Stathis Papaioannou writes: > There has been some discussion in recent posts about Tipler's Omega Point > theory, which postulates that an infinite amount of subjective time can > be squeezed into the last few moments of a collapsing universe. This > is straightforward mathematically using infinite series, but if time > is quantised, it would not work in reality; and it seems to be widely > accepted that time is indeed quantised. Is there a way around this > difficulty?
At http://www.sciam.com/askexpert_question.cfm?articleID=000A03B0-6000-1C71-9EB7809EC588F2D7 John Baez, a widely respected physicist, responds to the question, is time quantized: "The brief answer to this question is, 'Nobody knows.' Certainly there is no experimental evidence in favor of such a minimal unit. On the other hand, there is no evidence against it, except that we have not yet found it. There are no well-worked-out physics theories incorporating a fundamental unit of time, and there are substantial obstacles to doing so in a way that is compatible with the principles of General Relativity. Recent work on a theory of quantum gravity in which gravity is represented using loops in space suggests that there might be a way to do something roughly along these lines--not involving a minimum unit of time but rather a minimum amount of area for any two-dimensional surface, a minimum volume for any three-dimensional region in space and perhaps also a minimum 'hypervolume' for any four-dimensional region of space-time." So I think it is an oversimplification to say that it is widely accepted that time is quantized. It is pretty clear that something strange must happen as we go to smaller and smaller time and distance scales, but nobody knows what. Tipler's Omega Point theory is basically a theory of general relativity and I don't think it incorporates quantum mechanics. So it has to be viewed as extremely speculative on that basis, although the same thing might be said of the Big Bang, or of discussion of black hole singularities, both of which involve infinities much like the Omega Point theory does. I'll tell you something else about the OP that most people don't know. Many people may think of the universal collapse as providing an energy source and/or effective time speedup which leads to this prediction that an infinity of calculating can be done. But this is not the case. With overwhelming probability, a natural Big Crunch will not allow for infinite calculations, rather only a finite amount of computation is possible. The only way to get an infinite amount of calculation is for the collapse to take a very special and peculiar form, in which the universe oscillates unstably from one extreme shape to another. Instead of collapsing as a nice little ball getting smaller and smaller, the universe has to stretch in first one direction, then another, ever more extensively. Such wild gyrations will not occur naturally, yet they are the only way for infinite calculations to occur. Only this will create the ever more extreme temperature variations that can drive ever-faster calculations. Tipler's idea is that life itself will take over control of the universe's collapse. Just as we may some day control the weather by predicting its course with extreme accuracy and modifying inputs to make it do what we want, so, Tipler theorizes, life could control the very shape of the universal collapse by measuring it, making short and long term predictions, and then making small modifications to the energy and matter under life's control in order to shape the path. Since the universal collapse is a chaotic system, as is the weather, it might theoretically be possible. Life's task will become ever more difficult as each oscillation of the collapse occurs. With each gyration, life must move more quickly and accurately to keep the universe on its path. A single slip-up anywhere along the line and the potential for infinite calculation is lost. And meanwhile the temperature is rising exponentially, threatening the physical stability of whatever substrate of mass and energy life has adopted to provide for continuity of existence. Oh, and I forgot to mention that life at one side of the universe can't communicate with life at the other side. Infinite computation may be possible but not infinite communication. The photons won't get there before the collapse occurs. So all of this delicate balancing act must be accomplished without any global communication, each part of the universe must act on faith that every other part is going to perform exactly those steps required to make the whole thing come together and work perfectly. All this is without any pre-arrangment beyond what we can accomplish in this era. We better get our acts together before we head out colonizing. Given these immense challenges, which increase in difficulty and complexity literally without limit, improbability piled upon impossibility, we can throw in the still-unknown difficulties implied by quantum theory, and a wildly unlikely theory becomes that much less plausible. Then of course there is the new problem that the Big Crunch no longer is a plausible outcome, tossing Tipler's theories into the trash. In short, while the Omega Point theory was an interesting speculation on how infinite computation might be possible in a universe based on General Relativity, it was never very plausible and is much less so now. Hal Finney