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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.
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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,,
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-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
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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@
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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
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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.
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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
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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
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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.
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_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
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'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
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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
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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
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"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
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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.
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-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.
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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,
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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.
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