|
|
|
Quantum Mechanics, Local Causality, and Process Philosophy
by Henry Pierce Stapp
Henry Pierce Stapp works at the Lawrence Berkeley Laboratory,
University of California, Berkeley, California.
The following article appeared in Process Studies, pp. 173-182, Vol. 7, Number 3, Fall, 1977. Process Studies is published quarterly by the Center for Process Studies, 1325 N. College Ave., Claremont, CA 91711. Used by permission. This material was prepared for Religion Online by Ted and Winnie Brock.
SUMMARY
The author deals with Whitehead’s proposed theory of reality that provides a natural ontological basis for quantum theory. The basic elements of his theory are events that actualize, or bring into existence, certain definite relationships from among a realm of possibilities or potentialities inhering in the set of prior events.
(This essay was edited by William B. Jones, who teaches philosophy at Old Dominion University, Norfolk, Virginia.)
I. Science and Quantum Theory
Science can be pragmatic or fundamentalistic. The aim of pragmatic science is to make predictions about what will be observed in different situations. The aim of fundamentalistic science is to understand the fundamental nature of things. The choice between these aims is a matter of taste and interest.
The adequacy of quantum theory depends on which view of science is adopted. Pragmatically it is an adequate theory of atomic phenomena, but it eschews description of underlying realities and is hence fundamentalistically inadequate. In view of quantum theory’s silence regarding underlying entities the Copenhagen claim of completeness must be interpreted as a claim of pragmatic completeness (8:1098-116).
Pragmatic science and fundamentalistic science have different aims, but are mutually supportive. The former, through its study of detail, yields facts the latter must fit. The latter, through its search for unity, yields concepts the former can use. Thus each is justified by the standards of the other.
The basic problem in fundamentalistic science is to find a unified model of reality that is consistent with relativistic quantum theory. The aim of the present work is to adduce support for a model of reality similar to Whitehead’s from an examination of the constraints imposed by Bell’s theorem.
II. Bell’s Theorem
Bell’s theorem (1:195-200; 7:1306-308; 6:1-10; 2:526-35) is the most profound discovery of science. It shows that, if the statistical predictions of quantum theory are approximately correct, then, in certain cases, the principle of local causes must fail. This principle asserts that events in one region are approximately independent of variables subject to the control of experimenters in distant contemporary regions. The statistical predictions of relativistic quantum theory conform to this principle, but their character is such that the principle cannot hold for the individual events themselves.
The particular predictions of quantum theory upon which this conclusion rests follow directly from the most basic principles of quantum theory, independently of the detailed dynamics. And they have been experimentally tested and confirmed (3:938-41).
Bell’s theorem has focused attention on the possibility, not seriously considered before, that although the distance between two individual events may be too great for a light signal to traverse it during the time interval separating them, the character of one of them may yet depend upon that of the other, in spite of the fact that such "superluminal" connections disappear at the statistical level. The central mystery of quantum theory has always been the puzzling way that information gets around. Thus the new information provided by Bell’s theorem seems to be exceedingly pertinent.
Bell’s Theorem imposes a severe condition on models of reality, for it demands that an adequate model account simultaneously for the observed causal structure on the statistical level and the non-causal structure on the individual event level. Bell’s theorem shows that no theory of reality compatible with quantum theory can allow the spatially separated parts of reality to be independent: these parts must be related some way that goes beyond the familiar idea that causal connections propagate only into the forward light-cone.
III. A Modified Whiteheadian Theory of Events
Whitehead has proposed a theory of reality that provides a natural ontological basis for quantum theory. The basic elements of his theory are events that actualize, or bring into existence, certain definite relationships from among a realm of possibilities or potentialities inhering in the set of prior events. This model of nature accords with Heisenberg’s idea (5) that each quantum event actualizes a definite result from among a realm of possibilities and that the wave function describes the probabilities, or potentials, for the occurrence of the various possible results. Whitehead’s events have certain characteristics of mental events, and hence his theory accords, to some extent, with Wigner’s suggestion (11:284-302) that the actualizing of definite results is associated with mind or consciousness. However, Whitehead’s events are not confined to higher life forms, but constitute all of nature. Hence, Whitehead’s theory accords also with Heisenberg’s view (5:54) that in the observation of atomic phenomena the critical quantum event that actualizes one result, rather than a macroscopically different alternative, occurs already at the level of the experimental devices that detect the atomic disturbance, rather than at the level of the perceiving human observer.
It is fundamental to Whitehead’s theory that the potentia of each event is conditioned by the entire preexisting world. This feature corresponds to the fact, often stressed by Bohr, that in describing quantum phenomena, the whole experimental arrangement must be taken into account. Indeed, the basic conceptual problems of quantum theory disappear once it is admitted that the potentia for each event is conditioned by the entire preexisting world. For example, interference effects in optical experiments pose no problem in principle if the event of photon absorption by a particular grain in the photographic plate has a potentia to occur that is conditioned by the entire experimental setup.
No detailed dynamics of event generation was worked out by Whitehead, but the general ontological framework is broad enough to cope with the quantum facts.
The theory proposed here is not exactly the one proposed by Whitehead. In the first place it ignores the mental aspects and concentrates instead on the space-time and momentum-energy aspects, in order to bring the theory into contact with theoretical physics. However, this concentration on the nonmental aspects is not meant to deny that any theory claiming to be an ontological description of reality should have the potentiality of dealing adequately with the mind-body problem. Indeed, Whitehead’s detailed analysis of the mind-body problem in the framework of his theory constitutes a significant factor in the overall credibility of theories of this general kind. A second departure from Whitehead concerns a change in the space-time structure. This change is discussed below.
The following postulates define an ontology that is similar to that of Whitehead.
1. The creative process. There is a creative process that consists of a well-ordered sequence of individual creative acts called events.
Remark 1. -- This assumption affirms that there is a real coming into being, or coming into existence, and that the process of creation can be decomposed into a well-ordered sequence of individual creative acts. Whatever is created exists, and nothing else exists. Nothing passes out of existence, and at the end of each creative act the whole of creation is settled and definite: all that exists is unambiguously fixed.
Remark 2. -- This set of discrete events appears highly pluralistic. However, each event is assumed to "prehend" all prior events in the sequence. In particular, each event embodies within itself all of prior creation and establishes a new set of relationships among the previously existing parts. Thus each event embraces all of creation and endows it with a new unity.
Remark 3. -- The sequence of creative events is well-ordered. One event is "prior" to another if it precedes it in this primordial sequence. This primordial sequence, which contains all that exists, is defined without reference to the space-time continuum: existence is logically prior to space-time.
2. Space-time position. Each event has characteristics that define an associated region in a four-dimensional space. This mathematical space is called the space-time continuum. The region in this space associated with an event is called its location.
Remark 1. -- Space-time has no independent existence in this theory. Rather each event has characteristics that can be interpreted, theoretically, as a region in a four-dimensional mathematical space. For physical applications this metaphysical distinction is unimportant, and one can imagine the events to appear at a well-ordered sequence of locations in a pre-existing space-time continuum. The order of occurrence of events need not coincide with any particular temporal order.
Remark 2. -- The positions (i.e., centers) of the actual events are nowhere dense in the space-time continuum. Thus the actual events atomize space. However, the possible position of any event, before it is actualized, ranges over a continuum. Thus as regards potentiality space-time is continuous.
Whitehead’s ontology differs from the one described above in two important respects: 1) Whitehead does not specify that the set of events forms a well-ordered sequence. 2) Each of his events prehends (and is dependent upon) not all prior events, but only the events of its own "actual world." The actual world of a given event is the set of all actual events whose locations lie in the backward light-cone of its own location.
These differences between Whitehead’s ontology and the one proposed here originate in Whitehead’s attempt to bring his ontology into conformity with the demands of relativity theory. These demands are discussed next.
In prerelativity physics temporal ordering is considered to define the order in which things come into existence. But in relativity theory the temporal order of two space-like-separated events depends on the frame of reference, and hence it is not well-defined in an absolute sense. Thus if one tries to retain in relativity theory the notion that temporal order specifies order of coming into existence, then the order in which two space-like-separated events come into existence is not well-defined in an absolute sense. This line of thought leads to a relative concept of existence in which what exists depends on space-time standpoint.
An alternative point of view is that the space-time coordinates of an event merely label its position in the space-time continuum; they do not specify or determine the order in which events come into existence. This second point of view allows one to retain the absolute concept of existence, in which what exists does not depend on space-time standpoint.
Whitehead’s use of the concept of "actual world" suggests his acceptance of the relative concept of existence. In opposition to this relative concept the following points can be raised: (1) The observations dealt with by physicists depend, as far as we know, on the relative space-time positions of events, but not on the order in which they come into existence. Thus in pragmatic science the question of order of coming into existence is irrelevant: ontological questions need be answered only if one demands an ontology. Thus the theory of relativity, considered as a theory of physical phenomena, says nothing about the issue in question. (2) The 2.7’ K background radiation defines an empirically preferred frame of reference that can be used to define an absolute order of coming into existence. (3) Kurt Gödel (4:555-62) has remarked that all cosmological solutions of the Einstein gravitational equations have preferred systems of space-like surfaces that can be used to define an absolute order of coming into existence. (4) One of Whitehead’s chief aims was to fulfil the philosophical demand for unity of the world. This unity is destroyed if each event prehends, not all of creation, but only its own actual world. Thus Whitehead’s general philosophy should lead him to embrace the absolute concept of existence. (5) Bell’s theorem apparently requires some events to depend on events whose positions lie outside their backward light-cones. This would be contrary to White-head’s scheme. (6) A simple concept, if adequate, is preferable to a complex one. The relative concept of existence makes existence dependent on something else, namely space-time standpoint. This concept entangles existence with space-time and is much more complex than the absolute one, if indeed it can be understood at all (see Gödel’s remark).
One argument in support of the relative concept of existence is that one should refrain from introducing into the basic theoretical structure any noncovariant feature, because it will then be difficult to recover in a natural way the general covariance of the physical laws.
This argument has no force against the ontology proposed here because that ontology does not specify any one frame as preferred over any other, at the level of general principle. Of course, the actually existing world will be described in a particular way in a particular frame of reference, but we can (and shall) assume that the positions of the events are relational constructs that have significance only relative to one another.
A second argument for the relative concept of existence rests on the claim (1) that what exists for an event consists precisely of that upon which it depends and (2) that an event depends precisely on the events in its backward light-cone. Claim (1) goes far beyond usual ideas, which allow an event to depend only on a small part of what exists. Claim (2) seems to be contradicted by Bell’s theorem.
A third argument for the relative concept of existence rests on the fact that in prerelativistic thinking temporal order defines simultaneity, which in turn specifies order of coming into existence. The claim that this linkage should be maintained in relativity theory has no rational justification. For temporal ordering depends on arbitrary labeling conventions, whereas existence should be independent of arbitrary conventions. The natural way to deal with this disparity is simply to decouple the temporal order from the order of coming into existence.
The essential change wrought by the ontology proposed here is to make the process of creation manifestly global: the entire universe is regarded as an organic whole. This conceptualization is entirely in line with Whitehead’s general aims and ideas. However, Whitehead chose to reconcile his philosophic aims with the empirical facts by imposing special ad hoc conditions on his basic ontology rather than allowing the empirical facts to follow from his philosophic principles. These ad hoc conditions are complicated, unnecessary, and apparently incompatible with the quantum facts represented by Bell’s theorem.
For these reasons the ontology of Whitehead has been modified here to bring it into accord with his own general principles. The modifications entail a dependence of events on space-like-separated events, in accordance with the apparent implications of Bell’s theorem. However, no violation of the general principles of relativity theory is entailed by this change: the general covariance of physical laws can be maintained, along with the prohibition against faster-than-light signals.
3. Conservation of momentum-energy. Among the events prior to a given event are some events called its antecedents. Any event is a successor to each of its antecedents. The location of each event is connected to the location of each of its antecedents by a positive time-like geodesic (a straight line in space-time) that runs from the location of the antecedent to the location of the successor. Each geodesic is associated with a real mass-value m and also with a momentum-energy vector mv, where v is the four-velocity defined by the direction of the geodesic. The sum of the momentum-energy vectors associated with the geodesics coming into the location of a given event from the locations of its antecedents is equal 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 rather than mechanistic; it is formulated as a mathematical condition on the overall space-time structure of what emerges from the process of creation, not as a dynamical law that governs the detailed way in which reality unfolds.
IV. Bell’s Theorem and the Theory of Events
The noncausal structure of events demanded by Bell’s theorem is incomprehensible in the framework 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 E0, E1, and E2. Their locations L0, L1, and L2 lie in three well-separated experimental areas A0, A1, and A2. Experiment E0 is an antecedent of both E1 and E2. Thus there is a time-like geodesic from Lo to L1 and another from L0 to L2, as shown in FIG. 1. An experimenter in A1 can choose to perform experiment E11 or experiment E12. An experimenter in A2 can choose to perform experiment E21 or experiment’ E22. Now according to the ordinary idea of causality (i.e., the principle of local causes), the result of E21 (or E22) in A2 is independent of which experiment (E11 or E12) is performed in A, and vice versa. But Hell’s work shows this requirement to be incompatible with the statistical predictions of quantum theory.
According to the theory of events proposed here, one of the two events E1 or E2 is prior to the other. Suppose E1 is the prior event. When it occurs, the possibilities for events in A2 are radically changed. For example, if the locations L0, L1, and L2 are effectively points (compared to the large distances between them), then the two locations L0 and L1 determine the geodesic L0 L1, and hence the energy-momentum carried from L0 to L1. This fixes in turn the momentum-energy available for the geodesic from L0 to L2, which fixes this geodesic itself, assuming that the two geodesics exhaust the momentum-energy available from E0.
Fig. I. Space-time picture of Bell’s phenomena
Note from editor: the figure is not available
Thus after E1 occurs, the event in A2 is required to lie on a fixed geodesic that is determined by the events E0 and E1.
At this stage only space-time and momentum-energy considerations have been introduced, and Bell’s phenomena do not enter. The correlations between the events in A1 and A2 are just those expected from classical ideas: the course of events in A2 is correlated to what is observed in A1, but not on decisions made by the experimenter in A1.
Though 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 A2 is determined by what happens in the earlier region A0, whereas in the theory of events proposed here the possibilities for E2 are limited jointly by the prior events E1 and E0. This logical difference becomes important in experiments involving spin, which are the ones in which Bell’s phenomena occur.
Suppose the geodesics L0 L1 and L0L2 are associated with spin-s representations of the Lorentz group. Just as before, the possibilities for E2 are limited jointly by the prior events E0 and E1. Part of the information determined by E0 and E1 is represented by the momentum-energy four-vector associated with the geodesic L0 L1. However, these two events E0 and E1 determine also another vector associated with the geodesic L0 L1, namely a spin vector associated with the corresponding spin space.
The spin vector and the momentum-energy vector associated with L0 L1 are both determined jointly by E0 and E1. Thus it would be unnatural, in the framework of the theory of events, to treat them differently. It is accordingly assumed that these two vectors should be treated in the same way.
Treating the spin and momentum-energy vectors in the same way leads to very different effects with respect to the ordinary idea of causality. This difference stems from the fact that the two experimenters can independently manipulate the directions of the two spin vectors (modulo signs), but cannot do this with the two momentum vectors without disrupting the experiment. For the two momentum vectors are required by the conservation laws to be essentially parallel, whereas the two spin vectors (modulo signs) can be independently fixed by the two experimenters. Thus the directions of the two spin vectors are variables subject to the independent control of the experimenters in the two separated regions, whereas the directions of the two momentum vectors are not independently controllable. It is the availability of the independently controllable directions along which the spin is measured that is the basis of the phenomena dealt with by Bell’s theorem.
The spin vector associated with L0L1, like the momentum vector, is determined by events E0 and E1. But the experimenter in A1 can, by choosing the experiment to be performed, fix this spin vector, up to a sign. Thus, in the theory of events proposed here, the event E2 can depend on what the experimenter in A1 decides to do. This effect is contrary to the ordinary idea of causality, but conforms to the requirements imposed by Bell’s theorem.
This theory of events does not conform to the ordinary idea of causality. But it provides an alternative possible space-time picture of causality. This picture arises by regarding the geodesic associated with a spin-J representation of the Lorentz group as a conduit of spin-J information. This information flows from an event both forward to its potential successors and backward to its antecedents. For example, the determination in event E1 of the spin vector associated with geodesic L0 L1is viewed as being instantly communicated along L0 L1 to L0, where it can be tapped by geodesic L0 L2 in the assessment of a possible successor to E0 having location L2.
[Editor’s note: This essay was specially prepared for the readership of Process Studies from various published (9, 10) and unpublished articles authored by Professor Stapp. Support from the Old Dominion University Research Foundation for the editing is gratefully acknowledged.]
References
1. J. S. Bell, "On the Einstein Podolsky Rosen Paradox," Physics, 1/3 (1964), 195-200.
2. John F. Clauser and Michael A. Home, "Experimental Consequences of Objective Local Theories," Physical Review D, 10/2 (July 15, 1974), 526-35.
3. Stuart J. Freedman and John F. Clauser, "Experimental Test of Local Hidden-Variable Theories," Physical Review Letters, 28/14 (April 3,1972), 938-41.
4. Kurt Gödel, "A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy," pp. 555-62 in Paul Arthur Schilpp, ed., Albert Einstein: Philosopher-Scientist, New York: Tudor Publishing Co., 1951.
5. Werner Heisenberg, Physics and Philosophy, New York: Harper, 1958.
6. Henry Pierce Stapp, "Correlation Experiments and the Nonvalidity of Ordinary Ideas About the Physical World," LBL-5333, Berkeley, California, 1968.
7. Henry Pierce Stapp, "S-Matrix Interpretation of Quantum Theory," Physical Review D, 3/6 (March 15, 1971), 1303-20.
8. Henry Pierce Stapp, "The Copenhagen Interpretation," American Journal of Physics, 40/8 (August, 1972), 1098-116.
9. Henry Pierce Stapp, "Bell’s Theorem and World Process," II Nuovo Cimento, 29B/2 (October 11, 1975), 270-76.
10. Henry Pierce Stapp, "Theory of Reality," Foundations of Physics, 7/5-6 (1977), 313-23.
11. Eugene Paul Wigner, "Remarks on the Mind-Body Question," pp. 284-302 in Irving John Good, ed., The Scientist Speculates, London: W. Heinemann, 1961.
[Editor’s note: Stapp’s essay effectively singles out those aspects of Whitehead’s theory which can be handled by the techniques of contemporary physics, and then seeks to examine them in the light of the familiar conservation laws. These laws are apparently well established in physics, but Whitehead’s explicit theory provides no place for them.
Instead of Stapp’s broader usage of "prehension" to designate any "prior" event in his well-ordered series, let us think of a prehension in more Whiteheadian terms as comparable to a geodesic (world-line in space-time) linking a present event with one of the events in its causal past. Thus, as in Stapp’s illustration, A1 and A2 prehend A0, and, we shall assume for purposes of simplification, they alone prehend A0. If the momentum-energy of A0 is to be conserved, then A1 and A2 must jointly possess this. Hence, if in prehending A0, A1 prehends a larger share of this momentum-energy, there is less available for A2. A1 and A2 are contemporaries, but it seems that the portion of A0 which the prior event A1 prehends affects what is available for A2 to prehend.
It is not necessary to assume that the prehension of A1 affects the already past A0. The initial datum may well be undisturbed. What is affected is the sum total of objective data available for prehension by A1 and its associates. The sum total of objective data for whatever properties as are conserved, such as momentum-energy, must be equal in amount to the initial datum (A0).
This suggests a well-defined meaning for the immediate and the distant past for Whitehead’s theory, even though on other grounds he seems to have dispensed with this distinction. We can state these meanings conversely in terms of the immediate future for A0. It consists in all those occasions whose appropriations of A0 (i.e., whose objective data relative to A0) are precisely equal in amount to the initial datum A0. Any occasions influenced by A0, but lying beyond this immediate region, would be influenced only indirectly by A0 by means of those occasions directly influenced by A0. The conservation principle thus defines for us the meaning of immediate future. The immediate past of an occasion would consist in all those events in which such conservation factors would be decisive. The conservation principles would have to be satisfied in all situations, but there is no reason in principle why events which appear "distant" to a given one by other spatiotemporal criteria might not be the ones which complete a given locus of objective data equal to some initial datum.
Also, there seems a sense in which Stapp’s work requires that physical prehension be symmetrically internal, both to the prehending occasion and what is prehended. While the past initial datum remains unaffected, the way its present objective data (insofar as they must remain constant by the conservation laws) are ingredient in the world is affected by each prehension of that initial datum.]
SUMMARY
The author deals with Whitehead’s proposed theory of reality that provides a natural ontological basis for quantum theory. The basic elements of his theory are events that actualize, or bring into existence, certain definite relationships from among a realm of possibilities or potentialities inhering in the set of prior events.
(This essay was edited by William B. Jones, who teaches philosophy at Old Dominion University, Norfolk, Virginia.)
I. Science and Quantum Theory
Science can be pragmatic or fundamentalistic. The aim of pragmatic science is to make predictions about what will be observed in different situations. The aim of fundamentalistic science is to understand the fundamental nature of things. The choice between these aims is a matter of taste and interest.
The adequacy of quantum theory depends on which view of science is adopted. Pragmatically it is an adequate theory of atomic phenomena, but it eschews description of underlying realities and is hence fundamentalistically inadequate. In view of quantum theory’s silence regarding underlying entities the Copenhagen claim of completeness must be interpreted as a claim of pragmatic completeness (8:1098-116).
Pragmatic science and fundamentalistic science have different aims, but are mutually supportive. The former, through its study of detail, yields facts the latter must fit. The latter, through its search for unity, yields concepts the former can use. Thus each is justified by the standards of the other.
The basic problem in fundamentalistic science is to find a unified model of reality that is consistent with relativistic quantum theory. The aim of the present work is to adduce support for a model of reality similar to Whitehead’s from an examination of the constraints imposed by Bell’s theorem.
II. Bell’s Theorem
Bell’s theorem (1:195-200; 7:1306-308; 6:1-10; 2:526-35) is the most profound discovery of science. It shows that, if the statistical predictions of quantum theory are approximately correct, then, in certain cases, the principle of local causes must fail. This principle asserts that events in one region are approximately independent of variables subject to the control of experimenters in distant contemporary regions. The statistical predictions of relativistic quantum theory conform to this principle, but their character is such that the principle cannot hold for the individual events themselves.
The particular predictions of quantum theory upon which this conclusion rests follow directly from the most basic principles of quantum theory, independently of the detailed dynamics. And they have been experimentally tested and confirmed (3:938-41).
Bell’s theorem has focused attention on the possibility, not seriously considered before, that although the distance between two individual events may be too great for a light signal to traverse it during the time interval separating them, the character of one of them may yet depend upon that of the other, in spite of the fact that such "superluminal" connections disappear at the statistical level. The central mystery of quantum theory has always been the puzzling way that information gets around. Thus the new information provided by Bell’s theorem seems to be exceedingly pertinent.
Bell’s Theorem imposes a severe condition on models of reality, for it demands that an adequate model account simultaneously for the observed causal structure on the statistical level and the non-causal structure on the individual event level. Bell’s theorem shows that no theory of reality compatible with quantum theory can allow the spatially separated parts of reality to be independent: these parts must be related some way that goes beyond the familiar idea that causal connections propagate only into the forward light-cone.
III. A Modified Whiteheadian Theory of Events
Whitehead has proposed a theory of reality that provides a natural ontological basis for quantum theory. The basic elements of his theory are events that actualize, or bring into existence, certain definite relationships from among a realm of possibilities or potentialities inhering in the set of prior events. This model of nature accords with Heisenberg’s idea (5) that each quantum event actualizes a definite result from among a realm of possibilities and that the wave function describes the probabilities, or potentials, for the occurrence of the various possible results. Whitehead’s events have certain characteristics of mental events, and hence his theory accords, to some extent, with Wigner’s suggestion (11:284-302) that the actualizing of definite results is associated with mind or consciousness. However, Whitehead’s events are not confined to higher life forms, but constitute all of nature. Hence, Whitehead’s theory accords also with Heisenberg’s view (5:54) that in the observation of atomic phenomena the critical quantum event that actualizes one result, rather than a macroscopically different alternative, occurs already at the level of the experimental devices that detect the atomic disturbance, rather than at the level of the perceiving human observer.
It is fundamental to Whitehead’s theory that the potentia of each event is conditioned by the entire preexisting world. This feature corresponds to the fact, often stressed by Bohr, that in describing quantum phenomena, the whole experimental arrangement must be taken into account. Indeed, the basic conceptual problems of quantum theory disappear once it is admitted that the potentia for each event is conditioned by the entire preexisting world. For example, interference effects in optical experiments pose no problem in principle if the event of photon absorption by a particular grain in the photographic plate has a potentia to occur that is conditioned by the entire experimental setup.
No detailed dynamics of event generation was worked out by Whitehead, but the general ontological framework is broad enough to cope with the quantum facts.
The theory proposed here is not exactly the one proposed by Whitehead. In the first place it ignores the mental aspects and concentrates instead on the space-time and momentum-energy aspects, in order to bring the theory into contact with theoretical physics. However, this concentration on the nonmental aspects is not meant to deny that any theory claiming to be an ontological description of reality should have the potentiality of dealing adequately with the mind-body problem. Indeed, Whitehead’s detailed analysis of the mind-body problem in the framework of his theory constitutes a significant factor in the overall credibility of theories of this general kind. A second departure from Whitehead concerns a change in the space-time structure. This change is discussed below.
The following postulates define an ontology that is similar to that of Whitehead.
1. The creative process. There is a creative process that consists of a well-ordered sequence of individual creative acts called events.
Remark 1. -- This assumption affirms that there is a real coming into being, or coming into existence, and that the process of creation can be decomposed into a well-ordered sequence of individual creative acts. Whatever is created exists, and nothing else exists. Nothing passes out of existence, and at the end of each creative act the whole of creation is settled and definite: all that exists is unambiguously fixed.
Remark 2. -- This set of discrete events appears highly pluralistic. However, each event is assumed to "prehend" all prior events in the sequence. In particular, each event embodies within itself all of prior creation and establishes a new set of relationships among the previously existing parts. Thus each event embraces all of creation and endows it with a new unity.
Remark 3. -- The sequence of creative events is well-ordered. One event is "prior" to another if it precedes it in this primordial sequence. This primordial sequence, which contains all that exists, is defined without reference to the space-time continuum: existence is logically prior to space-time.
2. Space-time position. Each event has characteristics that define an associated region in a four-dimensional space. This mathematical space is called the space-time continuum. The region in this space associated with an event is called its location.
Remark 1. -- Space-time has no independent existence in this theory. Rather each event has characteristics that can be interpreted, theoretically, as a region in a four-dimensional mathematical space. For physical applications this metaphysical distinction is unimportant, and one can imagine the events to appear at a well-ordered sequence of locations in a pre-existing space-time continuum. The order of occurrence of events need not coincide with any particular temporal order.
Remark 2. -- The positions (i.e., centers) of the actual events are nowhere dense in the space-time continuum. Thus the actual events atomize space. However, the possible position of any event, before it is actualized, ranges over a continuum. Thus as regards potentiality space-time is continuous.
Whitehead’s ontology differs from the one described above in two important respects: 1) Whitehead does not specify that the set of events forms a well-ordered sequence. 2) Each of his events prehends (and is dependent upon) not all prior events, but only the events of its own "actual world." The actual world of a given event is the set of all actual events whose locations lie in the backward light-cone of its own location.
These differences between Whitehead’s ontology and the one proposed here originate in Whitehead’s attempt to bring his ontology into conformity with the demands of relativity theory. These demands are discussed next.
In prerelativity physics temporal ordering is considered to define the order in which things come into existence. But in relativity theory the temporal order of two space-like-separated events depends on the frame of reference, and hence it is not well-defined in an absolute sense. Thus if one tries to retain in relativity theory the notion that temporal order specifies order of coming into existence, then the order in which two space-like-separated events come into existence is not well-defined in an absolute sense. This line of thought leads to a relative concept of existence in which what exists depends on space-time standpoint.
An alternative point of view is that the space-time coordinates of an event merely label its position in the space-time continuum; they do not specify or determine the order in which events come into existence. This second point of view allows one to retain the absolute concept of existence, in which what exists does not depend on space-time standpoint.
Whitehead’s use of the concept of "actual world" suggests his acceptance of the relative concept of existence. In opposition to this relative concept the following points can be raised: (1) The observations dealt with by physicists depend, as far as we know, on the relative space-time positions of events, but not on the order in which they come into existence. Thus in pragmatic science the question of order of coming into existence is irrelevant: ontological questions need be answered only if one demands an ontology. Thus the theory of relativity, considered as a theory of physical phenomena, says nothing about the issue in question. (2) The 2.7’ K background radiation defines an empirically preferred frame of reference that can be used to define an absolute order of coming into existence. (3) Kurt Gödel (4:555-62) has remarked that all cosmological solutions of the Einstein gravitational equations have preferred systems of space-like surfaces that can be used to define an absolute order of coming into existence. (4) One of Whitehead’s chief aims was to fulfil the philosophical demand for unity of the world. This unity is destroyed if each event prehends, not all of creation, but only its own actual world. Thus Whitehead’s general philosophy should lead him to embrace the absolute concept of existence. (5) Bell’s theorem apparently requires some events to depend on events whose positions lie outside their backward light-cones. This would be contrary to White-head’s scheme. (6) A simple concept, if adequate, is preferable to a complex one. The relative concept of existence makes existence dependent on something else, namely space-time standpoint. This concept entangles existence with space-time and is much more complex than the absolute one, if indeed it can be understood at all (see Gödel’s remark).
One argument in support of the relative concept of existence is that one should refrain from introducing into the basic theoretical structure any noncovariant feature, because it will then be difficult to recover in a natural way the general covariance of the physical laws.
This argument has no force against the ontology proposed here because that ontology does not specify any one frame as preferred over any other, at the level of general principle. Of course, the actually existing world will be described in a particular way in a particular frame of reference, but we can (and shall) assume that the positions of the events are relational constructs that have significance only relative to one another.
A second argument for the relative concept of existence rests on the claim (1) that what exists for an event consists precisely of that upon which it depends and (2) that an event depends precisely on the events in its backward light-cone. Claim (1) goes far beyond usual ideas, which allow an event to depend only on a small part of what exists. Claim (2) seems to be contradicted by Bell’s theorem.
A third argument for the relative concept of existence rests on the fact that in prerelativistic thinking temporal order defines simultaneity, which in turn specifies order of coming into existence. The claim that this linkage should be maintained in relativity theory has no rational justification. For temporal ordering depends on arbitrary labeling conventions, whereas existence should be independent of arbitrary conventions. The natural way to deal with this disparity is simply to decouple the temporal order from the order of coming into existence.
The essential change wrought by the ontology proposed here is to make the process of creation manifestly global: the entire universe is regarded as an organic whole. This conceptualization is entirely in line with Whitehead’s general aims and ideas. However, Whitehead chose to reconcile his philosophic aims with the empirical facts by imposing special ad hoc conditions on his basic ontology rather than allowing the empirical facts to follow from his philosophic principles. These ad hoc conditions are complicated, unnecessary, and apparently incompatible with the quantum facts represented by Bell’s theorem.
For these reasons the ontology of Whitehead has been modified here to bring it into accord with his own general principles. The modifications entail a dependence of events on space-like-separated events, in accordance with the apparent implications of Bell’s theorem. However, no violation of the general principles of relativity theory is entailed by this change: the general covariance of physical laws can be maintained, along with the prohibition against faster-than-light signals.
3. Conservation of momentum-energy. Among the events prior to a given event are some events called its antecedents. Any event is a successor to each of its antecedents. The location of each event is connected to the location of each of its antecedents by a positive time-like geodesic (a straight line in space-time) that runs from the location of the antecedent to the location of the successor. Each geodesic is associated with a real mass-value m and also with a momentum-energy vector mv, where v is the four-velocity defined by the direction of the geodesic. The sum of the momentum-energy vectors associated with the geodesics coming into the location of a given event from the locations of its antecedents is equal 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 rather than mechanistic; it is formulated as a mathematical condition on the overall space-time structure of what emerges from the process of creation, not as a dynamical law that governs the detailed way in which reality unfolds.
IV. Bell’s Theorem and the Theory of Events
The noncausal structure of events demanded by Bell’s theorem is incomprehensible in the framework 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 E0, E1, and E2. Their locations L0, L1, and L2 lie in three well-separated experimental areas A0, A1, and A2. Experiment E0 is an antecedent of both E1 and E2. Thus there is a time-like geodesic from Lo to L1 and another from L0 to L2, as shown in FIG. 1. An experimenter in A1 can choose to perform experiment E11 or experiment E12. An experimenter in A2 can choose to perform experiment E21 or experiment’ E22. Now according to the ordinary idea of causality (i.e., the principle of local causes), the result of E21 (or E22) in A2 is independent of which experiment (E11 or E12) is performed in A, and vice versa. But Hell’s work shows this requirement to be incompatible with the statistical predictions of quantum theory.
According to the theory of events proposed here, one of the two events E1 or E2 is prior to the other. Suppose E1 is the prior event. When it occurs, the possibilities for events in A2 are radically changed. For example, if the locations L0, L1, and L2 are effectively points (compared to the large distances between them), then the two locations L0 and L1 determine the geodesic L0 L1, and hence the energy-momentum carried from L0 to L1. This fixes in turn the momentum-energy available for the geodesic from L0 to L2, which fixes this geodesic itself, assuming that the two geodesics exhaust the momentum-energy available from E0.
Fig. I. Space-time picture of Bell’s phenomena
Note from editor: the figure is not available
Thus after E1 occurs, the event in A2 is required to lie on a fixed geodesic that is determined by the events E0 and E1.
At this stage only space-time and momentum-energy considerations have been introduced, and Bell’s phenomena do not enter. The correlations between the events in A1 and A2 are just those expected from classical ideas: the course of events in A2 is correlated to what is observed in A1, but not on decisions made by the experimenter in A1.
Though 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 A2 is determined by what happens in the earlier region A0, whereas in the theory of events proposed here the possibilities for E2 are limited jointly by the prior events E1 and E0. This logical difference becomes important in experiments involving spin, which are the ones in which Bell’s phenomena occur.
Suppose the geodesics L0 L1 and L0L2 are associated with spin-s representations of the Lorentz group. Just as before, the possibilities for E2 are limited jointly by the prior events E0 and E1. Part of the information determined by E0 and E1 is represented by the momentum-energy four-vector associated with the geodesic L0 L1. However, these two events E0 and E1 determine also another vector associated with the geodesic L0 L1, namely a spin vector associated with the corresponding spin space.
The spin vector and the momentum-energy vector associated with L0 L1 are both determined jointly by E0 and E1. Thus it would be unnatural, in the framework of the theory of events, to treat them differently. It is accordingly assumed that these two vectors should be treated in the same way.
Treating the spin and momentum-energy vectors in the same way leads to very different effects with respect to the ordinary idea of causality. This difference stems from the fact that the two experimenters can independently manipulate the directions of the two spin vectors (modulo signs), but cannot do this with the two momentum vectors without disrupting the experiment. For the two momentum vectors are required by the conservation laws to be essentially parallel, whereas the two spin vectors (modulo signs) can be independently fixed by the two experimenters. Thus the directions of the two spin vectors are variables subject to the independent control of the experimenters in the two separated regions, whereas the directions of the two momentum vectors are not independently controllable. It is the availability of the independently controllable directions along which the spin is measured that is the basis of the phenomena dealt with by Bell’s theorem.
The spin vector associated with L0L1, like the momentum vector, is determined by events E0 and E1. But the experimenter in A1 can, by choosing the experiment to be performed, fix this spin vector, up to a sign. Thus, in the theory of events proposed here, the event E2 can depend on what the experimenter in A1 decides to do. This effect is contrary to the ordinary idea of causality, but conforms to the requirements imposed by Bell’s theorem.
This theory of events does not conform to the ordinary idea of causality. But it provides an alternative possible space-time picture of causality. This picture arises by regarding the geodesic associated with a spin-J representation of the Lorentz group as a conduit of spin-J information. This information flows from an event both forward to its potential successors and backward to its antecedents. For example, the determination in event E1 of the spin vector associated with geodesic L0 L1is viewed as being instantly communicated along L0 L1 to L0, where it can be tapped by geodesic L0 L2 in the assessment of a possible successor to E0 having location L2.
[Editor’s note: This essay was specially prepared for the readership of Process Studies from various published (9, 10) and unpublished articles authored by Professor Stapp. Support from the Old Dominion University Research Foundation for the editing is gratefully acknowledged.]
References
1. J. S. Bell, "On the Einstein Podolsky Rosen Paradox," Physics, 1/3 (1964), 195-200.
2. John F. Clauser and Michael A. Home, "Experimental Consequences of Objective Local Theories," Physical Review D, 10/2 (July 15, 1974), 526-35.
3. Stuart J. Freedman and John F. Clauser, "Experimental Test of Local Hidden-Variable Theories," Physical Review Letters, 28/14 (April 3,1972), 938-41.
4. Kurt Gödel, "A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy," pp. 555-62 in Paul Arthur Schilpp, ed., Albert Einstein: Philosopher-Scientist, New York: Tudor Publishing Co., 1951.
5. Werner Heisenberg, Physics and Philosophy, New York: Harper, 1958.
6. Henry Pierce Stapp, "Correlation Experiments and the Nonvalidity of Ordinary Ideas About the Physical World," LBL-5333, Berkeley, California, 1968.
7. Henry Pierce Stapp, "S-Matrix Interpretation of Quantum Theory," Physical Review D, 3/6 (March 15, 1971), 1303-20.
8. Henry Pierce Stapp, "The Copenhagen Interpretation," American Journal of Physics, 40/8 (August, 1972), 1098-116.
9. Henry Pierce Stapp, "Bell’s Theorem and World Process," II Nuovo Cimento, 29B/2 (October 11, 1975), 270-76.
10. Henry Pierce Stapp, "Theory of Reality," Foundations of Physics, 7/5-6 (1977), 313-23.
11. Eugene Paul Wigner, "Remarks on the Mind-Body Question," pp. 284-302 in Irving John Good, ed., The Scientist Speculates, London: W. Heinemann, 1961.
[Editor’s note: Stapp’s essay effectively singles out those aspects of Whitehead’s theory which can be handled by the techniques of contemporary physics, and then seeks to examine them in the light of the familiar conservation laws. These laws are apparently well established in physics, but Whitehead’s explicit theory provides no place for them.
Instead of Stapp’s broader usage of "prehension" to designate any "prior" event in his well-ordered series, let us think of a prehension in more Whiteheadian terms as comparable to a geodesic (world-line in space-time) linking a present event with one of the events in its causal past. Thus, as in Stapp’s illustration, A1 and A2 prehend A0, and, we shall assume for purposes of simplification, they alone prehend A0. If the momentum-energy of A0 is to be conserved, then A1 and A2 must jointly possess this. Hence, if in prehending A0, A1 prehends a larger share of this momentum-energy, there is less available for A2. A1 and A2 are contemporaries, but it seems that the portion of A0 which the prior event A1 prehends affects what is available for A2 to prehend.
It is not necessary to assume that the prehension of A1 affects the already past A0. The initial datum may well be undisturbed. What is affected is the sum total of objective data available for prehension by A1 and its associates. The sum total of objective data for whatever properties as are conserved, such as momentum-energy, must be equal in amount to the initial datum (A0).
This suggests a well-defined meaning for the immediate and the distant past for Whitehead’s theory, even though on other grounds he seems to have dispensed with this distinction. We can state these meanings conversely in terms of the immediate future for A0. It consists in all those occasions whose appropriations of A0 (i.e., whose objective data relative to A0) are precisely equal in amount to the initial datum A0. Any occasions influenced by A0, but lying beyond this immediate region, would be influenced only indirectly by A0 by means of those occasions directly influenced by A0. The conservation principle thus defines for us the meaning of immediate future. The immediate past of an occasion would consist in all those events in which such conservation factors would be decisive. The conservation principles would have to be satisfied in all situations, but there is no reason in principle why events which appear "distant" to a given one by other spatiotemporal criteria might not be the ones which complete a given locus of objective data equal to some initial datum.
Also, there seems a sense in which Stapp’s work requires that physical prehension be symmetrically internal, both to the prehending occasion and what is prehended. While the past initial datum remains unaffected, the way its present objective data (insofar as they must remain constant by the conservation laws) are ingredient in the world is affected by each prehension of that initial datum.]
|
|