Monthly Archives: March 2013

Maxwell’s Demon, Lions and semipermeable membranes

A few weeks ago I went to a talk based on http://arxiv.org/abs/1003.0179. The argument is that in thermodynamics it is wrong to treat particles as indistinguishable. If you have two different kinds of particles in a container, then in principle it is possible to separate them using a semipermeable membrane, and so there is an entropy of mixing, no matter how small the difference is. Why should there be a discontinuity when the difference is reduced to zero?

Talk of semipermeable membranes made me think of the following:
Catching lions in the desert
The thermodynamic method: We construct a semi-permeable membrane which is permeable to everything except lions and sweep it across the desert. (H. Pétard 1938)

It is possible to accept Diek’s argument, thinking of the particles as being physically identical, but each having a unique identifier. The entropy would then be different to what it is normally taken to be, but you also need to think about how the distinguishabilty of the particles might be detected. There would need to be some sort of Maxwell’s demon, reading the identifier for each. There would be an entropy cost to this – according to Landauer’s principle it is when the demon needs to forget what it has read. This would presumably cancel out the difference in entropy in this model.

I once saw a pair of capercaillies in a wildlife park in an enclosure split into two parts. Between the two parts there was a hole which the female could get through, but the male, being considerably bigger could not. Hence the female got to choose whether she spent time with the male or not. So this is a semi-permeable membrane, differentiating one animal from another.  Maybe the lion membrane isn’t so far fetched… But then to distinguish lions from everything else would need more than a hole of a given size, it would need a system which recognised lions – some sort of artificial intelligence.

My conclusion is that the claim that you can in principle find a semipermeable membrane to distinguish two different kinds of particles needs qualifying.  When the difference is substantial it will be a matter of physics, but as the particles become more and more similar, distinguishing them becomes more of a matter of computation – which is thermodynamically different to using physics to distinguish them. This argues against the idea that physical processes can be thought of as computations – Some systems may be thought of as making choices, but a hole which allows some particles through and not others shouldn’t be thought of as a computational device.

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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.

The Sleeping Beauty paradox

Last week I went to a talk based on the following paper (http://philsci-archive.pitt.edu/8556/). 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 one 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

Why not zero unemployment?

Microeconomics is about how individuals bargain with each other. There’s a bigger picture, macroeconomics, which looks at things on a large scale. Thus Keynesian economics tells of how a government deficit can be used to help promote employment. What I wonder is how individuals might be able to make a difference.

Classical economics predicts that unemployment should be zero (Well there was the argument that workers expected wages which were too high, but one is suspicious of this as presumably those putting it forward were all fairly well off). Zero unemployment isn’t a very realistic prediction, but one wonders… Is there some way that we as individuals could change our behaviour – moving away from the supposed microeconomic rationality – to make reality agree better with this prediction. In scientific experiments, one often has to make some effort to demonstrate what are supposedly fundamental laws. For instance, to demonstrate Newton’s first law one needs to get rid of friction. Maybe one also needs to make an effort to get reality to agree with economic ‘laws’ – it’s just a thought.