dl58 said:
The explosion may be uncertain to Alice but the example with Tom shows it is fixed.
You are assuming your conclusion. You can't just state that it is "fixed" in an absolute sense. My contention is that "fixed" is relative; it depends on which event you pick. You can't refute that by just claiming that "fixed" is absolute. You have to show how SR
requires "fixed" to be absolute, and you haven't done that.
dl58 said:
By fixed I mean Alice will not see something which contradicts what Bob saw
That's because you constructed the scenario that way: you stipulated that the events of the explosion, Bob seeing it, and Alice seeing it are all in the past light cone of Tom at some event. So of course they're all "fixed", by my definition.
But now suppose this: Bob sees the star explode. Bob also sees an image of Alice at that same event (i.e., the light from that image of Alice reaches him at the same event on his worldline as the light from the exploding star). Bob
predicts, based on those images, that Alice will see the exploding star at the event on her worldline that intersects his future light cone at the event where he sees the exploding star and the image of her.
However, Bob's
prediction turns out to be wrong: what he does not know is that an alien spacecraft , coming in at high deceleration, took Alice aboard and flew off with her at high acceleration in the opposite direction, at an event on her worldline just outside Bob's past light cone at the event where he sees the exploding star and the image of her. The alien ship's acceleration is high enough, in fact, that both the past and the future light cone of Bob at the event where he sees the exploding star are behind the alien ship's Rindler horizon. That means that no light from the approaching alien ship had reached Bob at that event, and the light from the exploding star that is passing Bob at that event will never reach Alice, because it can't catch up with the alien ship.
You may object that you didn't include all this in your scenario. But in the real world, you don't get to choose the scenario. You picked a scenario in which nothing of interest happens except the exploding star; but in the real world, you don't get to pick what things of interest happen. The point is that both "futures"--both sets of events involving Alice, the one you gave where she sees the exploding star and the one I gave where she gets taken away by the alien ship and never sees it--are consistent with what is in Bob's past light cone at the event when he sees the light from the exploding star. And that will be true of any event. Even at the event where Tom has all of this in his past light cone, so he knows which of the "futures" that were consistent with Bob's past light cone actually came to pass, there are still an infinite number of "futures" that are consistent with what is in Tom's past light cone at that event, and there is no warrant for claiming that anyone of them is "fixed and certain".