Tim May wrote: >Time for a digression. The classic urn experiment, with Price's objections. > >And let me throw in something several members of this list will likely >appreciate: a bet on the outcomes (a la Bayesian reasoning, a la market >processes, a la Robin Hanson's idea futures, a la probabalistic definitions >of the truth). > >Imagine two urns. Imagine, say, 500 black stones and 500 white stones. A >person is reaching inside one urn, removing a stone, transferring it to the >other urn, picking up a stone "at random" (a regrettably loaded term, but >one which will hopefully become clearer...imagine that the man is blind and >cannot possibly see the color of the stone he is picking up). > >A group of people is show two filmed sequences: > >In Sequence One, the two urns are filled with stones of mixed color at the >start of the film. As the main transfers stones, the number of black and >white stones in each of the urns fluctuates, but there are never, in this >particular film, any excursions outside the ratio 450 of one color to 550 >of the other. > >In Sequence Two, the the film begins rolling with one urn filled with white >stones and the other urn filled with black stones. The man reaches in, >takes a white stone, transfers it to the other urn. He reaches in, takes a >black stone, transfers it to the first urn. As the film progresses, the two >urns eventually reach a state where each has about 250 white stones and >about 250 black stones. > >The group is told that one of the films is presented in correct >chronological order while the other is presented in reverse chronological >order. > >The group is told that bets will be taken on which is which. Oddsmakers are >standing by. A terminal linked to the Idea Futures Market is available. > >(The Barbourian jumps up and yells "There is no time! All events happen at >the same time!" The organizer says "Fine, but I'm still taking bets. The >Barbourian sits down.) > >Which way would you bet? And what do think oddsmakers would make odds? > >Not surprisingly, nearly everyone will bet that Sequence Two was shown in >correct chronological order and that Sequence One, if one of the two >sequences was shown in reverse chronological order, must have been the one >that was reversed. > >(The Quibbler points out that Sequence One could easily be shown in >chronological order, just either a long time after the mixing started or >starting with an initially mixed set. "Sure," the organizer points out, >"but I told you one was in correct order, one was reversed, so place your >bets.") > >Now the urn example is one that does not use the "molecular chaos" that Huw >Price is so critical of in "gas mixing" examples, arguing that "molecular >chaos" is assuming the conclusion. > >Here we have a simple, discrete, mixing problem. > >Is urn mixing "reversible"? Sure, though very, very unlikely. Unless the >man doing the blind mixing (not looking at the color, or unable to see the >color, etc.), the odds of a reversal back to the original 500 white/500 >black configuration is a simple matter of odds calcualations--on the order >of 2^(-500). > >Now the Priceian would argue, from what I have read of his book, that while >he agrees that nearly all people would correctly bet which of the films was >time reversed and which was not, that they are missing the point, that the >real issue is how the urns came to have 500 white balls in one urn and 500 >black balls in the other urn in the first place. > >Feh. This crotchet, this hangup, is one of the main reasons I can't get >overly excited by Huw Price's analysis of time.
It's true that if one just wants to study the physics of how the world works now one can just take for granted a low-entropy initial singularity and not worry about why. But I think if one wants a complete cosmological theory that's a pretty big issue you'll want to explain. It all depends on your point of view. I agree that Huw Price would say the real issue in your scenario is how you got the balls segregated in the first place. If his point of view is correct, the only reason you see it as "natural" is because you are used to living in a universe with low-entropy initial conditions which allows for the existence of things like intelligent beings who are able to set up such ordered initial conditions. Consider a variation on this--say the video features two types of molecules instead of two types of balls, and instead of urns we're just dividing the screen into two halves and looking at how many of each type appear on each side. Again, if the video was shot in our universe then we'd expect the scenario with molecules starting out perfectly segregated and then gradually mixing as they bounce around must be the one shown normally while the one where they start about equally mixed and end about equally mixed was shown in reverse. But suppose we then find out the video was taken from a parallel universe which was in a state of maximum entropy, with no low-entropy initial conditions. In that case, there'd be no way to tell which video was shot in reverse; either way, the video showing the molecules "starting" segregated would represent a statistically unlikely fluctuation in entropy. Or what if the video was taken from a parallel universe which we knew had a *future* low-entropy boundary condition, but no such boundary condition in the past--then we'd bet that the video showing the molecules going from segregated to mixed was actually the one shot in reverse! A priori there is no reason why a universe with a future low-entropy boundary condition should seem any more or less weird to us then one with a past low-entropy boundary condition; for now we are equally clueless about how to explain either one in terms of known principles of physics. >And I certainly don't draw the same conclusions he draws about how the >initial low entropy state of such systems must come from Poincare/Boltzmann >recurrences. If I remember correctly Price did *not* suggest low-entropy initial conditions could be explained by Poincare recurrence--in fact I think he raised the exact same objection to this possibility that you did, pointing out that the anthropic principle would only guarantee the minimum entropy fluctuation needed to generate an intelligent observer, which is tiny compared to the fluctuation you'd need to explain a universe like ours with low entropy as far as the eye can see (and even lower entropy in the past). I think Price's suggestions were: 1. new time-asymmetric laws of physics 2. a "Gold universe" with time's arrow reversing during the contraction phase so the big crunch is a mirror to the big bang (Greg Egan wrote a cool short story about how living in such a universe could allow you to send messages into the past using light from stars in the contraction phase) 3. laws which guarantee that one end of the universe will be low in entropy while the other will be high, but are equally likely to lead to a low-entropy "future" condition as a low-entropy "past" condition (though observers in either type of universe will call the low-entropy end the 'past'). Incidentally, J. Richard Gott (who I think might have come up with the Doomsday argument, I'm not sure) in his book "Time Travel in Einstein's Universe" makes another interesting suggestion about how to explain low-entropy initial conditions. Combining the idea of wormholes spawning "baby universes" with the idea of wormholes as time machines, he suggests that the Big Bang might be such a baby universe spawned my a wormhole which originates in its own future history! As it turns out this "self-creating universe" model seems to naturally imply no advanced electromagnetic waves, only retarded ones, which is equivalent to saying that entropy must decrease in the past direction, not the future one. Quoting from p. 195-196: "The geometry of our time-travel model provides a natural explanation for the asymmetry between the future and the past that we observe in our universe. Suppose we live in the universe represented by the farthest right horn in Figure 27. [he refers to a diagram of a self-creating universe where the 'farthest right horn' is another baby universe that spawned from the original self-created universe] If we allowed light waves to go to the past, they would work their way down this branch to the branch to its left and eventually to the trunk, where they would enter a time loop at the bottom and circle the time loop counterclockwise an infinite number of times, leading to an infinite buildup of energy and causing the whole structure to blow up, creating a singularity. That is not the geometry we started with--the solution is inconsistent. The only way for a self-consistent model to work is if light waves always travel toward the future, just as we observe. (If photons created in the branches travel only toward the future, then these photons travel out the branches away from the time loop, creating no problem.) "Now consider a photon emitted within the time loop at the bottom. It could, in principle, circle the loop clockwise an infinite number of times. But each time it went around, it would lose energy because it would be traveling toward the future, in the same direction that the branch is expanding. Each time it circled, it would add only one 535th as much energy as on the previos circuit because the expansion stretches its wavelength by a factor of 535, robbing it of energy. The sum rapidly converges to a finite value. So, even though it circles an infinite number of times, it would not cause an infinite buildup of energy. However, a photon going backward in time (counterclockwise) around the loop would pick up energy on each circuit because in the counterclockwise direction the branch is always getting smaller, compressing its wavelength. A photon circling an infinite number of times toward the past would cause an infinite buildup of energy, causing the model to blow up. In fact, the only way to obtain a self-consistent solution is to have light waves, and gravitational waves, travel only to the future throughout the entire model. Thus, in our model, the asymmetry between the future and the past that we observe (in which causes precede effects) comes from the time asymmetry in the geometry of the Universe--it has a time loop in the beginning. "This arrow of time was not something we built into the model; it was implicit in the model, but its emergence quite surprised us. It's an important prediction by the model, which turns out to agree with our observations. "In the standard big bang model, by contrast, there is nothing to produce an arrow of time. In that model, the early universe is filled with radiation, and whether it is going forward or backward in time from its source does not matter. Waves going toward the past would increase in energy as they approached the big bang singularity, where they would blow up. But the density in the big bang model blows up there anyway, so it causes no problem. Waves going to the past are not forbidden, in principle, in the standard big bang model. But with a time loop in the beginning, self-consistency forbids waves going to the past--just as is observed today." Gott then goes on to show how the entropy arrow of time can be derived from the electromagnetic arrow of time, based on the fact that it implies higher temperatures as you go back in time. Anyway, this probably is not the most likely answer to the arrow of time question (there are a few other contenders), but it'd be pretty cool if it turned out to be true. --Jesse _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx
