ABSTRACT
It has long been remarked that ‘‘The Theory of Relativity’’ is a poor name
for the Theory of Relativity. The usual justification for the name looks
backward to pre-relativistic space-time structure: the absolute temporal and
spatial structures of (Neo-)Newtonian space-time (namely, simultaneity,
lapse of time between events, and spatial dimension of objects) all become
‘‘relative to the observer’’ in Einstein’s theory. But this masks the radical
nature of the shift to special and general relativity. In those theories,
simultaneity, lapse of time between events, and spatial dimensions of objects rather become physically non-existent. It is entirely incidental to the physics
that in special relativity the choice of an ‘‘observer’’ (which is nothing
more than the choice of a time-like vector at a point in space-time) allows
for the definition of a unique global reference system (a Lorentz frame)
which in turn supplies a global time function and a spatial metric on the
simultaneity slices of that function. In a generic general relativistic space-
time, choice of an ‘‘observer’’ does not pick out any such global reference
system, and indeed, no such system may exist. That is, it is evident in general relativity that ‘‘simultaneity’’ is not a physically-interesting-but-observer-
dependent notion; it is rather absent altogether from the physics. And the
same holds in special relativity, even though one can, as a purely formal
exercise, associate a global time function with an observer-at-an instant.
The moral of the theories of relativity is not that classical spatio-temporal
notions are rendered merely relative, but that they are expunged from physics
altogether.
