Approved For Release W01/03/26 : CIA-RQR96-00787ROW2000QQP§A-@@ 1", OF RE2,11TY IU ILen--y Pierce Z;taop La,:rren:--,z@ Elerkeley Laborato-,y University of California Berkeley, California 94720 April 29, 1915 -@3STIZACT Bell's theorem is.used to guide the formulaticn of a'unif-i-d theory of reality that incor-porateo- the basic princip-'-@!s of relativ- istic quantiza theory. I. iNTRODUCTION @@uantum theory is a t.heory of observations; the roalities it deals are certain,observat-L:)ns of' scienLIS'ks who --:se These observations are only a sl-all part of reality. Consequently quant= 'Ll'oory, considered as a theory cf reality, is incomplete, Prevailing Ity c , ad o -L .pinion holds, in fact, that no complete theory of real" ar e quately describe quantum phenomena. This opinion stems from the long history of failures of attempts to achieve this end. it is not clear, however, whether these failures arise fro--..I aa-L inadequacy of -the reality con--ept, or merely from a breakdol,,,n of the classical idea of causal sDaz,---tiii ic development. 3ohr cften emplhasl,zed the breakdown oil' t'rLis classicall idea in the realm of quantu-m ph@!non,:!na, and his point has "b-:-@en strikingly verified and clarified by the %vork of J. S. Bell. Bell's work was oriEiinall'y formulat-ed in ILhe astricted 2) hidden-variable tlhe-,ry. ljo!wever, it was soon realized by U.S. Ener8-y 1"e-search and Developr-,entu Adn.-inistratio.n. Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release W1103126: CIA-RDP96-00787RQV200080053-6 establi-,"ed -,,ras foliowinc, pro-Irr_,.._nd r@@,,a, 1-1 - L : The stat The statistical predictions of quantiLm theory are incompal.-ilble prin'. __). vrit'n the prin-,ip'Le of local causes. the _1, The principle of local causes asserts that what happens in one sPac6-tima re.-ion is appro,ximately independent of variables s@jbjec-., -to the control of an experimenter in a far-away space-like-seDarated. re 1@7 "on. This Drinci-Dle holds in relativistic qu,-@uitum, theory at th,@@ level of statistical predictions. Ho,,,iever, the character of these predictions is such that the principle must - fail at the level of the indi'vidual events. The statistical predictions from which -this result follov; come directly from the basic principles of quantum, theory, no-, frc:n the detailed dynamics, and they have been experimentally testolc@ and confirmed.(3) Bell's theorem shows that no theory of reality compatible wi-.-h quantum theory can allow the spatially separated parts of reality tc e 4 b independent: These parts must be related some way -that goes beyond the familiar idea that causal connections Provarrate only in-to the for-,.-ard light-cone. This conclusion will guide our thoughts. The first task of any general theory of reality is to formula-11-e tho connection between the ex-neriential or psychic a3pects of reality and 'I'le.material or space-time aspects. The debatue between Bohr and Ei 71-3 pointed to the importance of th-is qi,.estion, for Einstein ap--aled finally to the need for a comprehensible understanding of rela. V Sp@,_,@r Lirr.0 'ions, whereas Bohr appealed ullimately to the primacy of exreriential relations. A unified theory cC reality muct bring the-Se " w o L LI, @s,pects of reality into one coherent so-eme,, Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release W1103126: CIA-RDP96-00787RG40200080053-6 -3- Un.@ 11 tI',-"C3-y OC @';aality has beer. Yr Ac-ord@*n,c, tc -this theo@,,y r,:2aIitI*,- consls!@s cf d-iscrete even1@3. Each event-has a location, which is a firi-te s-.@ace- time region. it. also has certain experiential characteristics. To support the idea t1hat experience cornes in discrla-@e units who ;Friteo: (6) Vihitehead cites the authority of William Jazes, L "Either your experience is of no conklentij, of no ch.ange, or it is of a perceptible aaiount of content or chazirre. Your acque-intar.,ae with reality grolJS literally by buds or drops of perception. Intellec- I a. - tually mid on reflection you can divIde these into components, bu-I as immediatoly given -they come totally or not at all." To support -the idea that, physical processes consist of dis- Crete events .one may cite the authority of L'Iieis Bohr:(7) "(The essence of quanti-in theory) may be expressed in thel so- called quantum postulate, which attributes to any atomic proce@,s @@_ri essential discontinuity, or rather individuality, completely forei- 0__ to the classical theories and symbolized by Planck's quantum of a cti on. A reality consisting of discrete events seems hopelessly fragmented and,pluralistic, Yet 'Uhitehead's reality is unified. This u-nity is achieved by considering ea--h event to be a process in which all. prior events are brought to@@ether, cr "preherded", in a new oa,"'.orn. Reality -thus becomes tne process @Df creatic)n, in discrete Jual stlep,3, of an o' @'e 1, t @ @ns b i -AlvU otween thngs ... it are parts of this. samo crocess. !,Jental event, - s ara a part of th'is E;cnoral %%,orld process, arid they afford tin i.11,1,S@-ration OC 113.7 events can be processes that brlin,g to'gether prior in ne,,,, r,,j, t t- e r n s Approved For Release 2001103126: CIA-RDP96-00787ROO0200080053-6 Approved For Release Q&01/03/26 : CIA-RDP96-00787RQU200080053-6 Tach ev;@nl in the --acrld process prehen,-Ij via,:- evcr@- i)rior event, and hence 3ontains %-iithin its-3if, in a (-_%rtain sense, the whole of creaticn.' VFhitehead chose a model that did not attain the full unity just described. He believed that relativity 'Uheo--,-y req@L-red space-liLe- se-:@aratecl events to be causally independent, and hence decreed that each.event prehend, not all of,creatiori) but o.-Ily those events whose lo3ations lay in its backward ligh-t-cone. This mutilation of'the model destroys its natural unity and logical simplicity. Moreover, it is incomDatible with quantum theory, by virture of Bell's theorem. Th-as it must be undone. The result- is a philosophically attractive unified model of reality that provides a natural setting for relativ- ist-i-I quantum theory. II. THEORY OF EVENTS In this section a physical theory of events is erected on the mo-el of reality described above. This theory incorporates the basic pr-4--ciples of relativistic quantum -theory. The theory is set forth in eight assur.-iptions or postulates, which have physical, metaphysical, and mathematical aspects. The guiding principle. is maxii-.al simplicit.-. The aim is to use -the simplest and most economical metaphysical and mat`;emat I cal. structures consistent with what Ue IL-iow from experience. The postulates are as follows: 1. The creative process. There is a crea@ivc, process that, i c onsists of a well.-ordered sequence of individual creative acts called events. Remaz,k- This assumption affirms that there is actual creation, i.e., a --eal ccmilng into being, or a coming into existence, @Lnd t1hat the I C@ Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release iMl/03/26 : CIA-RD-P96-00787RW200080053-6 Or' can be (@,-_compo3ed into -?, s_e,j!_lqnce oft' a C ts . V! I, I *UCvor Is created -2,cis ts, a-cid not, h.Lnc- e is @ exis 1.t -i n o- p:_i,3s,e,3 out of existence. Ar, t1re end of' eac-a cr,@,ative act -the of creation is settled and definite all -that exists is una:fbiauously fixed. 1his simple logical structure can be contrasted ;,"ith ones in which all of creation, past, present, and future exists, a.-id is fixed, and change io some sort of ii:@-us'ion.- It may also be contrasted ones in which the creative process is not a single linear process but rather a multiple process that proceeds somehaa indepe ndently in different space-time regions, sotliat what exists is not globally well- defined but depends on the space-time point from which the determination of what exists is made. (These models bifurcate nat;ure: they posit either changing experiences of a pre-existincy world or a changing world in pre-existing space-tirqe.) 2. Space-time location. Each event has characteristics t..hat define an associated region in a four-dimensional mathematical space. This mathematical sDace is called the space-time continuum, and the region in this space associatled with an event is called its location. Remark Space-time has no irdependent existence in -this theory. Rather each event has characteristics -that can be interpreted as a region in a certain mathema.ical space. For physical applications this metaphysical distinction. is unimportant, and one may imac-ine a pre- L existinzr space-time ocn-Ulnuum., vd+.h the eventus sea Uerod -Lhrough it. 0 Definition An event is prior to another iT it occurs earlier in the sequence of creative acts dc-scribed in (1). It is subsec-Lient if it occurs later in this sequence. 3. Conservation of Tinior,-,entum-enerEy. kaong the events prior -to a given event are somne events called it,,,- anLt_-,re_de_.,its, Any eve@@t is Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release iW01/03/26 : CIA-RW96-00787RQ0200080053-6 a to each of its ant-ecedents. The location of cac@'. e'..@_-' is oonne,-Acd to the locat"ion of each of its antecedents b@- s, geodesic (a directed straight line in space-time) that runs from t.-e- location of the antecd.ent -to the location of the successor. Each geodesic is associated with a real mass-value m, and also with a n-.,omentum-enerEy vector p = mv, -.,There v ..is the four-veloclity defined by the direction of the geodesic. The sum of the mamentum-energy vectors associated with the geodesics cominc into the location oil a- given event from the locations of its antecedents is equnI to thE@ sum of the energies associated with the geodesics going out from the location of the event to the locations of its successors. Remark This physical assumption, like -those -that follow, is holistic r 'her than mechanistic; it is formulated as a mathema'ical co a@ U ndition on the overall space-time structure of what emerges from the procQSS of creation, not as a dynamical la,,,T that governs the detaile! way in which reality unfolds. Definition A system is a local space-tine pattern of events. 4. Lorentz Invariance. Probabilities are determined, by lo:!al conditions: under suitable conditions of isolation the statistical behavior of ensembles of systems defined by local specifications do not depend on the Lorentz frame used to relate the local specifications to global space-time. He.-7,@IrR The isolation condition requires a local systeja to be isolat-ed in the sense that outside sources of energy a-re negligible. The assumption is t1hat under this condition of isolation ensembles of subsystems defined by local specifications exhibit the- type of behavior characterized by probability functions. Moreover -.1hese probability functions are invariant under Lorentz tr-ansformations. Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release 2401/03/26 CIA-RDP96-00787ROQ0200080053-6 t an --is ic A r@.-,)re-sents th;@ local specifications tha eriz@errble and B represents the local specific,_t ions define a final ensemble and P[A; B) is the-probabilitly that B h--Ids un-der conditions A, then P[A; BI is independ-ant of the pace-tii,.ie coordinates occurring in Larentz fra-me used to relate the s the local specifications A and B .to physical space-time points. 5. Scattering formalism. The statistical results of scatter- ing experiments can be described by the formalism of classical rela tivistic statistical mechanics, with the geodesics identified .,iith the trajectories of classical point particles. Remark in the classical description each beam of initial particles is described by a probability or weight function w(p,x) and the detection system for each of the final particles is described by an efficiency function e(p,x). The expression fd3p d3x vi(p,x) e(p,x) P[VT' ej J I X0= -1. = gives the probability -that a particle in the beam described by w will be detected by the system described by e. (The time t can be chosen arbitrarily.) For a scattering of m particles into n Darticles the expression Approved For Release 2001/03/26 CIA-RDP96-00787ROO0200080053-6 Approved For Release ZD01/03/26 CIA-RDP96-00787RV200080053-6 3 3 P e e d P d V"'@2) ... wM; 1 2 n] x d.3 p d3x (P@'X@) j=1 x S(plj'xl@'-@Pm)x P, x ... )P"x (2) 1 J. n n 0 x X.01 gives the probability that if the initial beams are described by the weight functions wl., ... )W _M and the final-particle detection syst-emrs are described by the efficiency functions el,,,,,e n then all n final particles will be detected. (The times t i and t i can be chosen arbitrarily.) Each function wi(p,x) is a real function of the real mass- shell momentum-energy ver-tor p and the real four-vector x. It satisfies, for any X, wi(p, X) = wi(p, x + xp), (3) This condition arises from the fact that all the particles of momentum p move in the direction defined by p = mv; i.e., along p. Functions satisfying (3) can be constructed by specifying 0 w(p,x) at sonp- time, say x t, -and. then forming ""(P'X) f d3x' d(Xpo) "'T(P'x') 6 /'(xl - x of (4) x =t Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release W1/03/26 : CIA-RDP96-00787ROQ;,200080053-6 f.-no'l-Iier @-,,ay o' coz,structing solutions -to (3) is to Writ-2., f0r cc:i,.plcx function @(p) @,nd ouny real constant Ti, d4q I q) @*(M-v + q) (27r)3 f qx/h c, 6(q.v') (M (2 1 2) wher e v p/m and In 4 q 6. The quantum assumption. The functions W(P,X) occurririg in nature are sums of functions of the form (5), with different fluic- tions @(p) but with the same constant TA. This constant is Planc:@.'s constant. The analogous'formula holds for C(P,X). Rerr,,irk This assumption allows the scattering formula (2) to be trans- cribed in-to quantum mechanical form. (8) The S-matrix S(P.1'...'pm; P ...,Pnl) is then de-Cined in terms of the function appearing in (5). Conservation of probability implies n -the unitarity of S(ply...,P,). n 7. 1Macrocausality.(9). Itomentum-energy is transferred over macroscopic distances only by the stable systems: an event having an incoming geodesic not positive time-like or with mass not that of a stable system has a probability to occur -that falls off exponentially under space-time dilation. The size of the location of an event has a finite bound that depends only on the incoming geodesics. Rer.rnrk This i,-iacrocausality condition entails -that the S-matrix be an analytic func-tion at all real points (pl, '.,P' n except those lying on a set of well-defined surfaces called the positive-a 1,andau surfaces. The rule of continuation around each of (9) these singularity surfaces is also determined. Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release 2001/03/26 : CIA-RDP96-00787RO40200080053-6 _10- Madi.:,,a1 anaiytuicity. (10) The ar-alytic can'in@.,,ation of tile D . . . L U U matrix to complex )pl ) has only tholse sJ1ngu'arij.iQS 'that are required by the unitarity conditions. lze:nark Maximal analyticity is a principle of econo,,V; it asserts that the 8 matrix has no unnecessary singularities. Or it is a principle of simplicity; it asserts that the S matrix has -the simplest po@;Sible analytic structure. Any useful-physica-I theor.y must be based on some princip U le of economy or simplicity. There is no theore-lical'or experimental evidence for any singularity not required by unitarity. It seems entirely possible that the general principles of Lorentz invariance, unitarity, maorocausality, and maximal analyticity may determine in principle a unique complete relativistic quantum theory of elementary particles. (10) A few, constants may have to be determined empirically, at least in practice. If this theory is carried over to the nonrelativistic limit, where particle-creation is excluded, then it yields (11) the Schroedinger equation, and hence the concept of equations of motion. And the Schroedinger form of quantum theory reduces, in appropriate contexts and lintits, -to classical physics. It thus appears -that all of physics c,,u-i emerge from the eight assumptions listed above, together, perhaps, iAth a fe;,,r empirical consta-fits. III. BELLIS 'ZHEOR01 AND THEORY OF EXENTS The noncausal structu-re of eveats demanded by Bell's theorem is incomprehensible in the frame,,,iork of ordinary ideas, but is a natural consequence of the theory of events described above. In the simplest cases involving Bell's phenomena there are three (scattering) events EO, El, and E 2. Their locations LOY Lly Approved For Release 2001/03/26 : CIA-RDP96-007.87ROO0200080053-6 Approved For Release @DO1/03/26 : CIA-RDP96-00787RQW200080053-6 'Ued ex-cer-1 rzenfjal areas ind L iie in three well-epara A0, A, , and 2 L A2' ExPeriment E 0 is an antecedent of both E I and E 2- ' -1hus '.here is a timelike geodesic from *L to L and another from L to L 0 1 0 2@ as 3ho-wn in-Fig. 1. An experimenter in A, can choose to perform. ex-periment E11 or experiment E 12" An ex-,@erimenter in A2 c an choose to perform experiment E 21 or experiment E 22* Suppose E ljk JM-11- is the event (result) that cccuzs in experiment E if the ex ij menter in A 2 does experiment E 2k* Suppose E 2jk is the event (result) that occurs in E 21 if the experimenter in -.A, does experi- r-rent- E The ordinary idea of causality (i.e., the principle of local causes ) deTa-nds @hdt, t,'he _E ------- 4Q- I@ut J Bell's work shows this requirement to be incompatible with the statistical predictions of quantlxrn theory. According -to -the -theory of events one of the two events E_. or E is prior to the other. Suppose E is the prior event. "Frien 2 1 it occurs the possibilities for events in A 2 are radically changed. For example, if the locations LO, Ll, end L 2 are.effectively points (compared to the large dist a1rces between them) then the two locations L0 and L 1 determine -the geodesic L 0L,, and hence the energy- moment@un carried from L 0 to L 1, This fixes in -turn the momentum- energy available for the geodesic from L 0 to L 2Y vihich fixes this. geodesic itself, assuming tha@t the two geoClesics exhaust the momentum- energy available from E G Thus after E 1 ouci.Lrs the event in A 2 is required to lie on a fixe'd geodesic that is determined by the events E and E 0 1, At this stage only soace-time and mamentum-energy cb.-Isidera- tions have been introduced, and Bell's pheno,7,-:.,na do not enter. The correlations between -the cvr-:;.-ts in AI and A 2 are just those Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release -ZaDl/03/26 : CIA-RPf2@6-00787ROQ0200080053-6 Fig. 1. Space-time picture of Bell's phenomena. 0 e-,'Pected from classical ideas: the course of events in A 2 is correlated -to what is obserlied in A,, but not on decisions made by -the experimenter in A 1* Thou'(7h the results at this stage are similar to those of classical particle theory, -the logical structure is different. In the classical theory what happens in A 2 is determined by what happens in the earlier region A 0, whereas in the -theory of events the possi- bilities for E 2 are limited jointly by the prior events E and E This logical difference becomes important in experiments involvir_@@ 0' spin, which are the ones in which Bell's phenomena occur. Suppose the geodesics L L and L L, are associated with 0 1 0 2 spin representations of -the Lorentz group. Just as before -the possibilities,for E 2 are lLTnited jointly by the prior event s E 0 and E 1 Part of the information determined by H 0 and Ei 1 is rep- resented by 'the momentum-energj four-vector associated with "the Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release -ZgOl/03/26 : CIA-R_P@?6-00787RQU200080053-6 Ic L T T-1 0 r, these two events E 0 and E 1. also anDthar vectov associated vfi th the geodcjic LL, , nairn@ly a s-in vector ass3ciated with -the corresponding spin space. The spin vector ard the moment um-enerL7, voctor associated with L0LI are both de-termined joi-ntly by E 0 and E I' Thus it would be =atiiral, in the,framework.of the theory of events, to tre@at them differently. It is accordingly assumied -that these two vectors should be treated in the same way. Treating the spin and momentiLm-energy vectors in the s ame way leads to very different effects with respect to the ordinary idea of causality. Tlhis difference stems from the fact that the two experi- menters can independently manipulate the directions of the two spin vectors, modulo signs, but cannot do this with the two momentum vectors, vrithout disrupting the experiment. For the t-wo mornent,@Ln vectors are required by the conservation laws.to be essentially parallel,whereas the two spin vectors, modulo signs, car be indepen- dently fixed by the' two experimenters. The spin vector associated with L 0Ll, like the momentum vector, is determined by events E 0 and E 1* But the experimenter in A, can, by choosing the experiment to be performed, fix this spin vector, up to a sIgn. Thus, in the theory of events, the event E 2 depends on what the experimien@er in A 1 decides -to do. ("This effect is contrary -to the ordinary idea of causality, but conform3 -to the rcquirements imposed by Bell's theorem. The theory of events does not conform to -the ordinary idea of causality. But it. provides an alternative possible space-time picture of causality. 'Ihis picture arises by regardincr the geodesic associated with a spin-i re-presentation. of the Lorcnt.-, group as a conduit-of Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release QW1/03/26 : CIA-RQP,96-00787RGQ0200080053-6 "T * f ma-lan. This infonma'ion flo-,"s it.,3 pottntizl successors @--_-id bacllg@ard to ex,@?_mple, -the determination in,eventE1 of X wit,h goodesir L 11 is vie-.-iecl as beincr instantly 0 1 @ frt-)m all cv@jnt both fo-,,iard its antecedent3. Fo_- thc spin vect-,or assooiated communicated alono- 6 0 L0L1 ''to LOY where it can be tapped by geodesic L 0L2; in the assess- ment of a possible successor to E 0 havingg location L 2' IV.- CONCLUSIONS The basic proper-ties of relativistic quantum theory emerue in a natural way from a logically simple model of reality., In this model there is a fundamental creative process that proceeds by discrete steps. Each step is a creative act or event. Each event is associated with a definite snace-time location. The fundamental process is not local in character, but it generates local space-time patterns -that have mathematical forms amenable to scientific study. This theory of reality reconciles the positions of Einstein and Bohr. It conforms to Einstein's view that the complete basic -theory should be a complete 'theory of reality rather than a theory of observations; i.e., it should, describe "any real (individual) situation (as it supposedly exists apart- from any act of observation). The model described above attemplus to do exactly -that. In the model everything, -that exists is perfectly definite: Sobroddinger.'s cat is cither,dead or alive, not both, independently of any act of observation, or of' any choice of space-ti_-.e perspective. On the other hand, the theory is probably useless in the realm of atomic physics, and for essentially the reasons adva-rced by Bohr, namely that, "The element of wholeness,, syr.@bolilzed by Uhe quant-um of action and completely foreign to classical physical recourse to a Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release 401/03/26: CIA-RDP96-00787RO4W2OOO8OO53-6 -15- 0 + @.L m,)de of imperative il I A tionc of the o3currence of individual qucuitum effec-@L: in one ',av! -1 e s3J."'C' experimental arrangement This probable lack of utility of the model in the realm of atomIc physics does not necessarily mean that th-2 model has -no uses at all. In the realm of elementary particle physics the q'aantum -theoretical -Drinciples, thoug4.perhaps sufficient in princliple, are difficult to apply, and the insight provided by a model of the unler- lying reality might be useful. 'More important would be the possible uses in those realms of science -@,rhere the approximations essential- to the applicability of quantum theory fail. Bohr often stressed that -the wave function of a system has meaning only to the extent that the system can be regard.ed as isolated from the rest of the world,(14) i.e., only in those situations @,'@here the possible outside sources of energy-momentum can be ignored. When this idealization is inapplizable the wave function of the system is not definable, and even if it could be defined it would be undergoing continual quantum jumps, and no 'u_'!)T)s exists. adequate theory of quantum 0 - No system is completely isolated from the rest of the world, except -the whole world, which oannot be -treated byquan,tum theory since t",iere is no outside "observer". And most sys-tems of interest are not even approximately isolated from the resL of -the Jorld. One clasi of systems of special interest to iwari are living Systems. These require interactions their en,,,Ironments to sustain life, and consequently, as emphasized by Bohr, (15) they cazu-iot be fully described by quantum theo.-y. Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release QX1103126 : CIA-RDP96-00787RGQ0200080053-6 -ib- UrdIt-,-)- of understandin,gr is a natUral goal of J.n'-), to u-nify t1ae various bran@'--hes of scien,-,e and kno-;;Ied@r@@ p-ys-Lcs, bio-@cgy, psychology,, sociology, philosophy, etc., soM-9 o-iorarclaincr conceptual frame-work is required. It is be.g,in ,Ath the logically simplest model of reality that is Consi-ztent with all we ?.no'w. The -theory of events outlined abo,,,e is a logically sir.-.ple model of reality that is apparently consistent with all we know. Taken in conjunction with Whitehead's theory of process it is, as far as I know, the or-ly existing model of all of ri@ality thall- incorporates the basic principles of relativistic quantum. theoi@y. Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For Release QX1/03/26 : CIA-RDP96-00787RW200080053-6 ES 1 J. S. Bell, Physics ( N. 1, 195 ( 1964 2. IF. P. Stapp, Correlation'Experiments and tn.? 111cn,all-dity of Ordinary Ideas About the Physical World, Berk,@le.y (1968) and Phys. Rev. D3, 1303 (1971). The principle of lo-1-1 causes is introduced and analyzed in these works, -.,frere it is tacitly .assumed U -that counter e'fieiences are no' limited in principle, This assumption is made also in the present .-;ork. For a dis--.,ssion of this point see J. F. Clauser and M. A. Hoiaie, PIVs. Rev. D119, 526 (1974), and references cited there. 3. S. J. Friedman and J. F. Clauser, Phys. Rev. Lett. 28, 938 (11972). 4. 14. Bohr and A. Einstein in 11bert Einstein: Philosopher-3cie-tist (Tudo Publishing Co., Ne-a York, 1951). 5. A. N. Whitehead, Process and Reality (Macriud Ilan Co., Yorlk, 1929). 6. William James, quo-Led in Ref. 5. 7. N. Bohr, Atomic Theory and -the Description of Natlure (Cambridge University Press, Englan-d, 1934), p. 53. 8. 11. P. Stapp, Foundations of S-matrix Theory. I. Theory and TvTeasurement, Lw;rence Berkeley Laboratory LBL-759 Rev. (1972), or D. Iagolnitzer, Introduc-tion to S-matrix Theory, C.E.N.-Sa3lay, 1973. 9. D. lagolniLzer and 11. P. Stapp, Commu-n. Math, Phl,,s. 14, 15 (1969); and D. lagolnitzer, Ref. 8. 10. G. F. Chew, S-matrix Theory of Stror),-, Intera2tions (VI. A. Benjamin, Inc., New Yor'--:, 1c,161), and ilie 11-nalytic S-matrix (W. A. Benjamin, Inc., New Yor'_,-, 1966); H. P. Stapp, Phys. Rev. 125, Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6 Approved For ReleaseQK1/03/26 CIA-RDP96-00787RQ0200080053-6 2139 (196,22); j. Gunson, J. Math. Phjs. 6, 827 and `45 (Preprint in 1962). 11. R. BlanLei-@Dec-'Lcr, M. L. Coldber,-e-r, N. M. Khuri, and S. B. Treiz---:, Annals olf Phys. 10, 62 ( 1960). 12. A. Einstein, Ref. 4, p. 667. 13. N. Bohr, E'ssays 1958-1962 or Physics and Human PaAD'ai@,'d7e Ofiley, New York, 1963 ), p. 60. See also H. P. 'S tapp, Am. J. PhYs. 40, 1098 (1972), p. 1108. 14. N. Bohr, Pef. 7, p. 54. See also Ref. 2, p. 1308. 15. N. Bohr, Atoi-tiic Physics and Himan Kno-,vled@@re ('Xiley, New York, lr'-503"' P. 10. Approved For Release 2001/03/26 : CIA-RDP96-00787ROO0200080053-6