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.

1 comment:

  1. awesome dad!
    BUT WRITE ABOUT STARS!
    They're Interesting!

    ReplyDelete