Saturday, 2 March 2013

Thoughts about the multiverse

The idea of a multiverse has a lot going for it.  In quantum theory, the many worlds interpretation avoids some of the tricky problems of other interpretations.  More generally, the question of why the universe seems to be tuned for life to exist is easier to understand if there are many universes - naturally we will find ourselves in one which is suited to life, but there may be many more which have no life. However, I have my doubts about the benefits of postulating a multiverse.

Karl Popper objected to  Freudian psychology and Marxism because they had an answer to everything.  In particular, if you criticised them, then it couldn't be because they were wrong - it was because there was a problem with your mind. You had been brainwashed by bourgeois society or were suppressing an event in your past.  I see the many worlds idea as having a similar problem.  Other universes exist, but things are set up in such a way that your mind can't detect them.

I would look on multiverse ideas more favourably if there was a way to travel between universes. I just don't buy the idea that things can become separated so that there can never again be any communication between them.  Once it was thought that if mass fell into a black hole then it was gone forever.  But then came Hawking radiation - the mass in a black hole is in fact gradually returned to the rest of the universe.  I've also heard  a new postulate of thermodynamics proposed saying that for any two systems there will be some possibility of interaction between them.

Then there's the question of a Deity.  I'm not convinced that postulating a creator does anything to answer the question of why there is something rather than nothing, or why it seems to be tuned for life to exist.  Some have put forward the multiverse as an alternative to a creator.  I don't agree with this.  In the Narnia books by C.S. Lewis there is the 'wood between the worlds', a place (in Aslan's country seemingly) from which each of the different worlds can be reached.  If there is a multiverse then I would expect there to be a corresponding 'wood between the worlds'. Maybe, as in the Narnia books, travel between the worlds is more related to religion than to science. So I see the existence of a multiverse as supporting the possibility of a Deity, rather than arguing against it.

Friday, 1 March 2013

The Sleeping Beauty paradox

Last week I went to a talk based on the following paper (  I didn't really follow the argument that a quantum many-worlds version made the argument clearer, but it did get me thinking about the problem.

Beauty agrees to the following arrangement.  After she goes to sleep on Sunday a coin is tossed. When she wakes up she is asked how likely it is that the coin landed heads - with the following proviso.  If it landed heads she is just woken up on Monday, but if it is tails then after being woken on Monday she is hypnotised so she forgets that she has been woken up.  She is then woken again on Tuesday with the same question.  In no case does she  know what day it is when she is woken up.

The paradox is that on Sunday she believes that the coin will land heads with a probability of 50%.  She does not gain any new information when she is woken up, but if she makes a bet then the rational thing to do is to bet that is has landed heads with a probability of 33.3%.

When I came out of the talk I was convinced that the 'correct' probability had to be 50%. But then I began to construct an argument for this and I changed my mind - I now think that it is 33.3%

Suppose there were two 'sleepers' Peter and Paul. In fact they don't have to sleep, you just arrange as follows.  If the coin lands tails you ask each of them separately for the probability (so that the other doesn't know about it), but if it lands heads then you just ask one of them at random. In this case a probability of 33.3% is certainly correct, but the person being asked has got some new information - the fact that he is being asked.

Suppose now that there is just one person, but the arrangement is that you hypnotise him to make him think that he is Peter or Paul - if the coin lands tails you ask each persona, if heads then just one at random.  This seems equivalent to there being two people.  Maybe you could just show him his 'name' on a card when he is woken up - but what difference could knowing the name make to the probability of the coin landing heads.  So this must be just the same as with Beauty.  Hence her correct choice of probability is 33.3%. 

It seems to me that although in once sense Beauty does not gain any new information, in another she does, just as Peter or Paul gain new information when they are woken up and asked for the probability