> You are right about the need for a simultaneity plane which defines "now"
> absolutely. That doesn't exist in Einstein's preferred formulation of STR.
> But it did exist in his first formulation where time was a parameter and
> not a coordinate (dimension), and it does exist (at least the possibility
> is there) in Lorentz's empirically equivalent formulation of STR. The
> reason it disappears for Einstein is his positivism which led him to a
> wholly operationalist definition of time and simultaneity.
I'm not sure what you mean by some things here, but am also not
sure that they affect the argument. Whether you deal with SRT as
Einstein did in his 1905 paper or as Minkowski did in terms of
space-time, the Lorentz transformation eqns are the same. It doesn't
matter whether you call t a parameter or a coordinate, t = constant
isn't the same as t' = constant. Lorentz had a preferred frame, the
aether, so that the transformation eqns would hold between the aether
frame & any moving frame but not between 2 arbitrary inertial frames.
Thus the transformations between intertial frames wouldn't form a group.
(&, of course, no one has found the aether!)
You can choose an arbitrary frame & call it "preferred" - but
why? As I noted, the Incarnation makes it possible to speak
meaningfully of "God's rest frame".
Einstein moved away from positivism, & by 1920 called Mach "a
good mechanic but a poor philosopher". When he was asked near the end
of his life to contribute to the Carnap _Festschrift_ he declined with
some rather sarcastic remarks about positivism.
> Under some models of GTR, including the class of "physically realistic"
> solutions, a privileged reference frame is possible.
At any space-time event you still have the freedom of local
Lorentz transformations. The Friedman-Lemaitre models have a "cosmic
time", but the description of the model by an observer moving with
respect to the "privileged" observers is still valid.
> Even if we cannot do
> better than an operationalist notion of physical time, we still are not
> forced to give up the idea of absolute simultaneity.
We are unless we can keep people from moving.