Monday, December 20, 2004
What we know, and don't, and why
Reporting now from a rustic lodge deep in the forests of Minnesota, where a motley collection of physicists and philosophers have gathered to talk about the Arrows of Time. My job is of course to let people know that we have an explanation for the apparently low entropy of our observable universe. Once you have that, there are still a number of interesting questions, but I think that the cosmo-thermodynamic arrow is the origin of all the rest.
Actually the collection is not so motley; there are some very smart people here in the woods, including one Nobel laureate, Tony Leggett. The other night we shared the lodge with the holiday party of a local real estate firm, and let me tell you something: women swoon for Nobel prizewinners. Even (especially?) ones as gentle and soft-spoken as Tony. Trust me on this.
Physicists have a lot to learn from philosophers (and vice-versa). I learned something (or think I did) about the psychological arrow of time from David Albert. As you know (since even those who haven't been reading the blog from the start have gone back and combed through all the archives), I have previously mentioned the idea that the thermodynamic arrow of time -- the fact entropy is very small in the past, and tends to grow on purely statistical grounds -- is responsible for the fact that we can remember the past but not the future. But why is that exactly?
It's a tricky argument, and I'm still not sure I understand it correctly. But the basic idea hinges on the consistency of different hypotheses about what was going on in the far past. In particular, imagine a situation where we have three things: 1) a memory of receiving a new sweater for Christmas last year, 2) detailed knowledge of the laws of physics, and 3) complete ignorance about the initial conditions of the universe, i.e. a hypothesis that all conditions consistent with our current macroscopic state are equally likely. (Our macroscopic state is really everything we think we know about the present universe, including positions and properties of the macroscopic objects in it; but this knowledge is compatible with a huge number of microstates, which would correspond to a specification of the properties of each and every elementary particle comprising these objects.) Can we conclude, from these three pieces of information, that we probably did receive a sweater? No; in fact, it turns out to be incredibly unlikely. That's because, of all the ways we could have a memory of receiving the sweater, most involve very high-entropy conditions in the past, out of which we and our memory have appeared very recently as a random fluctuation. Random fluctuations of order from disorder are very rare; however, there are many many more ways to be disordered than to be ordered, so the number of ways to achieve order is dominated by trajectories that come from disorder, not trajectories that come from greater order. So if we really believe that all possible past configurations are equally likely, our "memories" are utterly unreliable.
What saves us from such a psychologically devastating situation is that this set of beliefs is cognitively unstable. That's because we used our knowledge of the laws of physics (not to mention the rules of logic, probability, and so forth) to reach this conclusion. But the reason why we believe these laws is that we have memories of experiments that count as evidence for them -- but these memories are completely unreliable! So we have no reason to think that we actually understand the laws of physics. Thus, this set of beliefs is self-undermining; if we hold it, we conclude that we have no reason to hold it.
The way out is to change our initial set of assumptions. We simply replace the assumption that any past configuration is equally likely with the "past hypothesis" -- the idea that the early universe is in a very special state (or one of a small number of special states) with very low entropy. This simple hypothesis removes from consideration all of the thermodynamically unlikely (but very numerous) possible histories in which we and our memories of Christmas past are just fluctuations from the surrounding chaos. Given that we have a memory of receiving a sweater, and that the universe began in a highly ordered state, it is quite likely that we actually did receive a sweater.
The lesson that we are supposed to learn from this is that the past hypothesis is a crucial part of our understanding of how the world works -- it has the status of a law of nature. In the picture that Jennie Chen and I have suggested of a universe in which our observed patch is just a small part of a bigger ensemble, this hypothesis is local and contingent, but still reasonable. There are other parts of the bigger universe which are close to thermal equilibrium, where the past hypothesis wouldn't be appropriate. But in regions of thermal equilibrium you won't have living beings, much less reliable memories.
David Albert is also known for being perhaps the sole respectable person to appear in the movie What the #$*! Do We Know?, a docu-drama about quantum mechanics and consciousness. (I haven't actually seen the movie, but Peter Woit has. FYI, "#$*!" is usually pronounced as "bleep", but more colorful renderings are allowed.) The movie was made by crackpots, who want to argue that consciousness and quantum mechanics are inextricably intertwined, to the extent that we can literally change reality by appropriately focusing our mental states. David was asked by the producers to sit for an extended interview about the mysteries of quantum mechanics, and he innocently agreed. After five hours of filming, in which he patiently explained to them that their views were completely crazy, they chopped up the footage into short sounds bites of quotes like "Yes, that's an important question," and interspersed them throughout the film. David is on record as saying that his views were dramatically misrepresented by the movie. Another lesson learned: if anyone wants to get you on film, you have to establish that you trust them not to twist your words against themselves.