Hal Finney writes:
>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
>time.
Does the "splitting" have to be a bifurcation? If the universe splits into
many (perhaps infinitely many?) universes rather than just two when this
experiment occurs, the probability distribution can be preserved if the
photon passes through the polarizer in 99% of these post-split universes.
> > (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.
This example reminds me of a moneymaking scam which goes like this. I spam
many thousands of people who are potential participants in a certain
lottery, offering them a list of what I claim will be the winning numbers. I
provide some pseudo-scientific explanation of how I came by these numbers,
but in reality the numbers have been randomly generated by my computer. I
ask for no money up front from the email recipients, but I suggest that if
they do use my numbers in the lottery and win, they should give me 1% of the
winnings. Now, you can see that if I send out enough emails, there are bound
to be some winners; and these winners will probably be so pleased that they
will happily hand over the 1%. It looks like a great deal - everything to
gain, nothing to lose - but of course, it is not. I have not increased the
spam scam victims' chance of winning at all, and in fact I have reduced
their expected gains by 1%. The error comes from the tacit assumption on the
part of the winners that I had singled them out to offer them the correct
numbers. If I had really done that, then they certainly should have been
impressed.
Returning to the many worlds example, if I provide you with random numbers
while claiming to be able to predict/rig this week's lottery result, then
purely by chance one in one million (say) of your future selves will win
using my numbers. To those fortunate future selves it will appear extremely
unlikely that they won purely by chance, and they will happily pay me the
promised $1000. As above, the error the winners make is to behave as if I
had singled out their particular world as the one in which my numbers win.
In this case, however, that would have been doubly impossible: the different
worlds do not come individually labelled, and the only necessary distinction
between them (leading to the splitting) need be the differences in lottery
results, which is the process we are examining.
Stathis Papaioannou
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Received on Sun Oct 10 2004 - 10:22:21 PDT