DAM%MIT-OZ@MIT-MC.ARPA (07/09/85)
Date: Monday, 8 July 1985 20:04-EDT From: mikes at AMES-NAS.ARPA (Peter Mikes) Some people believe that Einstein was right, rather then Bohr. I suggest that we do accept the fact that there is indeed a division of opinion concerning ... queastion whether QM is paradox free and logicaly consistent. Some people prefer not to see or face the problems - that's fine - but lets stop parroting the statement that 'all is fine and there is no paradox'. I joined this list with the hope of learning some physics and perhaps discussing some of the philosophical problems with quantum mechanics. I have been a little disapointed but maybe I can initiate the kind of discussion that I had hoped for. What bothers me about quantum mechanics is quite simple. Quantum mechanics is mathematically incomplete: there is no mathematically complete theory of what constitutes a physical system and how physical systems change over time. One approach is to say that physical systems are wave functions: points in a Hilbert space, and that the dynamics of such systems are governed by Schodingers equation. This is the most mathematically complete statement I have seen. However the Schrodinger's cat problem clearly shows that either this mathematical model is incomplete or we must accept multiple worlds. DeWitt, Hugh Everitt, and Wheeler endorse the multiple-worlds view. However most physicist seem to reject the idea that Schodingers equation is a complete model and instead choose to believe in the Copenhagen interpretation in which wave functions "collapse". In the Copenhagen interpretation the act of measurement causes the wave to change in manner not goverened by Schrodingers equation; the wave function collapses instantaneously and discontinuously into an eigenvector of the measured quantity. The problem with the Copenhagen interpretation is that there is no MATHEMATICAL theory of what constitutes a measurement; there is no mathematical theory governing wave function collapse. I would enjoy some discussion based on fairly sophisticated knowledge of the relevant mathematics. For example, if one accepts the DeWitt-Everitt-Wheller multiple worlds view then what are the philosophical consequences of the linearity of the wave function? The sum of any two solutions is a solution. Thus people "living in" one solution should not be aware of people living in another solution. Unfortunately the square-amplitute operator governing the probability distribution of the Copenhagen interpretation is non-linear. How can a non-linear effect arise from a linear equation? The square-amplitude operator is clearly important for understanding physical experiments. This seems to be a flaw in the multiple worlds view.
gjphw@iham1.UUCP (wyant) (07/13/85)
>
This is a brief comment on Peter Mikes' submission concerning the adequacy
of quantum mechanics. While I am not prepared to address all of the issues
Peter raised in his article, there are a few points that have been mentioned
previously in this news group.
First, A. Einstein's et al interpretation of quantum mechanics is in
jeopardy. The Aspect experiment, a test of Bell's Inequality, appears to be
an unequivocal demonstration that hidden variables and/or Einstein causality
cannot provide a proper explanation of phenomena in the quantum mechanical
realm. The significance of Bell's Inequality has been discussed in this news
group. I refer those interested to a very readable article by J. Rosen in a
recent PHYSICS TODAY that treats the interpretation and evaluation of the
Aspect experiment.
Second, a recent article in the AMERICAN JOURNAL OF PHYSICS (a journal of
physics demonstrations, history, and interpretations intended for college
level physics instructors) discussed the history and meaning of Bell's
Inequality, Einstein causality, and the completeness of quantum mechanics.
The author suggested that in addition to the two standard interpretations for
the measurement process in QM (wavefunction collapse and multiple worlds), a
third interpretation originally proposed by Max Born also deserves
consideration. I cannot claim to understand the "potentia" interpretation at
this time, but perhaps some other interested party could explain this to us.
Finally, I have difficulty understanding Peter's perspective on
completeness. Two possibilities occur to me. One is that I can ask all sorts
of questions, but if they cannot be answered by QM, then QM as it is currently
constructed is incomplete. Another possibility is that no matter what I may
want, if QM cannot answer it then there is no answer. This second operational
approach, used quite successfully in the Special Theory, would say that QM is
complete. Our interpretations are merely vain attempts to convert a
mathematical formalism into common language.
Personally, I am not very conversant with the measurement problem in QM,
having merely been content to turn in my homework sets on time. The
sophisticated discussion will have to come from elsewhere.
Patrick Wyant
AT&T Bell Laboratories (Naperville, IL)
*!iham1!gjphwgwyn@BRL.ARPA (07/15/85)
From: Doug Gwyn (VLD/VMB) <gwyn@BRL.ARPA> The "multiple worlds" view was shown to be observationally indistinguishable from the "collapsing wave function" view. Last time I read an interview with Wheeler, he had basically given up on the "multiple worlds" theory because of this. The linearity issue is an important one, although I worry more about other aspects than the one you mentioned (square of amplitude to get probability being nonlinear). There is no reason to expect probabilities to add linearly.
DAM%MIT-OZ@MIT-MC.ARPA (07/15/85)
I had heard that the multiple worlds view is experimentally indistinguishible from the Copenhagen interpretation. But the problem with probability being square amplitude still bothers me. I will read Hugh Everitt's article again more carefully and see if I can figure out how he solves the problem. The non-linear nature of probability seems (to me) to be a problem. Consider a wave function which is the sum of two "worlds" w1 and w2. The non-linearity of probability seems to imply that the likelyhood of a given experimental outcome performed in w1 depends on w2: w1 and w2 are not really independent.
gwyn@BRL.ARPA (07/15/85)
From: Doug Gwyn (VLD/VMB) <gwyn@BRL.ARPA> It is the superposition of "states" of the same system that is linear in the wave function, not a combination of systems. I agree that quantum probability and/or logic clashes with the classical versions. I hope to have the time to figure out how to resolve this. Maybe someone could save us some work and explain it?
franka@mmintl.UUCP (Frank Adams) (07/17/85)
I have a problem accepting the multiple worlds explanation for quantum mechanics. Let me state up front that I am not a physicist, and do not understand quantum mechanics in any detail. However, I think (hope) that I understand it well enough that what follows is not nonsense. If I am wrong, please tell me so. Basically, those who prefer multiple worlds over instantaneously collapsing probability fields seem to object to the fact that the latter transmit something which is rather like information at a speed faster than light. It seems to me that the multiple worlds explanation has the same problem -- the split into multiple worlds must take place at faster than the speed of light. That is, an event (measurement) at a point A causes a point B to be in one of two worlds (or each of two different worlds) before a signal from A can reach B. I suppose one would say that the seperation into different worlds is instantaneous - but what is instantaneous? One cannot say that the separation into multiple worlds took place BEFORE the measurement -- because then the state of the system would be determined in any one world, and we get the same predictions as are derived from the "hidden variables" explanation -- predictions which appear to be counter to the experimental evidence. (I also don't think that is what the multiple worlds explanation says, but (a) I'm not sure, and (b) I want to cut down on irrelevant comments.) I think what I'm saying is that the multiple worlds theory doesn't help AT ALL in explaining what goes on in any one world (which is all we have, ultimately). If it does, could someone please explain how?
brooks@lll-crg.ARPA (Eugene D. Brooks III) (07/18/85)
> It is the superposition of "states" of the same system that > is linear in the wave function, not a combination of systems. > > I agree that quantum probability and/or logic clashes with > the classical versions. I hope to have the time to figure > out how to resolve this. Maybe someone could save us some > work and explain it? The explanation is easy, the classical versions are WRONG! If we started teaching Quantum Field Theory as the first topic in physics curricula we could derive all else from "last principles" but then no one would be able to learn physics.
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (07/19/85)
> > I agree that quantum probability and/or logic clashes with > > the classical versions. I hope to have the time to figure > > out how to resolve this. Maybe someone could save us some > > work and explain it? > > The explanation is easy, the classical versions are WRONG! No, they aren't. Classical probability theory can for example be based on counting. It is defined on a Boolean lattice and works remarkably well in its domain. Why is QM a different case? (I admit that it's different; I want to know what is behind the difference!) > If we started teaching Quantum Field Theory as the first topic > in physics curricula we could derive all else from "last principles" > but then no one would be able to learn physics. Gee, I sure am glad that QFT explains everything. The books and papers I read on it did not give me that impression. No one is trying to stop you working physicists from doing your thing. We just want to understand what is going on, not to memorize what the current theory in vogue is.
DAM%MIT-OZ@MIT-MC.ARPA (07/22/85)
I agree that the multiple-worlds interpretation does not solve the "faster than light" problem; after all the multiple worlds interpretation is supposedly experimentally indestinguishable from the Copenhagen interpretation. A different motivation for the multiple worlds interpretation is the desire to understand the relationship between quantum mechanics and gravitation. Some people think that the multiple worlds interpretation will help us understand the nature of space-time.
davidson@sdcsvax.UUCP (Greg Davidson) (07/24/85)
The multiple worlds interpretation has some severe problems at the macroscopic human level. These problems were explored quite some time ago in fiction by Borghes in ``The Garden of Forking Paths'' and more recently, and more devastatingly, by Niven in ``All the Myriad Ways''. The basic problem is that if all quantum possibilities are followed, then the orderliness we seem to observe in our macroscopic lives is an illusion peculiar to the absurdly rare paths through the space of multiple worlds in which what we consider normal sequences of events happen to be preserved. For example, in some worlds, you hit 'n' to this article, in others, you were injured when your terminal spontaneouly imploded, in others you were unable to read the article because it had become garbled by quantum noise into (surprise) a perfect translation in Polish, etc. As soon as you take the multiple worlds interpretation seriously, you also didn't take it seriously, and so on. Any rational life, including the life of a physicist, becomes absurd under such circumstances. Because of this problem I must reject the multiple worlds interpretation, at least along all world lines that happen to allow me rational thought. _Greg Davidson Virtual Infinity Systems, San Diego
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (07/26/85)
> The multiple worlds interpretation has some severe problems ...
Not all the alternate worlds are equiprobable! There is no
observable difference between the alternate-worlds QM and the
Copenhagen QM. It happens that there IS a small chance that
your terminal would have imploded by now, but it is much more
likely that it hasn't. (And, a posteriori, it is certain that
it hadn't, but that was not a priori the case.)brooks@lll-crg.ARPA (Eugene D. Brooks III) (07/28/85)
> No, they aren't. Classical probability theory can for example > be based on counting. It is defined on a Boolean lattice and > works remarkably well in its domain. Why is QM a different > case? (I admit that it's different; I want to know what is > behind the difference!) What do you mean by "what is behind the difference"? > > > If we started teaching Quantum Field Theory as the first topic > > in physics curricula we could derive all else from "last principles" > > but then no one would be able to learn physics. > > Gee, I sure am glad that QFT explains everything. The books > and papers I read on it did not give me that impression. QFT, to the extent which it can be solved, is regarded to give an accurate description of everything except gravity. The comment made above is an analog of the similar farcical comment, "you can understand all of Chemistry and Biology by knowing the fundamentals of E&M." Of course, no one takes such comments seriously, at least I hope no one did. The fact that one cant "solve?" problems in QED using anything other that perterbation theory makes the possibilities of constructing the field operators for a baseball very remote.
king%Kestrel@sri-unix.ARPA (07/30/85)
From: king@Kestrel (Dick King)
The multiple worlds interpretation has some severe problems at the
macroscopic human level. These problems were explored quite some time
ago in fiction by Borghes in ``The Garden of Forking Paths'' and more
recently, and more devastatingly, by Niven in ``All the Myriad Ways''.
The basic problem is that if all quantum possibilities are followed,
then the orderliness we seem to observe in our macroscopic lives is an
illusion peculiar to the absurdly rare paths through the space of
multiple worlds in which what we consider normal sequences of events
happen to be preserved.
The basic reason why ordinary things happen most of the time is that
that although the common occurrence is only one "thing", the ordinary
events can happen in a great many more ways than bizzaire things.
Example: Suppose I sit in a room with a million air molecules, and I
will die instantly and horribly if my half of the room contains more
than 600K or less than 400K molecules.
There are 1000000!/500000!*500000! ways the air molecules can be
divided exactly evenly. This is an absurdly large number,
approximately 500000!. By contrast, there is only one way the air
molecules can all be in one half of the room.
Using the bionomial distribution, we see that the mean number of
molecules in each half is 500000, and the standard deviation is 1000,
so the portion of the distribution curve (of the possible numbers of
molecules in my half) that leads to my survival spans the center 200
standard deviations, allowing me to survive
99.999999999999999999999999999999999999...% of the time. (my tables
don't go that far.)
For example, in some worlds, you hit 'n' to this article, in others,
you were injured when your terminal spontaneouly imploded, in others
you were unable to read the article because it had become garbled by
quantum noise into (surprise) a perfect translation in Polish, etc. As
soon as you take the multiple worlds interpretation seriously, you also
didn't take it seriously, and so on. Any rational life, including the
life of a physicist, becomes absurd under such circumstances. Because
of this problem I must reject the multiple worlds interpretation, at
least along all world lines that happen to allow me rational thought.
True, but in the vast majority of worlds I peacefully read the message.
These possible worlds differ in minor detail; some of the terminal's
atoms moved in different directions, but I couldn't tell the difference.
_Greg Davidson Virtual Infinity Systems, San Diego
________________________________
-dickdavidson@sdcsvax.UUCP (Greg Davidson) (08/10/85)
>From: gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) >Subject: Re: Quantum Mechanics >Organization: Ballistic Research Lab >> The multiple worlds interpretation has some severe problems ... >Not all the alternate worlds are equiprobable! There is no >observable difference between the alternate-worlds QM and the >Copenhagen QM. It happens that there IS a small chance that >your terminal would have imploded by now, but it is much more >likely that it hasn't. (And, a posteriori, it is certain that >it hadn't, but that was not a priori the case.) The probability of the multiple worlds is irrelevant to the dwellers therein. Each world is a complete spacetime continuum separate from the others. In some moments, at some places, in some of them, there is an appearance of what we think of as normality. In others there is not. Maybe the latter worlds are less common, or maybe your thoughts of normality, including your notions of what is probable, are due to the peculiar accidents of your world. Once you accept the multiple worlds view, all action, including doing physics, becomes futile. If you live in a world where this wasn't turned into a recipe for Fettuccini by quantum mechanical accidents, consider yourself lucky! _Greg Davidson Virtual Infinity Systems, San Diego P.S. If all you want is a simple theory consistent with observation, consider the possibility that all possible patterns of particles and energy states exist with no time ordering, and you can have any universe you want, with any appearance of physical laws, merely by traversing them in the desired order. If you think about it, Occam's razor would prefer this above the conventional Multiple Worlds view. See Borghes' story ``The Library''. _JGD