I have been reading up on this subject a little bit and about the
quantum immortality, I believe it is a common misconception that this
means you will never die; if all future branches involve your death,
then you will die ... Quantum immortality does not imply that you can
dodge every bullet and that the "you of today" will still live
tomorrow, although the "you of yesterday" could still live tomorrow
whilst the "you of today" does not.
Also I personally do not believe ASSA favours a MWI interpretation of
quantum mechanics over a deterministic one because a "single MWI
universe" will be less probable than a "single deterministic universe".
But it might favour MWI over Copenhagen interpretation.
If the universe splits into 2 universes each second; I do not
necissarily see an issue as explained by Stathis Papaioannou in his
post. And it is even a fact that you are more probable to live in the
year 2000 than in the year 1000 because the human population has grown;
but once we go to infinities, the same approach might not work anymore
(although I am still debating about this myself) ...
Anyway, I do not believe that MWI favours later moments in time over
earlier moments in time. Although the number of universes increases,
their individual probability decreases, keeping the total probability
equal (although relativity might complicate a more rigorous approach).
A simple way of picturing this, would be that at the big bang; the
universe is 1 piece of paper, and from then on, every second, the
piece(s) of paper is cut in half; giving 1, 2, 4, 8, ... universes. The
total area of paper remains the same and all the pieces get smaller all
the time, this means that the chance of being in a particular universe
as the universe splitting progresses, even decreases :).
That's a good way to look at it. Everett originally called his interpretation
a 'relative state'; emphasizing that observed states were relative to the
observer. 'Multiple universes' is a convenient way of talking, but the idea
comes from holding onto the unitary evolution of the state vector in a Hilbert
space describing states of the universe. So there is only one universe and it
is the projection onto different semi-classical subspaces (the only kind we can
experience) that correspond to different 'universes'. In QM you can have
negative information (due to the correlations of entanglement) and so from the
Hilbert space view the total information may be zero, even though the
projection onto subspaces is very complex.
I also think that the modeling of the inner product in Hilbert space as real
number is probably and approximation. QM and general relativity together
imply that there are smallest units of time and space, the Planck units. When
a quantum theory of gravity is invented I think it may imply a smallest unit of
probability - so that the arbitrarily small probabilities required for Tegmark
to survive his machine gun will not exist.
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