INTERPRETING THE MANY WORLDS INTERPRETATION

8/21/2019 INTERPRETING THE MANY WORLDS INTERPRETATION

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D A V I D A L B E R T A N D B A R R Y L O E W E R

I N T E R P R E T I N G T H E M A N Y W O R L D SI N T E R P R E T A T I O N

I N T R O D U C T I O NHe re i s a pa r tia l l is t of the e lem enta ry pr inc ip les of Qu antu m Theo ry: 1

(I) An y i so la ted quan tum mechan ica l sys tem is charac te r izedby a state [unction $s( t).

(II) So long as S rem ains isola ted, Ss(t) evolves de te rminis t ic -a l ly in accordance wi th the Schrodinger equa t ion (or inaccordance wi th one of the re la t iv i s t ic genera l iza t ions ofthe Schr6dinger equa t ion) .

( I II ) For any com ple te com pat ib le se t of obse rv ables O of S , $scan a lways be expressed as a sum or a superp os i t ion ofeigensta tes of O, as fol lows:(1) $s = c 1 0 1 + c z 0 2 +wh ere the c~ a re com plex num bers , and the O~ represen tquantum s ta tes (e igens ta tes of O) of S in which O has thepart icular valu e oi such th at i f i ~ j then oi ~ %(IV) W hen a me asurem ent of O i s ca rr ied out on S in s ta te $sthe probab i l i ty of obta in ing O = ok i s equa l to the absolu tesquare of the ampli tude ck of Ok in the s ta te funct ion $.

(V) W hen a mea surem ent of O i s ca rr ied out wi th the resul ttha t O = ok then the s ta te of S col lapses , or i s red uc edinstantaneously into the e igensta te O~.

This l is t is sul l ic ient to show why quantum theory is phi losophical lyperplexing. The f i rs t pe rp lexi ty i s tha t quantum mechanica l super-pos i t ions a re not l ike any c lass ica l s ta te . When textbook wri te rsa t tempt to expla in wha t i t i s for an e lec t ron to be in , for example , thespin s ta te c11'x + c2~x they are re du ced to saying things l ike i t nei therhas x-spin up nor x-spin down but i s in some sense in both s ta tes andin nei ther . ( Tx represents the e igensta te of x-spin = +(up) e tc . ) Soone prob lem is to in te rp re t superpos i tions . Pa r t of an in te rpre ta t ionis g iven by IV which connec ts quantum s ta tes wi th the resul t s ofSynthese 77 1988) 195-213. 1988 by Kluwer A cadem ic Publishers


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196 D A V I D A L B E R T A N D B A R R Y L O E W E Rmeasurements. This brings us to the second difficulty, which is knownas the measurement problem . Suppose that M is a device formeasuring O on S. This means that there is an observable Q withvalues ql such that after M and S interact P O = oflQ = qk)= ~jk.(Thus M'S measurements of O are perfect. We make this assumptionthroughout our discussion.) It follows from the linearity of thedynamica l equations of quantum theory (as mentioned in II) that if thecomposite system M and S is isolated, then at the conclusion of themeasurement interaction the final state of M+ S is given by:

2 ) SM.S = Cl Q1M (~ 01S h- C2 Q2M Q 02s -I- .where QIM are the eigenstates of Q with eigenvalues qi.The problem is that equation (2) entails that at the conclusion of themeasuring process the measuring device is not characterized by aneigenstate of Q, rather, the final state of M+ S is a superposition ofproducts of the eigenstates of Q and O. But the usual account ofmeasurement (principles IV and V) stipulate that the state of M at theconclusion of the measurement will be some eigenstate of Q, and thatthe state of S at the conclusion of the measurement will be one of theeigenstates of O. The two treatments are flatly inconsistent with oneanother; and moreover there are, in principle, physically testabledifferences between the final states that these two different accountsentail. 2

A great deal of ingenuity has been expended over the years inattempting to say precisely how and when collapses might occur, andin attempting somehow to reconcile principles I, II and IV, V.Typically, such accounts involve claiming that measurements donot conform to I and II but instead produce a collapse of theobservable measured in accordance with V. We shall not pursue anyof these lines of thought here except to remark that (as is well known)they all face very serious difficulties.3 In particular, such accountsrequire a characterization of those interactions which are measure-ments and an account of how it is that measurements fail to satisfy theSchrodinger equation and instead instantaneously produce a collapseof the state of the system being measured.

THE MANY WORLDS INTERPRETATIONHere we want to discuss a response to the measurement problemcalled the many-worlds interpretation, first suggested by Evere tt


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I N T E R P R E TI N G T H E M N Y W O R L D S I N T E R P R E T T I O N 97

and later developed by DeWitt, Wheeler, and others. 4 The fundamen-tal idea of the many worlds interpretation is that measurements, andindeed all physical processes, must take place in accordance with theSchrodinger equat ion (or one of its relativistic variants). On this view,the state at the conclusion of a measurement process such as wasdescribed above is the uncollapsed state described by the right handside of (2).

The many worlds interpretation resolves the measurement problemsimply by denying that measuring O on S when the state of S is asuperposition of O-eigenstates brings about a collapse of the state-function of S into one of those O-eigenstates; that is, by denyingprinciple V. (The status of principle IV within the many-worldsinterpretation is, as shall presently be clear, a more complicatedmatter.) Consequently, there is simply no need, within this inter-pretation, to find an "explanation" of the collapse. One of the attrac-tions of the many worlds interpretation is that since it does not requirea division between measured system and measuring apparatus it is inprinciple possible to characterize the entire universe at any given timeby a state function like (1), a "universal wave function", the timeevolution of which is governed by a Schr6dinger equation. Thus theaccount has special appeal to cosmologists who may want to considerthe quan tum state of the universe. 5Although it may "solve" the measurement problem, the many-worlds interpretation faces difficulties of its own. The most obvious isthat it is difficult to square its claim that (in the measurement des-cribed above) the final, post measurement state of M+ S is not aneigenstate of O & O but a superposition of such states. How can thatbe? That the pointer on a measuring device is at some particularposition at the conclusion of a measurement is not, after all, atheoretical hypothesis which is open to question, bur rather (or so itwould seem), a straightforward empirical fact. When we look at thepointer (look to see the value of Q) it manifestly has a particularposition. 6 Moreover, when a human observer interacts with a systemlike M+ S in a state like the one on the right hand side of (2) byreading M's dial, then the Schr6dinger equation (for the systemObserver +M +S) entails that she (her brain, that is) evolves into asuperposition of belief states concerning the position of the pointerBut what can that mean? We certainly do not experience ourselves asin superpositions of belief states, or as evolving into them, when wemake observations


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198 D A V I D A L B E R T A N D B A R R Y L O E W E RTh ere is ano ther difficul ty with the many-w orlds c la im that (2)

correc t ly descr ibes the measurement of O. In (1) Ck is (according toIV) the probabil i ty that a measurement of O on S wil l yie ld the resul t0 = Ok These probabi l i t i e s a re the points a t which quantum theorymakes contac t wi th the outcomes of exper iments ; they a re absolute lyessent ial to our unders tanding of superp os i t ion and to the ap-pl icat ion and test ing of the theory. But i f the s ta te a t the end of ameasuring process is with c e r t a i n t y the one in (2), then what sense cani t make to say tha t when O i s measured the p r o b a b i l i t y of finding0 = Ok i s Ck? An d i f such s ta tements should turn out no t to mak e anysense a t a l l wouldn ' t tha t s imply pul l the rug out f rom under thethe ory?In addit ion to making the c la im that a l l physical processes aredescr ibed by a Sch r td ing er equa t ion , the many worlds in te rpre ta t ion i ssupposed to expla in how tha t c la im can be t rue whi le avoiding theproblems jus t ment ioned. I t i s jus t th i s which makes i t an in te r-pre ta t ion . We want to inqui re here whe ther or not the in te rpre ta t ioncan dea l wi th these problems; but thi s ta sk i s comp l ica ted a t the o utse tby the fact that i t isn ' t ent i re ly c lear just what the many-worldsinterpre ta t ion is . In an i l luminat ing art ic le , Ric har d He aly rem arke dtha t the in te rpre ta t ion i tse lf needs in te rpre t ing . 7 W e very m uchagree with him.

T H E S P L I T T I N G W O R L D S V I E WSo perhaps i t wil l be best to s tart off by c learing up a certa inconfus ion. There is a way of unders tanding the m any worlds in te r-preta t ion (a way one especial ly f inds in the popular l i tera ture onquantum theory) which, we wil l argue, is unsat isfactory. On thisin te rpreta t ion , which we ca ll the spl it ting worlds v iew , (SWV) whena quantum measurement occurs , the measur ing device and indeed thewhole l i tera l ly sp l i t s i n to tw o o r more (de pe nd ing on the numbe r o fposs ib le outcom es of the m easuremen t ) worlds . 8The fo l lowing passage by DeWit t sugges ts the SWV:The universe i s constan t ly sp l i tt ing in to a s tupendou s n umb er of branches , a l l resu l t ingfrom the measurement l ike in terac t ions be tween i t s myriads of components . Moreover ,every quantum t ransi t ion tak ing p lace on every s tar , in every ga laxy , in every remotecorner of the universe i s sp l i t t ing our loca l world on ear th in to myriads of copies ofitself. p. 161)


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I N T E R P R E T IN G T H E M A N Y W O R L D S I N T E R PR E T A T I O N 199On e w ay of unders tanding DeW it t ' s remark s i s as asse rt ing tha t thecomponents of the universa l s ta te func t ion of the universe a t a g ivent ime themse lves each represent a world a t tha t t ime . The t ime-dependence of the universa l s ta te func t ion i s taken to charac te r izesequences of such worlds or world h is tor ies . I f a t to @ is such aworld-component of the overa l l s ta te -func t ion, and i f an in te rac t iontakes p lace wi th in the world descr ibed by @, and i f tha t in te rac t ionresul t s in @1 and @2 be ing world-components a t the comple t ion ofthe in te rac t ion, then the SWV ins t ruc ts us to conce ive of the worldcorrespo nding to @ as having spl i t in to the two worlds , @1 and@ 2 .9

DeWit t says of th i s v iew:I still recall vividly the shock I experience d on first encountering this multiworldconcept. Th e idea o f 10 l+ slightly imperfect cop ies of oneself all constantly splittinginto further copies, which ultimately become unrecognizable, is not easy to reconcilewith common sense.D e W i t t a t t e mpt s t o re c onc il e t he SW V w i th c omm on se nse by argu ingtha t t o t he e x t e n t to w hic h w e c a n be re ga rde d s imply a s a u toma taand hence on a par wi th ordinary measur ing appara tuses , the laws ofquantu m mechan ics do not a l low us to fee l the spl it s (p. 161). Hisreason for th i s c la im i s as fo l lows: Suppose tha t an observer Ameasures the x-spin of an e lec t ron in st te c1/~x I C2~ x. A ssuming tha tA 's measurements a re perfec t ly accura te ( i . e . , P A believes spin =/spin = ) = 1) it fo llows tha t a t the conc lu s ion o f the m easur em entA + electron is in the sta te :

(3) c11'x Q BE L I 'x + c2 ~ (~) B E L ~(BE L I '~ is the s ta te of A 's be l ieving tha t the x-spin i s up , e tc . ) Onthe SW V this i s in te rpre ted as meaning tha t when A makes themea surem ent the world spli ts in to two worlds and tha t A literally splitsinto two successors, AL and AR. This is i l lustra ted in the fol lowingdiagram:

splitA prior to meas urem ent ~ (~'x + ~x)


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200 D V I D L B E R T N D B R R Y L O E W E RIn one world ( the one depic ted on the le f t ) AL correc t ly be l ieves tha tthe state of the electron is ~'x (since x-spin is up in that world) and inthe o the r world AR correct ly bel ieves that the s ta te of the e lectron is~,~. AL doesn ' t know about the sp l i t s ince she only remembers makingthe m easure men t and ob ta in ing the resul t tha t x-spin = t~ . An re-mem bers making the m easure men t and obta in ing x-spin = $~.) Fur-the rmore , i t fo l lows f rom the Schr6dinger equa t ion tha t subseque ntmeasurements by AL and o thers (same for AR) will confirm the resul tobta ined. So f rom AL's poin t of v iew the s ta te of the e lec tron appearsto be ~'~. It is ~ in he r world . And she has no knowledge of he r twinAR and the resul t of he r measurem ent . 1 Ev ere t t and DeW it t d i s-covered , surpr i s ingly , tha t even though the Schr6dinger equa t ion i sinconsistent with col lapses, i t predic ts tbat i t wil l appear to obse rvers(in the sense just expla ined) that col lapses occur. On the SWV,spl i t t ing plays the role of a col lapse by producing successors ofmeasur ing devices ( inc luding observers ) which record unique va luesof measurements . I t is this which leads one, and indeed led Everet t inthe f i rs t place , to think that th ere is som ething to the m any wo rlds idea.

There remains the problem of making sense of the probabi l i tyin te rpre ta t ion of the ampl i tudes on the SWV. The problem i s aformidable one because the dynamica l equa t ions a re comple te lyde te rminis t ic . So how does probabi l i ty ente r the p ic ture? DeWit tshows that i f we confine our a t tent ion to s i tuat ions in which, e .g. , Nindepend ent measu rements of the x-spin of e lec t rons in it ia lly prepar edin s ta te 1 /~(~ 'x + ~) a re made then as N goes to inf in ity the ampl i tudeof the sum o f sta tes in which sequen ce wi th a f requen cy d i f ferent f rom1/2 appear in the to ta l superpos i t ion converges to 0 . DeWit t sugges tsident i fying 0 amp li tude with 0 probabi l i ty. I t fol lows that the pro b-abi l ity of a seque nce wi th a f reque ncy d i f fe rent f rom 1/2 is 0 . DeW it tseems to think that this ident i f ica t ion solves the difficul ty concerningprobabi l i ty and remarks tha t the a rgum ent shows tha t the con-vent iona l probabi l i ty in te rpre ta t ion of quantum mechanics thusem erge s from the formalism i tse lf (p. 163).

There are many things wrong with the SWV. Our cri t ic isms wil ladvance us toward an interpreta t ion which, we wil l argue, is a moresa t i sfac tory way of unders tanding Ev ere t t ' s fundamen ta l idea; tha t a l lphys ica l processes a re governed by the dynamica l equa t ions as s t ipu-la ted by II . The fi rs t problem is the least subt le but perhaps the mostdestruct ive to the SWV. It is that the SWV is actual ly inconsistent


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I N T E R P R ET I N G T H E M N Y W O R L D S I N T E R P R E T T I O N 2 1

with the dynamical equations. For example, according to theSchr6dinger equation the total mass-energy of M+ S before and afterthe interaction are the same. This follows again from the linearity ofthe equations and the fact that in each of the states in the super-position the mass energy is the same before and after interaction.Similarly, the total number of particles comprising M + S is conserved.But on the SWV a measurement literally results in an astronomicalincrease of the number of particles and of the total mass-energy ofM + S. Of course it will be the case that this increase in the number ofparticles (or mass-energy) will go undetected by observers. But this inno way alleviates the main point that the splitting process is literallyinconsistent with the dynamical equations and so cannot be taken asan interpretation in which all physical processes are described bythem. No adequate many-worlds interpretation can countenance anysuch incompatibility with the dynamical equations.

The second difficulty concerns the understanding of probabilitywithin the SWV. Whatever merits DeWitt's argument for his claimthat the probability interpretation emerges from the quantummechanical formalism may have, it doesn't address the really difficultproblem that the dynamical equations are deterministic. 11 Since,according to the SWV, it is certain that all outcomes of the measure-ment will occur and will be observed by successors of A, what can bemeant by saying that the probability of a particular outcome = c2? Ifprobability is to be introduced into the picture, it must necessarily beby adding something to the interpretation. For example, we might saythat some of the worlds into which (2) splits are more ac tua l thanothers (or that one of the successors and not the other is really A .Then probability can be identified with the probability that the actualworld will follow a particular branch (or that A will find himself in aparticular world). The trouble with this suggestion is not only that it ismysterious (what distinguishes the more actual worlds from the lessactual ones?), but also that it gives up the central feature of the SWV,that the state-function entirely exhausts what there is to be said aboutthe physical world.

The third difficulty is called the problem of the democracy ofbasis . It concerns the way in which the worlds of the SWV arespecified. As stipulated by principle I the state of any system can bewritten as a linear combination of some complete set of basis vectors.According to the SWV the worms present when the system is in this


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202 D V I D L B E R T N D B R R Y L O E W E Rs ta te correspond to these bas is vec tors . For example , i f A measuresthe x-spin of an e lec t ron in the s ta te l /x /2( t~ + ~ ) then the pos t -measurement s ta te of A + e lec t ron wi l l be

(4) ~2 (1 ~ (~ B E L I ' ~ + ,l,x (~) BEL ] ,~ )where in the re a re , according to the SWV, two worlds , one in which Abelieves that spin is up and the spin is up and one in which A bel ievestha t spin i s down and the spin i s down. The problem is tha t the re a rean infinity of d is t inc t comple te se t s of bas i s vec tors in te rms of which(4) (and any such sta te) can be wri t ten. For example, (4) can a lso bewri t ten thus:

5) w he re

(--*A) = --~_ (B E L (t ~) + BEL(,I,x)),V 2((--A) = ~22 (B EL (t~ ) - BE L(~ x)),

In (5) the bas is vec tors , and consequent ly the worlds are --~A ~)---~and < ---a@ ~ 'x These are worlds in which the x-spin has no defini tevalue and A has no defini te bel ief about the value of x-spin. Thisspl i t t ing is certa inly not what the proponents of the SWV have inmind. Rather, they suppose that the l ines a long which the world spl i tswhen A measures the x-spin a re the ones tha t correspond to (4) andnot the ones that correspond to (5). At least in those si tuat ionsinvolving observers, they seem to suppose that the spl i t t ing process isa long l ines determined by brain sta tes associated with defini te bel iefsabout the measured sys tem. The problem is tha t in quantum theory the


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I N T E R P R E TI N G T H E M N Y W O R L D S I N T E R P R ET T I O N 2 3

choice of a se t of basis vectors in which to express a s ta te hasabsolute ly no phys ica l s igni f icance . So there i s nothing in quantumtheory i t se l f tha t suppor ts the representa t ion (4) over (5) . The MWVmust add something i f i t is to support i ts posi t ion that the worlds spl i ta long a preferred basis .The upshot of our d i scuss ion i s tha t the SWV is ce r ta in ly not anadeq ua te in te rpre ta t ion of the quan tum mechanica l formal ism. Thepos tu la ted spl i t t ing i s not fu l ly charac te r ized ( the democracy of bas i sproblem); i t i s incompat ib le wi th the dynamica l equa t ions i t i s sup-pose d to in te rpre t ( the conserva t ion of mass problem), and i t leaves usc omple t e ly i n t he da rk a bou t the meaning of probabil i ty c la ims (thede te rminism problem).

T H E M N Y M I N D S V I E W

The fundamenta l idea of the many worlds in te rpre ta t ion i s that allphysical processes whatsoever are governed by the SchriJdinger equationWe wil l construct an interpreta t ion which entai ls precisely this whileavoiding the problems tha t we found in the SWV. Our procedure wi l lbe to bui ld up to ou r in te rpre ta t ion in s tages , mot iva t ing i ts fea tures bycons ider ing solu t ions to problems tha t face the SWV.As we saw, the main d i f ficul ty tha t mus t be ov erc om e to implemen tthe fundam enta l idea is tha t th is idea enta i ls tha t m acrosc opic m easur-ing devices and indeed observers themse lves can be in superpos i t ions .W hat we want is an in te rpre ta t ion which explains how i t is tha t wealways se e (mistakenly so, i f the ma ny worlds interpre ta t ion iscorrec t ) macroscopic objec ts as not be ing in superpos i t ions and neverexper ience ourse lves as in superpos i t ions . The hear t of the problem istha t the w ay we conc e ive of menta l s ta tes , be l ie fs , memo ries , e tc . , i ts imply mak es no sense to speak of such s tates or of a mind as be ing ina superpos i t ion . When we in t rospec t fo l lowing an x-spin measurementwe never , a s apparent ly predic ted by the theory , f ind ourse lves in asuperposi t ion of thinking that spin is up and thinking that spin is down.If in t rospec t ion i s to be t rus ted , and i t seems par t of our very conceptof mental s ta tes that i t is t rustworthy at least to this extent , then we arenever in such superpos i t ions .

Le t ' s make th i s point sharper . Suppose :i) A is an obse rve r w ho c a n pe r fe c t ly me a sure x - sp in . (Tha t


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204 D V I D L B E R T N D B R R Y L O E W E R

(ii)

(iii)

i s : subse que n t t o a n x - sp in m e a su r e m e n t by i x iff Mbeliev es th at t~ and $~ if f M believ es th at Sx.)A c a n c o r r e c t ly r e po r t so m e o f he r m e n ta l s t at e s.Spec i f ica l ly , wh en A s ince re ly repor ts tha t she has a de f in i tebe l ie f abo ut the va lue of x- sp in ( i. e. , she repor ts : I t ise i the r the case tha t I be l ieve tha t sp in i s up , or i t i s the casetha t I be l ieve tha t sp in i s down, but i t i s no t the case tha tm y be l i e f s a bou t t he va lue o f x - sp in a r e in a ny wa y un -c e r t a in , o r il l -de f ine d , o r supe r pose d ) , t he n A doe s be l i e vetha t the x-sp in has a de f in i te va lue .The s t a t e whe r e in A be l i e ve s tha t t~ a nd the s t a t e whe r e inA be l ieves tha t ~ a re ident ica l wi th ce r ta in phys ica l s ta tesof A 's b ra in. W e wil l ca l l those sta te s B t and B~, .

I t tu rns out (and th is i s the sha rper form of our problem) tha t ( i i i ) i sinc ons i s t e n t w i th (i) a nd (ii) a nd qu a n t um m e c ha n ic s . Th e a r gu m e n tgoes l ike th is : le t A me asu re th e x-sp in of an e lec t ro n whic h i s in i t ia llyin the s t a t e c l t~ + c 2~ x. S ubse q ue n t t o tha t m e a s u r e m e n t , i f qua n tu mtheory and suppos i t ion ( i ) a re cor rec t , the s ta te of A + e lec t ron i s

8) c BL I t fo l lows f rom supp osi t ion ( ii) tha t A wi l l answer the ques t io n D oyou be l i e ve tha t t he x - sp in o f t he e l e c t r on ha s a de f in i t e va lue ?a f fi r m at i ve l y w h e n e v e r e i t h er o f t h e s t a te s B t x ~ ) t x o r B ~ ( ~ ) ~ob ta ins. A nd now i t fo l lows f r om the l i ne a r i ty o f t he qu a n tu mm e c ha n ic a l e qua t ions o f m o t ion , t ha t A wi l l a nswe r th i s que s t iona f f i r m a t ive ly whe ne ve r any l inea r superp os i t ion of B$~ (~)t~ andB~x (~)~x obta ins. So, in pa r t icul ar , i t fol lows from (i) and ( ii ) andquantum mechanics tha t when s ta te (8) obta ins , A wi l l a f f i rm tha t shebe l ieves tha t the x-sp in of the e lec t ron has a de f in i te va lue , e i the r upor down. But i f suppos i t ion ( i i i ) i s t rue then when (8) obta ins i t i s no tthe case tha t A be l ieves tha t x- sp in i s up , and i t i s no t the case tha t Abe l ieves tha t x- sp in i s down s ince A 's bra in i s in a superpos i t ion ofsta tes. So we have der ived a contradic t ion f rom ( i) , ( i i ) , ( i i i ) , andq u a n t u m t h e o r y .

I f we a r e to m a in ta in the f u nda m e n ta l i de a o f t he m a n y wor ldsin t e r p r e t a t ion a nd a l so m a in ta in ou r o r d ina r y c onc e p t ion o f m e n ta ls ta tes a s access ib le to in t rospe c t ion then we m ust g ive up (iii). Beca use


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I N T E R P R E T IN G T H E M A N Y W O R L D S I N T E R P R E T A T IO N 205(i i i ) identif ies mental s ta tes (e .g. , the sta te of believing that spin is up)wi th physica l s ta tes i t r e sul t s , g iven quantum theory and ( i ) , in thec onc lus ion th a t be l i e f s t a t e s c a n be in supe r pos i t ions . I f we d e ny tha tbe l ie f s ta tes can be in superpos i t ions (as ( i i ) seems to requi re us to do) ,the n we a r e de ny ing ( i i i ) . Th i s r e sponse toge the r w i th the a s sum pt iontha t a l l phys ic a l s t a t e s a r e qua n tum m e c ha n ic a l c om m i t s us to am ode s t ( so f a r ) non- phys ic a l i sm . Th i s non- phys ic a l i sm i s i ne v i t a b le inthe p r e se n t c on te x t . As long a s we m a in ta in bo th tha t we ha vein t rospec t ive access to our menta l s ta tes ( i . e . , a pe rson who says hebe l ieves tha t the sp in has a de f in i te va lue i s , o the r th ings be ing equa l ,c o r r e c t c onc e r n ing h i s be l i e f ) a nd tha t a l l phys ic a l s t a t e s a r e qua n tumm e c h a n i c a l , o u r a r g u m e n t s h o w s t h a t w e m u s t a c c e p t t h i s m u c hnon- phys ic a l i sm .

Here i s a way tha t we can g ive up ( i i i ) . Consider A aga in about tom e a su r e the x - sp in o f a n e l e c t r on . The e l e c t r on i s i n i ti a lly in s ta t ec11 x + c2+x an d A is ini t ia l ly in a sta te of readine ss. A t the co nc lus ionof the measurement A + e lec t ron i s the s ta te desc r ibed by (8) . We wi l lpos tu la t e th a t t he e v o lu t ion o f A s m e n ta l s t a t e in the c our se o f them e a su r e m e n t i s no t de te r m in i s t i c ( as i s t he e vo lu t ion o f A s bod y +e lec t ron) but i s probabilistic. A s mind s ta r t s out in a s ta te in which sheha s no be l ie f s a bo u t x - sp in a nd e nd s up e i the r in the s t a t e c o r r e spond-ing to Bl x or in the s ta te c or res pon din g to BJ ,~ ( tha t i s, ends u p e i th e rbe l ieving tha t sp in i s up or be l ieving tha t sp in i s down) but never i s ina superpos i t ion of be l ie f s ta tes . I t i s pos tu la ted , and th is i s a pr inc ip letha t i s a dde d to qua n tum the or y , t ha t(P ) t he p rob a b i l i t y t ha t A s mi nd e nds up be l i e v i ng t ha t sp i n i s up =cZ~ a nd t hep roba b i l i t y t ha t A s mi nd e nds up be l i e v i ng t ha t sp i n i s down = c 2.( P ) ge ne r a l i z e s to a ny pe r f e c t m e a su r e m e n t by a n obse r ve r .

This v iew, which we ca l l the s ingle mind v iew (SMV), so lyes someof the p r ob le m s tha t c on f r on t the S WV. On the S M V the e n t i r ephys ic a l wor ld i s a tho r ough ly qua n tum m e c ha n ic a l sys t e m a s de s -c r ibed by pr inc ip les ( I) and ( II ). P r inc ip le ( IV) i s sa t i sf ied by in te rp re t -ing qua n tum m e c ha n ic a l p r oba b i l i t i e s a s the p r oba b i l i t i e s tha t a nobse r ve r ( a m ind) w i l l ha ve c e r t a in be l i e f s a f t e r m a k ing a m e a sur e -m e n t . T h e w o r l d d o e s n o t s p l i t u p o n m e a s u r e m e n t ; r a t h e r , t h e m i n da ssoc ia t e d wi th a b r a in e nds up be ing in the m e n ta l s t a t e a s soc ia t e dwi th one o f the b r a in s t a t e s in the supe r pos i t ion o f B s t a t e s tha tdesc r ibes he r bra in . The probabi l i ty tha t the mind wi l l end up in apa r t i c u la r s t a t e i s c om ple te ly de te r m ine d by the phys ic a l s t a t e o f the


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206 D V I D L B E R T N D B R R Y L O E W E Robse r ve r + sys t e m m e a sur e d . E ve r e t t s a nd De Wi t t ' s o r ig ina l a r gum e n tto e xp la in why sys t e m s a ppe a r to c o l l a pse on m e a sur e m e n t i s e a s i lya d a p t e d b y t h e S W V . A f t e r m e a s u r e m e n t t h e m i n d s a s s o c a i t e d w i t hthe le f t hand par t of (6) wi l l a l l be l ieve tha t x- spin i s up . Fur therm e a s ur e m e n t s by the obse r ve r w i l l r e su l t i n " c on f i r m a t io n" s inc e thebra in s ta tes tha t a re pa r t of the overa l l s ta te a l l pe rce ive the sameva lue . The r e is no wo r r y a bou t the f a c t t ha t we ne ve r f e e l ou r se lve s tobe in o r in t r ospe c t supe r pos i t ions s inc e m e n ta l s t a t e s a r e ne ve r insupe r pos i t ions . An obse r ve r ' s s inc e r e r e por t s a bou t he r be l i e f s inc i rcumstances l ike (8) a re t rue . She cor rec t ly repor ts tha t she has adef in i te be l ie f about sp in because she does in fac t be l ieve i t to bee i the r up o r be l i e ve i t t o be down .Of c our se the s t a r t l i ng f e a tu r e o f the S M V i s i t s non- phys ic a l i sm .On the SMV, a l l but one of the e lements of a superpos i t ion l ike (8)r e p r e se n t , a s it we r e , m ind le s s b r ains ; a nd w hic h e l e m e n t r e p r e se n t s am ind i s no t de te r m ine d by the phys ic a l na tu r e o f the unde r ly ing b r a ins t a t e a n d c a n n o t b e d e d u c e d f r o m t h e q u a n t u m s t a t e o r f r o m a n yphysica l exper im ent . I t is c lea r f rom the d i lem ma g ene ra te d b y ( i), ( ii),and (iii) that a n y m an y wor lds in te rpr e ta t io n wh ich respec ts (ii) wi l l bec om m i t t e d to som e f o r m o f non- phys ic a l i sm , bu t t he non- phys ic a l i smof the SMV seems espec ia l ly pe rnic ious . I t en ta i l s tha t menta l s ta tesd o n o t e v e n s u p e r v e n e on bra in s ta tes (or physica l s ta tes genera l ly)s inc e one c a nno t t e l l f r om the s t a t e o f a b r a in wha t i t s s ing le m indbelieves.He r e i s a wa y to r e m e dy the s i tua t ion . S uppose tha t e ve r y se n t i e n tphysica l sys tem, every observer , has assoc ia ted wi th i t not a s inglem ind bu t r a th e r a n in fin i te se t o f m inds . ( The r e a son f o r the se t 's be inginf in ite wi l l soon b e a pparent . ) W e wi l l ca l l th is the " m an y mindsv ie w" ( M M V ) . W e suppose tha t whe n a n ind iv idua l ' s b r a in ( o r b ra in +e nv i r onm e n t ) i s i n s t a t e B * the ind iv idua l i s i n a c e r t a in m e n ta l s t a t eM k , i . e . , has ce r ta in be l ie f s , in tent ions , memor ies , exper iences , e tc .This supposi t ion i s p h y s i c a l i s t i c i n tha t i t s a ys tha t m e n ta l s t a t e s a r ed e t e r m i n e d b y o r s u p e r v e n i e n t o n b r a i n ( o r b r a i n + e n v i r o n m e n t )s t a t e s . The B ~ do no t f o r m a c om ple te ba s i s bu t t he y a r e a subse t o fone . So any bra in can be represented as in a s ta te :

(9) B = c l B * + c2 B 2 + c3 B * + whe r e the B ~ a r e the s t a t e s a s soc ia t e d wi th m e n ta l s t a t e s a nd theuns ta r r e d B s r e p r e se n t s t a t e s no t a s soc ia t e d wi th m e n ta l s t a t e s . Nowour proposa l i s to assoc ia te wi th each B* in (9) an inf in i te se t of minds


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I N T E R P R E T I N G T H E M A N Y W O R L D S I N T E R P R E TA T I O N 207in the corresponding mental state Mr and a measure P on the totalityof minds associated with all the B* such that the P of the set of mindsin state Mk = c~. P is a measure of the propor tion of minds in stateMk. Finally, each individual mind is supposed to evolve probabilistic-ally in accordance with postulate (P).

The individual minds, as on the SMV, are not quantum mechanicalsystems; they are never in superpositions. This is what is meant bysaying that they are non-physical. The time evolution of each of theminds on the MMV is, just as on the SMV, probabilistic. However,unlike the SMV, there are enough minds associated with the braininitially so that minds will end up associated with each of the elementsof the final superposition. An infinity of minds is required since ameasurement or a sequence of measurements may have an infinitenumber of outcomes. Furthermore, although the evolution of in-dividual minds is probabilistic, the evolution of the set of mindsassociated with B is deterministic since the evolution of themeasurement process is deterministic and we can read off from thefinal state the proportions of the minds in various mental states.Here is how the account works in the example of x-spin measure-ment. Suppose an observer is about to measure the x-spin of anelectron is in a brain state B wherein no mind has a belief that thevalue of x-spin is up (or that it is down) and that the electron is in statecl~x+c2~x: at the completion of the measurement the observer+electron is in the familiar state

1 0 ) ClB ~x ~ ~x + c2S~ (~ ~/xwherein the proportion of minds that have observed spin up (down) isc 2 (c2). Before making the measurement, each observer's mind canknow that (8) will be the post-measurement state and so can assign aprobability of c 2 to its observing spin up.We have purchased supervenience of the mental on the physical atthe cost of postulating an infinity of minds associated with eachsentient being. No doubt this talk of infinitely many minds soundscrazy. Perhaps it will seem less so after we see what it does for theinterpretation of quantum mechanics and how it compares with otherinterpretations.

First, and most important, the MMV (unlike the SWV) is in accordwith the fundamental idea of the many worlds interpretation--tha t theentire physical universe, and every physical system, is quantum


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208 D V I D LBERT N D B RRY LO EW ERmechanical in the sense of principles I and II. There is no need topostulate collapses or splits or any other non-quantum mechanicalp h y s i c l phenomena. And so there arises no conflict with conservationlaws as we saw on the SWV.

Second, the MMV entails that the time-evolution of the wholephysical world is completely deterministic, and that the global mentalstate of every sentient physical being (that is: the d i s t r ib u t io n ofmental states among the infinity of that being's minds) is uniquely fixedby the physical state of that being. Unlike the abandoned SMV, theglobal mental state is unambiguously determined by its physical stateand consequently the time-evolution of the global state is, likewise,deterministic.Third, the MMV is in accord with our very deep conviction thatmental states never superpose; consequently it is in accordance withthe claim that competent sentient beings can accurately report theirmental states.

Fourth, the MMV (unlike the SWV) entails that the choice of basisvectors in terms of which the state of the world is expressed has nophysical significance. There is always but o n e physical world in but o n equantum mechanical state on this account; and that state can beequally well written in terms of any complete set of basis vectors. Aslong as a brain is in a state which c n be represented as a super-position of B states it will have minds associated with it.

Fifth, there is no special problem on the MMV of interpretingprobability. Probabilities are completely objective although they donot refer to physical events but always to sequences of states ofindividual minds. The assertion, the probability that A will obtainresult l'x when measuring the x-spin of an electron in state c11'x +c2~ = c 2'' means simply that the probability tha t a mind associatedwith A will observe that x-spin is up = c 2 (recall that A's measure-ment is perfect . ) Although probabilities do not emerge from thequantum mechanical formalism we can adapt DeWitt's argument toshow from our postulate connecting the proportion of minds withamplitudes that the probability that a mind will believe that it residesin a maver ick world (i.e., has beliefs different from those in accordwith quantum mechanical probabilities) converges to 0 (but maverickminds will still be present).

Sixth, the account is re l i s t in the sense that it entails that there is auniquely correct state for the whole universe and in the sense that it


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I N TERPRETI N G TH E M N Y W O RLD S I N TERPRET TI O N 209does not suppose that the state of the universe in any way depends ona consciousness or on what observables an observer decides tomeasure. In this it contrasts markedly with some idealist inter-pretations which entail that consciousness, by bringing about a col-lapse or in choosing to measure certain observables, in some mys-terious way makes reality (perhaps different realities for differentobservers), u This realism, however, does have the consequence that amind's beliefs about the state of a system after measurement aretypically fal se. Thus, a mind associated with A that measures theX-spin of an electron in a superposition will at the conclusion of themeasurement believe, say, that the x-spin is up (of course some of A'sother minds will believe that spin is down). In fact, spin is neither upnor down but rather the system A's brain + electron (and of course theintermediary measuring devices, etc.) is in a superposition. So A'sbelief is strictly incorrect. However , it is, we might say pragmatical lycorrect , in the sense that subsequent measurements of the x-spin byA will, from the perspective of that mind, yield results which agreewith its initial measurement. 12

Not only is the MMV a realist interpretation of quantum mechanics,it also provides an account in which all interactions are local This issurprising because Bell's theorem is widely thought to rule out realist,local interpretat ion of quantum mechanics. 12 To see how the MMVallows for a local realist interpretation without violating Bell'stheorem, consider the sort of situation that Bell considers in provinghis theorem: A system consisting of two electrons is in the EPR state1 ,(EPR) ~ t (~) 2 - $1 Q t~).The electrons separate to distinct points 1 and 2 and an observer A1measures a component of the spin of electron 1 and an observer A2measures a component (not necessarily the same component) of thespin of electron 2. Bell's theorem says that there is no consistentdescription of the system which (a) assigns a state to a system in whichthe measured components have definite values (realism) and (b) inwhich the value obtained by one observer is independent of whichcomponent of spin the other observer decides to measure (locality),and which yields the correlations predicted by quantum theory for asystem in EPR. The MMV denies Bell's version of realism since


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210 DAVID ALBERT AND BARRY LOEWERaccording to i t the real s t a t e o f t he e l e c t ron+ obse rve r a f t e r ameasurement of spin on the system is s t i l l in a superposi t ion. Morespecifical ly, when A1 measures the x-spin of e lectron 1 his brain wil lgo in to a superpos i t ion corre la ted wi th the EPR s ta te . In th i s super-posi t ion, half his minds wil l bel iev e that spin is up and half wil l bel iev etha t spin i s down. S imi la r ly for A2 ' s measurement on e lec t ron 2 . Infac t the MMV enta i l s tha t a t the conc lus ion of Al ' s and A2 'sme a sure me nt s , no ma t t e r w hic h tw o sp in c ompone n t s t he y ma y ha vemeasured (even i f they measure d i f fe rent components) , 1 /2 of Al 'Sminds wi l l be l ieve tha t the resul t of the measurement he carr ied outwas up and 1/2 of his minds will bel ie ve that the resul t was do wn .Prec ise ly the same holds for A2. No corre la t ions wi ll have a r i sen atth i s point be tween the resul t s recorded in A~ 's minds and thoserecorded in A2 ' s minds , and indeed no ta lk of corre la t ions i s eveninte l l ig ib le . Those corre la t ions come in to be ing only when the obser-vers communica te the resul t s of the i r respec t ive measurements to oneanother. This communicat ion is , of course , a local dyna mic a l p roc e ssgoverned by the Schr6dinger equa t ion. I t i s then guaranteed tha t i f A1and A2 measured the same spin component they wi l l end up (a f te rcommunica t ion) be l ieving tha t they obta ined opposi te va lues . I f theymeasu red di f ferent spin com ponen ts , say x and x + 0, then the prob -abi l i ty tha t they wi l l end up be l ieving tha t they obta ined opposi tevalue s is cos z O. Th ese are the usual qu antu m mec hanica l p robabil i t iespredic ted by the theory . In thi s way the MM V permi ts a realist sincethe sys tem A1 A2 + electron1 + electron2 is a lways in som e part icularsta te , and local since interact ions are a l l local , descript ion.The preceding l is t seems to us suffic ient ly impressive to give theMMV a hearing in spi te of i ts dual is t commitments. In general i t canbe said that unl ike other accounts i t a l lows one to te l l complete lyexplic i t and inte l l igible stories, without employing non-classical logicsor myste r ious col lapses , about any quantum mechanica l process , in-c luding measurement ; s tor ies which a re ent i re ly cons is tent wi th pr in-ciples I and II and hence are local ly real is t ic . At the same t ime theaccount prese rves our ordinary (and perhaps a pr ior i ) concept ion ofmenta l s ta tes as access ib le to in t rospec t ion. The same cannot be sa idfor any oth er interp reta t io n . Of course , what a l lows for al l of this iswha t must be admi t ted to be an ext ravagant dua li sm. One m ay won derwhether i t may b e poss ib le to ge t away wi th less dua li s t commitmen ts .One assumpt ion, pe rhaps the most d i s turbing aspec t of the dua l i sm,


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I N T E R P R E T I N G T H E M A N Y W O R L D S I N T E R P R E T A T I O N 2

i s t h a t t h e r e i s a m a t t e r o f f a c t c o n c e r n i n g w h e t h e r o r n o t a m i n da s s oc i a t e d w i t h a b r a i n a t one t i me i s t he s m e mi nd a s one a s s oc i a t e dw i t h t he b r a i n a t a d i f f e r e n t t i me . T h i s a s s umpt i on v i o l a t e s t he s upe r -v e n i e n c e o f t h e m e n t a l o n t h e p h y s i c a l s i n c e t h e e v o l u t i o n o f t h ephys i c a l s t a t e o f t he un i ve r s e doe s no t de t e rmi ne s uc h i de n t i t i e s . (O nt he o t he r ha nd , a s w e p r e v i ous l y s a w , t he p ropor t i on o f m i nds i nva r i ous me n t a l s t a t e s a s s oc i a t e d w i t h a b r a i n a t a g i ve n t i me doe ss u p e r v e n e o n t h e p h y s i c a l s t a t e o f t h e b r a i n , o r b r a i n p l u s e n v i r o n -me n t . ) We c ou l d e f f e c t a pa r ti a l r e t r e a t f r om t h is dua l is m b y pos t u l a t -i ng t ha t a s s oc i a t e d w i t h a b r a i n a t a ny on e t i me is a s e t o f m om e n t a r ym i n d s w h i le n o t p o s t u la t i n g t h a t t h e r e i s a m a t t e r o f f a c t t h a t ami nd ( a s s oc i a t e d w i t h a pa r t i c u l a r b r a i n ) a t one mome n t i s t r a ns -t e mpora l i de n t i c a l w i t h a mi nd ( a s s oc i a t e d w i t h t he s a me b r a i n ) a ta n o t h e r m o m e n t . H o w e v e r , th e c os t o f s u r re n d e r in g t h e t r a n s - t e m -p o r a l i d e n t it y o f m i n d s w o u l d s e e m t o b e t h a t w e c a n n o l o n g e r m a k es e ns e o f s t a t e m e n t s l i ke t he p ro ba b i l i t y t ha t I w il l obs e rv e sp i n up onm e a s u r e m e n t is p s in c e s u c h s t a t e m e n t s s ee m t o p r e s u p p o s e t h a t itma ke s s e ns e t o t a l k o f a s i ng l e mi nd pe r s i s t i ng t h rough t i me . P e rha ps ,how e ve r , i t c ou l d be a rgue d ( t hough w e w i l l no t do s o he r e ) t ha t t hec onc e p t i on o f a m i nd pe r s i s t i ng t h rough t i me i s a n i l l u s i on ; one t ha tr e su l ts f r o m t h e f a c t t h a t m o s t m o m e n t a r y m i n d s w ill b e a s s o c ia t e dw i t h b r a i n st a t e s w h i c h r e c o rd a pe r s o na l h i s t o ry a nd so i t w il l s e e mto such a mind tha t i t has ex i s t ed as a pe rs i s t ing en t i ty .

C o u l d w e g o f u r t h e r a n d e l i m i n a t e a l l r e f e r e n c e t o m i n d s ? S u c h a ne l i mi na t i v i s m w ou l d e n t a i l a r a d i c a l l y d i f f e r e n t w a y o f t a l k ing a bo u tq u a n t u m t h e o r y a n d a b o u t o u r s e l v e s. T o d o s o w o u l d , si n c e q u a n t u mt h e o r y i s c o m p l e t e l y d e t e r m i n is t i c, g i v e u p a n y w a y o f m a k i n g s e n se o fq u a n t u m m e c h a n i c a l p r o b a b i l i t i e s . F u r t h e r , o n s u c h a n a c c o u n t t h e r ew o u l d b e n o m e n t a l s t at e s as w e o r d i n a r il y u n d e r s t a n d t h e m . T h e r ewi l l s t i l l be s t a t es , the bra in s t a t es B*, which reg i s t e r informat ion ands o ma y r e s e mbl e me n t a l s t a t e s , bu t t he s e s t a t e s w i l l no t be i n t ro -s pe c t i b l e i n t he w a y t ha t ( ii i) r e qu i r e s . W he t he r i t m i g h t be pos s i b le f o rus t o l e a rn s uc h a l a ngua ge , t ha t i s , t o l e a rn t o de s c r i be t he w or l de n t i r e l y i n q u a n t u m m e c h a n i c a l t e r m s , is a q u e s t i o n t h a t w e m u s t l e a v efo r a no t he r oc c a s i on , i s

N O T E ST h e a u t h o r s w o u l d l ik e t o t h a n k Y a k i r A h a r a n o v a n d D a v i s B a i r d f o r d i s c u s s i o n s o f

t h e m a n y w o r l d s i n t e r p r et a t i o n .


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2 1 2 D A V I D A L B E R T A N D B A R R Y L O E W E R

1 F or e xa mpl e , J . von Ne um a nn : 1955 , Mathematical Foundations of QuantumMechanics P r i nc e t on .2 W he n M + S is i n t he s ta t e de sc r i be d by (2) t he re i s a n obse rv a b l e R wh i c h i s i n a neigenst te R k On t he o t he r ha nd i f M + S is in one o f t he e i ge ns t a t e s i n t hesuperpos i t ion (2) then R i s in a superpos i t ion of Ri s ta tes . So in pr inc ip le one can te l lt he d i f f e re nc e be t we e n t he t wo pos t me a su re me n t s t a t e s by me a su r i ng R . I f t he s t a t e i s(2 ) we wi ll ob t a i n t he s a me va l ue e v e ry t i me we me a su re R on a sys t e m p re pa re d a sM + S i s. I f t he s t a t e i s one o f t he e i ge ns t a t e s o f (2 ) we wil l ob t a i n va r i ous va l ue s fo r R .H o w e v e r , t h e m e a s u r e m e n t o f ( R ) i s b e y o n d t h e m e a n s o f c u r r e n t t e c h n o l o g i e s b e c a u s eR i s ve ry uns t a b l e ; fo r e xa mpl e i t wou l d be d i s t u rbe d i f M+ S i n t e ra c t e d wi t h a s i ng l ea i r mo l e c u l e . S ome a u t ho rs a ppe a l t o t he i na b i l i t y t o de t e rmi ne whe t he r t he s t a t e o fM + S i s (2) o r on e o f i t s e i ge ns t a t e s t o a rgue t ha t t he m e a su re m e n t p rob l e m i s o f noi mpor t . B u t t h i s j u s t m i s se s t he po i n t . T he t wo s t a t e s a re d i f f e re n t.3 A d i s c us s i on o f va r ious a t t e mp t s t o de a l wi th t he me a su re m e n t p rob l e m c a n be foundi n B . d ' Espa gna t : 1971 , Conceptual Foundations o[ Quan tum Mechanics B e n j a mi n .4 T h e m a i n p a p e r s o n t h e M a n y W o r l d s I n t e r p r e t a ti o n a r e c o l l e c t e d in D e W i t t a n dGraham (eds . ) : 1973, The Ma ny Worlds Interpretation of Quantum Mechanics P r i n c e t o nUni ve r s i t y . P a ge r e fe re nc e s a re t o De W i t t ' s pa pe r s i n t h i s vo l ume .5 A c c o r d i n g t o t h e o r t h o d o x i n t e r p r e t at i o n e v e r y m e a s u r e m e n t p r e s u p p o s e s a d i s -t i nc t i on be t we e n t he sys t e m be i ng me a su re d (wh i c h i s de sc r i be d qua n t um me c ha n i c a l l y )a nd t he me a su r i ng a ppa ra t u s (wh i c h i s de sc r i be d c l a s s i c a l l y ) . On t h i s a c c oun t i t i sd i t ti c u lt t o s e e how qu a n t um t he o ry c a n be a pp l i e d t o t he who l e un i ve r se . In c on t ra s t t hema ny wor l d s i n t e rp re t a t i on a l l ows one t o spe a k o f t he qua n t um s t a t e o f t he e n t i r eun i ve r se a nd so s e e ms more su i t e d fo r c osmol og i c a l a pp l i c a t i ons . F o r a n e xa mpl e o fsuc h a n a pp l i c a t i on s e e D . Al b e r t , ' P os s i b il i ty t ha t t he P re se n t Qua n t um S t a t e o f t heU n i v e r s e i s t h e V a c u u m , f o r t h c o m i n g .6 I t is no t c l e a r wha t i t wou l d be t o s e e a ma c rosc op i c o bse rva b l e i n a supe rpos i t i ona l t hough some a u t ho r s i ma g i ne t ha t i t is li ke s e e i ng a b l u r.7 R i c ha rd He a l y : 1984 , ' How Ma n y W or l ds ' , Nous 18.s H e inz Page ls : 1984, The Cosmic Code B a n t a m , s e e m s t o u n d e r s t a n d t h e m a n y w o r l d si n t e rp re t a t i ons a s t he S W V. B ryc e De W i t t i n h i s pa pe r s i n t he book foo t no t e d i n 4 a l sounde rs t a nds t he i n t e rp re t a t i on t h i s wa y . Howe ve r , Eve r re t t ' s v i e ws a re muc h morea mbi guous , a t t i me s sugge s t i ng a spe c t s o f t he v i e w we l a t e r a dva nc e .9 T h e w o r l d s o f t h e S W V m a y r e m i n d o n e o f t h e p o s s i b l e w o r l d s w h i c h a r e di s c u ss e di n ph i l o soph i c a l l og i c. The y d i f f er a t l e a st i n t wo re spe c t s . A l l t he w or l d s o f t he S W V a ree qua l l y r ea l a nd n one a re a bs t r a c t . In t h i s it d if f e rs f rom t he c o mm on v i e w t ha t pos s i b l ewor l d s a re a bs t r a c t e n t i t i e s o f some k i nd , s e t s o f p ropos i t i ons o r p rope r t i e s . I t i s morel i ke Da v i d Le w i s ' r e al i sm a bou t pos s i b l e wor l d s e xc e p t t ha t on t he S W V wor l ds sp li t .S e c ond , t he ir wor l d s o f t he S W V a re qu a n t u m wor l ds i n t ha t som e obse rva b l e s a re i nsuperpos i t ions a t a world .l o F o r a n obse rv e r t o d i s c ov e r t ha t she i s i n a supe rpos i t i on l i ke (7 ) i nvo l ve s he r ma k i nga sell-measurement on a n obse rva b l e wh i c h i s i nc ompa t i b l e wi t h s t a t e (7 ) . I t fo l l owsf rom t he qua n t um me c ha n i c a l fo rma l i sm t ha t suc h a n obse rva b l e e x i s t s . S e e Al be r t ,D a v i d ' S e l f - M e a s u r e m e n t ' Physics Letters V o l . 9 8 A a n d ' A Q u a n t u m M e c h a n i c a lA u t o m a t o n ' , Philosophy of Science f o r t h c o m i n g .~ 1 De W i t t ' s a rgume n t f a l l s sho r t o f de mons t ra t i ng t ha t t he p roba b i l i t y i n t e rp re t a t i one me rge s f rom t he fo rma l i sm . In o rde r t o s e c u re a p roba b i l i t y i n t e rp re t a t i on he mus t


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I N T E R P R E T I N G T H E M A N Y W O R L D S I N T E R P R E T A T I O N 2 1 3ident i fy an ampl i tude converg ing on 0 and a probabi l i ty converg ing on 0 . This i s asubstan t ia l assumpt ion , and no part o f the quantum mechanica l formal i sm. Indeed ,DeWit t ' s a rgument , as he h imsel f seems to recognize , i s c i rcu lar . At one poin t hesuggests tha t mav eric k worlds (worlds wi th the wr ong frequencies) a re s implyabsent for the grand su perposi t ion . Th at i s , no t on ly i s the ampl i tude (probabi li ty ) o fsuch worlds 0 but they are physical ly impossible. However, this suggestion in confl ictwi th the gu id ing idea of the many worlds in terpre ta t ion tha t the Schrodinger equat iondescribes a l l physica l p rocesses , s ince acc ord ing to i t here wi ll be e leme nts of the overa l lsuperposi t ion which correspond to maverick worlds . There i s no escape from the fac ttha t any sequence of measu reme nts such as was descr ibed above wi l l invariab ly produc emav erick w orld h is tor ies (e.g ., some in which the resu l ts o f every x-sp in me asure men t i sIx).~2 Hi lary Putnam has pu t forward a v iew accord ing to which quan tum mecha nica len t it i es a re r ea l . . . b u t t h ey a re rel a t iv e t o an o b se rv e r . See 1 9 8 3, V o i . I I I o fPhilosophical Papers Camb r id g e .13 j. S. Bell: 1966, Rev. Mod. Phys 38.14 Loewer and Albert cont inue th is specula t ion in 'The Epis temology and Metaphysicsof the Many Worlds View' , in prepara t ion .D ep a r tm en t o f Ph i l o so p hyCo lu mb ia U n iv e rs it yNew York , NY 10027D ep a r tm en t o f Ph i l o so p hyRutgers Univers i tyNew Brunswick , NJ 08903

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INTERPRETING THE MANY WORLDS INTERPRETATION