Physics Today

Observant Readers Take the Measure of Novel Approaches to Quantum Theory; Some Get Bohmed Murray Gell‐Mann, James Hahtle, Robert B. Griffiths, Anton Zeilinger, Robert T. Nachtrieb, James L. Anderson, Allen C. Dotson, William G. Hoover, Henry M. Bradford, and Sheldon Goldstein

Citation: Physics Today 52(2), 11 (1999); doi: 10.1063/1.882512 View online: http://dx.doi.org/10.1063/1.882512 View Table of Contents: http://scitation.aip.org/content/aip/magazine/physicstoday/52/2?ver=pdfcov Published by the AIP Publishing

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.215.225.131 On: Mon, 24 Aug 2015 23:19:45 LETTERS Observant Readers Take the Measure of Novel Approaches to Quantum Theory; Some Get Bohmed n "Quantum Theory without Ob- beit discrete, intervals of time. How- DH, if two such quantities at the I servers—Part One" (PHYSICS TODAY, ever, he seems to think that we start same time do not commute, measure- March 1998, page 42), Sheldon Gold- with the union of many different fam- ments of them have to take place in stein discusses our work on the deco- ilies (with the possibility of inconsis- different alternative histories of the herent histories (DH) approach to tencies in statements connecting the universe.2 Our work is not com- quantum mechanics and the related probabilities of occurrence of various pletely finished, but the research work of Robert Griffiths and Roland histories) and are trying to find con- is not plagued by inconsistencies. Omnes. He describes correctly many ditions that will shrink this set to a aspects of the research and makes a single realm and its associated fam- References number of favorable remarks, such as ily thus eliminating inconsistencies. 1. R. Griffiths, Phys. Rev. A 54, 2759 "it seems likely that the program of That is not the case. Rather, we are (1996). R. Omnes, The Interpretation DH can be brought successfully to comparing the properties of different of Quantum Mechanics, Princeton completion." However, he seems to realms or families, while restricting U. P., Princeton, N. J. (1994). R. Grif- have misunderstood one important our statements in each case to a sin- fiths, J. B. Hartle, Phys. Rev. Lett. 81, gle family, thus encountering no in- 1981(1998). point, and as a result he mistakenly 2. M. Gell-Mann, The Quark and the Jag- attributes certain "inconsistencies" to consistencies along the way. uar , W. H. Freeman, New York (1994), the program at its present stage. It is worth mentioning that the fig- p. 172. We always consider a "realm"—a ure caption on the last page of the ar- MURRAY GELL-MANN set of mutually exclusive decoherent ticle is misleading. The photograph ([email protected]) histories with probabilities adding to shows Richard Feynman and one of Santa Fe Institute 1—and we typically impose some fur- us (Gell-Mann), and the caption de- Sante Fe, New Mexico ther conditions on a given realm. (A scribes Gell-Mann as "one of the most JAMES HARTLE "family," as discussed by Goldstein, sensible critics of orthodox quantum ([email protected]) consists of a realm and all its coarse theory" and Feynman as "one of its University of California, Santa Barbara grainings.) It is essential to restrict most sensible defenders." In fact, statements relating the probabilities both physicists held very similar heldon Goldstein's two-part article of occurrence of histories to a given views of quantum mechanics. Some S contains much valuable material. family containing them. 'Here, we months before Feynman's death in Unfortunately, his discussion of consis- have in mind statements such as the 1988, Gell-Mann described to a class tent histories is, in certain respects, following: If B happens at time U at Caltech the status of our work on misleading; at the very least, it is out and C at time t then A must have decoherent histories at that time. of date. (Goldstein, following Murray 3i Feynman was in attendance, and at happened at time tv) The restriction Gell-Mann and James Hartle, uses is necessary despite the fact that the the end of the class, he stood up, and the term "decoherent histories" for numerical probability of a given his- some of the students expected an ex- what Roland Omnes and I call "con- tory belonging to more than one fam- citing argument. But his comment sistent histories.") ily is independent of the family. This was, "I agree with everything you The logical structure of the consis- point has been stressed very strongly said." tent histories approach has been by Griffiths and Omnes.1 Inconsisten- There is no question that the "or- worked out in considerable detail by thodox" Copenhagen interpretation Omnes, and paying serious attention cies can arise if statements relating l the probabilities of occurrence of histo- works in measurement situations and to his "Rule 4" would have pre- ries are made while referring to differ- accurately predicts the outcomes of vented Goldstein from making the ent families in the course of a given laboratory experiments. It is not erroneous assertion that the consis- argument. That is true even if the wrong. Rather, it is a special case tent histories formalism is rendered histories involve only a single time. of the more general interpretation inconsistent by the results of An- Goldstein mentions our efforts to in terms of decoherent histories of drew Gleason; Simon Kochen and the universe. The Copenhagen pic- understand what is so special about Ernst Specker; John Bell; and Lucien ture is too special to be fundamental, 2 the "usual" realm defined by hydro- Hardy. My own recent work has and it is clearly inadequate for quan- led to a quite systematic treatment of dynamic variables averaged over small tum cosmology. the whole subject, in which consistent volumes and evaluated at short, al- As Goldsteins title suggests, DH is history "beables" (the physical refer- a formulation of quantum mechanics ents of the mathematical terms) are Letters submitted for publication should be in which observers do not play a fun- spelled out in considerable detail, and addressed to Letters, PHYSICS TODAY, damental role. We are working to the formalism is shown to be com- American Center for Physics, One Physics perfect that formulation. However, plete as a fundamental theory, with- Ellipse, College Park, MD 20740-3843 or we are not seeking, nor do we have, a out need of the additional principles to [email protected] (using your sur- formulation that implements Albert that Goldstein seems to think are nec- name as "Subject"). Please include your Einstein's idea of attributing "physical essary. Although the "primitive ontol- affiliation, mailing address and daytime reality" to all quantities for which ogy" (to use Goldstein's term) of con- phone number. We reserve the right to edit there are situations in which they sistent histories was not presented in letters. can be measured with certainty. In the earliest papers in as clear a form

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© 1999999 AJHAndiCV€ ! Imiiiuu? ui Pli) ^-220-6IP: 131.215.225.131 On: Mon, 24 Aug 2015 23:19:45FEBRUARY 1999 PHYSICS TODAY 11 as is now possible—a quite common to illustrate the inconsistency. that "inconsistencies can arise ... is occurrence when important new ideas For a certain quantum state ?//, say precisely the point of the example I are introduced into physics—the fun- at time t - 0, for a pair of spin-V2 par- used in the article and am using here. damental ideas have not changed, ticles, there are spin components A, Robert Griffiths is more explicit and more recent work has confirmed £, C and D (also at t = 0) for which about the cause of my having made the soundness of the basic strategy the DH approach yields the following "the erroneous assertion that the con- adopted by Gell-Mann and Hartle, four statements concerning joint prob- sistent histories formalism is ... in- Omnes and myself. (Readers inter- abilities P: consistent"—namely, my not "paying ested in pursuing the subject further 1. P(A = 1, B= l) = 0.09. serious attention to [Omnes's] Rule 4." may wish to consult reference 3, 2. P(A = 1, C# l) = 0. Here is the rule, as given on page which contains a response to various 3. P(B = 1, D^ l) = 0. 163 of the reference Griffiths men- criticisms and misunderstandings of 4. P(C = 1, D= l) = 0. tions: "Any description of the proper- consistent histories, as well as simple Corresponding to these four state- ties of an isolated physical system examples that may make some of the ments are four pairs of commuting must consist of propositions belonging ideas easier to follow.) observables and four decoherent together to a common consistent logic. There is one aspect of consistent families (the sort of families to which Any reasoning to be drawn from the histories that was perfectly clear in DH assigns probabilities): the AB fam- consideration of these properties the very first paper on the topic and ily, the AC family, the BD family and should be the result of a valid implica- in all our subsequent work: A quan- the CD family However, these fami- tion or of a chain of implications in tum history consists of a sequence of lies cannot be combined into, say, an this common logic.'1 What Omnes events at successive times, and these ABCD family, and thus DH does not calls a "consistent logic" amounts events correspond to subspaces of the supply us with probabilities for simul- more or less to a (decoherent) family quantum Hilbert space. In standard taneous values of A, S, C and D. I have always had great difficulty quantum theory, a wavefunction is as- It is important to appreciate that, with this rule. I don't understand sociated with a one-dimensional sub- for orthodox quantum theory (and, in what it actually means, in terms of space of the Hilbert space, whereas fact, even for Bohmian mechanics), both detail and basic meaning. Does subspaces of higher dimension corre- the four statements above, if used the description provided by the four spond to collections of wavefunctions. properly, are not inconsistent, because statements in my example, which re- Thus, wavefunctions are the building they then would refer merely to the quires reference to four families, vio- blocks out of which histories are con- outcomes of four different experiments, late this rule because the four state- structed, and it is difficult to under- so that the probabilities would refer, ments are on adjacent lines? What if stand why Goldstein asserts that, in in effect, to four different ensembles. they were on different pages, or were the consistent histories approach, "the However, the whole point of DH is made by different people? It can wavefunction is by no means the com- that such statements refer directly, hardly be expected that, when think- plete description of a quantum sys- not to what would happen were cer- ing about the same system, all people tem; it is not even the most impor- tain experimental procedures to be per- at all times will—by some peculiar tant part of that description." It is formed, but to the probabilities of occur- harmony—formulate statements con- Bohmian mechanics, not consistent rence of the histories themselves, re- cerning only the same common family. histories, that needs ("hidden") vari- gardless of whether any such experi- Besides, why are my four state- ables in addition to the standard Hil- ments are performed. Thus, the state- ments not a counterexample? They bert space of wavefunctions for its ments refer to a single ensemble of sys- are a description of precisely the sort beables, and in this respect the ap- tems, for about 9C7c of which, according that Rule 4 informs us "must" not be. proaches are actually quite different, to the first statement, both A and B This raises the question as to exactly despite Goldstein s efforts to find are 1; for none of which, according to what is meant in the rule by "must," some parallels. the second statement, can A be 1 with- and, in its next sentence, by "should." References out C also being 1; and so on. The real problem, I believe, is this: 1. R. Omnes, The Interpretation of Quan- As such, the four statements above If we "must" or "should" restrict our tum Mechanics, Princeton U. P., are obviously inconsistent, since it fol- descriptions and reasoning in the Princeton, N. J. (1994), p. 163. lows from statements 1, 2 and 3 that, manner described by Rule 4, it must 2. R. B. Griffiths, Phys. Rev. A 54, contrary to statement 4, in at least 9cc be because of the meanings of the 2759(1996). of the systems in the ensemble, C and statements under consideration and 3. R. B. Griffiths, Phys. Rev. A 57, D are both 1. This is the inconsis- the way the language expressing them 1604(1998). tency to which I referred in my article. is intended to function. For example, ROBERT B. GRIFFITHS Concerning this issue, Murray Gell- if (as would be appropriate in ortho- ([email protected]) Mann and James Hartle complain dox quantum theory) we were to use Carnegie Mellon University that I have "misunderstood one impor- the four statements above as an ellip- Pittsburgh, Pennsylvania tant point"—namely, that "it is essen- tical way of talking about results of tial to restrict statements relating the possible experiments, then it is appar- OLDSTEIN REPLIES TO GELL-MANN probabilities of occurrence of histories ent that we could get into trouble by gAND HARTLE AND TO GRIFFITHS: to a given family containing them" considering, at one time, several of The main complaint in these two let- because "inconsistencies can arise if these statements, should we slide into ters concerns my assertion that the statements relating the probabilities the mistake of thinking that the sev- decoherent histories (DH) approach is of occurrence of histories are made eral statements refer to a common inconsistent (unless the basic decoher- while referring to different families in experiment. ence condition is augmented by addi- the course of a given argument." I However, if, for DH, descriptions tional fundamental set selection prin- am puzzled by their response. Each such as those provided by the state- ciples). Before addressing this com- of my four individual statements con- ments above are to be understood plaint, though, I think it helpful to cerns only probabilities for a single with their usual meanings, then look again at the example I presented family (with, of course, a different Rule 4 is simply false, to the extent in my article (March 1998, page 45) one for each statement). And the fact that it has any meaning at all. And This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to 12 FEBRUARY 1999 PHYSICS TODAIP: Y 131.215.225.131 On: Mon, 24 Aug 2015 23:19:45 if the proponents of DH have some beyond supporting other meaning in mind for such state- the insinuation ments, they should so inform us and that DH involves supply this meaning—something that, only pure quan- as far as I am able to tell, they no- tum concepts, and where do. beyond sustaining V0 A&OVAT IT- /vto It may be argued that Rule 4 the illusion that, A should be regarded as merely a rule— unlike Bohmian occupy 7He that is, as merely defining a certain mechanics, it in- game. But then why must I play this volves no addi- game when analyzing the implica- tional "hidden" tions of DH? variables? —SG It is true that, to deduce or recog- nize that the four statements above heldon Gold- are inconsistent, we must consider a S stein conjec- collection of statements involving tures that more than a single family. If we obey "hardly anybody Rule 4 in our analyses, we will en- truly believes . . . counter, as Gell-Mann and Hartle say, anymore" in the "no inconsistencies along the way." Copenhagen inter- But the statements wall remain incon- pretation of quan- sistent even if we invoke and adhere tum mechanics, es- to rules that demand, in effect, that pecially in "the no- we ignore the inconsistency. tion that quantum In my article, I tried to present mechanics is the DH approach in what I deemed about observation the best possible manner. Whatever or results of meas- its vices, this version, based on an urement" (March augmented decoherence condition, 1998, page 42). has the virtue of consistency From discussions Griffiths finds it "difficult to under- with a number of stand" why I say that, for DH, the colleagues, I know PHYSICS wavefunction of a physical system that I am not the does not provide a complete descrip- only person to tion of the system. Let's focus, there- whom the Copenhagen interpretation ous misunderstanding. All the quan- fore, on the simplest possible example remains one of the most significant in- tum state is meant to be is a repre- to illustrate my point. Suppose that tellectual achievements of our cen- sentation of the catalog of our knowl- at, say, t = 0, a single spin-1/? particle tury. Therefore, Goldstein's conjec- edge of the system. It is precisely 1 is in a quantum state i with az = 1, ture is certainly incorrect. that catalog that is necessary to ar- and suppose we consider the single- I suggest that the very austerity of rive at the maximum possible set of time 'hence, decoherent) family corre- the Copenhagen interpretation, unsur- usually probabilistic predictions for sponding to the value of ax at this passed by that of any other interpreta- all possible future observations of the . time. Then, for about half of the tion of quantum mechanics, speaks system. members of a large ensemble of sys- very much in its favor. Indeed, its ba- The revolutionary new feature of tems in this state, the value of crx is sic attitude toward the fundamental quantum physics arises whenever 1, and for these individual systems role of observation represents a major there is no way, not even in principle, the quantum state i>, which is a su- intellectual step forward over naive to tell which of various possibilities is perposition of the eigenstates of a,, classical realism. In classical physics, the case. Then, instead of just hav- provides only partial information. observation is often regarded as a sec- ing to acknowledge our ignorance, as Griffiths claims that "wavefunc- ondary concept, with the elements of we would have to in classical physics, tions are the building blocks out of the real world being primary. Yet, it quantum superposition comes in as a which histories are constructed." In is obvious that any statement about qualitatively new property. If the con- the preceding example, the history nature has to be based on observa- dition above should ever be realizable ax= 1 can be regarded (ignoring the tion. What could then be more natu- for the dead and live states of a cat, other degrees of freedom) as corre- ral than a theory in which observa- its quantum state has to be a superpo- sponding to a wavefunction—namely, tion plays a more fundamental role sition of these states. That clearly the associated eigenstate. But this than in a classical worldview? What does not mean the cat is both alive wavefunction is by no means the could be more sensible than the the- and dead. It means only that no defi- quantum state \p of the system, which ory itself acknowledging that any nite statement can be made concern- remains, for DH, an incomplete de- statement about the physical world ul- ing the question of whether the poor scription of that system. Insisting timately is, at least implicitly, a state- animal is alive or dead. Upon obser- that histories be regarded as con- ment about observation? vation, we will find it in either state, structed out of wavefunctions makes Schrodinger's cat is paradoxical and thus the state assigned to the cat it more difficult to appreciate this only if one insists on pressing ortho- collapses into either possibility. fact and obscures the dynamical char- dox quantum theory into service—as It is not at all surprising that we acter of the role played for DH by the many naively do—to imply that (in have to change the representation of quantum state ip of a system. Goldstein's words) "the cat is some- our knowledge if that knowledge Why, indeed, does Griffiths insist how both dead and alive until an ob- changes because of information ob- upon so playing with words? Are server checks to see" (March 1998, tained by observation of the cat. The there any good reasons for doing so, page 43). Doing that reflects a seri- collapse of the state vector can be

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.215.225.131 On: Mon, 24 Aug 2015 23:19:45FEBRUARY 1999 PHYSICS TODAY 13 From JO kHz to 100 MHz The most powerful solid-state broadband amplifier made. 3500 watts CW Completely airField. 160 School House Road, Souderton, PA 18964-9990 USA • TEL 215-723-8181 • FAX 215-723-5688 In Europe, call EMV: Munich: 89-614-1710 • London: 01908-566556 • Paris: 1-64-61-63-29 www.ar'amps.com This article is copyrighted as indicated in the Copyrigharticle.t © Reuse 1997, Amplifie of AIPr Research content. Tin- ,,r.mni is subject- stripe ..n toAR the product termss is Reg at:. U.S http://scitation.aip.org/termsconditions.. Pat. ck Tm. Off. Downloaded to IP: 131.215.225.131 On: Mon, 24 Aug 2015 23:19:45 Circle number 9 on Reader Service Card seen only as a "measurement para- does not mean the cat is both alive vation, there is nothing in Zeilinger's dox" if one views this change of the and dead [but] only that no definite assertion that "any statement about quantum state as a real physical proc- statement can be made" on the ques- nature has to be based on observa- ess. In the extreme, it is often even tion, because we are, and must be, ig- tion" to suggest, or even make plausi- claimed that something happens to norant as to the fact; and that what ble the idea, that observation has a the cat because it is being observed. he calls a "natural understanding" of fundamental role to play in the formu- There is no basis for any such claim. the new quantum phenomena based lation, as opposed to the justification, In contrast, what can be more natu- on entanglement neither requires nor of physical theory. ral than to change the representation involves any "superluminal or instan- What Zeilinger terms "the auster- of our knowledge—that is, the quan- taneous transmission of information." ity of the Copenhagen interpretation" tum state—if we gain new knowledge These things are as true for Bohmian is very much like the austerity of sol- from a measurement performed on mechanics—to take my favorite quan- ipsism, and it suffers from similar de- the system? Any statement about tum theory7 without observers—as fects. What results from this auster- what is the case in the world can they are for orthodox quantum theory ity is not merely implausible, but also then be obtained only with explicit ref- as understood by Zeilinger. deficient in the theoretical simplicity erence to observation. Indeed, as in Even the last sentence of his let- afforded by an appeal to something the case of the measurement paradox, ter, while a bit too dogmatic for my outside ourselves. —SG the paradoxes constructed by oppo- taste, is one for which I have quali- nents of the Copenhagen interpreta- fied sympathy. However, his denigra- heldon Goldstein invokes the tion are always based on some realis- tion of "pre-quantum notions,"—which S Einstein-Podolsky-Rosen (EPR) tic pre-quantum notions about how can mean anything from what he paradox to suggest that "the quantum the world ought to be brought into calls "naive classical realism," to vari- mechanical description is not the whole the discussion through the backdoor. ables not definable (or defined) in story . . ." (March 1998, page 43). In fact, there is never a paradox if we terms of Hilbert space structure, to Although every college physics stu- realize that quantum mechanics is the possibility of any sort of observer- dent has heard of the EPR paradox, about information. Actually, such a independent reality—must be taken and most have read the original pa- view also leads to a most natural un- with a grain of salt as being merely per in Physical Review} far fewer stu- derstanding of new phenomena in an appeal to prevailing prejudices. dents of quantum mechanics have quantum computation and quantum But does Zeilinger truly believe read the rebuttal to EPR that was communication, such as quantum en- that "quantum mechanics is about in- printed in Physical Review a year tanglement, quantum nonlocality or formation"? Information is always in- later by Yale University professor quantum teleportation. Then, no need formation about something. There- Henry Margenau.2 Margenau showed whatsoever arises to allude to such fore, shouldn't quantum mechanics be that Einstein's objections to quantum notions as superluminal or instantane- regarded as being about that some- mechanics relied on the von Neu- ous transmission of information. thing? Quantum mechanics tells us mann projection postulate, which says It is very much to the credit of pro- about atoms and chemical bonding that the measurement procedure "col- ponents of alternative approaches and high-temperature superconductiv- lapses" the state of the system to the such as Goldstein that, beginning ity. Of course, it also provides us eigenstate of the measured observable with Albert Einstein in the early 20th with information about these things. with the recorded eigenvalue. As century, they have realized—often in But it does so precisely because it is Margenau made plain, the EPR para- a much deeper way than have the ad- about the things themselves. dox vanishes if the von Neumann pro- herents of the orthodox view—how And does Zeilinger really wish to jection postulate is abandoned. novel and counterintuitive some fea- deny that the change of the state vec- Margenau and his student James tures of quantum theory are. Yes, I tor that occurs during the measure- Park proved that the von Neumann submit, real progress necessitates full ment process is "a real physical proc- projection postulate is simultaneously acceptance of these novel and counter- ess," even when it leads to the de- "absurd, false, and useless."3 intuitive features, including the funda- struction of the possibility of interfer- 1. Why the postulate is "absurd." The mental role of observation and of re- ence? Can quantum interference be concept of a quantum state is inher- sults of measurements, rather than genuinely understood by invoking a ently statistical. "Quantum state" re- trying to return to pre-quantum no- wavefunction that is nothing more than fers to the identical preparation of an tions and concepts. "a representation of our knowledge'? ensemble of identical systems. One ANTON ZEILINGER Moreover, it would not be at all determines the state by recording the ([email protected]) sensible for a theory to acknowledge eigenvalues (in principle an infinite University of Vienna that "any statement about the world number of times) to get expectation Vienna, Austria has to make reference to observa- values of a "quorum" of observables. tion," since Zeilinger's assertion is Doing so in effect describes the prepa- OLDSTEIN REPLIES TO ZEILINGER: plainly false. Statements about his- ration that yielded the state of the G Because of the strong disagree- tory are not statements about history systems in the ensemble (before the ment expressed by Anton Zeilinger in books, and statements about dino- measurement). the first two paragraphs of his letter, saurs are not statements about fossil- However, the projection postulate I was surprised to find myself agree- ized dinosaur bones. And even state- says that a measurement on a single ing with much, if not most, of what ments concerned with the present, system determines the state of the he said after that—namely, that though they are typically based system (after the measurement). But Schrodinger's cat paradox is indeed a rather directly on observations—if not this contradicts the statistical nature consequence of what Zeilinger terms our own, then somebody else's—are of the quantum state. By itself, a sin- "a serious misunderstanding" of the usually not about those observations. gle measurement in quantum mechan- role of the quantum state; that when Although it is presumably true that ics cannot disclose a state unless one the quantum state of the cat is in a the justification of any statement has additional information not pro- superposition of dead and alive, then about the world must be based, at vided by that single measurement. (in Zeilinger's words) "that clearly least in part, on experience or obser- continued on page 89 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.215.225.131 On: Mon, 24 Aug 2015 23:19:45FEBRUARY 1999 PHYSICS TODAY 15 The truth probably lies somewhere be- tery of the Copenhagen interpretation LETTERS (continued from page 15) tween these extremes. However, re- is avoided by using this approach. Park gave the example of a school gardless of the status of the projec- Bohm summarized his analysis by where one knows that all the stu- tion postulate, it is not true that, as concluding that "we are able to obtain dents are of the same gender; a Nachtrieb claims, abandoning it "re- a complete objective description of the measurement on a single student solves the EPR paradox." This is be- process of the measurement, which determines the gender of the whole cause the EPR argument does not re- does not involve human observers in student population. quire the invocation of this postulate. any way at all" (page 607). 2. Why the postulate is "false." Real- What it does require, in addition to The notion that a measuring appa- istic measurement procedures exist the assumption of locality, is merely ratus is itself a physical system is not that violate the projection postulate.4 the quantum mechanical predictions unique to quantum mechanics. Many For example, some measurements de- for the correlations between the out- of the difficulties one encounters in, stroy the state completely, such as a comes of certain experiments—predic- for example, both special and general photon hitting a phosphorescent tions that have repeatedly been con- relativity—such as the so-called clock screen (measuring position), or a sil- firmed. Recent formulations of the paradox—can be avoided by dispens- ver atom hitting a plate in a Stern— EPR argument rarely, if ever, appeal ing with the assumption that ideal Gerlach experiment (measuring spin directly to the projection postulate. clocks measure proper time and by and position). And even in the original EPR paper, introducing simple physical models Other measurements could not pos- a version of the argument that made for clocks. I would argue, in fact, sibly yield an eigenstate of the observ- no such appeal was presented (along- that no physical theory is complete side one that did). unless it contains a complete descrip- able since the eigenstate would contra- 2 dict certain aspects of the experimen- In my article, moreover, I referred tion of the measurements it describes. tal setup. For example, if recording to the EPR paper merely to quote its One puzzle remains: Why did an eigenvalue of the momentum op- conclusion, that "the wave function Bohm in effect renounce BQMI by in- erator of a one-dimensional particle-in- does not provide a complete descrip- troducing BQMII, given that BQMII a-box left the particle in a momentum tion of the physical reality. ..." To requires certain postulates—such as eigenstate, elkx, the particle would no support that conclusion, I neither re- ad hoc restrictions on initial condi- longer be in the box, even if the walls lied upon nor mentioned the EPR ar- tions—that are not needed in BQMI? were infinitely high; the particle gument, but rather invoked entirely Furthermore, what problem was would be distributed uniformly over different considerations. solved by BQMII that could not be all space. As another example, if re- I note that if it could be argued dealt with by BQMI? To the best of cording an eigenvalue of the position convincingly that the projection postu- my knowledge, there is no way to dis- operator of a free particle left the par- late is "absurd," it would hardly be tinguish between the two. Thus, a ju- ticle in a position eigenstate, Stx-x^, necessary to argue that it is also dicious application of Occam's razor the particle would subsequently suffer "false and useless." But it is none would surely favor BQMI over BQMII. infinitely quick diffusion. of those things. Rather, it is merely As a postscript, I urge anyone in- 3. Why the postulate is "useless." No limited, an idealization useful for the terested in the measurement problem quantum mechanical calculations re- analysis of a restricted class of ex- (and even those who are not) to read quire the invocation of the von Neu- perimental situations. —SG chapter 22 of Bohm's book. mann projection postulate. Axiomatic quantum mechanics works just fine heldon Goldstein describes several References with the standard axioms: (a) defini- S reformulations of quantum me- 1. D. Bohm, Quantum Theory, Prentice- tion of the quantum state, repre- chanics that attempt to do away with Hall, New York (1951). sented by a density operator in Hil- the notion of an observer. He has, I 2. J. L. Anderson, Relativity Physics, Aca- bert space (unit trace, Hermitian, non- would argue, overlooked a much sim- demic Press, New York (1967), chap. 6. negative and so on); (b.) representation pler formulation than any of those he JAMES L. ANDERSON of most observables by linear, Hermi- discussed—namely, what I shall call ([email protected]) tian operators in Hilbert space; and Bohmian quantum mechanics I Stevens Institute of Technology (c) some form of equation of motion to (BQMI), to distinguish it from the Hoboken, New Jersey evolve the state in time. Bohmian mechanics (BQMII) dis- Abandoning the von Neumann pro- cussed in the second part of his OLDSTEIN REPLIES TO ANDERSON: jection postulate resolves the EPR article (April, page 38). G I very much agree with James paradox without having to concoct a The fundamental feature of BQMI, Anderson's assertion that "no physical new quantum mechanics. described in David Bohm's great book theory is complete unless it contains Quantum Theory,1 is the analysis of a complete description of the measure- References the measurement process as a physi- ments it describes," at least insofar 1. A. Einstein, B. Podolsky, N. Rosen, cal process. In this analysis, Bohm as potentially fundamental physical Phys. Rev. 47, 777(1935). recognized that a measuring appara- theories are concerned. However, in 2. H. Margenau, Phys. Rev. 49, 240 (1936). tus is itself a physical system whose the final chapter of his great book 3. J. L. Park, Philos. Sci. 35, 205 Q968). dynamics is also described by the (page 625), Bohm concluded that 4. H. Margenau, Philos. Sci. 25, 23 (1958). laws of quantum mechanics. A meas- "without an appeal to a classical ROBERT T. NACHTRIEB urement is then considered to be an level, quantum theory would have no ([email protected]) interaction, again described by the meaning. We conclude then that quan- Massachusetts Institute of Technology laws of quantum mechanics, between tum theory presupposes the classical Cambridge, Massachusetts the observed system and the appara- level and the general correctness of tus. No additional postulates are classical concepts in describing this OLDSTEIN REPLIES TO NACHTRIEB: needed to determine the consequences level; it does not deduce classical con- G Whereas the projection postu- of the measurement process, such as cepts as limiting cases of quantum late is, for Zeilinger, a triviality, for an assumed collapse of the wavefunc- concepts' (emphasis in original). Robert Nachtrieb it is an absurdity. tion. In particular, much of the mys- Bohm's comment points to an im- This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.215.225.131 On: Mon, 24 Aug 2015 23:19:45FEBRUARY 1999 PHYSICS TODAY 89 portant distinction between BQMI and BQMII, and it helps us under- stand why, little more than a year af- ter finishing his book, Bohm did in fact "renounce BQMI by introducing BQMII." Moreover, the abstract of the paper in which Bohm presented BQMII concludes as follows: "In any case, the mere possibility of such an interpretation proves that it is not necessary for us to give up a precise, rational, and objective description of individual systems at a quantum level of accuracy"1 BohnVs idea that, in Anderson's words, "a measuring apparatus is it- self a physical system whose dynam- OLDSTEIN REPLIES TO DOT- ics is also described by the laws of GSON: Concerning Allen quantum mechanics"—a notion that Dotson's quibble about meas- goes back at least to John von Neu- urement versus observation, I mann or Nevill Mott and certainly could have called my article did not originate with Bohm—is re- "Quantum Theory without Ob- quired for the very formulation of the servers or Measurements"; measurement problem, not its resolu- however, the title I chose is tion. As far as the measurement awkward enough. problem is concerned, this idea, with The work of Bell and which I agree, is part of the question, Hardy to which Dotson refers not part of the answer. u is very interesting, particu- Anderson implies that I wish to larly with regard to nonlocal- do away with the notion of an ob- ity. But it is not very rele- server." I do not. vant to deciding between, say, Reference Bohmian mechanics and ortho- dox quantum theory, which ac- 1. D. Bohm, Phys. Rev. 85, 166 (1952). count for the phenomena dis- —SG cussed by Bell and Hardy in a heldon Goldstein should realize surprisingly similar manner: S that standard quantum mechanics For both of those theories, the in itself is technically observer-free: "dynamical variables" (corresponding to the outcomes of the experiments) This identification provides an in- As Goldstein notes, it predicts, for an tuitively satisfying description of open observable, "the distribution of the that Bell and Hardy discuss should be regarded as "defined in connection systems with more or less unidirec- value that would be found were the tional particle flow—two-slit interfer- appropriate measurement performed" with specific experimental arrange- ments," to use Dotson's phrase. —SG ence, for example—in which the (March 1998, page 45). Thus, no fringes are formed by objectively real observers are actually required. particles following deterministic trajec- Naming the winner of the debate t first glance, Bohmian mechan- between Niels Bohr and Albert Ein- A ics and its "explanation" of the tories. However, it does not produce stein is still at issue, despite Gold- two-slit experiment (April 1998, page a satisfactory description of hidden stein's assertion favoring Einstein. 40) look marvelous. But isn't there trajectories in bound systems such as As Goldstein notes, Einstein believed some difficulty in applying these atoms, in which some or all of the that quantum mechanics might be su- ideas to problems involving tunneling, components of the probability current perseded some day by a more com- where the (quantum) kinetic energy are zero (under such circumstances, plete theory. However, it can be ar- is negative? flow velocities reveal little about hypo- gued that the current evidence, includ- WILLIAM G. HOOVER thetical particle velocities). The ing that stemming from the work of ([email protected]) Bohm interpretation ascribes this con- John Bell and Lucien Hardy, is most University of California at dition to electrons that are stationary simply explained by some form of Davis (Livermore campus) under the influence of counterbalanc- Bohr's conception of quantum states. Li verm ore, California ing gradients of the classical potential In that conception, dynamical vari- and a quantum potential—at least in ables that characterize a quantum egarding part two of Sheldon some directions. Although this pic- state are defined in connection with R Goldsteins article (April 1998, ture is self-consistent, a static model specific experimental arrangements, page 38), it should be noted that the of atomic electrons does not have the rather than as elements of reality as- de Broghe-Bohm theory derives hid- intuitive appeal of a dynamic one, sociated solely with the object, as Ein- den particle trajectories and veloci- and intuitive appeal is the point of stein would have wanted. ties that are compatible with Schro- such models, since we cannot observe ALLEN C. DOTSON dinger s equation by identifying them the trajectories. (dotson@ta rtan. sapc. edu) with the quantum mechanical prob- Eventually, a dynamic model of the St. Andrews Presbyterian College ability current and flow velocity, atom may be discovered that has hid- Launnburg, North Carolina respectively. den trajectories that are both comput- This article is copyrighted as indicated in the article. 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This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 131.215.225.131Circle numbe rOn: 87 oMon,n Reade 24 Augr Servic 2015e Car23:19:45d able and compatible with quantum which to base major scientific pro- mechanics. Meanwhile, it may be bet- Journal's History and gress of the future. This risk is espe- ter to just say that we are at liberty cially serious for the science of cell to postulate hidden deterministic par- Peer Review Process physiology, a field that is still in its ticle trajectories that more or less fol- Were Misrepresented infancy and in which revolutionary low the probability current in open upheavals are ongoing. systems (such as the two-slit interfer- am surprised to find myself mis- Recognizing all this, the editors of ence experiment), and that form closed I quoted—and to see certain other Physiological Chemistry and Physics orbits in bound systems (such as at- errors—in Paul Moran's response to and Medical NMR (formerly Physi- oms) consistent with some or all of the two letters to the editor (December ological Chemistry and Physics) have components of the probability current 1997, page 102) commenting on a long held to an official policy based being zero—and to leave it at that. book review he had written for your on the belief that scientific issues HENRY M. BRADFORD magazine. The following are five rea- should be settled by investigations (hen ry.bra dford@ns. sympa tico. ca) sons for my surprise. and open debate, not by appeals to Wolfville, Nova Scotia, Canada First, although Moran attributes anonymous judges. To achieve this to me two quotes about Raymond OLDSTEIN REPLIES TO HOOVER AND Damadian and alleges that they come goal, the editors have established G BRADFORD: My answer to Wil- from a casual conversation he and I over time a set procedure for evaluat- liam Hoover's question is, no. A parti- had back in the early 1970s, I do not ing submissions to the journal. It in- cle moving according to the Bohmian remember any such conversation cludes giving the author of a rejected equations of motion can do things that taking place. article the right to (1) rebut the rea- would be impossible classically. That Second, Moran quotes me as refer- sons given by the reviewers for rejec- is because Bohmian mechanics is not ring to Damadian as "Ray" but that is tion, (2) recommend to us a list of al- classical mechanics. Tunneling is a simply not something I would do, be- ternative competent reviewers and (3) prediction of—not a problem for— cause I know that nickname to be offen- in the case of ultimate rejection, have Bohmian mechanics. It should be re- sive to Damadian. Thus, I question us publish a brief priority note de- garded as a virtue that such seemingly that Moran's conversation was with me. scribing the article's key points and paradoxical behavior is explained Third, I don't recall that, as Moran its date of receipt by the journal. with so little difficulty—as, in fact, it alleges, Damadian published primar- The initial step in this procedure, is in Bohmian mechanics. Moreover, ily in Physiological Chemistry and however, remains the obligatory use the explanation does not involve any Physics (the journal's name in the of the orthodox peer review system. appeal to imaginary velocities. 1970s; Moran got that wrong too). The full procedure is described on the Henry Bradford faults the Bohm Rather, I remember his publishing front pages of each issue. interpretation because what it yields in such journals as Science, the Bio- physical Journal and the Proceedings It was thus with astonishment and is sometimes too simple. Atomic elec- dismay that we discovered that PHYS- trons in certain stationary states are, of the National Academy of Sciences, for Bohmian mechanics, at rest. Brad- as well as in what 111 call PC&P for ICS TODAY has been made into a tool ford complains that this is nonintui- short. I believe you will find that to publicize a \dlifying statement to tive. What this presumably means is Damadian's first publication in the effect that our journal does not that it conflicts with our classical in- PC&P did not occur until 1975. use the orthodox review system. The tuitions, as well as with the Solar Fourth, contrary to Moran's asser- statement appears in Paul Moran's re- System model of the (Bohr) atom that tions, all manuscripts submitted to ply to a couple of letters to the editor. we first learn. In other words, the PC&P were reviewed using orthodox In making such a spurious statement, behavior is unfamiliar. But why reviewing procedures. Moran—who evidently knows so little should a new theory predict only Fifth, although Moran claims that about our journal that he cannot even familiar behavior? I told him in the early 1970s that get the name right, let alone our By suitably complicating its defin- Damadian had already acquired the evaluation procedure—defames not ing dynamical equations, we could rights to publish PC&P, Damadian's only those of us who have run the transform Bohmian mechanics into acquisition did not occur until later in publication (I am the current editor-in- a theory in which atomic electrons that decade. Furthermore, although chief) but also all the scientists who move in a manner more consistent the journal's name was changed at have published their work in our with our prejudices. But such consis- that time {"and Medical NMR" was pages over the last three decades. tency would be of far less value to added), no change was made in the journal's editorial policy. GILBERT N. LING me than the simplicity sacrificed to ([email protected]) obtain it. CARLTON F. HAZLEWOOD Physiological Chemistry I would not say that the point of

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