Sunday, June 14, 2009

Statistical Mechanics

Most people these days have heard of quantum mechanics, and how it somehow brings chance and probability into physics on a basic level. This is a misleading truth, because actually quantum mechanics is perfectly deterministic, and not probabilistic at all, until we come to measure anything. Then the probabilities come in, and only then. The problem is that quantum measurement is a very subtle thing that is far from fully understood. And one thing we do know is that inferring how things really are, from how things look, is uniquely tricky in quantum mechanics.

To appreciate the subtlety of quantum mechanics, it helps to know about the older and less tricky place that probability has in physics: statistical mechanics. I doubt that most non-physicists have ever heard of statistical mechanics. In many places one can even earn a Bachelor's degree in physics without ever taking a course in it. This is unfortunate, because statistical mechanics is so important, that a physicist who doesn't know about it is like a Scout who doesn't know that fire needs air. Statistical mechanics is a sort of post-processing stage that has to be performed on virtually all the rest of physics — even including quantum mechanics — in order to make sense of anything but the very simplest and most controlled experiments.

Mechanics without statistics is the physics we learn in school. A rock flies through the air, falling under gravity. Ignore air friction, and model the rock as a point with a given mass — a particle. Apply Newton's Laws to particles: that's mechanics.

'In principle,' we may be told, 'the universe is a large number of particles, governed by Newton's Laws.' In practice, of course, most of these particles are beyond our control, beyond our observation, or at least beneath our notice. We do not see the vast swarms of air molecules that surround us and fill our lungs. And even if we could mark their paths, solving Newton's equations for so many interacting particles is far beyond our computational power. Thus do we see the vast gap between the pristine principles of physics, and the practical real world.

Bah. Physics doesn't care about pristine. Sure, part of physics is about trying to reduce everything, 'in principle', to some elegant little Theory of Everything. We're writing one big long footnote to Plato, who wanted everything to boil down to the five regular polyhedra. But that whole grand unified simplicity thing is really the hood ornament of physics, not the engine. The thing that drives physics is putting principles into practice, and codifying practice into principle. So no, the fact that we can't follow every atom does not make a huge gap between physics and reality. There is a whole huge branch of physics which is all about the principles and the practice of dealing with huge numbers of particles that cannot be individually observed, predicted, or controlled.

And that is the branch of physics called statistical mechanics. It uses probability theory to get the best results we can from what we do know, in spite of what we don't. Whether or not God plays dice with the universe, physicists do, to make up for the fact that we're not God.

Saturday, May 30, 2009

Time Reversal

Physics is conflicted about whether the future is fully determined and just waiting for us to reach it, or is perhaps at least partly undetermined. The undetermined viewpoint is represented in statistical mechanics, and to some extent in quantum mechanics. The deterministic position is taken by all the rest of physics, including most of quantum mechanics. This raises questions about whether physics supports predestination or free will, but I don't want to look at these now. I want to focus instead on the difference between future and past. Why can't I remember tomorrow?

Most of physics says that future and past are both completely determined by the laws of nature, and so are both equally and completely definite. Most of deterministic physics even goes so far as to have 'time reversal symmetry' — the future and the past are fully equivalent. This really makes it hard to see why I can't remember tomorrow.

Time reversal symmetry is a startling fact. Suppose I have a system in an initial state — for example, a piece of paper that has just been touched by a flame. Over some time interval, the system develops (physicists usually say 'evolves', though this has nothing to do with Darwin) into some other state. In our example, the paper will of course catch fire and burn. Let's stop the clock once the flames have died down, and call the little pile of ash our final state. In fact the final state is not just the pile of ash: it includes emitted light and dust and carbon dioxide molecules, and everything that resulted from the paper burning. For simplicity we can consider the final state to contain light, smoke, and ashes, letting the smoke and light stand for everything else that is also involved. Let's imagine there are no walls around, so the flashes of light from the flames just continue flying outwards.

Burning is easy. Unburning is not.
Now consider a hypothetical 'mirror state' to this final state, in which every particle and light wave is in the same position, but moving in the opposite direction. Of course it would be very difficult to make this mirrored state in reality. It's easy to make a pile of ash surrounded by rising smoke and outgoing light. Just burn some paper. But it's hard to make a pile of ash surrounded by falling smoke and incoming light.

Still, the mirrored final state of our burnt paper is in principle a possible state of reality, as far as we can tell. Suppose we could somehow achieve it. What would happen next? If burning of paper is governed by laws that have time reversal symmetry, then what would happen would be exactly the burning process, in reverse. The light and smoke would fall inwards onto the ashes, and these would re-assemble themselves into paper. Plumes of hot gas would form over the re-assembling ashes during the unburning process, but these time-reversed flames would be only faintly visible, for they would only be emitting as much light as ordinary flames absorb; the copious light that normal flames emit, these time-reversed flames would be absorbing instead. In the end, though, the motion-mirrored ashes would have unburnt into crisp white paper.

Okay, such a bizarre process is in principle possible. Should we be surprised? In a world full of unthinkably huge numbers of particles and waves all jostling together, it may be no wonder that all kinds of things are in principle possible. We have acknowledged, however, that this unburning which is possible in principle would be difficult to achieve in practice, because it would be very hard to assemble the time-reversed mirror state of the light, smoke, and ashes. In fact it would be extremely hard, because not just any state of incoming light and smoke falling onto ash would do. We would need the precise mirrored version of the final state from burning. So all the smoke particles have to be lined up so they will fall exactly into place on the ashes, and the incoming light has to have exactly the right waveforms to meet the ashes at the right time to drive the chemical reactions to separate oxygen from CO2 and assemble the carbon into cellulose, and so on. The precision of control that would be needed is ridiculously unfeasible. Out of all the possible states that include ashes, falling smoke, and incoming light, all of which would be difficult states to create, only a fantastically tiny fraction are actually time-reversing mirror states for burnt paper.

The conclusion seems therefore to be only the reasonable one, that ashes unburning into paper is a stupendously unlikely event. Paper burning into ash, in contrast, is not at all uncommon; it is quite easy to arrange this. So, in spite of time reversal symmetry, there remains a clear difference between past and future. Yesterday's paper becomes tomorrow's ash, and never the other way around, because paper that is about to burn into ash is nothing special, while ash that is about to unburn — that is, the time-reversed mirror state of freshly burnt paper — could only be a fantastically fine-tuned set-up.

But here's the point. For every initial state of paper that is about to burn into ash, there is a precise final state of ash, rising smoke, and outgoing light. For every such state there is a precise mirror state of ash, falling smoke, and incoming light. And that is a state of ash that is about to unburn into paper. So for every possible initial state of paper that is about to burn into ash, there is a state of ash that is about to unburn into paper; and conversely, there are only as many ways to burn paper as there are to unburn it. So how can burning be nothing special while unburning is fantastic? How can it be that paper-about-to-burn states are so much more commonly seen than ash-about-to-unburn states? There are exactly as many of each kind of state, for they match one-to-one. If one kind of state counts as a fantastically fine-tuned set-up, why is the other one any less bizarre?

How can it be that burning is so much more common than unburning? Obviously it is. But why?

This is the puzzle of time reversal symmetry.

Saturday, May 9, 2009

Remember Tomorrow?

I can remember yesterday, so why can't I remember tomorrow? This may sound like a pretty silly question, but it's one that physics can't yet answer.

The apparently obvious answer is that yesterday has already happened, whereas tomorrow hasn't yet. But this isn't really an answer at all, because the real point of the question is just to ask, what is the difference between 'already happened' and 'going to happen'? And insist as one may that this difference is obvious, that does not amount to an explanation of exactly what the difference is.

Drifting on the river of time
Where is yesterday when it is gone? We can imagine that each moment simply vanishes as it passes. So perhaps yesterday does not exist at all, and our present memories of it might just as well be legends of an imaginary world. Or we can imagine that the past is just the country that stretches behind us as our awareness drifts steadily forward on the river of time. So perhaps yesterday is still there, and our memories are souvenir sketches of a real landscape to which we will never happen to return.

We can think of the future in the same two ways. Perhaps it doesn't exist at all until it becomes the present. Or perhaps it is all there waiting for us to arrive.

There seems to be some truth in both pictures of the future. Some future events occur as anticipated, while others appear as sudden surprises. Yet we can find the same mixture of definiteness and indefiniteness in the past, as well. Important experiences remain vivid in memory, but obscure details fall into oblivion as soon as they pass. So the distinction between future and past is not as simple as one being real where the other is only potential. The difference between how real the two are seems to be only a difference of degree, not of kind.

The difference of degree is there, however. Memory may be fallible, but it is usually more accurate than prophecy. We have to say that the landscape behind us on the river of time seems more detailed than the terrain still ahead.

Why can't we remember tomorrow? The answer really isn't obvious after all. It has something to do with causality. Perhaps it also has something to do with how some things are more important than others. And that's really the bottom line of what physicists can say, right now, about this startlingly basic question.

Starting Out

There are several other 'cold heat' sites on the Web, and they are fine sites dedicated to various things, but I think this is the only one that is literally about cold heat. It's about heating and heat flow in gases cooled to within a millionth of a degree above absolute zero temperature. (Even though they are so cold, the gases don't become solid, because they are kept at extremely low pressure.)

This is an active research field in current physics, and has been for about fifteen years. In 2001 the Nobel prize was awarded for a big experimental breakthrough on this stuff. It's a pretty technical topic, but I'm going to try to make it understandable.

Why read this? Well, the technical details of quantum gases are pretty heavy going, but the basic questions we're investigating are really profound. They go right to the heart of what matter is, what physics is, and how things really are.