Why Physics Needs Quantum Foundations

7/29/2019 Why Physics Needs Quantum Foundations

1/4

arXiv:1003.5008v1[quant-ph]25Mar2010

Why Physics Needs Quantum Foundations

by Lucien Hardy and Robert Spekkens

Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, Canada N2L 2Y5

Quantum theory is a peculiar creature. It was born as atheory of atomic physics early in the twentieth century, butover time its scope has broadened, to the point where itnow underpins all of modern physics with the exception ofgravity. It has been verified to extremely high accuracyand has never been contradicted experimentally. Yetdespite its enormous success, there is still no consensusamong physicists about what this theory is saying aboutthe nature of reality. There is no question that quantum

theory works well as a tool for predicting what will occurin experiments. But just as understanding how to drivean automobile is different from understanding how itworks or how to fix it should it break down, so toois there a difference between understanding how to usequantum theory and understanding what it means. Thefield of quantum foundations seeks to achieve such anunderstanding. In particular, it seeks to determine thecorrect interpretation of the formalism. It also seeks todetermine the principles that underlie quantum theory.Why do we have a quantum world as opposed to a classicalworld or some other kind of world entirely?

There are many motivations for pursuing foundational re-search. One is the development of quantum technologies,such as quantum computation and quantum cryptography.A better understanding of the theory facilitates the iden-tification and development of these new technologies, theharnessing of the power of nonclassicality. Another moti-vation is that quantum theory is likely not the end of theroad. If we are to move beyond it, then it is important toknow which parts can be changed or generalized or aban-doned. Finally, there are the personal motivations of indi-vidual researchers: because quantum theory is very mys-terious and counterintuitive and surprising and it seems todefy us to understand it. And so we take up the challenge.

Operationalism and realism

Broadly speaking, researchers in quantum foundations canbe divided into two camps. There are the operationalistsand there are the realists. For the operationalist, operatorsin Hilbert space represent preparation and measurement

procedures, specified as lists of instructions of what to doin the lab. They are recipes with macroscopic activities asingredients. The theory merely specifies what probabilitiesof outcomes will be observed when a given measurementfollows a given preparation. For the realist, there issome deeper reality underlying the equations of quantumtheory that ultimately accounts for why we see the relativefrequencies we do. For the realist, quantum theory needsan interpretation. Does the wave function describe a real

entity? Are there extra hidden variables in addition to thewave function needed to fully describe a quantum system?

A classic example of the power of applying operationalthinking is Einsteins approach to special relativity. Bycarefully considering how to synchronise distant clocks, hewas led to abandon the hitherto cherished notion of ab-solute simultaneity. A good example of the successful ap-plication of realism is the atomic hypothesis. In this case,John Dalton and others were right to insist on the realityof atoms (in opposition to operationalists such as ErnstMach). It led to a theory for Brownian motion(Einsteinagain), the theory of statistical mechanics, and ultimately

much of modern physics.

Historically, both approaches were important in the de-velopment of quantum theory. Heisenbergs 1925 paperon matrix mechanics, which ushered in the modern ageof quantum theory, began with the sentence The presentpaper seeks to establish a basis for theoretical quantummechanics founded exclusively upon relationships betweenquantities which in principle are observable. This was op-erational thinking. In parallel to this, de Broglie positedthe existence of waves to describe quantum phenomenaand Schrodinger found an equation for their motion. Thiswas realist thinking.

In modern research into the foundations of quantum the-ory, both operationalism and realism are alive and well. Bythinking operationally, a general mathematical frameworkhas been developed which can accommodate a wide varietyof probabilistic theories. Quantum theory fits very com-fortably into this framework as a special case and so canbe easily understood in operational terms. Much progress
http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1http://arxiv.org/abs/1003.5008v1


2/4


has been made recently in understanding the deeper math-ematical structure of quantum theory in the context ofthis mathematics of operationalism. For example, manyfeatures of quantum theory (such as the impossibility ofbuilding a machine that can clone quantum states) turnout to be features of any non-classical probabilistic the-ory. These tools also contribute to the program of recon-structing quantum theory deriving its abstract mathemat-ical structure from natural postulates, just as the Lorentztransformations are derived from Einsteins postulates forspecial relativity.

But operationalism is not enough. Explanations do notbottom out with detectors going click. Rather, theexistence of detectors that click is the sort of thing that wecan and should look to science to explain. Indeed, scienceseeks to explain far more than this, such as the existence

of human agents to build these detectors, the existence ofan earth and a sun to support these agents, and so on tothe existence of the universe itself. The only way to meetthese challenges is if explanations do not bottom out withcomplex entities and everyday concepts, but rather withsimple entities and abstract concepts. This is the view ofthe realist. Without adopting some form of realism, it isunclear how one can seek a complete scientific world-view,incorporating not just laboratory physics, but all scientificdisciplines, from evolutionary biology to cosmology. It istrue of course that all of our evidence will come to us inthe form of macroscopically observable phenomena, butwe need not and should not restrict ourselves to these

concepts when constructing scientific theories. For therealist, then, we need an interpretation of quantum theory.

There are already plenty of candidates to choose from.There is the pilot wave model of Louis de Broglie andDavid Bohm in which the wavefunction guides the motionof actual particles according to a well defined equation.There is the many worlds interpretation of Hugh EverettIII in which the universe is regarded as splitting into manycopies every time the wavefunction evolves into a superpo-sition of distinct situations. There are also collapse modelsin which extra terms are added to the Schrodinger equationto cause a collapse of the wavefunction when sufficiently

macroscopic possibilities become superposed. Many moreideas for interpretations are in the making today. Caseshave been made for each by their respective proponents,but none has yet proven sufficiently compelling to achievea scientific consensus. So research on these issues contin-ues.

Ultimately, we expect that both operationalism and real-

ism will play an important methodological role in futureresearch. Operationalism is, at least, a useful exercise forfreeing the mind from the baggage of preconceptions aboutthe world, as Einstein did when he showed that the no-tion of absolute simultaneity was unfounded. As such itcan provide a minimal interpretation, some conceptual andmathematical scaffolding on which to build. On the otherhand, the extra commitments, constraints and details ofa realist model can also be a virtue. Realist models aremore falsifiable, they typically suggest new and interestingquestions (questions that may uncover novel consequencesof a theory), and they often suggest avenues for modifyingand generalizing the theory.

The foundational roots of quantum

information theory

The field of quantum foundations provides many examplesof how basic research guided by a desire for deeperunderstanding can lead to discoveries of great practicalinterest. Quantum information science serves as thebest example. To first approximation, it was born oftwo communities: on the one hand, computer scientistsand information theorists, and on the other, physiciststhinking about the foundations of quantum theory. Ifthe name of a field indicated its parentage, then theQuantum in Quantum Information would refer toQuantum Foundations.

Since those early days, there has been a slow but steadymarch towards quantum technologies becoming practical.Quantum cryptographic systems, for instance, are nowavailable commercially. Meanwhile, progress on the theo-retical side has shown how one can achieve stronger formsof security than previously conceived. One of the mostcelebrated cryptographic applications of quantum theoryis key distribution: the ability to establish a shared se-cret key among distant parties over a public channel insuch a way that one can reliably detect the presence ofan eavesdropper. Recent work has shown that under thevery conservative assumption that superluminal signalling

is impossible, one can achieve key distribution even ifthe would-be eavesdropper has the advantage of provid-ing the very devices that are used by the communicatingparties.[1,2]

This is practical stuff, but the path that led to such resultsstarts with foundational research. In 1964, John Bell wasconsidering the question of whether there is an interpreta-tion of quantum theory in terms of hidden variables. He

2 Physics in Canada


3/4


had been pondering the argument by Einstein, Podolskyand Rosen in favor of the incompleteness of the quantumdescription and thinking about various theorems that pur-ported to show the impossibility of such completions. Hewas also studying the pilot wave model of deBroglie andBohm. He noted that this theory postulated superluminalcausal influences and wondered whether this might be trueof all realist models of quantum theory. Once the questionwas asked, it was not long before he was able to provethat this is indeed the case a theorem that now bears hisname.[3]

Bells theorem is a profound result because it demonstratesa tension between the two pillars upon which modernphysics is built quantum physics and relativity theory.Since its discovery, physicists have been puzzling over it.One such person was Artur Ekert. In 1991, he realized that

the statistical correlations central to Bells theorem couldbe used to achieve secure key distribution.[4] Although adifferent quantum protocol for key distribution had beendeveloped seven years earlier by Charlie Bennett and GillesBrassard[5], it was Ekerts protocol that ultimately led tothe results mentioned above the possibility of achievingsecurity regardless of the provenance of the devices.

The theory of entanglement the property of quantumstates that is critical to the Einstein-Podolsky-Rosen ar-gument and Bells theorem is another example of thepractical payoff of foundational thinking. In 1980, WilliamWootters had just completed a Ph.D. thesis on a founda-

tional question: from what principles can the Born ruleof quantum theory be derived? Important to his consid-erations was a task known as quantum state tomography.This is an attempt to infer the identity of a quantum stateby implementing many different measurements on a largenumber of samples of it. In the fall of 1989, Asher Peres,another foundational researcher, asked whether joint mea-surements on a pair of systems might yield better tomogra-phy than separate measurements. They were able to findstrong numerical evidence that this was indeed the case.[6]

It seemed, therefore, that if a pair of similarly preparedparticles was separated in space, an experimenter would beless able to identify their state than if they were together.

In other words, there is a limit to how much informationabout the state can be accessed by local means a kindof nonlocality. In 1992, Charlie Bennett heard a talk byWootters on the subject and asked whether the nonlocal-ity that seemed to be inherent in entangled states mightprovide a way of achieving state tomography on separatedsystems with the same success that could be achieved ifthey were proximate.

Again, once the question was asked, it took only a fewdays for Wootters, Bennett, Peres and their co-workers(Gilles Brassard, Claude Crepeau and Richard Jozsa) toanswer it. Yes, it could be done.[7] The key insight wasthat by consuming a maximally entangled state (i.e. us-ing it in a manner that ultimately destroys it), the quan-tum state of a system could be transferred from one partyto another distant party using only local operations andclassical communication. The trick was dubbed quan-tum teleportation by its authors. Several discoveries inquantum information theory (including Ekerts key distri-bution protocol) had shown that entanglement was useful,and with the discovery of teleportation, it became espe-cially obvious: entanglement was a resource. This changein perspective prompted researchers to ask many new andinteresting questions about entanglement. The result hasbeen a dramatic increase in our understanding of the phe-

nomena, leading to applications across all subdisciplinesof quantum information science (cryptography, communi-cation and computation) and further afield (for instance,in new density matrix renormalization group methods forsimulating quantum many-body systems).

One final story. Early in the history of quantum infor-mation theory, when most researchers were still thinkingabout quantum theory as imposing upon us additional lim-itations relative to what we would face in a world thatwas governed by a classical theory, David Deutsch wasthinking differently. He was looking to identify tasks forwhich quantum theory provided an advantage. In the mid-

eighties, his unique perspective led him to write one ofthe very first articles on quantum computation, an arti-cle that prepared the ground for important subsequentdiscoveries.[8] What led Deutsch to perform this seminalwork? He was thinking about the information-processingconsequences of Everetts many worlds interpretation ofquantum theory.

Quantum foundations meets quantum

gravity

Perhaps the holy grail of modern physics is a theory ofquantum gravity. We need to find a theory that reducesto quantum theory in one limit and to general relativity inanother, and that makes new predictions which are sub-sequently verified in experiments. This has been an openproblem since the birth of quantum theory, yet we still donot have a theory of quantum gravity. The problem is diffi-cult because there are deep conceptual differences betweengeneral relativity and quantum theory. Consequently, the

Physics in Canada 3


4/4


two theories have very different mathematical structures.

In the past, when two less fundamental theories have beenunified into a deeper, more fundamental theory, the unifi-cation has typically required an entirely new mathemati-cal framework, motivated by conceptual insights from thetwo component theories. If this is the case for quantumgravity, then foundational thinking is likely to be useful.Does quantum gravity call for a new type of probabilistictheory? Which of the postulates of quantum theory (inwhatever formulation) will have to be modified or aban-doned, if any? A similar type of conceptual thinking aboutthe foundations of general relativity is also likely to be sig-nificant. If we have a mathematical framework that is richenough to contain a theory of quantum gravity (in muchthe same way that the mathematics of Hilbert space is suf-ficient for quantum theory and the mathematics of tensor

calculus is sufficient for general relativity) then we couldexpect that a few suitably chosen postulates would narrowus down to the right theory. It is in the construction ofthis framework and the selection of these postulates thatthe conceptual and mathematical tools of quantum foun-dations are likely to be useful.

Send off

The field of quantum foundations does not merely existto tidy up the mess left behind after the physics has beendone. Rather it should be regarded as part and parcel ofthe great project of theoretical physics - to gain an everbetter understanding of the world around us.

In particular, researchers in the field are striving toachieve a deeper understanding of the conceptual andmathematical structure of quantum theory. It is atestament to the importance of this sort of pure enquirythat the ideas of quantum foundations have found such acompelling application in the field of quantum informationscience. It was John Bell thinking about hidden variablesthat ultimately led to many practical results in quantumcryptography; it was William Wootters asking Why the

Born rule? that guided us down the last stretch of thepath that culminated in understanding entanglement asa resource, and it was David Deutsch thinking about themany worlds interpretation of quantum theory that laidthe foundations of quantum computing.

We should not expect that quantum information theorywill be the only substantial application of ideas fromquantum foundations. They may well play a significant

role in the construction of a theory of quantum gravity.They may even spawn entirely new fields of research thatwe cannot currently predict. Thinking about foundationspays off in the long run. David Mermin once summarizeda popular attitude towards quantum theory as Shut upand calculate!. We suggest an alternative slogan: Shutup and contemplate!

ACKNOWLEDGEMENTS

Research at Perimeter Institute is supported by the Gov-ernment of Canada through Industry Canada and by theProvince of Ontario through the Ministry of Research andInnovation.

REFERENCES1. J. Barrett, L. Hardy, and A. Kent, No Signaling and

Quantum Key Distribution, Phys. Rev. Lett. 95, 010503(2005).

2. A. Acn, N. Gisin, Ll. Masanes, From Bells Theorem toSecure Quantum Key Distribution, Phys. Rev. Lett. 97,120405 (2006).

3. J. S. Bell, On the Einstein-Podolsky-Rosen paradox, Physics(Long Island City, N.Y.) 1, 195 (1964).

4. A. K. Ekert, Quantum cryptography based on Bells theorem,Phys. Rev. Lett. 67, 661 (1991).

5. C. H. Bennett and G. Brassard, Quantum Cryptography:Public key distribution and coin tossing, in Proceedings of

the IEEE International Conference on Computers, Systems,and Signal Processing, Bangalore, p. 175 (1984).6. A. Peres and W. K. Wootters, Optimal detection of quantum

information, Phys. Rev. Lett. 66, 1119 (1990).7. C. H. Bennett, G. Brassard, C. Crpeau, R. Jozsa, A. Peres,

W. K. Wootters, Teleporting an Unknown Quantum Statevia Dual Classical and Einstein-Podolsky-Rosen Channels,Phys. Rev. Lett. 70, 1895 (1993).

8. D. Deutsch, Quantum theory, the Church-Turing principleand the universal quantum computer, Proc. R. Soc. Lond. A400 97 (1985).

4 Physics in Canada

Documents

Why Physics Needs Quantum Foundations