Comments on Comments on Comments: A Reply to Margenau and Wigner Hilary Putnam Philosophy of Science, Vol. 31, No. 1. (Jan., 1964), pp. 1-6. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28196401%2931%3A1%3C1%3ACOCOCA%3E2.0.CO%3B2-2 Philosophy of Science is currently published by The University of Chicago Press.
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Philosophy of Science
VOL.
January,
31
I 964
NO. I
DISCUSSION : COMMENTS ON COMMENTS ON COMMENTS A REPLY TO MAWGENAU AND WIGNER* HILARY P U T N A M Massachusetts Institute of Technology
T h e Margenau and Wigner "Comments" [2] on my "Comments on the Paper of David Sharp", [3, 41 is a strange document. First the authors say, in effect, "had anything been wrong (with the fundamentals of quantum mechanics) we should certainly have heard". Then they issue various obiter dicta (e.g., the "cut between observer and object" is unavoidable in quantum mechanics; the-highly subjectivistic -London-Bauer treatment of quantum mechanics is described, along with von Neumann's book, as "the most compact and explicit formulation of the conceptual structure of quantum mechanics"). My assumption 2 (that the whole universe is a system) is described as "not supportable", because "the measurement is an interaction between the object and the observer". T h e "object" (the closed system) cannot include the observer. The issues involved in this discussion are fundamental ones. I believe that the conceptual structure of quantum mechanics today is as unhealthy as the conceptual structure of the calculus was at the time Berkeley's famous criticism was issued. For this reason-as much to emphasize the seriousness of the present situatioil in the foundations of quantum mechanics as to remove confusions that may be left in the mind of the general reader upon reading the Margenau and Wigner "Commentsv-I intend to restate the main points of my previous "Comments", and to show in detail why the Margenau and Wigner remarks fail completely to meet them. 1. The main point. Let S be a system which is "isolated" (as well as possible) during an interval to < t < t,, and whose state at to is known, let M be a measuring system which interacts with S so as to measure an observable 0 at tl, and let T be the "rest of the universe". In quantum mechanics, a physical situation is described by giving two things: a Hamiltonian and a state function. T h e usual way of obtaining an approximate description of the situation of the system S is simply to set the interaction of M T with S equal to zero for the interval to < t < t,. This, of course, is only an approximation-rigorously, the interaction between S and M T never completely vanishes, as Sharp and I both pointed out in our papers. What then is the rigorous description of the system S ? The answer, surprisingly, is that usual quantum mechanics provides no rigorous,
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* Received
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October, 1962.
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HILARY PUTNAM
contradiction-free account at all ! (The parallel with the 18th century situation in the foundations of the calculus is surprisingly close: setting dx = 0 after one has divided by dx "works". But mathematically this procedure is wholly unjustified, and it took the work of Weierstrauss and the development of the concept of a limit to provide a rigorous, thoroughly justifiable procedure.) In fact, if we take account of the fact that S is not strictly isolated (i.e., Hamiltonian (interaction between M T and S ) # 0), then, by an elementary calculation1, S cannot be assigned any state function. Also, since M T generates a field (however weak) which would have to be exactly known to describe the situation of S by means of a Hamiltonian, and by quantum mechanics itself, one cannot exactly know this field, since one cannot know the simultaneous positions and momenta of its sources, S cannot be assigned a Hamiltonian either. So the "approximation" made in quantum mechanics-setting Hamiltonian (interaction M T and S) = 0--is like the "approximation" setting dx = 0, and not like the legitimate approximations in classical mechanics, which can always in principle be dispensed with. I t is an algorithm which "worlis", but which has not, to date, been grounded in a consistent and, in principle, mathematically rigorous theory.
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2. T h e Margenau-Wigner reply. Margenau and Wigner reply: "Overall consistency of all parts of quantum mechanics, especially when that theory is forced to make reference to 'the entire universe' has never been proven or claimed." This is the only reference to the main point of my "Comments", and it gives the erroneous impression that the point we have just reviewed depends on treating "the entire universe" (S M T) as a system with a $-function of its own.
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3. Cosmological p r o b l e m s n o t relevant. Margenau and Wigner's phraseology"especially when that theory is forced to make reference to 'the entire universe' " (italics mine)-suggests that by 'the entire universe' I must have meant the cosmological universe and that I sought to embroil quantum mechanics in the problems of cosmology. Nothing could be wider of the mark. Footnote 1 of my paper made it clear that the question is whether quantum mechanics can consistently treat measurement as an interaction taking place within a single closed system (containing the observer). There is no objection to "idealizing" by setting Hamiltonian (T, M S ) = 0. After all, it is purely contingent that T is not just empty space. But it is not purely contingent that M is not just empty space: empty space cannot make measurements. If we do attempt to treat all measurements-that is to say, all the measurements we are interested in-as taking place within one closed system (as we would in classical physics), then we must imagine that the "rest of the universe", T, is just empty space, or at least that no measurements are carried out by observers in T upon M S. Otherwise, (1) the main point (see above) is not taken care of at all, and (2) we are not imagining that all measurements relevant in the context take place in one closed system (which is the question at issue). Margenau and Wigner write, "In fact, if one wants to ascertain the result of the measurement, one has to observe the measuring apparatus, i.e., carry out a measurement on it." As an argument against the "one closed system" view this is worthless, since it presupposes that the observer is not part of M.
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4. It is n o t t r u e t h a t "the object c a n n o t b e t h e whole tiniverse". Margenau and Wigner also state that Von Neumann's axioms for quantum mechanics are in-
' Cf. 141, p. 227, equation (4), and p. 230 ff.
COMMENTS ON COMMENTS ON COMMENTS
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compatible with the assumption that a closed system which contains the observer (the "entire universe") is a system in the sense of quantum mechanics. I t is true that if we make the assumption that "measurement" involves the interaction of the system under consideration with an outside system, then we cannot also assume that "the entire universe" is a system. Must we make this assumption ? In my "Comments", I suggested that it might be possible to give it up, but I did not give details. Since this is the point (the "cut" between observer and object) that Margenau and Wigner say is central to all of quantum mechanics, I will now be more explicit on this point. Let M and S be as before, and let T be empty (so that the "entire universe" consists of M S for present purposes). Von Neumann postulates that when M measures an observable 0 in S , then S is thrown into a new state, an eigenstate of the observable 0. Which eigenstate of 0 S is in is determined by M. According to Bohr, this is done in a wholly classical manner-that is, the process by which some macro-observable in M (say a pointer reading) comes to register the value corresponding to the 0-state S is in can be explained by classical physics. In particular, M can be treated using classical physics a l o n e ~ n l yS has to be described quantum mechanically. Of course, the "cut" can be shifted-that is, a proper part of M (always including the observer) can be taken as the measuring system M', while the rest of M can be adjoined to S to make the new observed system St.But, however we make the "cut", the measured system S is thought of as obligingly "jumping" into an eigenstate of 0 so that a classical system M can measure 0 in a purely classical way. This is not only implausible on the face of it, but inconsistent since S cannot, strictly speaking, have states of its own, as has already been pointed out. What is consistent and what also seems to avoid the whole difficulty, is to say that the interaction between M and S causes the entire system M S to go into an eigenstate of 0. In other words, assume: 0-measurement causes the entire universe to go into an eigenstate of 0. This assumption is consistent with the mathematical formalism of quantum mechanics-in fact, more consistent than the assumption that S alone jumps into an eigenstate of 0, as we have seen-and expresses the view that the measuring system is a part of the total system under consideration, and not an "outside" system.
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5. Quantum mechanics and classical physics. In the preceding section, I referred to a well-known peculiarity of the received interpretation of quantum mechanics (the so-called "Copenhagen Interpretation")-namely, S is ascribed a #function, and treated according to the laws of quantum mechanics, while the measuring system or "observer", M, is treated as a classical object. Thus quantum mechanics
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HILARY PUTNAM
classical physics." ([I], p. 209). "The quantum mechanics formalism represents a purely symbolic scheme permitting only predictions, on the lines of the correspondence principle, as to results obtainable under conditions speczjied by means of classical concepts." ([I], p. 21 1, italics mine). Specifically, the point that we neglect the "atomic" (quantum mechanical) structure of the "observer" is made by Bohr: "The neglect of the atomic constitution of the measuring instruments themselves, in the account of actual experience, is equally characteristic of the applications of relativity and of quantum theory." ([l], p. 238). The Russian physicist Landau has recently gone so far as to argue that it is not strictly true (as is usually maintained-e.g., by Margenau and W i p e r ) that classical physics is reducible to quantum mechanics, for just this reason-that, although classical physics is dedz~cedon the "object" side of the "cut", it is assumed on the "observer" side. As we saw before (cf. "the main point"), neglect of the "atomic constitution" of M T is fundamental in even setting up a Hamiltonian for S. How can we overcome this unsatisfactory state of affairs ? London and Bauer would like to reduce the "observer" to a disembodied "consciousness", but Margenau and Wigner admit this is not yet successful. "Present-day physics" (sic!) is not applicable to the "consciousness". The alternative suggested in the preceding section is much more direct and unmetaphysical. Namely, we should treat M S as a single closed system obeying the laws of quantum mechanics. If 0 is the observable being measured, and 0' is the correlated macro-observable (e.g., the position of the pointer), then at the end of the interaction 0 and 0' (considered now as observables in M S, even though 0 depends only on S and 0' only on M) will have the same spectrum of eigenfunctions. These eigen-functions will have (approximately) the form #,X,, where #$ is an eigen-function of 0 in S and X, is the corresponding eigen-function of 0' inM.2 This is a purely quantum mechanical characterization of measurement-no use is made at all of classical physics or of the classical description of M. T o complete the account, we need only postulate that the entire system M S goes into the state #,xi with the corresponding probability lc,j"but no reference to "classical concepts" is thereby introduced.
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6. Remark on "quantum jumps". The standard interpretations of quantum mechanics accept the so-called "Projection Postulate"-that measurement "throws" a system into an eigenstate of the observable measured. In my paper I included a brief argument for the necessity of this principle. Margenau and Wigner of course accept the conclusion-that one must postulate a process of measurement, distinct from and not reducible to "motion" (continuous change of state, governed by the Schrodinger equation) in a single closed system-indeed, this is just their "cut between the observer and the object". However, they misunderstood my argument, which was, indeed, too briefly stated in my "Comments". My argument was just this: Let E be an electron which is free3 during the interval to < t
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COMMENTS ON COMMENTS ON COMMENTS
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position at to and at t,, and that "the whole businessyy-the position measurement at to, the free movement of the electron in the interval to < t < t,, and the position measurement at t,-is treated as a case of "motion" in one closed system. Then the state function of the whole system must be an eigen-function of the position of E at to and at t,. On the other hand, the electron E is not interacting with the rest of the system during to < t < t,, so the state function of the whole system must have the form #$, during the interval to < t < t,, where # is the state function of a free electron (subject to the constraint that $J (q,, q2, qs, to) is a &function), and $ is the state function of the rest of the system. But # (q,, q,, qs, t) is spread out over all space at every t > to, (in non-relativistic quantum mechanics) so that the state function of the whole system cannot be an eigen-function of the position of E at t, ("reduction of the wave packet") except by possessing a discontinuity at t,. In a nutshell, the Schrodinger equation is first order in the time, and thus we are not free to impose boundary conditions at two or more different times. This is a perfectly correct argument to a conclusion Margenau and Wigner accept (the need for the Projection Postulate) from premisses they accept. Ilowever, the argument loses part of its force if we renounce my assumption 1 (which is just the "cut" assumption) and revise the Projection Postulate (as suggested above) to say that measurement sends M S, and not just S, into an eigenstate of the observable measured. In this case it is still true that we cannot say the Schrodinger equation is obeyed when to < t < t, except at the price of introducing by "fiat" (the revised Projection Postulate) a "reduction of the wave packet" at t,; however, we can say that "the whole business"-including the applications of the Projection Postulate-takes place in a single closed system which contains the observer. A defect of my interpretation is that it does not explain just why and how measurement (construed as a physical process, in my interpretation) causes a "reduction of the wave packet". However, the London-Bauer interpretation is subject to even worse defects. On their interpretation the measuring system is always outside the system S and includes a "consciousness". However, London and Bauer do not go so far as to make it just a "consciousness"-it must also have a "body", so to speak. Thus the main point applies in full force to this interpretation. Ignoring the interaction between M and S prior to the measurement is not just a useful "approximation", but is indispensible in this theory. Secondly, the "reduction of the wave packet" depends on "measurement" which is ultimately just the "direct awareness" of a fact by a "consciousness", in this interpretation. Subjective events (the perceptions of an "observer") cause abrupt changes of physical state ("reduction of the wave packet"). Questions: What evidence is there that a "consciousness" is capable of changing the state of a physical system except by interacting with it physically (in which case an automatic mechanism would do just as well) ? By what laws does a consciousness cause "reductions of the wave packet" to take place ? By virtue of what properties4 that it possesses is "consciousness" able to affect Nature in this peculiar way ? No answer is forthcoming to any of these questions. Ideally, perhaps, we would prefer a theory which was free of the need for postulating et quantum jumps". However, if we are going to accept the Projection Postulate, the theory suggested here will do-there is neither reason for nor plausibility in making quantum mechanics dependent upon an inconsistency producing "cut between observer and object" or upon "consciousness".
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I am indebted to Abner Shimony for raising this question.
HILARY PUTNAM REFERENCES
[I] N. BOHR,"Discussion with Einstein on Epistemological Problems in Atomic Physics," in A. Schilpp (ed.), Albert Einstein Philosopher-Scientist, Tudor, 1951, New York. and E. P. WIGNER,"Comments on Professor Putnam's Comments," [2] H. MARGENAU Philosophy of Science, vol. 29, no. 3, July 1962, pp. 292-293.
"Comments on the paper of David Sharp," Philosophy of Science, vol. 28, no. 3, [3] H. PUTNAM, July 1961, pp. 234-239. [4] D. H. SHARP,"The Einstein-Podolsky-Rosen Paradox Re-examined," Philosophy of Sciencl , vol. 28. no. 3, July 1961, pp. 225-233.
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[Footnotes] 1
The Einstein-Podolsky-Rosen Paradox Re-Examined David H. Sharp Philosophy of Science, Vol. 28, No. 3. (Jul., 1961), pp. 225-233. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28196107%2928%3A3%3C225%3ATEPR%3E2.0.CO%3B2-8 3
Comments on the Paper of David Sharp Hilary Putnam Philosophy of Science, Vol. 28, No. 3. (Jul., 1961), pp. 234-237. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28196107%2928%3A3%3C234%3ACOTPOD%3E2.0.CO%3B2-6
References 2
Comments on Professor Putnam's Comments H. Margenau; E. P. Wigner Philosophy of Science, Vol. 29, No. 3. (Jul., 1962), pp. 292-293. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28196207%2929%3A3%3C292%3ACOPPC%3E2.0.CO%3B2-C
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Comments on the Paper of David Sharp Hilary Putnam Philosophy of Science, Vol. 28, No. 3. (Jul., 1961), pp. 234-237. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28196107%2928%3A3%3C234%3ACOTPOD%3E2.0.CO%3B2-6 4
The Einstein-Podolsky-Rosen Paradox Re-Examined David H. Sharp Philosophy of Science, Vol. 28, No. 3. (Jul., 1961), pp. 225-233. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28196107%2928%3A3%3C225%3ATEPR%3E2.0.CO%3B2-8
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