The article "A Test Theory of Special Relativity: I. Simultaneity and Clock Synchronization"
by Reza Mansouri and Roman U. Sexl, published in 1977, contains at
least two statements that are pertinent to my current investigation into
the role of convention in Einstein's light speed principle.
The
first is that "one of the most debated problems in special relativity
is the role of convention in the definition of simultaneity of distant
events and the related question of first-order experiments (first order
in v/c)" (p. 498).
"One
of the most debated problems in special relativity"! As is clear from
my last few posts, that's not exactly reflected in some recent textbooks
on special relativity purportedly focusing on conceptual issues.
Mansouri
and Sexl quickly make it clear that they believe convention plays an
important role in clock synchronization and thus in the definition of
simultaneity. They state, for example, that "Einstein's procedure to
synchronize clocks at different space points is but one of several
possible alternative conventions".
Mansouri
and Sexl are thus effectively saying that the synchronization of clocks
is a matter of convention. They do not give any particular reason for
this statement beyond listing a number of clock adjustment procedures
which they all label synchronization procedures.
And
that's the crux of the matter. I think it's important to be absolutely
clear about what exactly is conventional in Einstein's theory: it's the
choice of clock adjustment procedure. Anybody is free to adjust distant
clocks any way they like, and some such procedure may be adopted by a
whole community or even the whole world as the one to be applied by
convention. But, and this is a big but, not every clock adjustment
procedure is a synchronization procedure.
To
prove that point, it is sufficient to give examples of clock adjustment
procedures which are not synchronization procedures, and I have done
this in, for example, this and this
post. Drawing on those examples, I have argued that in general terms an
Einstein-like clock adjustment procedure using signals is a
synchronization procedure if and only if the signals used are emitted
and propagate in symmetrical conditions in all directions. And I have
concluded that on that basis Einstein's clock adjustment procedure is
not and cannot be a synchronization procedure.in all uniformly moving
frames of reference.
All
that may seem straightforward enough. But there is a possible objection
to my line of reasoning which I think I need to address in greater
detail than I have done.
The
objection broadly goes like this: "True, there may have been a time
when the idea of simultaneity was based on that of sending out signals
in symmetrical conditions, but that concept of simultaneity has become
untenable because it's emerged that it's impossible to distinguish
between frames of reference in which such symmetry pertains and frames
in which it doesn't. Therefore physicists have redefined
the concept and have agreed to call distant events with the same time
stamp according to Einstein-adjusted clocks "simultaneous". Even if that
definition hasn't filtered through into general usage, it's a technical
definition of the kind scientists use all the time to ensure their
concepts are precise and can be applied operationally. For example,
mathematicians talk about "groups" and "rings" in algebra in a very
precise technical sense, and they're perfectly free to do so even though
the concepts of a "group" or "ring" are used in very different ways in
non-mathematical contexts."
Indeed.
Absolutely. Physicists are free to do this. But then they shouldn't be
using the concept of "simultaneity (physics)" in contexts in which only
the symmetry-based concept of simultaneity makes sense. Just like
mathematicians shouldn't - and to the best of my knowledge generally
don't - use their concept of a "group (algebra)" to talk about group
dynamics in social situations, for example.
To
be more specific: I think the concept of simultaneity is closely linked
to concepts such as synchronization, symmetry, existence, signal,
speed, and cause and effect. This link is established in the way people
generally think, talk and write about these various concepts. It is thus
ingrained in the English language as currently constituted. Similar
considerations probably apply to many other languages in which similar
concepts exist.
I think the following statements exemplify some of the relationships between those concepts as currently constituted:
1)
Events in two places A and B are simultaneous if and only if
synchronized clocks located at A and B show the same time when the
events occur.
2)
Clocks in A and B can be synchronized by setting them to the same time
when identical signals emitted in opposite directions from the mid-point
M between A and B arrive at the clocks, provided the signals propagate
in symmetrical conditions.
3)
Signals sent from A to B cannot arrive in B at an earlier time than
when they were emitted as measured by synchronized clocks in A and B.
4)
If a signal emitted from A arrives in B at an earlier time than when it
was emitted, according to clocks positioned in A and B, then those
clocks aren't synchronized.
5)
A cause in a location A always precedes its effect at a distant
location B provided the clocks used to measure time in A and B are
synchronized.
6)
The one-way speed of a signal between A and B is the distance between A
and B divided by the time the signal needs to travel from A to B as
measured by synchronized clocks in A and B.
Some
of the meaning of "simultaneity", "synchronization", "symmetry",
"signal", "speed" and "cause and effect" is established in these
relationships.
It
is thus not possible to "redefine" one such concept and expect its
relationship with other, related concepts to be unaffected. For example,
I would hold that the concept of cause and effect relies on a
symmetry-based concept of simultaneity and becomes inapplicable in some
circumstances if the requirement of symmetry is given up.
And
this is exactly what happens if Einstein's clock adjustment procedure
is adopted: while we may not know whether light signals propagate
symmetrically in any particular uniformly moving frame of reference, we
do know that if they propagate symmetrically in a first frame then they
do not propagate symmetrically in other frames that move relative to the
first, at least not locally. The result is that the concept of cause
and effect, for example, becomes inapplicable in the context of special
relativity if superluminal speeds are involved.
Suggestions that superluminal speeds lead to cause and effect or the flow of time being "reversed", as they keep being made
in relation to recent neutrino experiments at CERN, are thus misguided:
they are the result of uncritically and unwittingly applying concepts
that rely on a symmetry-based concept of simultaneity to a theory in
which that concept has been abandoned.
After
this little digression, it's time to mention the second statement made
by Mansouri and Sexl that is pertinent to my investigations. This is the
"remarkable result", as the authors describe it, that "a theory maintaining absolute simultaneity is equivalent to special relativity" (Mansouri/Sexl's emphasis, p. 503).
My discussion of this statement will, however, have to wait until my next post.
