O PINION Quantum Theory Needs No ‘Interpretation’

Christopher A. Fuchs and Asher Peres ecently there has been a spate of of our experimental activity, then we carry an umbrella. Probability theory Rarticles, reviews, and letters in must be prepared for that, too. is simply the quantitative formulation TODAY promoting various The thread common to all the non- of how to make rational decisions in “interpretations” of quantum theory standard “interpretations” is the the face of uncertainty. (see March 1998, page 42; April 1998, desire to create a new theory with fea- We do not deny the possible exis- page 38; February 1999, page 11; July tures that correspond to some reality tence of an objective reality independ- 1999, page 51; and August 1999, page independent of our potential experi- ent of what observers perceive. In par- 26). Their running theme is that from ments. But, trying to fulfill a classical ticular, there is an “effective” reality the time of quantum theory’s emer- worldview by encumbering quantum in the limiting case of macroscopic gence until the discovery of a particu- mechanics with hidden variables, phenomena like detector clicks or lar interpretation, the theory was in a multiple worlds, consistency rules, or planetary motion: Any observer who crisis because its foundations were spontaneous collapse, without any happens to be present would acknowl- unsatisfactory or even inconsistent. improvement in its predictive power, edge the objective occurrence of these We are seriously concerned that the only gives the illusion of a better events. However, such a macroscopic airing of these opinions may lead understanding. Contrary to those description ignores most degrees of some readers to a distorted view of desires, quantum theory does not freedom of the system and is neces- the validity of standard quantum describe physical reality. What it does sarily incomplete. Can there also be a mechanics. If quantum theory had is provide an algorithm for computing “microscopic reality” where every been in a crisis, experimenters would probabilities for the macroscopic detail is completely described? No have informed us long ago! events (“detector clicks”) that are the description of that kind can be given Our purpose here is to explain the consequences of our experimental by quantum theory, nor by any other internal consistency of an “interpre- interventions. This strict definition of reasonable theory. John Bell formally tation without interpretation” for the scope of quantum theory is the only showed3 that any objective theory giv- . Nothing more is interpretation ever needed, whether ing experimental predictions identical needed for using the theory and by experimenters or theorists. to those of quantum theory would nec- understanding its nature. To begin, Quantum probabilities, like all essarily be nonlocal. It would eventu- let us examine the role of experiment probabilities, are computed by using ally have to encompass everything in in science. An experiment is an active any available information. This can the universe, including ourselves, and intervention into the course of include, but is not limited to informa- lead to bizarre self-referential logical Nature: We set up this or that exper- tion about a system’s preparation. paradoxes. The latter are not in the iment to see how Nature reacts. We The mathematical instrument for realm of physics; experimental physi- have learned something new when we turning the information into statisti- cists never need bother with them. can distill from the accumulated data cal predictions is the probability rule We have experimental evidence a compact description of all that was postulated by Max Born.1 The conclu- that quantum theory is successful in seen and an indication of which fur- siveness of Born’s rule is known today the range from 10–10 to 1015 atomic ther experiments will corroborate to follow from a theorem due to radii; we have no evidence that it is that description. This is what science Andrew Gleason.2 It is enough to universally valid. Yet, it is legitimate is about. If, from such a description, assume that yes–no tests on a physical to attempt to extrapolate the theory we can further distill a model of a free- system are represented by projection beyond its present range, for instance, standing “reality” independent of our operators P, and that probabilities are when we probe particle interactions interventions, then so much the bet- additive over orthogonal projectors. at superhigh energies, or in astro- ter. Classical physics is the ultimate Then there exists a r physical systems, including the entire example of such a model. However, describing the system such that the universe. Indeed, a common question there is no logical necessity for a real- probability of a “yes” answer is tr(rP). is whether the universe has a wave- istic worldview to always be obtain- The compendium of probabilities rep- function. There are two ways to able. If the world is such that we can resented by the “” r cap- understand this. If this “wavefunction never identify a reality independent tures everything that can meaningful- of the universe” has to give a complete ly be said about a physical system. description of everything, including CHRIS FUCHS , previously the Lee DuBridge Here, it is essential to understand ourselves, we again get the same Prize Postdoctoral Fellow at Caltech, is now a Director-Funded Fellow at Los Alamos that the validity of the statistical meaningless paradoxes. On the other National Laboratory. His daytime research nature of quantum theory is not hand, if we consider just a few collec- focuses on theory and restricted to situations where there tive degrees of freedom, such as the quantum computation. ASHER PERES is the are a large number of similar systems. radius of the universe, its mean den- Gerard Swope Distinguished Professor of Statistical predictions do apply to sin- sity, total baryon number, and so on, Physics at Technion— Institute of Tech- gle events. When we are told that the we can apply quantum theory only to nology, in Haifa, Israel. He is the author of probability of precipitation tomorrow these degrees of freedom, which do not Quantum Theory: Concepts and Methods is 35%, there is only one tomorrow. include ourselves and other insignifi- (Kluwer, Dordrecht, 1995). This tells us that it is advisable to cant details. This is not essentially

70 MARCH 2000 PHYSICS TODAY © 2000 American Institute of Physics, S-0031-9228-0003-230-0 Downloaded 25 Sep 2012 to 162.105.13.196. Redistribution subject to AIP license or copyright; see http://www.physicstoday.org/about_us/terms different from quantizing the mag- teleportation process.4 In order to spond to quantum states. This analo- netic flux and the electric current in a teleport a quantum state from one gy is misleading: Attributing reality SQUID while ignoring the atomic photon to another, the sender (Alice) to quantum states leads to a host of details. For sure, we can manipulate and the receiver (Bob) need to divide “quantum paradoxes.” These are due a SQUID more easily than we can between them a pair of photons in a solely to an incorrect interpretation of manipulate the radius of the uni- standard entangled state. The exper- quantum theory. When correctly used, verse, but there is no difference in iment begins when Alice receives quantum theory never yields two con- principle. another photon whose polarization tradictory answers to a well-posed Does quantum mechanics apply to state is unknown to her but known to question. In particular, no wavefunc- the observer? Why would it not? To be a third-party preparer. She performs tion exists either before or after we quantum mechanical is simply to be a measurement on her two photons— conduct an experiment. Just as clas- amenable to a quantum description. one from the original, entangled pair sical cosmologists got used to the idea Nothing in principle prevents us from and the other in a state unknown to that there is no “time” before the big quantizing a colleague, say. Let us her—and then sends Bob a classical bang or after the big crunch, so too examine a concrete example: must we be careful about using The observer is Cathy (an “before” and “after” in the quan- experimental ) who tum context. enters her laboratory and sends Quantum theory has been a photon through a beam split- accused of incompleteness ter. If one of her detectors is because it cannot answer some activated, it opens a box con- questions that appear reason- taining a piece of cake; the able from the classical point of other detector opens a box with view. For example, there is no a piece of fruit. Cathy’s friend way to ascertain whether a sin- Erwin (a theorist) stays outside gle system is in a pure state or is the laboratory and computes part of an entangled composite Cathy’s wavefunction. Accord- system. Furthermore, there is no ing to him, she is in a 50/50 dynamical description for the superposition of states with “collapse” of the wavefunction. some cake or some fruit in her In both cases the theory gives no stomach. There is nothing answer because the wavefunc- wrong with that; this only rep- tion is not an objective entity. resents his knowledge of Cathy. Collapse is something that hap- She knows better. As soon as pens in our description of the one detector was activated, her system, not to the system itself. wavefunction collapsed. Of “What do you mean, ‘a quantum fluctuation?’ Likewise, the time dependence course, nothing dramatic hap- Didn’t we discuss cause and effect?” of the wavefunction does not pened to her. She just acquired represent the evolution of a the knowledge of the kind of food she message of only two bits, instructing physical system. It only gives the evo- could eat. Some time later, Erwin him how to reproduce that unknown lution of our probabilities for the out- peeks into the laboratory: Thereby he state on his photon. This economy of comes of potential experiments on acquires new knowledge, and the transmission appears remarkable, that system. This is the only meaning wavefunction he uses to describe because to completely specify the of the wavefunction. Cathy changes. From this example, it state of a photon, namely one point in All this said, we would be the last is clear that a wavefunction is only a the Poincaré sphere, we need an infin- to claim that the foundations of quan- mathematical expression for evaluat- ity of bits. However, this complete spec- tum theory are not worth further ing probabilities and depends on the ification is not what is transferred. The scrutiny. For instance, it is interesting knowledge of whoever is doing the two bits of classical information serve to search for minimal sets of physical computing. only to convert the preparer’s informa- assumptions that give rise to the the- Cathy’s story inevitably raises the tion, from a description of the original ory. Also, it is not yet understood how issue of reversibility; after all, quan- photon to a description of the one in to combine quantum mechanics with tum dynamics is time-symmetric. Can Bob’s possession. The communication gravitation, and there may well be Erwin undo the process if he has not resource used up for doing that is the important insight to be gleaned there. yet observed Cathy? In principle he correlated pair that was shared by However, to make quantum mechan- can, because the only information Alice and Bob. ics a useful guide to the phenomena Erwin possesses is about the conse- It is curious that some well-inten- around us, we need nothing more quences of his potential experiments, tioned theorists are willing to aban- than the fully consistent theory we not about what is “really there.” If don the objective nature of physical already have. Quantum theory needs Erwin has performed no observation, “observables,” and yet wish to retain no “interpretation.” then there is no reason he cannot the abstract quantum state as a sur- reverse Cathy’s digestion and memo- rogate reality. There is a temptation References ries. Of course, for that he would need to believe that every quantum system complete control of all the microscop- has a wavefunction, even if the wave- 1. M. Born, Zeits. Phys. 37, 863 (1926); 38, ic degrees of freedom of Cathy and her function is not explicitly known. 803 (1926). 2. A. M. Gleason, J. Math. Mech. 6, 885 laboratory, but that is a practical Apparently, the root of this tempta- (1957). problem, not a fundamental one. tion is that in classical mechanics 3. J. S. Bell, Physics 1, 195 (1964). The peculiar nature of a quantum phase space points correspond to 4. C. H. Bennett, G. Brassard, C. Crépeau, state as representing information is objective data, whereas in quantum R. Jozsa, A. Peres, and W. K. Wootters, strikingly illustrated by the quantum mechanics Hilbert space points corre- Phys. Rev. Letters 70, 1895 (1993). ᭿

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