Stathis Papaioannou writes:
> Hal Finney writes:
> >Not to detract from your main point, but I want to point out that
> >sometimes there is ambiguity about how to count worlds, for example in
> >the many worlds interpretation of QM.  There are many examples of QM
> >based world-counting which seem to show that in most worlds, probability
> >theory should fail.
> I'm not sure what examples you have in mind here,

The specific kind of example goes like this.  Suppose you take a
vertically polarized photon and pass it through a polarizer that is
tilted slightly from the vertical.  Quantum mechanics predicts that
there is a high chance, say 99%, that the photon will pass through,
and a low chance, 1%, that it will not make it and be absorbed.

Now, the many worlds interpretation can be read to say that the universe
splits into two when this experiment occurs.  There are two possible
outcomes: either it passes through or it is absorbed.  So there are two
universes corresponding to the two results.

However, the universes are not of equal probability, according to QM.
One should be observed 99% of the time and the other only 1% of the

The discrepancy gets worse if we imagine repeating the experiment multiple
times.  Each time the multiverse splits again in two.  If we did it, say,
20 times, there would be 2^20 or about 1 million universes.  In only
one of those universes did the photon take the 99% chance each time,
yet that is the expected result.  By a counting argument, the chance
of getting that result is only one in a million since only one world
out of a million sees it.  This is the apparent contradiction between
the probability predictions of orthodox quantum mechanics and the MWI,
assuming that we count worlds in this way.

> but this is actually the 
> general point I was trying to make: probability theory doesn't seem to work 
> the same way in a many worlds cosmology, due to complications such as 
> observers multiplying and then not being able to access the entire 
> probability space after the event of interest.
> Consider these three examples:
> (A) In a single world cosmology, I claim that using my magic powers, I have 
> bestowed on you, and you alone, the ability to pick the winning numbers in 
> this week's lottery. If you then buy a lottery ticket and win the first 
> prize, I think it would be reasonable to concede that there was probably 
> some substance to my claim (if not magic powers, then at least an effective 
> way of cheating).
> (B) In a single world cosmology, I announce that using my magic powers, I 
> have bestowed on some lucky gambler the ability to pick the winning numbers 
> in this week's lottery. Now, someone does in fact win the first prize this 
> week, but that is not surprising, because there is almost always at least 
> one winner each week. I cannot reasonably claim to have helped the winner 
> unless I had somehow tagged him or otherwise uniquely identified him before 
> the lottery was drawn, as in (A).
> (C) In a many worlds cosmology, I seek you out as in (A) and make the same 
> claim about bestowing on you the ability to pick the winning numbers in this 
> week's lottery. You buy a ticket, and win first prize. Should you thank me 
> for helping you win, as in (A)? In general, no; this situation is actually 
> more closely analogous to (B) than to (A). For it is certain that at least 
> one future version of you will win, just as it is very likely that at least 
> one person will win in the single world example. I can only claim that I 
> helped you win if I somehow identified which version in which world is going 
> to win before the lottery is drawn, and that is impossible.

I'm afraid I don't agree with the conclusion in (C).  I definitely should
thank you.  To see this, let's make my thanks a little more sincere,
in the form of a payment.  Suppose I agree in advance to pay you $1000
if you succeed in helping me win the lottery.  I say that is a wise
decision on my part.  It doesn't cost me anything if you don't help,
and if you do have some way of rigging the lottery then I can easily
afford to pay you this modest sum out of my winnings.

But I think your reasoning suggests that it is unwise, since I will win
anyway, so why should I pay anything to you?  I don't need to thank you
in this way.  Do you agree that this follows from your reasoning?

Hal Finney

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