[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.