Galileo's Predicament

Albro Swift wrote:
 There's no difference between the Galilean and Einsteinian methods
 of synchronizing clocks.  In both cases, to synchronize events at 
 the two ends of a uniform stationary rod, we can simply tap the rod 
 at its midpoint and let the sound waves (in the rod) propagate out 
 to the ends, where they will arrive simultaneously.

Brian Jones wrote: 
 Thanks for your sincere reply, but I must note that you missed the
 main point. In other words, where is your proof that these sound 
 waves will arrive simultaneously?

I understood your point.  You advocate a definition of simultaneity 
that results in a unique sequence of time slices for all frames of 
reference.  In fact, that IS your proposed definition of simultaneity.  
However, your presentation was misleading in it's historical references, 
and I think it lacked the proper emphasis on the main epistemological 
point as well.

You referred to your proposed definition as the "classical" one, 
and suggested that it was founded in the Galilean tradition.  This 
is historically problematical at best, because your proposed definition 
of simultaneity implies anisotropic lengths within uniformly moving 
reference frames.  We normally presume the lengths of physical 
objects are invariant under spatial rotations in any unaccelerated 
frame of reference.  This was certainly Galileo's assumption, and 
it's entirely consistent with classical Galilean invariance.  
However, it's strictly INconsistent with your proposed definition 
of simultaneity.  

Classical theorists assumed they could have BOTH absolute simultaneity 
AND spatial isotropy in all inertial frames, and no one can say 
which of those two deep-seated assumptions (intuitions) they would 
have preferred to give up, had they realized they were incompatible.  
Therefore, it's historically misleading to equate your proposed 
interpretation with the "classical" Galilean outlook.  

Of course, if you want a historical precedent for your proposal 
you don't have far to look.  Your proposed interpretation was 
invented by H. Lorentz around the turn of the century in order 
to reconcile a complex of new experimental results that were 
inconsistent with classical predictions.  On the other hand, you 
may be slightly unconfortable citing this precedent, in view of 
the fact that Lorentz eventually aknowledged (albiet reluctantly) 
the elegance and power of the interpretation you are disparaging.

The epistemological point in your presentation that I think deserved 
more emphasis concerns your comment

  "Why do we need a substitute for [B. Jones's proposed
   synchronization procedure]?  The answer is simple:  No one 
   has yet presented ... a way to produce [such synchronization].

This is admirably candid, but after such a devastating admission one 
would expect to see some argument to suggest why your proposal is not 
as jejune as it appears to be.  Instead, you simply present a review of 
some elementary texts, and then conclude by announcing

   "The lack of (absolute) clock synchronization is the only 
    reason relativity theory stands today."

This is badly worded, because it implies sufficiency when you could 
only mean necessity.  In essence, you assert that if our experience
of the physical world provided us with a basis for a coherent and 
operationally meaningful definition of absolute velocity, then our
physical theories would reflect this fact.  Presumably so, but the
relevance of this contra-factual proposition to the universe in which
we find ourselves is unclear.

I must say, this entire discussion has a strong ironic element,
because in the age-old debate between absolute and relational theories 
of space, time, and motion, the theory of relativity represents the 
absolute side.  It's well known (outside of internet discussions) that 
the theory of relativity is most definitely NOT a relational theory of 
motion, i.e., it does not attribute all physical effects to the relations 
between material bodies.  The effects are ultimately determined by the 
absolute background metric, which is affected by, but is not determined 
by, the distribution of material objects (except arguably in some 
specific cosmological models that are not currently in favor among 
cosmologists).  Thus, relativity, no less than Newtonian mechanics, 
relies on space(time) as an absolute entity in itself, exerting 
influence on material bodies.  (This is typically introduced to 
relativistic treatments by a set of boundary conditions necessary 
to determine a solution of the field equations.)

There actually have been attempts to create true *relational* theories 
of motion, notably the interesting work of Barbour and Bertotti in the 
1970's.  It's just an unfortunate historical accident that the name
"relativity" was given to Einstein's theory.  The word actually refers 
to the covariance of spatial and temporal intervals, not to any 
Leibnizian notion that only the relations between material objects 
are physically significant.  Admittedly Einstein was sympathetic to 
this philosophy, especially early in his career, and entertained 
hopes of banishing absolute space from physics, but like Newton 
before him he was forced to abandon this hope in order to produce 
a theory that satisfactorily represents our observations.  It is
therefore doubly ironic to see Einstein daily excoriated in this 
newsgroup for foisting a relational theory of motion on the world.