niin:
1) time doesn't physically exist?
There's some subtlety to this. I was reminded the other day when I read an article about Hogfather see
Sky One where Terry Pratchett was talking about justice. He said you could grind the Universe down to a powder and
you wouldn't find a single atom of justice. It's the same with lots of things that we talk about. Like weather, entropy, colour, sound. These are things that we experience, and as such we can say they exist. But whether they really physically exist becomes a matter of language and definition. I'd say time is like heat, and is a derived effect of motion, and cop out by saying it isn't fundamental because it isn't what you think it is.
2) spacetime doesn't exist?
I think here I'd say no, it doesn't. Spacetime comes with some "fundamental" baggage, and if time isn't fundamental, I've got to say that space exists, but not spacetime.
3) Einstein did not believe in spacetime?
The quotes I found say he had issues with Minkowski, doubts when he was formulating general relativity, and more when he was hanging out with Godel. I think he wavered, and ended up thinking spacetime was space. But I can't prove this.
4) Einstein believed in the ether?
Maybe not "the" aether. Definitely not the aether Michelson and Morley were looking for. But see the Leyden address of 1920. He definitely believed in "an" aether. Basically he was saying that space is a kind of aether.
5) Special Relativity can be used to prove that time doesn't exist?
That's a bit black and white. It's more like Special Relativity can be "interpreted" in terms of space rather than spacetime. Here's a paper that goes some way to illustrate what I mean:
A New Interpretation of Special Relativity
Note the following excerpts:
Let us consider what relativity principal would hold in general if distances were always measured by wave propagation times (or conversely if time were defined in terms of wave propagation distance).
With this definition of distance, the constant c is simply a scaling factor which relates the units of distance to the units of time.
Let us take this as an alternative postulate for special relativity: matter consists of waves which propagate at the speed of light.
it makes little difference whether we assume that Lorentz invariance is truly a property of time and space or whether it is merely the result of using matter waves to make measurements.
It's got aether written all over it, though he doesn't actually use the word. I wonder if there's any rebuttals kicking around? I was reading another more relevant paper, but it's late and I can't find it. Time for bed.