Month: April 2005

(Attention conservation notice (hat tip to Cosma for the term): This post requires some familiarity with Maxwell’s equations to make much sense.)

A recent post by Dave Bacon reminds me of a beautiful old idea by John Wheeler for explaining the electron (and other charged particles) as a combination of non-trivial geometry, and the free electromagnetic field.

Suppose we start with ordinary flat spacetime. Now insert a pair of tiny little punctures, and a little tube connecting those punctures. The tube and the punctures will be used to represent an electron / positron pair.

Now suppose that we have a divergence-free electric field going into one puncture, passing through the tube, and out the other end of the tube.

From the point of view of an observer in the bulk, who is unaware of the puncture, it will look like the electric field has non-zero divergence around each puncture, i.e., it the punctures look like charges.

There are several beautiful things about this picture:

• The charges of the two punctures are equal and opposite.
• It puts the electric and magnetic fields on an equal footing – there is no charge for either.

Unfortunately, the idea leaves us wondering (a) why we don’t see magnetic charge in the bulk; (b) why charge is quantized ; and (c) what the dynamics of the tubes is supposed to be.

Still, I really like the idea as a simple example of how non-trivial geometries can give rise to interesting physical phenomena.

When giving a talk, and I realize 10-15 minutes before the end that I’m not going to cover everything, don’t speed up. There’s this oddball temptation to “cover everything”, but it’s a chimera – if I speed up, chances are very good that most of my audience doesn’t follow, so what have I gained? Nothing.

The better stategy is to pause for moment to gather my thoughts, decide what the most important remaining point is, and then spend 5-10 minutes making that point in the clearest way possible. Hard to remember in the heat of the moment, with the illusion of completeness beckoning.

The University of Queensland Department of Physics is advertising a position as either a Lecturer or Senior Lecturer in Theoretical Physics. We are encouraging applications in condensed matter and quantum information. See the description at the above link for more details.

(Just to translate the level of those positions: rough US equivalents are Assistant and Associate Professor.)

Note: To people who’ve seen this before, I posted this yesterday, but the link worked only with cookies set from my computer. My apologies to people who tried to click through, and got an error message.

Ben Powell, guest blogging at Illuminating Science, writes:

Recently I had a rather interest discussion with Andrew White. […]

The discussion/argument/whatever started out about the physics curriculum at UQ but quickly moved on to a discussion about what where the truly original contributions to physics in the twentieth century. Andrew claimed that there where only two. The theory of quantum mechanics and the theory of relativity. For the record I should say that many (perhaps most) other physicists would agree with Andrew. I don’t. I think that the existence of emergent phenomena is equally fundamental and probably more important than either quantum mechanics or relativity.

Working with the criteria of beng fundamental and important, rather than “truly original”, which I don’t understand, I’d still disagree, because (a) emergence wasn’t discovered in the 20th century; and (b) it’s not an empirical discovery, as such, but rather a property of many simple rule systems, not just the laws of physics. I’d place it more in the category of mathematics than of physics.

Furthermore, I can’t think of any specific example of an emergent phenomena that rivals the discovery of quantum mechanics or relativity in importance.

None of which, of course, is to say that the fact of emergence is not fantastically important and interesting.

Let me illustrate emergence with a very old example – time’s arrow. The so-called fundamental laws of physics (i.e. quantum mechanics and relativity) do not care about which way you run time. That is if you think of the world as a movie then, if I played the movie backwards everything should, according to these ‘fundamental’ laws, be the same. Clearly your everyday experience contradicts this prediction (you can’t make an omelet without breaking some eggs – but you certainly can’t make an egg by ‘un-breaking’ an omelet). So – if science is to be based of empirical evidence shouldn’t we reject these ‘fundamental’ laws.

The answer is that when we many particles acting together the begin to behave in new ways that we could never expect from studying a single particle. Such new behaviours are called emergent behaviours. In this case the emergent property is called entropy. Entropy is a measure of disorder – the more disordered a system is the higher its entropy. Something given the rather pompous name of ‘ the second law of thermodynamics‘ says that the entropy of the universe can never decrease. That is the universe as a whole is always getting more disorder. This is easy to misunderstand. Small parts of the universe can decrease their entropy, but then the entropy of the rest of the universe has to increase, so that the total entropy of the universe does not decrease. Actually as you’re sitting here reading this your body is busy decreasing its entropy, however all the body heat that is following out of you is disordering the rest of the universe and
increasing the entropy of the rest of the universe.

However, it is important to realise that when physicists first discovered entropy they did not derive it from a ‘fundamental’ theory, instead they found that, in they’re theories on many particles they had to include entropy to make the theory agree with nature. This century we found that when classical (or Newtonian) mechanics was replaced by quantum mechanics we still need to worry about the role entropy plays in large systems. In fact we can go further than that. We do not know how to derive the second law of thermodynamics from any ‘fundamental’ theory. And yet we believe it to be true. Einstein went so far as to say that “it is the only physical theory of universal content which I am convinced, that within the framework of applicability of its basic concepts will never be overthrown.” So what made him so sure of this?

According to Ed Jaynes’ derivation of thermodynamics, the general applicability of the second law is a trivial consequence of adopting a Bayesian view of probabilities, together with the reversibility of the fundamental dynamical laws. Carl Caves has a nice explanation of this point of view. (The original papers by Jaynes are in the 1957 Physical Review).

Personally, I’m not entirely sure this approach gets at the whole physical content of the second law, but if you believe Einstein might have entertained similar thoughts, then it does give an appealing answer to the question “Why was Einstein so certain of the general applicability of the second law, even in new physical theories”. It’d be interesting to look through his other writings to see if there’s any evidence he did or did not hold these sorts of views.

The important thing to understand is the second law of thermodynamics is true regardless of the details of the ‘fundamental’ theory – be that classical physics, quantum physics or some future theory that we do not know about yet. Therefore Bob Laughlin (who won the 1998 physics Noble prize) and David Pines have called principles such as the second law of thermodynamics ‘higher organising principles’.

The second law of thermodynamics is just the best know of these ‘higher organising principles’, we know know that many physical phenomena can only be described in terms of such ‘higher organising principles’. Examples include superconductivity, Bose-Einstein condensation, the quantum Hall effect, protein folding, most of chemistry, all of biology and life to name a few.

Finally we come to my last point. There is a general acceptance in science, which I must point out is not shared by many philosophers, of a reductionist world view. That is to say the view that we can materials physics in terms of particle physics, chemistry in terms of materials physics, biology in terms of chemistry, psychology in terms of biology and the humanities in terms of psychology. It seems to have become increasingly clear, over the course of the twentieth century that, if this is true then these ‘explanations’ can only be made in terms of higher organising principles because all of the things begin explained are emergent phenomena.

Remember more is different.