torek@umich.UUCP (Paul V. Torek ) (01/22/86)
Ken Rimey (>> > and >) writes: >> >You may have noticed that, in describing a theory in which the >> >universe is deterministic and measurement is not a fundamental >> >idea, I sure refer to measurement and probability a lot. The >> >point is that these ideas are involved only in the interpretation >> >of the mathematical object that represents the state of the universe. >> >They don't clutter up the theory of how to calculate that object. >> >In particular, in the Many-Worlds view, wave functions don't "collapse". >> >> >Many-Worlds is indistinguishable experimentally from the more popular >> >variant of quantum mechanics that talks about wave functions >> >collapsing. Then why is Many-Worlds interesting? Indeed, Many-Worlds >> >is less a theory than an argument that some of the conventional >> >postulates of quantum mechanics are not fundamental. >What I mean is that it is unnecessary to postulate that wave functions >collapse during measurements. Measurements are ordinary physical >interactions of matter with matter, and are adequately described by >ordinary equations of motion. OK, fine, except for one thing. You speak of "a theory in which the universe is deterministic." Then how come, when one performs a measurement on a "mathematical object that represents the state of the universe", the outcome is only *probable*. That is, given two electrons (fired in sequence through the famous "two slits") represented by the same mathematical equation, and using a single measuring device, one nevertheless can get different measurements. So, while this interpretation of QM may show that observers aren't so special, I don't see how it can affirm a deterministic universe. [Whoops! I deleted a sentence of Rimey's here, thereby misleading my readers by making them think I was responding to the one below. I wasn't. I have inserted bracketed clarifications into my own posting below to remove the confusion] >> >Many working >> >physicists will, if you ask them, express doubt as to whether quantum >> >mechanics is really applicable to cats and such. [RIMEY] >> >> And one interpretation of QM has it that it [QM] doesn't [crucially depend >> on an "observer"], because macroscopic >> objects like cats and such involve entropy (i.e. when the cat dies, entropy >> is increased, thus an irreversible process has taken place). [TOREK] >That is not an interpretation of QM. It is simply wrong. It is? What's your evidence? (Or were you misinterpreting me? What I meant was that one could assume that wave packets collapse whenever entropy is increased (or maybe it's, increased *by a sufficient amount*). Thus, one can admit wave packet collapse without deifying observers and encouraging crackpots.) --Paul V. Torek torek@umich
rimey@ernie.BERKELEY.EDU (Ken &) (01/24/86)
>>What I mean is that it is unnecessary to postulate that wave functions >>collapse during measurements. Measurements are ordinary physical >>interactions of matter with matter, and are adequately described by >>ordinary equations of motion. > >OK, fine, except for one thing. You speak of "a theory in which the universe >is deterministic." Then how come, when one performs a measurement on a >"mathematical object that represents the state of the universe", the outcome >is only *probable*. That is, given two electrons (fired in sequence through >the famous "two slits") represented by the same mathematical equation, and >using a single measuring device, one nevertheless can get different >measurements. Nevertheless, abstractly, the theory only tells us how to calculate one future, one that incorporates both outcomes of the experiment. That is the only mathematical theory we have. The values of the probabilities we observe in the real world stare us in the face when we calculate that deterministic future, but to interpret them as probabilities and contradict the deterministic nature of physical law is beyond the mathematical theory. It would be nice to have something more to say, but we don't. People talk of nondeterministic collapse of wave functions, but that is only vague mumbling unrelated to any mathematical model of the universe. The reason that this gap in our understanding is not a handicap is that all the calculations, the numbers, the meat, is contained in the deterministic theory. >>> >Many working >>> >physicists will, if you ask them, express doubt as to whether quantum >>> >mechanics is really applicable to cats and such. [RIMEY] >>> >>> And one interpretation of QM has it that it [QM] doesn't [crucially depend >>> on an "observer"], because macroscopic >>> objects like cats and such involve entropy (i.e. when the cat dies, entropy >>> is increased, thus an irreversible process has taken place). [TOREK] > >>That is not an interpretation of QM. It is simply wrong. > >It is? What's your evidence? (Or were you misinterpreting me? What I meant >was that one could assume that wave packets collapse whenever entropy is >increased (or maybe it's, increased *by a sufficient amount*). Thus, one >can admit wave packet collapse without deifying observers and encouraging >crackpots.) Entropy is a statistical concept, like standard deviation. There is much arbitrariness in defining it, though this doesn't make any difference in practice for macroscopic systems. The familiar thermodynamics definition is funny because it is history dependent and not a function of the current state of the system. Entropy can play no role in the fundamental laws of the universe. It is not a physical thing. (Well, I challenge anyone else to say it better. Please.) Ken Rimey
torek@umich.UUCP (Paul V. Torek ) (01/26/86)
rimey@ernie.UUCP (Ken Rimey) writes: >>when one performs a measurement on a "mathematical object that represents >>the state of the universe", the outcome is only *probable*. That is, >>given two electrons (fired in sequence through the famous "two slits") >>represented by the same mathematical equation, and using a single >>measuring device, one nevertheless can get different measurements. [TOREK] > >Nevertheless, abstractly, the theory only tells us how to calculate >one future, one that incorporates both outcomes of the experiment. >That is the only mathematical theory we have. The values of the >probabilities we observe in the real world stare us in the face when >we calculate that deterministic future, but to interpret them as >probabilities and contradict the deterministic nature of physical law >is beyond the mathematical theory. "The deterministic nature of physical law"? Aren't you begging a question there? What I find disturbing -- incoherent, even -- about the Many Worlds Interpretation as described by you, is that it doesn't take measurements seriously. Now see here: measuring devices are part of reality too, and so are human minds. You can try to get out of "wave packet collapse" by saying that measuring devices exist in an "uncollapsed" state too, but when you get to the experimenter your position breaks down. The experimenter thinks "aha, the result was E1" or "aha, the result was E2", but not both, not neither, not in-between (etc.). (Unless you start postulating multiple, branching universes, but you said you weren't going to do that.) Let me put it this way: how can a deterministic theory have it that the very same initial conditions (particle, measuring device setup, etc.) lead in different trials to the different outcomes experimenter-thinks-"E1!" and experimenter-thinks-"E2!"? >It would be nice to have something more to say, but we don't. People talk >of nondeterministic collapse of wave functions, but that is only vague >mumbling unrelated to any mathematical model of the universe. Vague mumbling? One can derive the probabilities from the math. >all the calculations, the >numbers, the meat, is contained in the deterministic theory. Except that the deterministic theory can't predict what I'll be thinking after I perform the experiment. Again -- the point bears repeating -- my thoughts are events in the universe too. --------------------[different issue]------------------------- >Entropy is a statistical concept, like standard deviation. There is much >arbitrariness in defining it, though this doesn't make any difference in >practice for macroscopic systems. OK, I see your point here. But suppose instead of entropy, it's a difference in energy between "pure states" that matters; that is, perhaps wave packets collapse whenever the difference in energy exceeds a certain value. (For greater detail, see a recent article by N. Maxwell in *Philosophy of Science* -- I'll post a more complete reference next time, I promise, plus a few choice passages.) The point being, one can make sense of wave packet collapse without giving aid to "crackpots" (making "observation" a fundamental notion) and without resorting to multiple universes or (worse) taking measurement too lightly. --Paul V. Torek torek@umich
rimey@ernie.BERKELEY.EDU (Ken &) (01/27/86)
Paul Torek writes: >You can try to get out of "wave packet collapse" by >saying that measuring devices exist in an "uncollapsed" state too, but when >you get to the experimenter your position breaks down. The experimenter >thinks "aha, the result was E1" or "aha, the result was E2", but not both, >not neither, not in-between (etc.). (Unless you start postulating multiple, >branching universes, but you said you weren't going to do that.) You misunderstood me. Both happen. In one universe. It is very wrong to say that the various possible outcomes take place in corresponding independent branching universes. The possible outcomes constructively or destructively interfere with each other. It is often argued that macroscopically different outcomes will not interfere noticably with each other. Though this may not be true for superfluids, superconductors, and such, it is probably accurate when the different outcomes involve different behaviors of a macroscopic classical system like a human. The fiction of a branching universe may therefore be approximately correct on the scale of human experience, but the fiction confuses more people than it enlightens. They think it has something to do with what they read in science fiction books. Maybe all this discussion will only confuse more people. Maybe the only people who could safely be entertained by it are those who already understand quantum mechanics on a formal mathematical level -- Hilbert space, not Schrodiger's equation. Not really a snob, Ken Rimey
torek@umich.UUCP (Paul V. Torek ) (01/28/86)
Ken: You obviously know a lot more quantum physics than I do. I don't know the mathematics of Hilbert space, for instance. But I'm still going to argue with you... In article <11561@ucbvax.BERKELEY.EDU> rimey@ernie.UUCP (Ken Rimey) writes: >>You can try to get out of "wave packet collapse" by >>saying that measuring devices exist in an "uncollapsed" state too, but when >>you get to the experimenter your position breaks down. The experimenter >>thinks "aha, the result was E1" or "aha, the result was E2", but not both, >>not neither, not in-between (etc.). (Unless you start postulating multiple, >>branching universes, but you said you weren't going to do that.) [TOREK] > >You misunderstood me. Both happen. In one universe. > >It is very wrong to say that the various possible outcomes take place >in corresponding independent branching universes. The possible >outcomes constructively or destructively interfere with each other. In other words, I *didn't* misunderstand you: you *don't* want to postulate multiple universes. You assert that in one universe, the experimenter BOTH thinks "aha, the result was E1" and "aha, the result was E2". But that's manifestly false -- at least it's manifest to the experimenter, because he knows damn well that he's only thinking ONE of those thoughts. UNLESS: unless you suppose that after the experiment, two consciousnesses inhabit the one body (presumably corresponding to two brain states superposed in the same brain). Well, you can avoid contradictions that way, but the resulting view is -- to put it nicely -- weird. I note, not quite in passing :->, that your position can be entirely recast in multiple-universe talk if one allows that the branching universes can interfere with each other. This may constitute a slight redefinition of the word "universe", but I think it shows that your position is not really so different from the branching-universe notion after all. --Paul V. Torek torek@umich
weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (01/30/86)
>You assert that in one universe, the experimenter BOTH thinks "aha, the result >was E1" and "aha, the result was E2". But that's manifestly false -- at least >it's manifest to the experimenter, because he knows damn well that he's only >thinking ONE of those thoughts. UNLESS: unless you suppose that after the >experiment, two consciousnesses inhabit the one body (presumably corresponding >to two brain states superposed in the same brain). Well, you can avoid >contradictions that way, but the resulting view is -- to put it nicely -- >weird. So what? For decades now, physics has been weird. Even from the physicists' point of view, it's weird. ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720