Alfredo Tifi said:
I believe Hawking is exaggerating in telling us (page 83):
«...the Universe doesn't have just a single history, but every possible history, each with its own probability; and our observations of the current state affect its past and determine the different histories of the Universe, just as the observations of the particles in the double slit experiment affect the particles' past.»
Do you agree?
I may come closer to agreeing with this than most. If you follow the Multi World Interpretation (MWI) - in the sense that the universe is continuously spawning slightly different copies of itself that do not further interact, then I have no counter argument for you. Otherwise, consider this:
The first problem with "changing the past" is the notion of choosing an observation - acting independently of "predestination". Let's say that we have two copies of the universe, one where you (Alice) observe something at noon, the other where you observe something different at noon. Would it be safe to say that these universes were the same up until noon? That's certainly what we had in mind when we set up the experiment (notwithstanding that this experiment cannot actually be set up).
But when we test this in the only ways we can, we sometimes find a violation of the Bell inequality. Alice makes measurements "randomly", and when her choices and results are compared to those of Bobs, it appears that Alice mucked with the past. Of course, the results are symmetric, Alice can accuse Bob of mucking with the past as well.
But since we apparently only end up with a single copy of the past, whose to say that it has changed? And we have an equal problem with the future. Just as we can't duplicate the universe, we can't really inject information into it from "outside" either.
So if we allow ourselves to claim that either the present or the future are not specific, why should we treat the past any differently?
To a large extent, this is a matter of semantics. We can all agree on what restrictions QM places on experimental results. But when we go from the Math to the English language, we discover that English has ambiguities that are well tolerated in common affairs - but work poorly in describing the Physics.
Let me describe the Bell Inequality by moving "cause" into the future. Remember that the only purpose of this is to change the English semantics describing the QM results. I am not claiming that this is a "better" description - only a consistent one:
Both Alice and Bob make their measurement choices of the entangled particle independently. Since Alice did this based on a telescope facing the Northern sky and Bob did it based on the Southern sky, we presume that no information has yet been exchanged between them. But we will allow for an indefinite present, so Alice may not have measured the result, and if she did, it may be + or -. Similarly, Bob's may be any of the three as well. When they compare results, certain Alice/Bob combinations are inconsistent with QM and will not persist. They can be made to violate Bell's inequality without any FTL issue.