[FOM] Re: 206:On foundations of special relativistic kinematics 1

[Timothy Y. Chow]

I looked up Mackie's paper, "Three Steps Toward Absolutism," reprinted in
the book "Logic and Knowledge," a collection of Mackie's papers.  It's
been over ten years since I learned of this paper, so it's about time I
actually read it!  I'll discuss it from my own, somewhat biased
perspective.

Let X be a point in spacetime and suppose that two photons P1 and P2
originate at X and move off in diametrically opposite directions.
Mackie's key claim is that there is a canonical bijection between the
worldlines of P1 and P2.  From this he derives a concept of "absolute
rest" as follows.  Any observer that passes through X and that travels at
constant velocity relative to an inertial reference frame can define a
bijection between the worldlines of P1 and P2: He simply associates
*simultaneous* points on these worldlines with each other.  Since
simultaneity depends on the reference frame, different observers will
define different bijections.  The observer whose bijection coincides with
the canonical one is deemed to be the one at "absolute rest."

But where does the canonical bijection come from?  How is it defined?
Mackie clearly states that there isn't any way to define this bijection
experimentally.  But if it can't be defined experimentally, isn't it
meaningless?  No, says Mackie, that would be a verficationist error.

I personally think that Mackie confuses himself because he relies heavily
on a diagram that looks like it yields a canonical bijection, when in
reality the diagram has a built-in choice of reference frame.  But here's
one way we might argue that there is a canonical bijection: All photons
are alike, and any two photons that are born at X must pass through the
exact same stages in its life history.  So I can define a correspondence
by associating a particular instantaneous stage in the life history of P1
with the *exact same stage* in the life history of P2.  By a stage in the
life history, I mean something intrinsic to the photon, not determined by
its interactions with other things in the world.  (Although Mackie
doesn't argue exactly in this way, several things that he says seem to
suggest that this is the idea in the back of his mind.)  Never mind that
I can't establish this correspondence experimentally, as long as it makes
*theoretical* sense.

I don't find Mackie's argument compelling and I doubt that many people do.
However, if we weaken his claim slightly and assert that there is nothing
to stop us as theorists from picking a particular reference frame and
declaring by fiat that it is privileged, then I don't think that it can
be directly refuted.  Physicists would probably shrug and say O.K., you
can add irrelevant entities to your theory; I don't see the point, but
as long as you predict the same experimental results then I don't really
care.

I wonder if a foundational treatment of special relativity should
adjudicate such disputes, e.g., should it rule out Mackie's view on
the grounds of simplicity, or should it leave such "philosophical"
questions unresolved?

Tim