cosmology. But there would be a problem of quantum cosmology even if spacetimewere flat and there were no gravity. And there is a problem of quantum gravity evendisregarding quantum cosmology. The two problems are logically independent, andwe might be able to find a consistent quantum theory of gravity even within theframework of current quantum theory, with its distinction between quantum systemand classical observer.

One final light note of disagreement: Lee expresses the hope that the differentschools of thinking in quantum gravity will ultimately all turn out to be (at least inpart) right. As for me, I often worry they might all turn out, ultimately, to be wrong!(But, after all, Lee is an optimistic American, and I a disenchanted Europeany)

I am sure the reader will find his or her own reasons to disagree with Lee’s ideasand speculations. But, if anything, this increases the interest of this challenging andstimulating book. Lee raises problems, and is able to effectively introduce thereader—the cultivated thinker, as well as the scientifically illiterate reader—into theflowering of the ideas of contemporary fundamental physics, as well as into itscontroversial aspects. Best of all, the book clearly conveys, with humility, theenthusiasm involved in the best of current theoretical activity in physics.

C. RovelliCPT, Universite de Aix-Marsille II,

Case 907 Luminy, F-13288 Marseille, France

E-mail address: rovelli@cpt.univ-mrs.fr

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From physics to philosophy

J. Butterfield and C. Pagonis (Eds.); Cambridge University Press, Cambridge, 1999,235 pp., UK d40.00 hardback, ISBN 0-521-66025-4

The philosophy of physics has emerged in recent years as a vibrant and importantinterdisciplinary branch of science. It is a ‘hard’ subject, combining the best impulsesof its component parts—the mathematical rigour of theoretical physics, andphilosophy’s concern for conceptual clarity. The latter is lamentably missing frommuch of contemporary theoretical physics.

Despite the obvious fact that their subject has been shaped by the philosophicalmores of its founders (as well as by social and political factors, but that is anotherstory), many physicists react with suspicion to ‘mere philosophy’, an area theyperceive as unlikely to be of use to them in their work. Yet, of course, knowingly ornot, they are drenched in philosophy—in outlook, in language, and in the veryrejection of certain categories of investigation as irrelevant. Examples where thismatters are legion. For example, Bohr’s philosophical musings on the interpretationof the uncertainty principle dominated a generation of textbooks, to the detriment of

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the presentation. And the new science of quantum information is fundamentallyrooted in Einstein and Schrodinger’s analysis of the implications of entanglement inthe context of interpretation. Part of the remit of the philosophy of physics is tobring out and analyse the fundamental role of philosophy in these sorts of cases.

Calling attention to the philosophical biases and underpinnings of science is anhonourable and necessary tradition, but is modern philosophy of physics more thanjust carping from the sidelines, a kind of jolt to the conscience of those physicistswho happen to notice it? It does not need to be, of course, but I believe it is more;many of its practitioners are active participants in the thick of current problems oftheoretical physics, and the insights being offered are of practical relevance there, aswell as in philosophy. This admirable volume, a collection of essays honouringMichael Redhead on his retirement, illustrates the point. Moreover, the book is agood place to find out what contemporary philosophers of physics regard asimportant problems. It is good, not just because of the breadth of topics discussed,and the fact that, without exception, the articles are well written and stimulating, butbecause some contain important results I have not seen elsewhere.

An example of the latter is Arthur Fine’s analysis of Lucien Hardy’s (1993)‘without inequalities’ demonstration that quantum mechanics is nonlocal. Hardy’swork was a remarkable step, but the interpretation of mathematical theorems inquantum mechanics is notoriously subtle. Fine argues that Hardy’s argumentinvokes not just a locality assumption about any putative hidden variables, but alsotacitly assumes conditions on their joint distributions which are, in general, alreadyinconsistent with quantum theory. He even gives a local hidden-variable modelcovering the Hardy example. Hence, a test confirming quantum mechanics in thiscontext would not establish ‘nonlocality’. These are important observations,although unlikely to be the final word.

Other notable observations are made in this book. Harvey Brown discusses avariety of issues connected with the objectivity of quantities in quantum mechanicsin the context of symmetries of the theory, particularly gauge and coordinatetransformations. In the process, he corrects many misconceptions about basic issues,such as the transformation laws of position and momentum, or the assumptions thatgo into the gauge principle which give it physical content. Brown points out thatmany physical quantities, such as stationary states and the geometric phase, are notinvariant with respect to elements of the Galilean group. He shows that the notion ofa precise value of an observable is a relational property in that sharpness is notpreserved under a translation of the coordinates. These results do not mean thatparticular inertial frames are singled out, or cast doubt on the objective character ofthe quantities considered. They emphasize, rather, the strongly relational characterof objectivity in quantum mechanics. One cannot help feeling that much of thismaterial should be in physics textbooks.

The fundamental role of group theory in quantum mechanics is discussed in adifferent context by Steven French. His purpose is to illustrate a scheme that aims toformalize the relationship between mathematics and physics by embedding the latterin a certain mathematical structure. This is part of a programme to develop a ‘theoryof theories’. As a physicist, I have a nagging Feyerabendian doubt when presented

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with such schemes that, if they are sufficiently sensitive to the almost infinitely subtlerelations between the various components of science, they will at most apply to oneexample. I am unfamiliar with this field, but would guess, since mathematics is butone component of the language of physics, that there are formidable problemsinvolved if one aims to make reference in the scheme to actual physical practice—which involves a variety of additional informal and often unstated concepts (thismay be what the author intends by the idea of partial isomorphism). Perhaps a goodtest of the value of the scheme would be application to other examples.

A clutch of articles address issues connected with the introduction of ‘beables’ inthe quantum theory—quantities for which a measured value is a pre-existingpossessed value—the celebrated example being the de Broglie–Bohm theory. In oneof these articles, Rob Clifton sets out to distil in an algebraic context the keycharacteristics of a general theory of quantities that might be afforded beable status.Clifton aims to include the possibilities that not all observables are beables (therebycircumventing, for example, ‘no-hidden-variable’ theorems), and that the choice ofbeables may be dependent on the quantum state (thereby including, for example,modal interpretations). This is a somewhat abstract construction based on C*-algebras and the author wisely checks his results along the way by referring back tothe Bohm theory. But the approach captures other theories that have apparently notbeen investigated before, a notable property being that, in general, the beables do notcommute. Clifton’s construction is impressive, but presumably this is only the firstinstalment in that the theory needs to be completed by specifying the dynamicalequations obeyed by the beables. The author draws inspiration from John Bell’scomments on the form a beable theory should take. Bell argued, in particular, that inBohm’s theory, spin is an example of an observable that should not be regarded as abeable. This is a rather subtle question, for there exists a Bohm-like theory in whichspin is attributed to a particle at the outset through possessed values of orientation(as well as location). One might argue that the additional variables simply extend theposition-beable configuration space, and it is not clear whether one can ‘measure’ theadditional angular variables; but this does, nevertheless, seem to be a putativecounterexample to the usual claim about the treatment of spin in Bohm’s theory.Moreover, and perhaps ironically, it is conceivable that this type of theory fallswithin the orbit of Clifton’s algebraic construction.

A second article on the Bohmian theme, by Jim Cushing and Gary Bowman, looksat ways of distinguishing the Bohm and Copenhagen interpretations. At present, thequestion of whether these interpretations are empirically equivalent is somewhatmurky, so the authors concentrate on the distinct insights provided by the Bohmtheory that might prompt new avenues of physical enquiry. These are reviewed in thecontext of the closely connected problems of the classical limit of quantummechanics and quantum chaos. The authors argue that the specification of theconditions under which classical-like or chaotic behaviour may be generally expectedto occur has not been satisfactorily solved within the conventional quantumformalism. In contrast, the conceptual and mathematical machinery of the Bohmtheory naturally allows one to state precise criteria to determine when one is enteringthese regimes.

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The Bohm theory exhibits several interesting properties; for example, that chaosmay be obtained in a quantum context where it is absent in the classical case, andvice versa. However, in the act of making precise the conditions under whichclassical behaviour will be obtained as a special case of quantum behaviour, ittranspires that certain valid parts of the classical description cannot be obtained aslimiting cases within the Bohm model. Actually, this should not necessarily beregarded as a ‘problem’ in the sense of a defect that must be remedied. Rather, it maybe an insight of Bohm’s interpretation that quantum mechanics is not a universaltheory. As the authors state, this is currently an open question. In this connection,however, it should be mentioned that there is another property of the Bohm theorythat the authors do not mention that is relevant to the issues they discuss and whichdoes appear to be a problem: the nonuniqueness of the Bohm theory. There isconsiderable underdetermination in this theory in that many different choices ofguidance law can be postulated compatible with the same quantal distribution ofparticle positions. Indeed, it may be shown, starting from relativistic considerations,that when applied to electrons, the original non-relativistic de Broglie–Bohm law isincorrect. The problem of underdetermination may not impinge on generalconsiderations on the relation between the classical and quantum descriptions, butit surely does modify the detailed structure of the trajectories, such as is involved inclassifying the conditions for the onset of chaos. Therefore, it may be premature toapply trajectory ideas in areas such as chaos until the issue of uniqueness is sortedout; the pertinent features of the congruence implied in the original de Broglie–Bohmmodel may be artefacts in that they are not exhibited by a flow determined by analternative guidance law.

In a further thoughtful article that directly addresses the Bohm theory, SimonSaunders investigates the ontology of the relativistic pilot-wave theory. He argues asfollows. First, he notes the virtue of the pilot-wave theory is that it provides asolution to the measurement problem. This it does successfully in non-relativisticquantum mechanics. Now how does it fare in the relativistic case? Saundersinvestigates the two possibilities: treat matter in terms of particle trajectories, or fieldtrajectories. In both cases, he assumes that the trajectories are integral curves of thecorresponding quantum-mechanical currents. There are, he opines, defects in bothapproaches. In the particle ontology, the model is objectionable for the (rather odd!)reason that it does not appear to suffer from all the defects of the standard theory(e.g., in the Dirac single-particle case, the particle never acquires negative energy,whatever the quantum state). The particle approach does, however, admit a theoryof measurement, and there are possibilities for interpreting it in terms of Dirac’s orFeynman’s models. In contrast, in the field ontology, if one requires that fieldsshould become classically localized in the context of describing measurementoutcomes, then, as far as we know, they do not. Saunders concludes that, although ithas defects, the best current candidate for a relativistic beable theory is the particleontology, interpreted according to Dirac’s hole theory.

One might respond in the following way to this argument. First, on a minor point,it seems that the contention that the pilot-wave theory is at heart just a theory ofmeasurement is questionable—surely, although the solution of the measurement

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problem was a triumphant application, de Broglie and Bohm invented their theory todescribe what happens between measurements (cf. the iconic image of particletrajectories in the two-slit experiment). The point was to relegate measurement to aparticular application of the theory, a special but typical many-body process (it isnevertheless true that the theory must somehow achieve a theory of measurement).On the more substantive point, it is not clear whether the only options availablefor a particle ontology are Dirac or Feynman. The truth of the matter is thatinsufficient work has been done on the relativistic pilot-wave theory—in particular,pursuing the implications of the trajectory model to its logical conclusion (e.g.,it was only recently established that the trajectory theory for a many-fermionsystem can be made Lorentz covariant, albeit nonlocal). No one has yet attemptedto give, for example, a detailed account of creation and annihilation processesfor fermions, starting from a general state of a collection of particles andantiparticles. In this approach, one would aim to introduce a new ‘beable’-likequantity corresponding to particle number that would have a fixed (integer) value fora Fock state but vary for a superposition of states. If this programme could becarried through, there is the possibility of a novel insight into these processes quitedistinct from either Feynman’s or Dirac’s models. A further point that deservesattention is the assumption that the physical paths of a particle or field should bedefined in terms of the quantum currents. There is always the possibility that thesepaths are actually the configuration-space projections of an underlying phase spaceflow whose individual trajectories may have very different properties from the meancurrent.

The problem of defining localized particle variables in relativistic quantummechanics is by no means confined to the Bohm and related theories. It has been adifficulty in the formalism itself since the inception of quantum mechanics. And therelation between the apparently different notions of localization employed in hidden-variable theories and in the quantum formalism (particle trajectories or concentratedfields in the hidden-variable case, localization properties of self-adjoint operators inthe quantum formalism) has not been investigated very far. The essay by GordonFleming and Jeremy Butterfield is the sort of analysis one needs to read prior toundertaking such a task. This long article has the character of a mini-monographand the authors might think about turning it into a fully fledged one. For it raises ina clear way, and seeks to answer, the thorny questions associated with the concept oflocalization in relativistic quantum mechanics and quantum field theory, particularlyin relation to defining a satisfactory position operator (they do not discuss therelation with hidden-variable interpretations).

The authors start by explaining what the problem is, for both the Klein–Gordonand Dirac equations (and more general systems). First, if one includes the fullenergy spectrum in the quantum state, one obtains the usual ‘na.ıve’ positionoperator (with delta-function eigenstates), but this has conceptual and technicalproblems. Suppose, then, one restricts to just the positive energy spectrum, where theappropriate position operator is the Newton–Wigner operator. Some of theproblems associated with the na.ıve operator are avoided, but the Newton–Wigneroperator has two properties that look somewhat damning: its associated localized

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eigenstates expand superluminally, and they delocalize under a Lorentz transforma-tion. Fleming and Butterfield then ask if physical sense can be made of these features.Although the results obtained are perhaps not as conclusive as promised at thebeginning of the paper, their approach does look promising. The authors start bygoing back to classical relativistic mechanics and examining how the evolution ofposition variables may be described using various equivalent parametrizations. Oneof them, involving a particular hyperplane dependence of the position variables, ispreferred in that it allows a relatively trouble-free quantization procedure to becarried through. The resulting position operator is illustrated by application toquantum field theory, and the relation with the Newton–Wigner operator isestablished. The authors claim that, although their position operator possesses thesame attributes of superluminality and delocalization as the Newton–Wigneroperator, sense can be made of this through the additional structure offered bythe hyperplane dependence. A reason why this proposal is not fully conclusive is thatthe components of the new position operator do not commute for space-likeseparations; further work is needed to establish that this does not imply causalanomalies.

It has happened that physicists have taken the lead in addressing philosophicalproblems of their subject where philosophers have been slower off the block, or evenignorant of the discussion going on in physics. This is argued by Gordon Belot andJohn Earman, who illustrate the point by assessing the reaction of each camp toEinstein’s hole argument in general relativity (unfortunately, they do not pause toreview for us what this argument is!). The authors argue that the philosophy ofspace-time acquires particular relevance in the context of the problem of time inclassical and quantum gravity. As they explain, technically this is a problem becausegeneral relativity has a particular gauge and Hamiltonian structure which impliesthat in its quantum version a physical system is static. But underlying this areconceptual problems of classical general relativity (which, somewhat like quantumtheory, apparently admits different interpretations compatible with the samepredictions). Moreover, one’s predilection for a solution of the quantum problemis likely to colour one’s view of the initial classical theory that was quantized. So,philosophy matters: not just in interpretation, but in the very technical constructionof a theory.

Abner Shimony discusses, by way of analysing the writings of some of theprincipal proponents of the idea, whether fundamental natural laws might resultfrom some natural evolutionary process analogous to that employed in Darwinism(involving the concepts of variation, selection, and inheritance). That is, not only dothe configurations of matter evolve, as required by Darwin, but the laws that definethe configurations, regarded as forming an invariant backdrop in Darwinism, mayalso evolve. The idea is attractive because of the great difficulty in explaining in otherterms the necessity of natural laws. The author is careful to distinguish this notion ofevolution from the historical development of science, to which one might also seek toapply evolutionary ideas (as was done, for example, by Popper). Actually, I am notentirely convinced one can fully make this distinction. It is we, after all, who changethe laws of physics that we regard as fundamental—are they all supposed to be

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evolutionary products? A comparable argument carried out a century ago wouldhave wanted to make Newton’s and Maxwell’s equations the fruits of evolution,whereas now it is the equations of particle physics. And what do we do in caseswhere one set of laws (e.g., quantum mechanics) supersedes another set (e.g.,classical mechanics), but we still turn to both according to the problem at hand, andwhere, in any case, the relation between them is not fully understood (for the latter isnot simply a special case of the former)?

Despite these caveats, the conjecture of evolving laws is an interesting one; forexample, if the laws of physics do change by virtue of a set of governingenvironmental laws that are themselves immutable (as they must be, since variationcan only occur with respect to a fixed background), what brings the latter intoexistence? Shimony examines the views of two philosophers, Pierce and Whitehead(whose remarks on this topic are, frankly, pretty vague), and two physicists, Smolinand Wheeler. Smolin, for example, seeks to implement a restricted version of theidea: he assumes the standard model of elementary particles, but seeks to develop anevolutionary explanation for the particular values taken by the free parameters in thetheory. He argues that, in an ensemble of possible universes, the range of parametervalues will be sharply peaked on those that have a propensity for producing blackholes, and which are also conducive to life. This is a notable result but, as remarkedby Shimony, the results do not provide an explanation for the fundamental laws ofphysics. It might also be added that the programme appears to start from thereductionist idea that the elementary particle laws are necessary and sufficient toestablish a link between physics and a theory of ‘life’. At present, we do not knowwhether either of these assumptions is true. It is an old criticism of the particlephysics programme that, starting from its premises alone, one cannot deduce orpredict (without further assumptions) the simplest of macroscopic phenomena. Thelaws governing ‘life’, if indeed there are any in the sense we understand the term, maybe entirely unconnected with particle physics. We do not even possess a fullyfunctioning theory of systems that combine classical and quantum properties (suchas DNA).

In general, these are not introductory-level essays. And the book does notconstitute a fully comprehensive overview of current ‘philosophy of physics’,exhibiting a heavy bias towards quantum theory. But the essays contain somethought-provoking stuff, and this stimulating volume is unquestionably a valuableaddition to the canon of the philosophy of physics. Philosophers have seen therelevance of physics to their subject. Hopefully this book will contribute to anevolving exchange of ideas between the disciplines, and will stimulate more physiciststo make the return trip.

Peter HollandGreen College, University of Oxford,

Woodstock Road, Oxford OX2 6HG, UK

E-mail address: peter.holland@green.ox.ac.uk

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