Putnam. Comments on Comments on Comments

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Comments on Comments on Comments: A Reply to Margenau and WignerAuthor(s): Hilary Putnam

Reviewed work(s):Source: Philosophy of Science, Vol. 31, No. 1 (Jan., 1964), pp. 1-6Published by: The University of Chicago Press on behalf of the Philosophy of Science AssociationStable URL: http://www.jstor.org/stable/186740 .

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Philosophyf Science

VOL. 3I January, I 964 NO. I

DISCUSSION: COMMENTS ON COMMENTS ON COMMENTS

A REPLY TO MARGENAU AND WIGNER*

HILARY PUTNAM

Massachusetts Institute of Technology

The Margenauand Wigner "Comments"[2] on my "Commentson the Paper ofDavid Sharp",[3, 4] is a strange document. First the authors say, in effect, "hadanything been wrong (with the fundamentalsof quantum mechanics) we shouldcertainlyhave heard". Then they issue various obiter dicta (e.g., the "cut betweenobserverandobject"is unavoidable n quantummechanics;the-highly subjectivistic-London-Bauer treatment of quantum mechanics is described, along with vonNeumann's book, as "the most compactand explicit formulation of the conceptualstructure of quantum mechanics"). My assumption 2 (that the whole universe is asystem)is describedas "not supportable",because"the measurement s an interaction

between the object and the observer". The "object" (the closed system) cannotinclude he observer.

The issues involved in this discussion are fundamental ones. I believe that theconceptualstructureof quantummechanicstoday is as unhealthyas the conceptualstructureof the calculus was at the time Berkeley's amous criticismwas issued. Forthis reason-as much to emphasize the seriousness of the present situation in thefoundationsof quantummechanicsas to remove confusions that may be left in themind of the generalreaderupon readingthe Margenauand Wigner"Comments"-Iintend to restatethe main points of my previous "Comments",and to show in detailwhy the MargenauandWignerremarks ail completelyto meet them.

1. The main point. Let S be a system which is "isolated" (as well as possible)duringan intervalto < t < t1, and whose state at tois known, let M be a measuringsystem which interacts with S so as to measurean observable0 at tl, and let T bethe "rest of the universe". n quantum mechanics,aphysicalsituationis describedbygiving two things:a Hamiltonianand a state function.The usual way of obtaininganapproximatedescriptionof the situationof the systemS is simplyto set the interactionof M + T with S equalto zero for the intervalto < t < tl. This, of course, is onlyan approximation-rigorously,the interactionbetween S and M + T never com-pletely vanishes, as Sharp and I both pointed out in our papers. What then is therigorousdescriptionof the system S?

The answer, surprisingly,is that usual quantum mechanicsprovidesno rigorous,

* Received October, 1962.



2 HILARY PUTNAM

contradiction-freeaccountat all! (The parallelwith the 18th centurysituation n the

foundationsof the calculusis surprisinglyclose: setting dx 0= afterone has divided

by dx "cworks".But mathematicallyhis procedure s wholly unjustified,and it took

the work of Weierstraussand the developmentof the concept of a limitto provide arigorous, horoughly ustifiableprocedure.) n fact, if we takeaccountof the factthatS

is not strictlyisolated(i.e., Hamiltonian(interactionbetween M + T and S) # 0),then, by an elementarycalculation',S cannot be assigned any state function. Also,

since M + T generatesa field (howeverweak)which would haveto be exactlyknown

to describe the situation of S by meansof a Hamiltonian,and by quantummechanics

itself, one cannotexactly know this field, since one cannot know the simultaneous

positionsandmomenta of its sources,S cannot be assigneda Hamiltonianeither. So

the "approximation"made in quantummechanics-setting Hamiltonian(interaction

M + T and S) = 0--is like the "approximation" etting dx = 0, and not like the

legitimateapproximations n classicalmechanics,which can always in principle be

dispensedwith. It is an algorithmwhich "works",but which has not, to date, been

groundedin a consistentand, in principle,mathematicallyrigoroustheory.

2. The Margenau-Wigner reply. Margenauand Wigner reply: "Overall con-sistency of all parts of quantummechanics,especiallywhen that theoryis forced to

make reference o 'the entire universe'has never been provenor 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.

3. Cosmological problems not relevant. MargenauandWigner'sphraseology-"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 cos-

mologicaluniverseand that I sought to embroilquantummechanicsin the problemsof cosmology. Nothing could be wider of the mark.Footnote 1 of my papermade it

clearthat the questionis whetherquantummechanicscan consistentlytreatmeasure-

ment as an interactiontaking place within a single closed system (containing the

observer).There is no objection o "idealizing"by settingHamiltonian T, M + S) =

0. Afterall, it is purelycontingentthat T is not just emptyspace. But it is not purely

contingentthat M is not just empty space:empty space cannotmake measurements.If we do attemptto treat all measurements-that is to say, all the measurementswe

are interestedin-as taking place within one closed system (as we would in classicalphysics),then we must maginethat the "rest of the universe", T, is just empty space,or at least that no measurementsare carriedout by observersin T upon M + S.

Otherwise, 1) the main point (seeabove) s not taken careof at all, and(2)we arenot

imagining that all measurementsrelevant in the context take place in one closed

system(whichis the questionat issue).Margenauand Wigner write, "In fact, if one wants to ascertainthe result of the

measurement,one has to observe the measuringapparatus, .e., carryout a measure-

ment on it." As an argumentagainstthe "one closed system"view this is worthless,since itpresupposeshat the observer s notpart of M.

4. It is not true that ""theobject cannot be the whole universe". Margenauand Wigner also state that VonNeumann'saxiomsfor quantum mechanics are in-

1 Cf. [4], p. 227, equation (4), and p. 230 ff.



COMMENTS ON COMMENTS ON COMMENTS 3

compatible with the assumption that a closed system which contains the observer(the "entire universe") s a system in the sense of quantummechanics.It is true thatif we make the assumption hat "measurement" nvolves the interactionof the systemunder considerationwith an outsidesystem, then we cannot also assume that "theentire universe" is a system. Must we make this assumption? In my "cComments",I suggestedthat it might be possible to give it up, but I did not give details. Sincethis is the point (the "cut" between observerand object) that Margenauand Wignersay is centralto 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"consistsof M + S for presentpurposes).Von Neumann postulatesthatwhen M measuresanobservable0 in S, then S is thrown nto a newstate,aneigenstateof the observable0.Which igenstateof 0 S is in is determinedby M. Accordingto Bohr,this is donein awhollyclassical manner-that is, the process by which some macro-observablen M(say a pointer reading) comes to register the value corresponding o the 0-state S is

in can be explained by classicalphysics.In particular,M can be treatedusing classicalphysics alone-only S has to be described quantum mechanically.Of course, the"cut" can be shifted that is, a proper partof M (always ncludingthe observer)canbe taken as the measuring ystem M', while the rest of M canbe adjoined o S to makethe new observedsystemS'. But, howeverwe make the "cut", the measuredsystem Sis thoughtof as obligingly ""jumping"nto an eigenstateof 0 so that a classicalsystemM can measure0 in a purelyclassicalway.This is not only implausibleon the faceofit, but inconsistentsince S cannot, strictly speaking, have states of its own, as hasalreadybeen pointed out. What is consistent and what also seems to avoidthe wholedifficulty,is to say that the interaction between M and S causes the entire system

M + S to go into an eigenstateof 0. In otherwords, assume: 0-measurement ausesthe entireuniverse ogo into an eigenstate f 0.This assumptionis consistent with the mathematical ormalism of quantum me-

chanics-in fact, more consistent than the assumptionthat S alonejumps into aneigenstate of 0, as we have seen-and expressesthe view that the measuringsystemis apart of the total system underconsideration,and not an ""outside"ystem.

5. Quantum mechanics and classical physics. In the preceding section, Ireferred to a well-knownpeculiarityof the received interpretationof quantumme-chanics (the so-called "CopenhagenInterpretation")-namely, S is ascribed a 0-function,and treatedaccording o the lawsof quantummechanics,whilethe measuring

system or f"observer, M, is treatedas a classicalobject.Thus quantum mechanics"ctreatshe world asconsistingof two kindsof objects-classical objectsand quantummechanicalobjects-with the formermeasuring he latter",as I wrotein my previouspaper.

Of course, any classicalsystem can also be taken as the object,and then the laws ofclassicalphysics are forthcomingas special cases of the laws of quantummechanics,in an appropriate imiting sense. However, according to the usual account, someother classicalsystem has then to play the role of "observer",and this other systemhas then to be treated classically.In their paragraphon this point, MargenauandWigner refer to the classical limit theorems and the Bohr correspondenceprinciple.

But these imply only that any classicalsystem can be treated as the object, whichwas never at issue. Indeed, this point has been made sharplyand againand againbyBohrhimself. E.g., "The account of the experimentalarrangement nd the resultsofthe observationsmust be expressed... with suitableapplicationof the terminologyof



4 HILARY PUTNAM

classical physics." ([1], p. 209). "The quantum mechanics formalismrepresentsa

purelysymbolicschemepermittingonlypredictions,on the lines of the correspondenceprinciple, as to results obtainable under onditionspecified y means f classical oncepts."

([1], p. 211, italicsinine).Specifically, he point thatwe neglectthe "atomic"(quantummechanical) tructure

of the "observer" s made by Bohr: "The neglect of the atomic constitutionof the

measuring instruments themselves, in the account of actual experience, is equallycharacteristicof the applicationsof relativityand of quantum theory." ([1], p. 238).

The RussianphysicistLandauhas recentlygone so faras to argue that it is not strictly

true(as is usuallymaintained-e.g., by Margenauand Wigner)that classicalphysics

is reducible to quantum mechanics, for just this reason-that, although classical

physics is deduced n the "object"side of the "cut", it is assumed n the "observer"

side. As we saw before (cf. "the main point"), neglectof the "atomicconstitution"of

M + T is fundamental n even setting up a Hamiltonian or S.

How canwe overcomethis unsatisfactory tateof affairs? Londonand Bauerwouldlike to reduce the "observer"to a disembodied"consciousness",but Margenauand

Wigneradmitthis is not yet successful."Present-dayphysics"(sic!) is not applicable

to the "consciousness".The alternativesuggested in the precedingsection is much

more direct and unmetaphysical.Namely, we should treat M + S as a single closed

systemobeyingthe lawsof quantummechanics.If 0 is the observablebeingmeasured,

and O' is the correlatedmacro-observable e.g., the position of the pointer), then at

the end of the interaction0 and O' (considerednow as observables n M + S, even

though 0 dependsonly on S and O' only on M) will have the samespectrum f eigen-

functions.These eigen-functionswill have (approximately)he form V'Xj'wherey? is

an eigen-functionof 0in

Sand

Xiis the

correspondingeigen-functionof O' inM.2

This is a purely quantummechanical haracterizationf measurement-no use is made

at all of classicalphysicsor of the classicaldescriptionof M. To completethe account,

we need only postulatethat the entiresystemM + S goes into the state IiXiwith the

correspondingprobability ICI12-butno referenceto "classicalconcepts" is thereby

introduced.

6. Remark on ""quantum jumps". The standard interpretationsof quantummechanics accept the so-called "ProjectionPostulate"-that measurement"throws"

a system into an eigenstate of the observablemeasured.In my paper I included a

brief argumentfor the necessity of this principle. Margenauand Wigner of course

accept the conclusion-that one must postulate a process of measurement,distinctfrom and not reducible to "motion" (continuous change of state, governed by the

Schr6dingerequation) n a singleclosedsystem-indeed, this is just their "cutbetween

the observerandthe object".However,they misunderstoodmy argument,whichwas,

indeed, too brieflystated in my "Comments".My argumentwas just this: Let E be

an electron which is free3 during the interval to < t <tl. Suppose E has a sharp

2 Note that whether Oi or OtbXs called an eigen-function of 0 depends on which Hilbert

space one is using-the Hilbert space of S or of S + M. The statement that 0 and O' have

the same spectrum is true only in the Hilbert space of S + M.

3 In [3] I neglected to say that E should not interact with the rest of the system during theinterval to < t < tL, and my use of the phrase "any physically realizable Hamiltonian" un-

fortunately gave rise to the contrary impression. The point was that the above argument is

quite independent of the nature of the interaction between M and E at to and at tl.



COMMENTS ON COMMENTS ON COMMENTS 5

position at toand at t1, and that "the whole business"-the position measurement at to,the free movement of the electron in the interval to < t < t1,and the position measure-

ment at t1-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 andat tl. On the other hand, the electron E is not interacting with the rest of the system

during to < t < t1, so the state function of the whole system must have the form 0b,during the interval to < t < t1, where b s the state function of a free electron (subject

to the constraint that b(ql, q2, q3, to) is a 8-function), and 0 is the state function of the

rest of the system. But b (ql, q2, q3, 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 t1 ("reduction of the wave packet")

except by possessing a discontinuity at t1. In a nutshell, the Schr6dinger 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 Margenauand Wigner accept (the need for the Projection Postulate) from premisses they accept.

However, 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 Schr6dinger

equation is obeyed when to < t < t1 except at the price of introducing by "fiat" (the

revised Projection Postulate) a "reduction of the wave packet" at t1; however, we

can say that "the whole business"-including the applications of the Projection Postu-

late-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 measure-

ment (construed as a physical process, in my interpretation) causes a "reduction of thewave 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 indis-

pensible in this theory. Secondly, the "reduction of the wave packet" depends on

ccmeasurement" which is ultimately just the "direct awareness" of a fact by a "con-

sciousness",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 "reduc-

tions of the wave packet" to take place ? By virtue of what properties4that 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

"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".

4 I am indebted to Abner Shimony for raising this question.



6 HILARY PUTNAM

REFERENCES

[1] N. BOHR, "Discussion with Einstein on Epistemological Problems in Atomic Physics," in

A. Schilpp (ed.), Albert Einstein Philosopher-Scientist, Tudor, 1951, New York.[2] H. MARGENAU and E. P. WIGNER, "Comments on Professor Putnam's Comments,"

Philosophy of Science, vol. 29, no. 3, July 1962, pp. 292-293.

[3] H. PUTNAM, "Comments on the paper of David Sharp," Philosophy of Science, vol. 28, no. 3,

July 1961, pp. 234-239.

[4] D. H. SHARP, "The Einstein-Podolsky-Rosen Paradox Re-examined," Philosophy of Scienc,

vol. 28. no. 3, July 1961, pp. 225-233.

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Putnam. Comments on Comments on Comments