[Brian Skyrms] Possible Worlds, Physics and Metaph(BookFi.org)

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B R I A N S K Y R M S

P O S S I B L E W O R L D S , PHY S I C S A N D M E T A PH Y S IC S *

(Received 24 December, 1975)The idea that many possible worlds may exist, not merely as abstract stmc-tures but in a concrete and robust a manner as our own has long been familiarto fans of science fiction. Recently, it has acquired proponants from twodistinct areas. David Lewis, in his book, Counferfactuals argues for just sucha view:I believe that there are possibIe worlds other than the on e we happen to inhabit ... Iemphatically do not identify possible worlds with respectible linguistic entities; takethem to be respectible entities in their own right. When I profess realism ab ou t possibIeworlds, I mean to be taken literally. Possible worlds are what they zre and no t someother thing. i f asked what sort of thing they ate, I cannot give the sort of reply myquestioner p roba bly exp ects: th at is, a proposal to reduce possible worlds to somethingelse.I can only ask him to admit that he knows what sort of thing a ctual worfd is, and thenexplain that other worlds are more things of that sort, differing not in kind b ut onlyin what goes on a t them. O ur actual world is only o ne world am on g others.'

But it is not only metaphysically-minded modd logicians who support amany-worlds view. Some physicists have argued that such a view is requiredfor a correct interpretation of quantum mechanics. IkWitt and Graham, intheir preface to The h n y - h r l d s nterpretation o m n m m Mechanicswrite:

Hugh Everett 111, propounded a new inttrprrtation of quantum mechanics tha t deniesthe existence of o *parate clasdcal nalm and asserts that it makes sense to talk about astate vector for the entire u n i v e ~ e .The state vector n m r cohpws , and hens t reafiWas a whole s rigaously deterministic, This rtaiity, which t &scribed jointly by thedynamicol variables and the state vector is not the reailty we customaiiy think of , bu ta reality composad of rnarsy worlds. By virtue of the temporal d e v e l o p m n t of th hd~nrtrnicral variabbs the sate vector decornpaseg natur4.b rs orttacygonal vectors,reflecting a cantinun1 rglitting of the universe into a multitudc of mutual ~ n ~ b w m a b kbut equally rcd worlds ...n light of such suggestions, the f~Uowing uestions of 'pldosogkcal science-fiction' take an.a wider significance.

PhiIosophicgI Studief 30 2976) 23 -332. AZZ Righa Rmc~edCopyright 43 1976 by D. Reidel i 2bhin.gCompany, Dodrccht-fi iknd

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more than one possible world exists (in the1. Is the contention that cr=7fisistenf?sense ou r own)11. If it is Consistent, how do r;Ne fmd out the facts of the matter?

In order to answer these questions, wemust be clear about just what sorts ofpossible worlds are a t stake. 1f a possible world need only be a mathematicalstructure which is a model for a dven language, then the co-existence ofm a n y possible worlds poses no conceptlid problem But it is clear that it isnot that sort of possible world existence is at issue here. Neitherphysicist not science fiction writer is interested in such pale and abstractpossibnities, and Lewis explicitly says that he isn't either; I cannot believethat our o m world is a purely m a hematical entity. Since do not believethat other worlds are different in a n d from ours, I do not believe that theyare either."4 What I take kw o e saying, and what makes his claim reallyexciting, is the content ion that p ~ ~ ~ i b l eorlds are red asAfghanistanor the emter of the Sun r A- Lewis, DeWitt and the typical sciencefiction story all claim that possible worlds exist in ust as ~ ~ ~ c r e t eMY asOur O I W . f Suggest that we take tm as mplying &at more One possibleworld is real in the following sense: world is real if-and-only if every propo-sition true-in-that-world is m e 5

h i s seems a modest requi rement , designed only to separate genuine physi-cal or metaphysical c]-s from metap hofica fl~resented rnode1 theory- Butthis innocent requirement imediateJy leads to difficulty. It is plausible toadopt the following principle of individuation for possible worlds: A worldw s identical to a world w if and only if exactly the same propositions aretrue-in-wl as are tme-in-w, ~~t n m f two possible worlds are disrinct thenthere is a proposition wlrich is tme-&-one and whose denid is tmt-bethe-other; and if two distinct worl& aarc m d hen there is s propositon such thatboth it and its denid arc? tme. m many-worlds hypothesis is prima JPcieinconsistent

The situation is reminiscent of ;i?az old metaphysical problem, the problemof rhge. Change involves apdmf ie contradiction- f i t Fa, then -Fa -with the first a d econd &uations being quite red. Some phifosophers havetaken this d i f f i e d ~s showing change;is impossible. Others have condudedthat contradictions me possible. Neither of these views is now much favored,

P O S S I B L E W O R L D S P H Y S I C S A N D M E T A P H Y S I C S 325Rather, it is generally held that the appearance: of contradiction n the dem ip-tion of change arises from an incomplete specification of the statements in-volved. We do not have 'Fa' and '-Fa' both being true. Rather, we have a ruethe relational statements Fat, and -r;irtz3where 'tl'and t3 refer to differenttimes. 'Socrates is young at tt ' no more contradicts Socrates is old at t2 than'Socrates loves Alcibiades' would contradict 'Socrates cares not for Democritus',This medicine is such a successful treatment for the paradox of change that it hhard to resist trying it out on the paradox of many real worlds. We will say thatwhat we took to be 'Fa' is really E;izwlY a d what we took to be -Fayis eally-Fav, . Thus 'Socrates is wise in wodd 1 no more contradicts Socrates ia silly

in world 2 than Socrates is young at tl' contradicts 'Socrates is old at t2'.7But now, we no longer have two distinct possible worlds in the sense laiddown. What has happened is that what looked from an earlier perspective

(the Fa; -Faperspective) like distinct possible worlds, have from the later( F w , , -Fmz) erspective been incorporated into a single 'supr-world'.Thus, the answer t o question 1 is: yes and no. It is strictly inconsistent tomaintain that two distinct possible worlds are real. But is always B consistentto take what, from a certain perspective are distinct possible worlds; incor-porate them as indicated into a single 'super-world'; and contend that thatsuper-world is real.

More precisely, we see that the notion of a possible world is language-rehtive. Relative to the language in which Fa is a closed sentence w havetwo distinct worlds, but relative to the richer language in which F i i 3 s aclosed sentence they are but objects; a part of the substance of the world.A language L ,can always be replaced by a richer language, L , in this mannerso that the worlds relative to L re objects relatiye to L . Consequently, thaclaim that more than one po~ribleworld sxistJ must be taken ss s~sertinghattome language, L, s not adequate to d e s r i h mality but that a richer Lwhich requires many worlds-nlative-to-l m n g ts objecb ir .&qua&.

t us examine the reasons adduced by both mtaphysicima d hysicia,insupport of hais claim. Lewis writes:If an argument is wanted, it is this 1 i s u n e o n t r o v o d y true that thin s nt@t haken o t h ~ m i mhan they am We , md xr 13o you, that thin caW hare hemWesn t in countlea ways. But what dues this arm O r d h w pellmits; thep m p w : these many ways that things mdd haw hen b e a s he sully t h y

are. n fre face of it this sentenm ismi exkbntid q ~ ~ c s t i o nt says at

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326 BRIAN SKYRMSthere exist many entities of a certain description, to wit ways things could have been ,I believe things could have. been different in countless ways; I believe permissible para*phrases of what I believe; taking the paraphrase at its face value, I therefore believe inthe existence of entities that might be called ways things could have been . I prefer tocall them possible world^ .^Taken at face value, this argument seems rather cavalier. Are there then 'waysin which things could not have been (e.g. triangles having 4 sides) which areimpossible worlds? Etc. But, Lewis redly has a more sophiticated argumentin mind. Thus:I do not make it an inviolable principle to take seeming existential quantifications ofordinary language at their face value. But I do recognize a presumption in favor of takingsentences at their fa ce value, unless ( I ) taking them at face value is known 5 0 lead totrouble and 2) taking them some other way is known not to ...1 do not n o any success-ful argument that my realism about possible worlds ieads to trouble ...All the alter-natives I know, on the other hand, do lead t o t r o ~ b l e . ~M a t this argument comes to, I think, is the contention that the most viablesernanticd theory for our ordinary counterfactual and modal discourse isone which assumes the co-existence of ma ny ac tual possible worlds,

Even if this contention were correct, it would constitute a weak argument.If I were convinced that the smoothest sernantical theory that could makesense of o r d i n q talk about the Easter rabbit; goblins; angels; and Pegasuswas one which assumed that such things really existed, would not therebybe convinced of their existence. Rather, I would hold such ordinary talksuspect. I have no reason to believe that emantical theory for ordinarydiscourse is a reliable guide in these matters. What require here are physic lreasons (rabbit track, etc,). What about possible worlds? If possible worldsare supposed to be the wme sorts of things as our actual world; i they aresupposed t o eds t in as concrete and robust a sense as our own they ares u p p e d to be as real as Afghanistan, or the center of the sun or Cygnus A ,then they require th same sort o midence for their a istence es otherconsti mbs. ufphysicaI rmZity. What is required t o show at thr: sort ofpossible wodds Lewis wants exist, is their presumption in the best phyrsimltheory.Furthemore, the contenticin that this sort of robust realistic theory ofpossible worlds provides f;he ost viable foundation for r =mantical th oryfor rnodiils and counkdi tc tuds seems t o me quite clearly false. h e reasonis that abstract mathematical structures Lewis them Ersatz possibleworlds ) w d o just as weZI as the pasible-worlds in 'possible-world-w m n t i ~ ' or modal and counterfactud logic. fn act, this is just the cwtom-

P O S S I B L E WORLDS, HYSICS N D METAPHYSICS 327ary way of doing possible-world-semmtics . One must admit, on thisapproach,that the real world is not a 'possible-world'. But to insist that it must be isperhaps to take a metaphor too literally. Lewis' robust realistic theory ofpossible worlds is not required by possible-world-semantics; it is rather anintellectual adventure su gested by possible-world-semantics. Finally, it isnot at aU clear why Lewis' truism, things could have been otherwise shouldnot apply also t o the en riched language which numbers among its things thepossible worlds relative t o t he initial language; and thus gnera te a runawayontology.'0

This metaphysical-semantical line of argument, then, fails both internally,and because it is an inappropriate kind of argument for deciding what isessentially a physical question. A compelling argument for a reality com-posed of many worlds would have take the form of a demonstration tha t thebest physical theory available required such an expanded reality. (If, forexample, a new physical theory required a 5-dimensional reality, we couldregard it as a reality composed of many 4-dimensional worlds, wit theappropriate topological and causal relations holding between them.) Suchnews from physicists would be important and exciting, but would not, Ithink, satisfy Lewis. F or Lewis assumes that the initial language is the anguageof physics, whatever it is and that his worlds are worlds relative to t t an-guage. He thus forecloses access to the only sort of evidence that couldsupport his robust realism.

M a t n ew s h e n , d o we h m rom physicha concerning the existence ofmany worlds? Quantum mechanics, under the Everett-Wheeler interpretation,has the initial appearance of being just theory of many worlds. In fact,hwit t md Graham have chwen to cntide their coflaction of afticlex of theEversttWheeler interpreta tion '?Re Many-Worldr Inferpretntion of QzLantum~'cknics.' In languags reminescent of Lewis, DeWitt dtscribes the manyworlds:Our univttxse m w t be viewed i constantly splitting into a stupndous number ofbnhches, all resulting from the m ~ u r t n r t n ~ ~nterntion etween its my ofCOragponcn.ts, ecause there exists neither a mchanism within the f-w~rk offoraamm nor, by definition, an entity outride of tfit universe th t de h whhhbranch of the gmad superposition is the 'real' world, U bmcfies must be remded asq w y eal 1=

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328 B RI A N S K Y R M SWhy then, do we n ot ob serve such splits? Everett expliiins:In reply to a preprint of this article, some correspondents have raised the question ofthe rfrm ition7 from possible to actual,' arguing that in 'reality' there is as our ex-pri enc e testifxes - no such splitting of observer states, so that only one branch can everactually exist. Sincc this point may occur to other readers the following is offered ine x p b t i o n .The whole issue of the transition from 'possible' to 'actual' is taken care of in the theoryin a very simple way-there is no such transition, nor is such a transition necemry forthe theory to be in accord with our experience. From the viewpoint of the theory a&elements of a superposition (all 'branches') are 'actual', none any more 'red' than therest. It is m e e e s w to suppose that aU but one are somehow destroyed, since an theseparate elements of a superposition individually obey the wave equation with completeindiffercnae to the prepence or absence ('actuality' or not ) of any other elements. Thistotal lack of effect of one branch on another also implies that no observer wig ever bea w m of any spjlitting p r m m . lZBut if the Everett theory is only one interpretaiiun of quantum mechanics;if othe r interpretations require only one world; and if the E verett interpreta-tion is observ tion lly indistinguishable from other interpreations ; houldn'tthe Everett interpretation simply be eliminated by Ockham's Razor? Thematter is no t qu ite so straightforward. In a standard formulation of q uantummechanics, the s tate function, J may change either (1) continuously, accord-ing to the Schrodinger wave equation or (2) discontinuously, as a result ofa measurement, according to the projection postulate. In the Everett theory,only p r o m s 1 is allowed; the projection postulate is denied. The entireuniverse may be treated qu antum m echanically in the Everett theory, but no ton t he standard theory. Thus it is strictly incorrect t o speak here of two dif-ferent interprsalions of the same theory. What we redly have are two dis-tinct, incompatible theories. The Everett theory cannot then, simply bedismissed as quantum mechanics plus metaphysical puffery. It m ust be ration-ally evaluated a s a genuine alternative theo ry.I do not want to pursue that evaluation here, but only to ask what sort of'many-world pictun the Everett theory docs give us. Everet t propats toregard wave mechanics as a complete theory, Thus measurement must bereg;lr&d ;ts an interaction between two subsystems of a composite system,whicfi must itrdf be regarded from the standpoint of wave mechanics. Thus:I ?& k s ht conqaaeaa tjuit i the sets {tf 1 and fT@S2 ) ~ - ~ m ~ l e t @f i o ~ o ~sets o tates fos , ruidS, respectively, then the g3~nera.l tate of S c nb~written assuperporzitim:

8= x j S. nisz

POSSIBLEWORLDS HYSICS ND METAPHYSICS 329although S is in st definite state 8, he subsystemsS andS, do not posses mythinglike defiite states independently of one anotherWe c n however for any choice of a state in one subsystem wigueiy assign a car-respondingrektive state in the other subsystem

For any choice of basis in S , , gi it is always possible to r e p ~ m the st tc of S s asingle superposition of pairs of states each consisting of a sta b from fie bwb { t i ) nS and its relative state in S, I3Given an ideal measuring interaction between a measured 'object' subsystemand a measuring 'apparatus7 subsystem, for each state of the apparatw sysbmits relative state is the corresponding eigenstate of the apparatus system. Forthe composite system there is then ;

a representation in terms of a superposition, each element of whkh contains a &finitobserver s t t e and a corresponding system state. Thus,with each suco b~d iibservation(or interaction) the observer state 'bmch w' into a number of different Jhtcr. fi chb m c h represents a different outcome of the measurementavrd tho c or re ~n dh g k n -state for the object system state . bm ches exist simultaneously in the superpositionafter m y given sequence of obs@;rvations.'*For purposes of illustration, consider the Schrodinger Cat paradox. The cat-geigercounter subsystem measures the radioactive source subsystem. Tneyare co orelate d 30 tha t the relative state of 'cat d ead' is radioactire decay~ ~ ~ u r r e d 'nd the relative stale of 'cat alive' is 'radioactive &my didn toccur'. The state of the composite system is a superposition containing thesepairs of states. Thus we are led to talk of a reality containing one world withradioactive decay and dead cat, and another with no radioactive decay andfive cat,

Here then, are the many worlds of the many-wotids interpntation ofquantum mechanics'. What kind o worlds me thq An unauphis.kicatedreader might jump, from the example of Schrodinger7s ~ t ,o fhc ~ o o c ~ w i ~that they an classical worlds. But, of course, the uncertainty principk hmediately show that this cannot be so. A world cannot haw g g l ~ d t f e ~for both a position md a momentum of a partide at a tim ach world itquite th~mughlyquantum mechanical, md may be thought of a ~ ~ f t ~in Hnbrt rpaos. Ks un i ~mf mpny wad m y lwr be o@t of s?r avwttw inHilbsrkspace. Now then, do the worldsand fhefr nlttiw constitute

larger reality U we c n wy in the u n h r e ~f wad hmch that it erm ber ~ p e m t E ds a m p p m f the compi&mf.w with m f i ~fm a n One may wonder at this point whether this b a theory of r n tycomposd of many ~oddnn tbe sew s t orth at the bcgi.dagofW prpr .

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330 BRIAN S K Y R M S POSSIBLE WORLDS PHYSICS A N D METAPHYSICS 33I think that it is not. The argument that I will ofler is an old one, and in noway orignal; but I think that for the concerns of this paper it should beunderlined once more.

It is evident, that if a universe of worlds U1 ontains at least one world,W, hich is not contained in a univeme Ll , hen U1 and U2 re distinct. Forinstance, if we tried taking numbers as worlds, and the 'universe' containingseveral 'worlds' as just their sum, it would not wash for then the Zlniversecontainh g just 2 and 3 would be identical to the one containing ust 1 and 4.The same point applies generally to taking vectors as 'wo rlds'a nd their vec torsum, or a superposition of the m with various coefficie nts as 'universe'. Nowin quantum mechanics, the decomposition of the state vector is likewise no tunique. The state vector might be written in terms of p osition eigenvectors ormomentum eigenvectors (or in t e r n of some other basis). The idea ofEverett-Wheeler is to disambiguate by using eigenvectors of th e m easurementactually performed, The performan ce of a perfectly sharp position measure-ment then splits one world into non -i nt er fe ~g ranches, each of which regs -ten a sharp position . What is important for us here, however, is that a pe rfect-ly sharp position measurement is an idealization t never really happens.What we have instead are imperfect approximations to this model, where theworld docs not split c l e d y into non-interfering branches. But now, there isno ma9011 not to decarnpose in t e rns of momentum mther than position,and by our previous a rgument, we have one qua ntum mechanical world ratheran many (just as we did before the imperfect measurement). From this

standpoint, d l the 'garden of the forking paths' talk is an appealing metaphorwhich provides some nsight into the theory of measurement, rather than anaccurate description of the reality posited by the theory. I am not suggestingthat the physic&@who are propanan& of the Everett-Wkedcr interpretationare deceived They know t is all very well. But we would be deceived ifwe took the reladve4tate formuIot ion of q w tu m . mchmicrr to be a theoryof may polasible wonlds ln Pht mnse at issue in thb paper.In smw ens l s a sense jn which the con ten ti or^ at many pmibte

teat. MebphysicaI mdmoammntid a m c n ef to d the 43taXiCXi b t s required to %Upp~t*%he =y-wsficon ntion is n demonstnrtion h t he b e ~ t hysical theory requires a richerreality, w from the starsdgmkt of o u r c u m n t penpctcti~e,s a = ey fm ny worlds. t k quite pcssible at them might be such a physid theory.But Everett's bEa&cf State' fum~latjolz fqmtu~lrmme~hmicdi n o t meh

a theory. To the best of our present knowledge, the hypothesis that morethan one possible wor ld is actual fails.Llniy of Illi~~ist Chicago Circle

NOTESThis paper grew out of a talk entitled 'Parakl Worlds and the Principle of Planitatatasgiven at Various times at University of Wisconsin; University of Chicago; fhlgblry Uni-versity; U.C.L.A. and U.C. Berkeley, in which I presented, md then criticizeda positionmuch Like that of David Lewis. That paper, more than thls exhibited my ambivlrlsmato a many-worlds view of reality which 1 find aesthetically attractive but, in final

analysis, philosophically indefensible. Thank?; or hefpful comments m due t6 theaudiences at each of these talks and also to Jim de Jong; Terry Patsons; Bas van F m n ;David Kapfan; David Lewis;Arthur Fine; Neal Grossman; Abner Shimony; Paul Teller;Ernest Adams; Phil Quinn; Gail Stein; Nancy CarWright and ladie Tharp (none ofwhom are to be taken as ensorsing the following). This paper is not an attack on modallogic. This paper is not an attack on the Everett-Wheeler interpretation of qwmmmechanics,Recent examples: Asimov, The Th em l v e s , various episodes of DY.W h , BC-TV.David Lewis,Counrerfactuals(Harvatd University Press: Cambridge, 1973),pp. 84-85.Bryce I)eWitt and Neill Graham (eda.), l%t Many-Worilds inteqmtarion of QuantumMechanics (Princeton UniversityPress: Princeton, 13731, p. v.Lewis, Countmfacnurb, p. 84.ibis definition, and the following argument are due to a suggestion of Terry M s o ~ .stated, the c le fi ti on s and the argument depend on a rather platonisticv kw of propa-sitions. Otherwise, there wouldn't be enough of them to fully characterize a world.Those who feel more comfortable with sentences might modify the argument as follows:ffa worldis real then every sentence true-in-hit-world is true. Two worlds are d i rmfb lydistinct if and only if there isa snt en ce true&-one but not the other. A theow of m31Iydiscernibly di sh ct worlds then falls into the same difficulties; while a theory of ma~Iydistinct but indiscernible worlds is not too interesting.' The Bnalogy between possible worlds and moments of time has Men pointed out byPrior, Montague, Kaplan, and Lewis, among others.NO@ that we cannot yet out of thcr general difficulties n h d withJust some buaincuabout sountsrparrt. Consider the u where ( 3 ~ )r is trusinu, and its denirlis trus

f z *David hw ,Cosurt~~~facmbr. 84.David b w h , Cb~lntrtfocttdaik, , 90.We slw that in order to wnsistcrntly rnrintnln that many paajibfrr worlds rrcwe musf incoq3~rat.athem into a sfn Q xwfity; a sir hprworbl'. M& q enow mppaar at the lava1 of surparworw Lewis blicvhs that o w mdtyk stppemrldhccapgorat;ingmany g d b h world. A mom convcntianrrl vbw hoMs h t BK d t yincogorates only one pmdbla? worM. Ff as I howwed this i i ultj'saak a f3-ath@ntpk~siePlquastion, we would want to s y hat it is p-bb that b w i ~sMt andthat h~ is wrong. That s to my, n polpplik-world-a, that thcn kmem hsnA consistent d t ust then hold t at m y upe,~ar are real, sadhmQ~mtthem into an even richer reality, a augm-super w0tI.d. ft L c h hat t irPFoccor ~ G Y W T top. NO naattt:rhow rick lp gy thc rdkt portktkter, ( m a f a

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332 BR I A N S K Y R M Sgoes to the trouble of postulating supenvorlds of transfinite order), we can always askthe modal question "Is it possible that reality is different from that postulated by therealist". And given that the reasonable answer is 'yes', the realist must postulate an evenricher reaEty. The point is, that this regress is embarrassing to a realist in a way that it isnot to a theorist who views possible worlds simply as mathematical structures. The latterneeds only to be able to find appropriate mathematical structures given any reasonablemodal language. The former must have a reality rich enough to accomodate all modalh g ~ ~ g e s .ut by the foregoing argument, whatever reality the realist postulates cannotbe r i c h enouah.-One might remark that the ontological situation here is no worse than that for settheory. Indeed But it is one thing to take a conceptualistic attitude towards sets, andanother to trike such an attitude towards physical reality.For proof that no language rich enough to contain arithmetic can express i ts ownConcept of necesdty, sea Montague, LSyntacticalTreatments of Modality, with Corollor-ies on Reflection Principles and Finite Axiornatizability', in ftoceedings of a oZZoquium0 and Many alued Logics: Aero Filosofiur Fennieo (Helsinki, August 19621,pp. 153-167.i Bryce DeWitt, The Many-Universes Interpretation of Quantum Mechanics', in DeWittand Graham . 178.Hugh ~vere t tII Relative State Formulation of Quantum Mechanics', Reviews oodem hysics 29,454-462, reprinted in DeWitt and Graham p 146-147.s Everett, "Relative State" Formulation of Quantum Mechanics', p. 143.

l Everett, ' "Relative State" Fo~rnulation f Quantum Mechanics', p. 146.I S ?dore correctly, the vector represents the state of the world at a time, but this doesnot affect the armmenf8 w -------See DeWitt's discussion of imperfect measurements in T h e Many-Universes Inter-pretation of Quantum Mechanics', in DeWitt and Graham, pp. 210-215.