From Aaron Sloman Fri May 10 08:38:48 BST 1996 To: adrienne@dvir.weizmann.ac.il Subject: Classical physics and determinism Dear Adrienne, I've been having some inconclusive discussion with Henry Stapp about the differences between classical physics and quantum physics, and one of your recent comments seems to me to be relevant to the point I am groping to make: To me (working on turbulence) the behaviour of the cup of coffee is complicated but not so very complex: we have its equation of motion, and believe it to be fully specified by a few parameters and the initial conditions, and in the stirred case the functional form of the stirring. The only problem is that the equation of motion is non-linear and so the specification of the initial conditions to sufficient accuracy is impossible. I've been trying to extend that notion to show that classical mechanics has two lives, (a) one, the "official theory" which is deterministic and (b) implicit actual theory that physicists and engineers use which was not deterministic (because it was "obvious"(?) that reality could not be, because of the nature of initial conditions.) Here's the argument, which is part of a larger exercise attempting to understand the role of ideas about possibility in our thoughts about mechanisms of many kinds: ======================================================================= Statistical mechanics has been important in classical physics as I understand it (remember I'm very much an amateur) for at least about 100 years. Now one way of looking at that is to say that that's just because we don't know enough, and if we had truly exact measures of everything then we could feed them into our equations and everything would be completely deterministic (even if not all the equations could be solved analytically....) I'd like to offer an alternative view, namely that the very notion of infinite precision of measurement is a sort of *metaphysical* ideal for which there is no scientific basis and never has been. In particular a complete specification of a point on the real continuum in some sense requires (in general) an infinite amount of information (except for the tiny subset of points that can be determined algorithmically). (E.g. there are infinitely many points in the real unit interval whose infinite binary representation is non-computable, i.e. not definable by a Turing machine. In fact, far more are non-computable than are computable: only countably many are computable.) Why should we assume that there is anything in the physical universe that has an infinite amount of information embodied in it, such as the size or position of a particle? Of course classical mechanics uses equations such that *if* you had the information then *in principle* you can feed it into the equations, and get infinitely precise results. But since no classical physicist ever had access to any measuring device with infinite precision, it is arguable that in a sense they never really assumed or even needed the availability of such information, except in their philosophical moments (e.g. Pascal). Moreover it was commonplace in physics labs to play with devices that demonstrated the statistical nature of reality. One I remember first seeing as an undergraduate in the 50's was an array of pins on a vertical panel, above a row of vertical tubes, and a sort of funnel above the pins through which a lot of ping-pong balls could be dropped onto the pins. It's impossible to ensure that one drops a ball through the funnel in such a way that it lands in a designated tube after hitting various pins on the way down. And yet if you pour a lot of balls through the funnel, without taking much care, they always form the same shaped histogram in the tubes (corresponding to a certain probability distribution). Do you recognize this familiar teaching toy from my description? I don't think I have heard ANY good argument in support of the claim that, in a device like that, every individual ball has a set of properties when it goes through the funnel that determines precisely which tube it will end up in. (More precisely the claim would be that the combination of ball and array of pins and tubes has an initial set of properties that determines the precise outcome. I am saying there has never been any justification for such a claim - only philosophical prejudice.) Admittedly, the array of pins through which the ball falls is such as to enormously amplify slight differences in initial conditions, but why should we believe that two balls that follow different paths really did have different initial states if we have no hope of being able to measure such differences? (Similar comments can be made about chaotic systems, which can appear to be indistinguishable at a particular time and yet behave very differently a short time later.) If the state of a ball coming down the funnel is not determined with infinite precision, then instead of saying that the array of pins determines the consequences of the initial state, we could say that the ball has an *indeterminate* initial state, which is equally compatible with ending up in a number of different tubes, and the geometry of the array of pins together with gravity (along with thermal and other motions that prevent a ball sitting forever on a pin or bouncing up and down indefinitely on the same pin) "forces a selection". What I am trying to do is suggest that the notion of infinitely precise state may not have been an essential feature of classical physics, just a philosophical interpretation favoured by deterministic philosophers. Once the idea is abandoned, we have the alternative view that mechanisms known long before quantum mechanics can force selections between possibilities that are not predetermined. (I would claim that gambling casinos contain many such devices.) Does that make any sense? I wonder if it is possible to start from a view of classical physics which is like the one I've sketched (i.e. objects have states whose precision is limited, so that in some experimental situations their future possibilities are not determined, and yet physical apparatus can force a selection to be made, but only in a statistical fashion, not a deterministic fashion), and then go on to say exactly what quantum mechanics adds to that? (Maybe that would enable me to understand quantum mechanics at last?) Or is my picture of classical physics already inherently quantum mechanical? I suspect not, since, for example, it has no notion of quanta: it says precision is not unlimited, but it does not specify any bounds to the precision. The lack of definite bounds might be another example of something that has no precise measure. However, in quantum mechanics there are precise laws regarding uncertainty of measurement. So that might be a difference: i.e. QM adds some determinism to classical mechanics conceived my way ???? Henry's answer is that I am just wrong about classical physics. But even if that is the case, then it still leaves open the question whether there is a view of physics which is intermediate between classical and quantum physics. My suspicion is that many people working with classical physics must implicitly have had such a view. I think it was implicit in the way I was taught physics many years ago. Aaron ======================================================================= From Aaron Sloman Fri May 10 09:56:30 BST 1996 To: adrienne@dvir.weizmann.ac.il Subject: Re: Classical physics and determinism Dear Adrienne, Isn't email amazing? Thanks for such a rapid response. Just one further comment to feed your weekend ponderings: > ....there IS > inherent imprecision at the smallest scales due to thermal vibrations, This assumes that there is a perfectly precise value for relevant physical variables (e.g. position, velocity, mass, diameter, etc. of particles) but that these are changing too fast or too irregularly to be capable of precise measurement. I want to consider an alternative, namely that there's nothing precise to be blurred by motion. I am wondering about the implications of giving up the idea of perfect precision. So even if we ignore thermal vibrations and the like is there any reason to believe in these infinitely precise values? One answer is that the equations of classical physics presuppose their existence. But I wonder whether that's actually so. The equations can propagate ranges of imprecision as well as perfect values, and that's how they have to be used in practice, which works very well for engineering desing, and much useful prediction till you get non-linear feedback loops and chaos, etc. On this view we get various kinds of small scale and large scale indeterminism out of something close to classical physics, but without any of the mysteries of quantum mechanics, no consciousness making choices, etc., just things like the geometry of a configuration allowing only N possible outcomes with nothing in between, etc. I guess if there is a residual mystery it's where the regularities in the distributions of outcomes come from. Why don't you ever get 100 balls falling into one column and none in the rest? Or do you believe that if you try often enough you eventually will? Could it be a brute physical fact that that's just impossible given the way decision-forcing mechanisms interact with inherently imprecise values? (I have to confess that I don't know whether I'm talking complete nonsense!) Cheers. Aaron ======================================================================= From Aaron Sloman Thu May 9 19:30:19 BST 1996 To: STAPP@theorm.lbl.gov Subject: Re: Comments on your paper. Henry, Thanks for the comments. > The idea that possibilities are actualities in classical mechanics > sounds odd, but may be sensible in some way: it brings us closer. that's what I felt -- but I wasn't sure whether it was illusory, for the reasons you mention. > But choices seem to have no ontological status: everything just > automatically unfolds, and the possibilities, considered as things like > elasticity, just feed into this automatic continuous process. The > experiential qualities still seem to be a superfluous add-on. I think that's an "official theory" of classical physics. The reality may be different, for the following (possibly weak??) reasons. Statistical mechanics has been important in classical physics as I understand it (remember I'm very much an amateur) for at least about 100 years. Now one way of looking at that is to say that that's just because we don't know enough, and if we had truly exact measures of everything then we could feed them into our equations and everything would be completely deterministic (even if not all the equations could be solved analytically....) I'd like to offer an alternative view, namely that the very notion of infinite precision of measurement is a sort of *metaphysical* ideal for which there is no scientific basis and never has been. In particular a complete specification of a point on the real continuum in some sense requires (in general) an infinite amount of information (except for the tiny subset of points that can be determined algorithmically). (E.g. there are infinitely many points in the real unit interval whose infinite binary representation is non-computable, i.e. not definable by a Turing machine. In fact, far more are non-computable than are computable: only countably many are computable.) Why should we assume that there is anything in the physical universe that has an infinite amount of information embodied in it, such as the size or position of a particle? Of course classical mechanics uses equations such that *if* you had the information then *in principle* you can feed it into the equations, and get infinitely precise results. But since no classical physicist ever had access to any measuring device with infinite precision, it is arguable that in a sense they never really assumed or even needed the availability of such information, except in their philosophical moments (e.g. Pascal). Moreover it was commonplace in physics labs to play with devices that demonstrated the statistical nature of reality. One I remember first seeing as an undergraduate in the 50's was an array of pins on a vertical panel, above a row of vertical tubes, and a sort of funnel above the pins through which a lot of ping-pong balls could be dropped onto the pins. It's impossible to ensure that one drops a ball through the funnel in such a way that it lands in a designated tube after hitting various pins on the way down. And yet if you pour a lot of balls through the funnel, without taking much care, they always form the same shaped histogram in the tubes (corresponding to a certain probability distribution). Do you recognize this familiar teaching toy from my description? I don't think I have heard ANY good argument in support of the claim that, in a device like that, every individual ball has a set of properties when it goes through the funnel that determines precisely which tube it will end up in. (More precisely the claim would be that the combination of ball and array of pins and tubes has an initial set of properties that determines the precise outcome. I am saying there has never been any justification for such a claim - only philosophical prejudice.) Admittedly, the array of pins through which the ball falls is such as to enormously amplify slight differences in initial conditions, but why should we believe that two balls that follow different paths really did have different initial states if we have no hope of being able to measure such differences? (Similar comments can be made about chaotic systems, which can appear to be indistinguishable at a particular time and yet behave very differently a short time later.) If the state of a ball coming down the funnel is not determined with infinite precision, then instead of saying that the array of pins determines the consequences of the initial state, we could say that the ball has an *indeterminate* initial state, which is equally compatible with ending up in a number of different tubes, and the geometry of the array of pins together with gravity (along with thermal and other motions that prevent a ball sitting forever on a pin or bouncing up and down indefinitely on the same pin) "forces a selection". What I am trying to do is suggest that the notion of infinitely precise state may not have been an essential feature of classical physics, just a philosophical interpretation favoured by deterministic philosophers. Once the idea is abandoned, we have the alternative view that mechanisms known long before quantum mechanics can force selections between possibilities that are not predetermined. (I would claim that gambling casinos contain many such devices.) Does that make any sense? I wonder if it is possible to start from a view of classical physics which is like the one I've sketched (i.e. objects have states whose precision is limited, so that in some experimental situations their future possibilities are not determined, and yet physical apparatus can force a selection to be made, but only in a statistical fashion, not a deterministic fashion), and then go on to say exactly what quantum mechanics adds to that? (Maybe that would enable me to understand quantum mechanics at last?) Or is my picture of classical physics already inherently quantum mechanical? I suspect not, since, for example, it has no notion of quanta: it says precision is not unlimited, but it does not specify any bounds to the precision. The lack of definite bounds might be another example of something that has no precise measure. However, in quantum mechanics there are precise laws regarding uncertainty of measurement. So that might be a difference: i.e. QM adds some determinism to classical mechanics conceived my way ???? > Yes, in my picture conscious experiences are a very high-level form of a > general type of beingness that is associated with the reduction of wave > function, generally. I would like to see that notion explained without making any assumptions about our ordinary notion of consciousness, experience, perception, thinking, etc. being brought in, i.e. it should be explained at a level at which the dynamics could operate in the physical world without any human beings or other experiencers like them. Then, when the two different notions have been separately defined, it might be possible to show how there's some deep affinity. Otherwise it looks like sleight of hand, importing a familiar concept into territory where it's application is totally unjustified. >.... If it is agreed that states are not infinitely precise, then there can be differences not entailed by the actual. >.... ======================================================================= From Aaron Sloman Thu May 16 00:15:27 BST 1996 To: STAPP@theorm.lbl.gov Subject: Re: Comments on your paper. Dear Henry, Thanks for your comments received a few days ago. > I think we must realize that we cannot speak with much precision or authority > or knowledge about the world itself: we can debate endlessly. But we can speak > of our theories about nature in precise terms. Up to a point I agree, though there are often degrees of imprecision in the theories themselves (even in pure mathematical theorems and proofs, as was shown very nicely by Imre Lakatos' work in the 1960s (Proofs and Refuations -- including a detailed analysis of Euler's theorem regarding relations between number of vertices, edges and faces of polyhedra).). Scientific theories are subject to even more imprecision since they refer to entities that cannot be fully defined in mathematical terms. Of course I assume you are not claiming that scientists can talk only about theories, for unless the theories referred to somthing there would be nothing to disagree about, no point in observing reality to settle disputes, and all theories would be equally good candidates for truth. I have the impression that some of the people you quote in your paper did not grasp this matter.(E.g. Bohr?) > Classical theory, as a theory, > has certain mathematical properties, and determinism etc. are among > them. The equations are deterministic, I agree. But what I was suggesting was that the inputs (boundary conditions, measurements) etc. may never have been sufficiently determinate for the equations to have fully deterministic consequences. Moreover, I suspect that that is exactly how physicists and engineers applied and thought about classical physics whether they acknowledged the fact explicity or not. The discovery of chaotic systems, where the deterministic equations can amplify indeterminacy of initial states to an extraordinary degree, eventually forced the realisation on them. .... My point was mainly about the nature of the classical theory. I.e. it is normally presented as being fully deterministic when perhaps it wasn't, and I think that was brought out in part by some of the experiments with "toys" that amplified the indeterminacy. Aaron From Aaron Sloman Thu May 16 00:25:28 BST 1996 To: STAPP@theorm.lbl.gov,adrienne@dvir.weizmann.ac.il Subject: Indeterminism in classical physics Dear Henry and Adrienne, By a strange coincidence I have recently stumbled across an article pointing out that there's a history of attempts to bring out the interminism in classical physics. The article, in Mind Vo,105, no 417, Jan 1996 (pages 80--83) is by Jon Perez Laraudogoitia, He refers to earlier work by J. Earman, a book A Primer on Determinism, Reidel 1986, which I have not read. I am still trying to recall what it was that I was taught about this in the 50s when I was a physics undergraduate in Cape Town, but the memories are too vague, except that I have vague recollections that statistical mechanics could not really work properly without an assumption that at some level of detail reality was inherently probabilistic rather than deterministic. Maybe I should become a physics student again and try to catch up. cheers. Aaron ======================================================================= From A.Sloman@cs.bham.ac.uk Thu May 16 08:15 BST 1996 Date: Thu, 16 May 1996 08:14:58 +0100 From: A.Sloman To: STAPP@theorm.lbl.gov Cc: A.Sloman Subject: Re: Comments Henry, Quick greetings thanks an a short response before I have to rush off > It has always seemed to me that trying to make classical mechanics seem > nondeterministic by talking about the fact that we cannot measure things > accurately and hence cannot have exact knowledge about initial conditions > is a muddying of the waters. That could be so, though the heart of my argument was not just a point about what we can measure but a suggestion that infinite precision is something for which there may actually be no room in reality. That's a very old idea and one of the roots of atomic theory, back in ancient Greece I think. So if some classical physicists had that idea then there could be a variant of classical physics wthout one of the components that make the other variants deterministic. The important question then is whether that could be a coherent theory, whether it is better or worse supported by evidence than the fully deterministic classical physics, and how such a theory might cope with the removal of indeterminism of end states in some of the experimental situations like the balls and tubes experiment. But I accept that such questions may be of little interest to someone who believes that all forms of Co are false anyway. I guess my interest in it is connected with trying to understand the nature of the processes of science. What kinds of conceptual apparatus are available physicists to build theories that have or might have had in the past at least a prima facie case for being taken seriously and what are the alternatives to full determinism outside the QM context, and whether those alternatives have been fully considered in the context of QM. My recollections of a talk given by Roger Penrose a couple of years ago suggests that he may be thinking along similar lines, in claiming that it's the interaction of large scale and small scale phenomena that causes the collapse. Anyhow, ignore my ramblings I need to do more studying of physics, though whether I'll ever find the time, is another matter Thanks for your patience. Aaron See also http://www.cs.bham.ac.uk/~axs/misc/real.possibility.html