Is Boltzmann Entropy Time's Arrow's Archer?Howard Barnum, Carlton M. Caves, Christopher Fuchs, Rüdiger Schack, Dean J. Driebe et al. Citation: Phys. Today 47(11), 11 (1994); doi: 10.1063/1.2808690 View online: http://dx.doi.org/10.1063/1.2808690 View Table of Contents: http://www.physicstoday.org/resource/1/PHTOAD/v47/i11 Published by the AIP Publishing LLC. Additional resources for Physics TodayHomepage: http://www.physicstoday.org/ Information: http://www.physicstoday.org/about_us Daily Edition: http://www.physicstoday.org/daily_edition

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March 1994 PHYSICS TODAY was thebest to date. I've been reading theseroundtables for years, and past partici-pants have inevitably blamed our pre-sent problems on (a) Congress, (b) thePresident, (c) uneducated business ex-ecutives, (d) lazy graduate students and(e) everyone else except us, the physicscommunity. It was refreshing to readof colleagues who finally realize thatthey (a-e above) are not the problem,but that we are, and that until andunless we fix ourselves, things are notgoing to get any better.

Reading the discussion, two addi-tional thoughts came to mind. First,all the participants seemed to agreethat the day of the stereotypical ar-rogant physicist, who is incapable ofinteracting with other human beings,is over. So it seems only reasonablethat universities start to implementadmission standards at both under-graduate and graduate levels that re-flect this understanding. Members ofadmissions committees can start toask, "Well, candidate X has perfectGRE's and straight A's, but what arehis human resources skills?" This ap-proach will go a long way towardcreating a pool of physicists for themodern research environment. AsAnthony Johnson of AT&T Bell Labsdescribed at the roundtable, in today'sindustrial teams it doesn't matterhow smart you are if you can't workwith other people.

Second, it seems that the time hascome to establish a political actioncommittee that represents physicists.Whether or not this is done as an APSoffshoot needs to be determined.Whatever your feelings about the eth-ics of PACs, they are a political real-ity. If every name in the APS direc-tory contributed $1.00 per week, therewould be considerable resulting finan-cial clout. (If you think $1.00 perweek is too much for job and researchfunding security, see you at the un-employment office.)

JEFFREY H. HUNTChatsworth, California

Is Boltzmann EntropyTimes Arrows Archer?Ludwig Boltzmann's ideas on irre-versibility are as controversial todayas they were at their introduction ahundred years ago. In the article"Boltzmann's Entropy and Time'sArrow" (September 1993, page 32),Joel Lebowitz, by giving a modernexposition of Boltzmann's ideas,tries to assure us that the controversyis unwarranted. Readers left unper-suaded should know that they are not

alone. Boltzmann's ideas are indeedcontroversial, because Boltzmannfailed to place them on a firm concep-tual foundation. Today a firm foun-dation can be provided—the key ideasare Claude Shannon's statistical in-formation1 and Edwin Jaynes's prin-ciple of maximum entropy2—but Le-bowitz's update, instead of providingthe necessary clarification, recapitu-lates the same murky concepts inmodern language.

Lebowitz addresses how time-asymmetric behavior of macroscopicvariables arises from time-symmetricmicroscopic equations. He partitionsphase space into macrostates, coarse-grained cells M, (of phase-space vol-ume |FM |) defined by the values ofthe macroscopic variables of inter-est—for example, the numbers of par-ticles within identical cubes that fillconfiguration space. To each phase-space point, or microstate, in M, heassigns the Boltzmann entropyS^{Mt) = k log |FM |. If the system isinitially confined to a small phase-space cell, then when the constraintsare released, it will tend to wanderinto larger cells. Lebowitz quantifiesthis behavior in terms of theBoltzmann entropy, which tends toincrease along a "typical" trajectory.

The problem here is not the story somuch as the commentary; for someoneoutlining an avowedly statistical the-ory, Lebowitz betrays an odd mistrustof probability concepts. He stressesthat he is dealing with the typicalbehavior of individual systems, notwith average behavior within an en-semble. But how can one charac-terize typical behavior without refer-ence to a probability distribution?Furthermore, he dismisses the Gibbsentropy SG = -k \dT p log p of a phase-space probability distribution p as ir-relevant to nonequilibrium phenomena,partly because it remains constant un-der Hamiltonian evolution, but also be-cause it relies on probabilities. Yetwhat is the significance of the increaseof the Boltzmann entropy when it hasan interpretation as a physical quantityonly in thermodynamic equilibrium?Indeed, why attribute a Boltzmann en-tropy to each phase-space point whenthe Boltzmann entropy is wholly aproperty of the coarse-graining?

Dealing with these questions en-tails using probabilities. Lebowitzimplies that probabilistic predictionsapply only to physical ensembles. Tothe contrary, when probabilities aresharply peaked, as they are for cer-tain macroscopic variables, they makereliable predictions for individual sys-tems. Probabilities provide the onlyway to define typical behavior for in-dividual systems and to assess just

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LETTERShow typical it is.

The phase-space probability distri-bution p(t) at time t follows from ap-plying the system dynamics to a uni-form distribution on the initial cell.The statistics of the macroscopic vari-ables at time t, determined by theprobabilities pt (t) = \M dF p(t) to be incell Mh are unaffected if p{t) is re-placed, within each cell M,, by a uni-form distribution containing prob-ability pj(t). This coarse-grainedphase-space distribution can be char-acterized uniquely as having themaximum Gibbs entropy given theprobabilities pt(t), the maximum be-ing EG = -kZ,p, lnp, + S ,Pl SB(M,).

Lebowitz's insistence on the pri-macy of Boltzmann entropy overGibbs entropy is thus stood on itshead. The Gibbs entropy SQ of thecoarse-grained distribution generallyincreases. Moreover, the increase hasa compelling interpretation: SinceSrjk is Shannon's statistical informa-tion, the difference between SQ andthe initial Gibbs entropy is theamount of information discardedwhen one retains only the statisticsof the macroscopic variables. The av-erage Boltzmann entropy does con-tribute to SQ, but this appearance ofthe Boltzmann entropies has nothingto do with entropies of individualphase-space points; rather, it is a di-rect expression of having discarded allinformation about the details of p(t)within the coarse-grained cells.

As Jaynes has emphasized,2 firmconceptual foundations are requiredfor progress in physics. The shakyfoundations provided by Boltzmannand Lebowitz obscure both what hasbeen accomplished and what remainsto be done. Boltzmann's ideas canindeed be used to derive time-asym-metric equations for macroscopic vari-ables, once they are supported withinthe solid framework of Gibbs, Shan-non and Jaynes; the Gibbs entropyBQ explains the time asymmetry as aconsequence of discarding microscopicinformation that is unnecessary forpredicting the behavior of the macro-scopic variables. Yet this explana-tion, like all good ones, immediatelyraises other questions: Why coarse-grain? Why discard information?These questions, the true puzzles ofirreversibility, provide the arena forfurther work.3

References1. C. E. Shannon, W. Weaver, The Mathe-

matical Theory of Communication, U. ofIllinois P., Urbana (1949).

2. E. T. Jaynes, Papers on Probability, Sta-tistics and Statistical Physics, R. D.Rosenkrantz, ed., Kluwer, Dordrecht,The Netherlands (1983).

3. W. H. Zurek, Phys. Rev. A 40, 4731(1989). C. M. Caves, Phys. Rev. E 47,4010(1993).

HOWARD BARNUMCARLTON M. CAVES

CHRISTOPHER FUCHSRUDIGER SCHACK

University of New MexicoAlbuquerque, New Mexico

Joel L. Lebowitz's article "Boltzmann'sEntropy and Time's Arrow" purportsthat consideration of the Boltzmannentropy gives a complete resolution ofthe apparent irreconcilability of theobserved irreversible behavior of sys-tems in nature with the time-revers-ible dynamical laws governing theevolution of trajectories. Lebowitz iscorrect in pointing out that the Gibbsentropy is constant in all processesand so is not appropriate as a non-equilibrium entropy. However, con-sideration of the Boltzmann entropydoes not give a complete explanationof the problem of irreversibility.

The main virtue of the Boltzmannentropy that is touted in the articleis that it "captures the separationbetween microscopic and macroscopicscales." If the scale-separation argu-ment were the whole story, then irre-versibility would be due to our ap-proximate observation or limitedknowledge of the system. This is dif-ficult to reconcile with the construc-tive role of irreversible processes.1Furthermore, where the scale separa-tion takes place is not well defined.When the Boltzmann entropy appar-ently works, as in a gas, it describesonly the approach to equilibrium ofthe velocity distribution for certaininitial conditions and does not de-scribe the appearance of correlations.2

For these reasons the Brussels-Austin group of which I am a memberhas for some years proceeded in adifferent direction. Irreversibility isnot to be found on the level of trajec-tories or wavefunctions but is insteadmanifest on the level of probabilitydistributions. Both classical andquantum mechanics therefore have tobe formulated on the level of prob-abilities for the classes of dynamicalsystems where irreversibility takesplace. This led to the theory of sub-dynamics, which allowed the treat-ment of irreversible processes interms of both the velocity distributionand correlations.3 The aim has beento obtain a formulation of the laws ofnature in terms of a complex spectralrepresentation of the time-evolutionoperator for probability densities thatis not implementable for trajectoriesor wavefunctions. This aim has nowbeen fulfilled for classes of chaoticsystems4 and so-called large Poincare

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LETTERSsystems5 by extending the Liou-ville(-von Neumann) operator togeneralized functional spaces. Themeaning of entropy becomes clear inthis new, extended formulation ofdynamics, where the original revers-ible group splits into two distinctsemigroups; as a result, broken timesymmetry appears already at themicroscopic level.

Also, a crucial point that is ne-glected in Lebowitz's article is thatirreversible processes are well ob-served in systems with few degrees offreedom, such as the baker and mul-tibaker transformations.14 Hence,many degrees of freedom is not anecessary condition for irreversiblebehavior. It is the chaotic dynamics,associated with positive Lyapunov ex-ponents or Poincare resonances, thatcauses the system to behave irre-versibly.

In conclusion, the arrow of time isnot due to some phenomenological ap-proximations but is an intrinsic prop-erty of classes of unstable dynamicalsystems. For these systems the dy-namical laws may be formulated inextended functional spaces to includethe arrow of time. In this formulationprobability appears in an irreducibleway. This is of special interest forquantum mechanics, as it leads to aunified formulation avoiding the col-lapse of the wavefunction (since thebasic laws are now given on the levelof density matrices).

However, dynamics cannot answerwhy all semigroups in nature are ori-ented in the same way. The orienta-tion must be mutually compatible,though, because all systems "commu-nicate"; that is, there are no trulyisolated systems in nature. The com-mon orientation of the semigroups ex-presses the unity of nature.

References1. I. Prigogine, From Being to Becoming,

Freeman, San Francisco (1980).2. D. J. Driebe, T. Y. Petrosky, J. Stat.

Phys. 67, 369 (1992). E. T. Jaynes,Phys. Rev. A 4, 747(1971).

3. I. Prigogine, C. George, F. Henin, L.Rosenfeld, Chem. Scripta 45, 5 (1973).I. Prigogine, T. Petrosky, H. Hasegawa,S. Tasaki, Chaos, Solitons and Fractals1, 3 (1991). I. Antoniou, S. Tasaki, Int.J. Quantum Chem. 46, 425 (1993).

4. H. H. Hasegawa, W. C. Saphir, Phys.Rev. A 46, 7401 (1992). P. Gaspard, J.Phys. A 25, L483 (1992). I. Antoniou, S.Tasaki, J. Phys. A26,73 (1992); PhysicaA 190, 303 (1992). H. H. Hasegawa,D. J. Driebe, Phys. Lett. A 168, 18(1992); 176,193 (1993); Phys. Rev. E, toappear (1994).

5. T. Petrosky, I. Prigogine, S. Tasaki,Physica A173,175(1991). I. Antoniou,I. Prigogine, Physica A 192, 443 (1993).T. Petrosky, I. Prigogine, Physica A175,

146 (1991); Proc. Natl. Acad. Sci. USA90, 9393 (1993); Chaos, Solitons andFractals 4, 311 (1994).

DEAN J. DRIEBEInternational Solvay Institutes

for Physics and ChemistryBrussels, Belgium

and University of Texas, Austin

Joel Lebowitz's accurate and enter-taining account of Boltzmann's classicexplanation of macroscopic irre-versibility emphasizes isolated sys-tems. Gibbs's ensembles made it pos-sible to widen this explanation toinclude microscopic systems interact-ing with thermal reservoirs. And in1984 Shuichi Nose discovered a re-versible dynamics1 describing Gibbs'sthermostatted systems and leading toa new and seminal view of micro-scopic irreversibility.

Nose's dynamics makes it possibleto generate nonequilibrium ensem-bles, characterizing nonequilibriumsteady states. Strain rate and heatflux can be specified, as well as com-position, energy and volume. Gener-ally, these nonequilibrium ensemblesoccupy fractal (fractional dimen-sional) portions of Gibbs's equilibriumphase space. The nonequilibriumphase volume is completely negligiblerelative to the phase volume of thecorresponding Gibbs's equilibrium en-semble—that with the same numberof particles, same energy and samevolume, but without the nonequili-brium fluxes.2

The negligible phase volume of thenonequilibrium states results fromthe multiplicity of constraints implicitin a "steady state." In a system un-dergoing steady shear at the strainrate e, for instance, not only de/dt butalso all the higher derivatives (d2e/df2,d3s/dt3, . . . ) must vanish. It is re-markable that Nose's thermostattedequations of motion are strictly timereversible. And their time behavioron velocity reversal is exactly thatdescribed by Lebowitz for isolated sys-tems: The time-reversed flow is lessstable with time reversal than is theforward-in-time evolution. This differ-ence in (Lyapunov) stability has re-cently been rigorously quantified for arestricted set of homogeneouslythermostatted nonequilibrium sys-tems.3 Our own very recent numericalinvestigations suggest strongly thatthis asymmetry between the two timedirections in steady-state nonequili-brium ensembles can only increase asthe homogeneity restriction is relaxed.4

References1. S. Nose, Prog. Theor. Phys. 103, 1

(1991).continued on page 115

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LETTERScontinued from page 152. B. L. Holian, W. G. Hoover, H. A. Posch,

Phys. Rev. Lett. 59, 10 (1987).3. S. Sarman, D. J. Evans, G. P. Morriss,

Phys. Rev. A 45, 2233 (1992).4. W. G. Hoover, H. A. Posch, Phys. Rev. E

49, 1913 (1994).WILLIAM G. HOOVER

University of California, DavisHARALD POSCH

University of ViennaVienna, Austria

BRAD LEE HOLIANLos Alamos National Laboratory

Los Alamos, New Mexico

In his interesting article "Boltzmann'sEntropy and Time's Arrow" Joel Le-bowitz claims, following Boltzmann,that macroscopic irreversibility is ex-plained by the large number of de-grees of freedom involved. This viewis incomplete. A set of time-symmet-ric equations evidently cannot leaduniquely to a time-asymmetric solu-tion. There must be another cause.

This cause rests in the fact thatwe are always concerned with initial,not with terminal, conditions. Themechanical problems we are solvingare of the form that at some initialtime, say t = 0, some macroscopic pa-rameters are given and other vari-ables are random. We then follow thedevelopment for t > 0. Following thesolution for negative times, the en-tropy would also be larger than att = 0; in other words it decreases withtime.

The extension to negative times is,however, not of practical interest, be-cause it does not describe a possiblesituation. In the laboratory this isdue to the fact that we can rememberthe past and make plans for the fu-ture, but not vice versa. As regardsthe world around us, it is no doubtdue to the fact that it all started fromthe Big Bang. Here lies the real rea-son for the asymmetry.

This is reflected in Boltzmann'sStosszahlansatz. This Ansatz isbased on the seemingly innocuous as-sumption that the number density ofmolecules moving in a certain direc-tion in a volume element from whichthey will in a given time collide witha scattering center is the same as inany other volume element, because"they do not know they are going tocollide." However, the molecules thathave just collided (which, in the time-reversed situation, would be the onesabout to collide) have a different dis-tribution, because they have beenscattered. Thus the "arrow of time"is included in Boltzmann's treatment,and it is not surprising that it isreflected in the solution.

Lebowitz's discussion demon-

"You have little understanding of probability, causation and coincidence."

strates that our preference for follow-ing evolution forward in time is sostrongly ingrained that we do not al-ways realize that this is a choice notforced upon us by the equations ofmechanics.

I have discussed these argumentsin detail.1 Similar arguments weregiven by Feynman.2 The intention isnot to detract from Boltzmann's meritfor having clarified so much of theproblem but to point out that an extrastep is needed for a complete accountof the situation.

References1. R. Peierls, Surprises in Theoretical

Physics, Princeton U. P., Princeton,N. J. (1979), sec. 3.8.

2. R. P. Feynman, The Character of Physi-cal Law, BBC Publications, London(1965).

RUDOLF PEIERLSOxford, England

LEBOWITZ REPLIES: Let me deal firstwith Rudolf Peierls's letter. (I wasnot aware of his very nice articlewhen I wrote mine.) I agree entirelywith him about the importance of in-itial conditions and I believe that thisis stated clearly in my article; see thesection "Initial conditions." I also be-lieve that he will agree thatBoltzmann said it very elegantly inone of his responses:1

From the fact that the differen-tial equations of mechanics areleft unchanged by reversing thesign of time without anythingelse, Herr [Wilhelml Ostwaldconcludes that the mechanicalview of the world cannot ex-

plain why natural processes al-ways run preferentially in adefinite direction. But such aview appears to me to overlookthat mechanical events are de-termined not only by differen-tial equations, but also byinitial conditions. In directcontrast to Herr Ostwald I havecalled it one of the most bril-liant confirmations of the me-chanical view of Nature that itprovides an extraordinarilygood picture of the dissipationof energy, as long as one as-sumes that the world began inan initial state satisfying cer-tain conditions. I have calledthis state an improbable state.The other three letters (a subset of

those received) unfortunately illus-trate how much confusion still existsabout the problem of macroscopic ir-reversibility. Each of these lettersoffers a different solution. Accordingto Howard Barnum and his colleaguesthe solution lies in information the-ory; Dean J. Driebe believes that wemust reformulate the laws of natureusing the mathematics of subdy-namics; and according to William G.Hoover and coworkers it is Nose dy-namics that saves the day.

In my opinion information theory,subdynamics and Nose dynamics allcontain interesting and useful ideasand can be illuminating when prop-erly applied. I believe, however, thatthey are neither needed for nor reallyrelevant to the problem of the asym-metry of observed macroscopic behav-ior. Boltzmann's ideas adequately ex-

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Each film scene depicts a scientific principle, or its violation, reinforcing con-cepts that are taught in more traditional ways. The chapter Electricity andMagnetism discusses the use of computers in Blade Runner. Under astronomy,2007 is examined as it relates to ancient astronauts. In the chapter Evolution,Planet of the Apes is studied in detail.

Helpful end-of-chapter exercises, together with more than 20 movie stills, fur-ther aid readers to grasp the technical material. Nonscience majors, science fic-tion enthusiasts, and film buffs will find this work both enjoyable and instructive.

1993,400 pages, ISBN 1 -56396-195-4, paper, illustrated$40.00 Members $3200

T h e P h y s i c s o f G o l fTheodore P. Jorgensen

In The Physics of Coif, you'll leam how to apply the principlesof dynamics and energy to perfect your golf stroke, to choosethe right dubs, and to make the handicap system work optimal-ly. Using stroboscopic photographs and an ingenious mathe-matical calculation, the author shows you how small changes inyour swing can increase the distance the ball travels.

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Time MachinesTime Travel in Physics, Metaphysics, and Science FictionPaul J. \ahin

Time Machines takes you on an exhilarating journey throughthe intriguing theories of scientists and the far-flung imagina-tions of writers. Explore the ideas of time travel from the firstaccount in English literature — Samuel Madden's 1733 Memoir:of the Twentieth Centun/— to the latest theories of physicistssuch as Kip Thome and Igor Novikov.This accessible work covers a variety of topics including the his-

tory of time travel in fiction; the fundamental scientific conceptsof time, spacetime, and the fourth dimension; time-travel para-doxes; the speculations of Einstein, Richard Feynman, KurtGodel, and others; and much more.

1993, 512 pagesJSBN 0-88318-935-6, cloth, illustrated$45.00 Members $36.00

"Most of the GDDCJ Stuff"M e m o r i e s o f R i c h a r d F e y n m a nLaurie M. Brown and John S. Rigden

Prominent physicists such as John Wheeler, Freeman Dyson,Hans Bethe, Julian Schwinger, Murray Gell-Mann, DavidPines, and others offer intimate reminiscences of their col-league and perceptive explanations of Feynman's trail-blazingwork. These essays uncover the precocious undergraduate,the young scholar at Cornell, the theoretician in his prime atCaltech, and the mature teacher andmentor.

Highlighting both the charm andthe brilliance of Feynman, "Most ofthe Good Stuff" is an engrossing col-lection for enthusiasts—scientists andnonscientists alike—awed and enter-tained by one of the century's great-est minds.

1993,181 pages, illustratedISBN 0-88318-870-8, cloth$35.00 Members $28.00

"Most of theGood Stuff"

Memories OfRICHARD

FEYNMAN

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LETTERSplain these observations without re-quiring reliance on ignorance or modi-fication of the laws of nature. Ofcourse such modifications may comeabout for other reasons—relativityand quantum mechanics are suchmodifications that came afterBoltzmann's work—but this is not theissue discussed in the article or in theletters.

What Driebe and Barnum and co-workers i and some other writers ihave in common is their refusal toaccept what to me seems an obviousfact: that irreversible behavior is ob-served in the evolution of a singlemacroscopic system that can be ade-quately described as isolated duringthe relevant period, be it ajar of fluidor the solar system. Thus when wepour some blue ink into a glass of redink (of the same density1 and seal upthe glass tightly 'making it an "iso-lated" system^ we always see it be-coming a uniform color. We don'tneed to repeat the experiment manytimes to get an ensemble or a prob-ability distribution, nor do we need torefer to ignorance about the exactmicroscopic state of the system—anymore than we would have neededsuch considerations to predict the fateof Comet Shoemaker-Levy after it hitJupiter. Both events are described bydeterministic. time-asymmetric mac-roscopic laws.

In deriving such time-asymmetriclaws one of course has to use prob-ability theory to characterize the typi-cality of the initial microstate of thesystem with respect to the initialmacrostate discussed earlier. Oneshows i or proves i then that the re-sults for macroscopic observations areso highly peaked that for large macro-to-micro ratios they amount to cer-tainties. In this way probabilities orensembles are convenient tools for de-scribing "typically" observed phenom-ena. This is discussed in my articleand in the references there: see inparticular the section "Notions ofprobability."

This excessive obsession with prob-abilities is the source of Driebe's con-tention that irreversibility is observedin a system whose microscopic stateis specified by a point X in the unitsquare evolving under the baker's dy-namics—a paradigm of the confusionsurrounding the subject. The macro-scopic state of such a system i speci-fied, say. by which half of the squarethe point X is in i will keep on chang-ing back and forth with time as itsmicroscopic state X jumps all over thesquare. No observations on such asystem will produce anything thatlooks time asymmetric, just becausethe svstem does not have many de-

grees of freedom. As put by Maxwell.The second law is continually beingviolated . . . in any sufficiently smallgroup of molecules. . . . As the num-ber . . . is increased . . . the prob-ability of a measurable vari-ation . . . may be regarded aspractically an impossibility."'-1

Turning now to Nose dynamics andits various generalizations, these areuseful for computer simulations andexhibit interesting analytic behavior.But as I have said in other places"there is no reason to believe that theyhave anything to do with the actuallaws governing the dynamics of themicroscopic constituents of our actualworld. So while it is interesting tospeculate on what the world wouldlook like with such dynamics. I be-lieve it is confusing to bring them intothe discussion of the conceptual prob-lem of macroscopic irreversibility.

References1. Quoted in E. Urod&.LudwigBoltzmann,

Man-Physicist-Philosopher. Ox BoxPress. Woodbridge. Conn. (1983). p. 74.

2. G. Eyink. J. Lebowitz. in MicroscopicSimulations of Complex HydrodynamicPhenomena. Proe. NATO Adv. StudyInst.. M. Mareschal. B. L. Holian. eds..Plenum. New York > 1992 '. p. 323.

3. J. C. Maxwell. Nature 17. 257 ilSTS>.JOEL L. LEBOWITZ

Rutgers UniversityNew Brunswick, New Jersey

Working RetirementsCan Open Up JobsWe need to create more openings inphysics research and physics teach-ing, both for the benefit of those youngpeople who have the vocation and forthe health of our physics enterpriseand institutions. Older physicistswho regret the dearth of employmentopportunities for young scientists atuniversities and national laboratoriescan help by voluntarily retiringaround the traditional age of 65 andcontinuing to work unpaid if that iswhat they want to do. Many physi-cists have done that, and I speculatethat many more would follow them iftheir institutions made the workingconditions attractive. It can be done,and financial incentives are not nec-essarily the decisive issue.

In the physics division at ArgonneNational Laboratory, six of us haveretired but continue to work unpaid,making it possible for a similar num-ber of young people to join the divi-sion. (For comparison, we have about40 regular scientific staff, i

The following perceptions andopinions are my personal ones. I de-

scribe the Argonne physics divisionexperience because I know it. Oursis by no means the only institutionwhere working retirement is prac-ticed, although we may have astronger tradition than others.

There is no financial incentive toretire at Argonne. Voluntary retire-ment works well in the physics di\i-sion because the retirees are treatedthe same as others. The consumptionof facilities and other resources byretirees has to be justified by produc-tivity, just as it does for other staff,although the standards can be relaxedsignificantly because the cost is somuch less. No Argonne policy is in-volved. We serve at the pleasure ofthe division director. However, nodivision director is likely to discour-age a practice that benefits the labo-ratory and the profession.

In fact it also benefits the retireesby permitting us to work less hard orless steadily if we so choose, althoughthat benefit is severely limited. Aperson cannot justify occupying facili-ties or even space idly. Besides, peo-ple who are active in research can'treally reduce their momentum verymuch without losing it.

Financial fears appeal* not to be amajor deterrent for most people. TheTIAA-CREF retirement system,which we share with many universi-ties and laboratories, works well. Theretirees I have asked at Argonne andat a few universities all say the moneyis adequate. Of course there are in-dividuals whose financial needs or re-sponsibilities are much greater thanthose of the majority, and such aperson cannot reasonably be expectedto retire voluntarily. There are insti-tutions where unusually low salariessystematically put people in that cate-gory. There are also persons whosework situations are incompatible withretirement, especially leaders of pro-jects whose funding will collapse ifthey retire. I believe the great ma-jority do not fall into any of thosecategories.

From conversations with col-leagues at universities. I have theimpression that voluntary retirementaround age 65 is relatively uncommonin most places and that the primarydeterrent is most often anticipatedlack of respect, not financial concernsor insensitivity to the ethical advan-tages. Amenities ranging from officespace to secretarial service may bewithheld from or offered grudginglyto a retiree, or the indi\idual maysimply be made to feel unwelcome. Aretiree may receive less departmentalsupport for research and professionalcosts than a paid colleague doingequally valued work.

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