Absolutely (i.e., Correctly or Truly)

Brian Jones wrote:
 In SRT, clocks are set according to Einstein's definition of
 'synchronization.' In classical physics, clocks were assumed to be
 absolutely (i.e., correctly or truly) synchronized, in which case the
 Galilean transformation applies. Given comoving (same frame) clocks,
 the only difference between Galilean transformation clocks and
 'Lorentz' transformation clocks is that the former are correctly
 synchronized whereas the latter are not, as we shall soon see.

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.  

In this way both Galileo and Einstein establish simultaneity for two
spatially separate points, enabling us (conceptually) to associate 
a synchronized clock with each point in space.  A set of events
consisting of all these clocks having the same reading defines a 
locus of simultaniety in space.

Up to this point the methods of Galileo and Einstein are in complete
accord.  The difference between the two views is simply that Galileo
assumed the synchronization procedure just described gives a unique
result, regardless of the state of (uniform) motion of the frame in
which it is carried out.  Einstein asserted that this assumption is
both unjustified and evidently contradicted by experience.  Moreover,
if we replace this "unique simultaneity" assumption with a "constant
light speed" assumption (suggested by experience) we immediately
arrive at a beautifully unified view of Maxwell's electromagnetism,
Lorentz's electrodynamics, AND ordinary dynamics.  In addition, 
the theory of special relativity, particularly in the Minkowski
interpretation, has proved itself to be a tremendously powerful 
heuristic aid in the development of new theories, including 
quantum field theory and (of course) general relativity.

In retrospect it's easy to see that the "Galilean" view was never
entirely free of conceptual difficulties.  Uneasiness with the
"Galilean" view of space, time, and motion goes back at least to Zeno
in the 5th century B.C., who pointed out the fallacy of thinking that
an arrow in motion is "instantaneously" identical to an arrow at rest.
Unfortunately, neither Zeno nor anyone else could think of a viable
alternative... until Maxwell's equations of electromagnetism provided
the clue.

On an even more fundamental level, it's clear that Galilean invariance
was unsatisfactory because it didn't provide a logical structure for
quantifying a definite and complete separation between any two events.
It allows us to consider spatial separations *only* between strictly
simultaneous events, because the spatial separation between any two
NON-simultaneous events separated by a time increment delta_t is 
totally undefined, i.e., there exist perfectly valid reference frames
in which those two events are at precisely the same spatial location,
and other frames in which they are infinitely far apart.  Still, in
all of those frames, the time interval remains delta_t.  Thus, there
is no definite *combined* spatial and temporal separation, in spite of
the fact that we clearly intuit a definite physical difference between
our distance from "the office tomorrow" and our distance from "the
Andromeda galaxy tomorrow".  Admittedly we could postulate a universal
preferred reference frame for the purpose of assessing the true and
complete separations between events, but such a postulate is entirely
foreign to the logical structure of Galilean space and time (to say
nothing of the fact that it's operationally meaningless without some
prescription for actually determining the preferred frame, which
classical mechanics never provided).

If we were to attempt to remedy this, we would naturally need to think
of a "conversion factor" c relating a certain amount of temporal
separation to an "equivalent" amount of spatial separation.  On the
other hand, we certainly know that "time" is not just another
dimension of space, but must always be, in a sense, orthogonal to all
the space directions.  These considerations lead very directly to a
combined metrical interval of the form (cdt)^2-(dx)^2-(dy)^2-(dz)^2.
As Minkowski said,

 "This being so, and since the [Poincare group] is mathematically
  much more intelligible than [Galilean invariance], it looks as
  though the thought might have struck some mathematician, fancy-
  free, that after all, as a matter of fact, natural phenomena
  do not possess invariance with the [Galilean] group, but rather
  with the [Poincare] group, with c being finite and determinate,
  but in ordinary units of measure extremely great.  Such a
  premonition would have been an extraordinary triumph for pure
  mathematics."

In any case, with our "stair-case wit" we can see that the Minkowski
metric automatically resolves Zeno's concerns, provides a definite
absolute separation between every two events in space and time, and 
is in complete accord with every observation made to date, as well 
as being perfectly consistent with the beautiful theory of
electromagnetism and the even more beautiful theory of general
relativity.