, in his
1905 “relativity” paper, selected a convention for synchronizing clocks. This
convention stated that if one sent a light signal from to A to B and it was
reflected back to B, then the time for going from A to B would equal the time
for going back from B to A. Thus, the time it took for light to go from A to B
would be ½ the time for the complete round trip. This convention is consistent
with and, in fact, is required by the 2^{nd} relativity postulate that
the speed of light is isotropic in all inertial frames. The 2^{nd}
postulate and this synchronization convention are, of course, part of the
foundation of Special Relativity.
However, Prof. Selleri, in Chapter 5 of his book “Weak
Relativity”, notes that professors H. R. Reichenbach
and Max Jammer have shown that one can choose the ratio of the time it takes
for light to go from A to B to the time for the complete round trip to be any
fraction between 0 and 1 and that will yield a theory that is as valid as
Special Relativity. Using “e” as the ratio that Einstein chose to be ½, Reichenbach showed that any value for e, where 0 < e
<1, would likewise be adequate and could not be considered false. Jammer agreed with Reichenbach
and wrote, "The thesis of the
conventionality of intrasystemic distant simultaneity
... consists in the statement that the numerical value of e need not necessarily be 1/2, but may be any
number in the open interval between 0 and 1, i.e., 0 < e <1, without ever leading to any
conflict with experience." None
of these choices for e would lead to a theory that described what was happening
physically as they would all be based on a premise that was, in general, false.
Hence, the
selection of e = 0.5 for all directions in all frames is a convention that does
not represent what’s happening physically. For the unique frame where
the speed of light is isotropic, the selection of e = 0.5 would be
accurate. However, Einstein’s convention simply tries to make every frame simulate
the unique frame so, when the conventions of Special Relativity are followed,
each observer (erroneously) observes the world as though he were at rest
in the unique frame.
It is,
therefore, recommended that the physics community seriously consider the
construct of a unique physics frame and the associated construction of what’s
happening physically in addition to Special Relativity’s description of each
observer’s conflicting views.
References
H. Dingle, Science at the Crossroads (Martin Brian
& O'Keeffe, 1972),
Downloadable from the World Science Data Base  Click Here
F. Selleri, LA
RELATIVITA' DEBOLE La fisica dello
spazio e del tempo senza paradossi (Melquiades, Milano 20072010) [The online English version, "Weak
Relativity" is downloadable.]
H. R. Reichenbach, The Philosophy of
Space and Time (Dover, New York, 1958)
H. R. Reichenbach, Philosophie der RaumZeitLehre, (Berlin, 1928) p. 224
M. Jammer, Concepts of Simultaneity (The John
Hopkins University Press, 2006)
M. Jammer. at page 205 of G. Toraldo di Francia, ed., Problems
ni the Foundations of Physics (Societa Italiana di Fisica, Bologna and North Holland, Amsterdam, 1979)