[bdonlan]

It really depends on your interpretation. The math just gives you a continuum of possibilities, each with an amplitude. If you choose to interpret this continuum as being actually real and applying to the entire universe, you don't need spooky action at a distance or FTL travel. You also don't need quantum randomness; the universe always travels down every path of possibility it can, so it never needs to make a random choice. However, this does mean you end up in a 'many worlds' interpretation - but with an amplitude ('measure') attached to each world (corresponding to the square root of the classical probability of that world coming to be). The philosophical implications of this interpretation are quite interesting as well - what happens to all of the 'you's that live in a world in which entropy spontaneously reversed, at an incredibly low measure?

If, on the other hand, you assume that at some point, the universe rolls a die and picks a final outcome, then yes, you do need what is effectively FTL communication of this random roll of the die. This interpretation is easier to understand for many people, since it most closely matches what we think we see. However, it cannot be exploited for transmitting any actual information; the math conspires to ensure the information transmitted is _truly_ random (you provably cannot encode any data under your control onto this channel). You don't even know when the choice is made - indeed, the concept of 'when' the choice might be made here is ill-defined; it may appear to happen after the observation of the result, for some frames of reference.

[ajuc]

Is there any difference between these 2 situations?

I have paper with sentence "Earth will be destroyed as of 2012.12.21 24:00 UTC". I am at Andromeda. The truth of the sentence changes from 0.000000001 % (or sth, bear with me) to 0% or 100% instantly, at the moment such time passes on Earth. But this doesn't transmit any information, and I still need to wait for regular light to come from Earth to check how exaclty the truth of this sentence changed.

I'm at Andromeda, I have qubit entangled with qubit on Earth. Someone on Earth changes his qubit, and my qubit changed, but I have to wait for regular bits of information, to be able to read these changes from my qubit.

[bdonlan]

There is a difference between those two situations. In the many-worlds-ish interpretation, the Earth _never_ goes to either 0 or 100%. Instead, once the moment of reckoning passes, observations of earth return _both_ 'destroyed' and 'non-destroyed' values, entangled together. When you observe this at Andromeda, your own waveform ends up containing "you, having observed Earth's destruction" and "you, having observed Earth not being destroyed" simultaneously. Note that this doesn't require FTL - the combined waveform from earth arrives after however many light-years it takes to get to Andromeda.

The key is, you can never observe that this quantum-mechanical weirdness happened to you, because your point of view only admits a single result at a time. In otherwords, "you" observe everything simultaneously, but each observation happens independently, so you can never think about two mutually exclusive results at the same time.