carrier@brahms (Stephen Carrier) (11/04/86)
This is cross-posted from talk.philosophy to sci.physics. In article <47@cartan.Berkeley.EDU> gsmith@brahms (Gene Ward Smith) writes: (in response to, in response to,... well, you can imagine.) >> ... Call the first moment of the universe time 0. >>No events exist before time 0, so that there is no time to relate one of >>these events to another. In this picture, time does not antecede existence >>(which statement sounds like utter nonsense anyway). Yes. Here's another point. Time is a coordinate, to some of us. If time is without beginning and without end, then are all real numbers the coordinate of some `point' of time? Not necessarily. Suppose that only the strictly positive numbers are the coordinate of some point of time. Then for any point of time t=t0, there is a previous time say t=t0/2. Then time is still without a beginning or ending moment (since t=0 is not included in this proposed time continuum), but, there is no point of time with a negative coordinate. What's it all mean? That there is _no_ difference between "Time has a beginning" and "Time has no beginning"? Not exactly. The scale of time is fixed by the desideratum that some simple, even linear, laws of physics should apply. My proposed distortion of time (for specificity's sake, say (My time)=42 raised to the power of (Ayn Rand time)), really messes up the laws of physics. (or of Ayn Rand?) But if our only concern is with the before-after relationship, and not with any particular standard way of measuring intervals, then yes, "Beginning" and "No beginning" are the same! In mathspeak: The real numbers are homeomorphic to the open ray {x: x>0} when each is given the interval topology. If one _does_ insist that the local scale of the time coordinate has some physical properties, then the problem of time's beginning becomes a well defined physics problem instead of a poorly defined metaphysics problem. (It has always been a historical problem, in the sense that it's mostly over now.) So let's look at the physics problem. Let's take for granted the big-bang theory, because I say to. The fact remains that physicists, or maybe just me, have no or little idea what could have been happening in the epoch before when t-coordinate= 10 to the -43 seconds when the density of the universe is believed to have been > 10 to the 93 grams per cubic centimeter. (Numbers off by at most 10 orders of magnitude. Small potatoes.) This is because general relativity collides with quantum theory. So, whatever goes/went on in this `open' interval probably doesn't obey laws similar to the ones we are familiar with. Suppose we knew the `true' linear laws, supposing such things exist, or even some merely `nice' laws which describe _both_ the very very early realm and our everyday realm (with quasars, quarks, and us.) And such that the laws we think we understand today are actually only linear approximations of these `true' laws. (In the same way that Newtonian physics is a linear approximation of Einsteinian physics, and is valid in a narrower realm which does _not_ include quasars and quarks.) If our concept of `time' has a correlate concept `pseudo-time' then the big-bang universe might turn out to be open-ended as pseudo-time goes to negative infinity. (But who could live in such a neighborhood?) (Funding for big-bangs in the laboratory is woefully inadequate, and the Rifkins would stop us with a court order, anyways. Therefore there will probably not be an answer to these questions in a `short' `time.') This is cross posted to sci.physics because maybe they can help, not that it's a problem, I mean, _I'm_ not losing any sleep over it. I think some similar speculations might exist in the physics community, although on solider ground, I guess. ucbvax!brahms!carrier Stephen Carrier/UCB Math Dept/Berkeley CA 94720 I am not a mystic, but I sure ain't no fuzz-brained rationalist, either.