Bell’s Theorem and Stapp’s Revised View of Space-Time

by Charles Hartshorne

Charles Hartshorne taught at the University of Texas where he was Ashbel Smith Professor of Philosophy. He had a distinguished career at several other universities, particularly the University of Chicago and Emory University. His most recent book, Creative Synthesis and Philosophic Method, was published by Open Court.

The following article appeared in Process Studies, pp. 183-191, 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.


Physicists now say what Whitehead said rather long ago: that nature consists, in the last analysis, of “events, not things.” Physicists as such can hardly be expected to see also that causal inheritance is prehensive.

In much recent philosophy, including mine hitherto, space and time have been considered primarily as they appear either to common sense or to relativity physics. But quantum physics suggests important qualifications. This should not surprise us. For it is only in quantum physics that science arrives at long last at the true idea of single "happenings," events not reducible to a series of subevents. This corrects or qualifies the idea of space-time as continuous. Actual happenings are discrete, not instantaneous or indefinitely extended temporally or spatially, and only the potentiality of happenings is continuous. In general (as Peirce saw, but in his "Synechism" partly forgot) continuity is the order of possibility, rather than of actuality. Pure geometry deals with possible, not actual events. Heisenberg seems to have seen more clearly than some, e.g., Schroedinger, the importance of the idea that a quantum "jump" is a single event, not a continuous series of events. Before the jump occurs, there is only a probability of its happening, and the wave function gives this probability.

The attempt to reduce probability to a mere matter of our ignorance has led nowhere in the fifty years since Heisenberg’s famous paper. The future is the aspect of reality that is definite only as probability, while the past is definite -- period. What happened happened, whether we know it or not. Becoming is creation of definite actualities. Peirce and Bergson had said this before the discovery of quanta, and for good reasons, but in quantum physics science discovered factual evidence that, if it did not prove these philosophers right, at least made it much easier for such views to get serious consideration.

Nature keeps making what amount to decisions (mostly not conscious as such), each causally conditioned but not causally determined. Every event has a cause if "cause" means necessary condition; no concrete definite event has a cause if "cause" means sufficient or determining condition, for that would make the result as necessary as the condition. Only for certain more or less abstract or approximate features of events, for instance statistical uniformities, can there be sufficient or necessitating conditions. Since the classical view that ultimately equates necessary and sufficient conditioning is no longer operative in science, there is no point either in affirming the compatibility of human freedom and classical determinism or in introducing ad hoc exceptions to determinism in the case of human decisions. Relevant also is the truth noted by Bohr that quantum physics applies strictly only to isolated systems, which at best are idealizations, and is not without further qualification applicable to organisms. Thus even quantum statistical determinacy is not absolute.

Quantum physics of course limits the precision with which spatiotemporal localization can be assigned to events, or to world-lines, that is, event sequences or careers. In 1964 a more radical correction of traditional views was discovered by J. S. Bell.1 In a personal communication Stapp writes:

What Bell’s theorem shows is that, contrary to the suggestion of relativity physics, it cannot be assumed that events controlled by an experimenter in one spatial region can influence events in a distant spatial region only after sufficient time has elapsed for some form of radiant energy to pass with the speed of light from one region to the other. Rather there are situations where quantum effects require that certain changes in events controlled by experimenters in one region be accompanied by changes of events in a distant region at times prior to the arrival there of any signal that travels at the speed of light from the location of the controlled events.

Whether or not this result reinstates absolute simultaneity is another question. What does follow, again in the words of Stapp, is that "spatially separated parts of reality must be related in some way that goes beyond the familiar idea that causal connections propagate only into the forward light-cone." Thus the famous Einsteinian concept of the space-time structure, standard for nearly sixty years, receives at last some qualification.

Peirce’s or Popper’s fallibilism, or Whitehead’s dictum, "seek simplicity and mistrust it," should have led us to expect something like this. To quote Stapp once more, "causal effects can be transmitted over large distances without the possibility of material conveyance. Admirers of Whitehead will recall his qualification, "provided physics keeps to its denial of action at a distance." It has not kept to it. Only so far as nonquantum effects are concerned is causal influence confined to the forward light cone, leaving a mass of contemporaries for any given event E, although most of these contemporaries of E are not contemporary with one another. ("Contemporary with" here means "mutually independent of.") This relativistic conception is quite different from older concepts not only of simultaneity but also of contemporaneity. It is one of the strangest ideas ever introduced by science. No wonder some physicists almost went out of their minds trying to assimilate it. By accepting it as ultimate, Whitehead rendered the great doctrine of events as summing up the influences of the past distressingly ambiguous. For "past" has no clear meaning in relativity physics. There is the "absolute past" of a given event and its absolute future, but between them a "present" teeming with relations of before and after.

For philosophy there was another difficulty. The conception of events related only by the nonrelation of independence implies the idea of purely external relations, not to be found in any of the events but sprawling somehow "between" them. I believe I have shown elsewhere that monistic arguments against wholly external relations and pluralistic arguments against wholly internal relations are equally cogent and that the solution to the problem of relating events is to be found only in a theory of asymmetrically internal-external relations, constitutive of one term but not of the other. Such relations are vulnerable to neither of the objections to which the symmetrical extremes are exposed (5).

In spite of these considerations, relativity physics has seemed to compel us to accept the symmetrical independence of spatially separated events. For decades I suffered philosophically from this seeming necessity. Now, may Allah bless him, Bell has done away, it seems, with the problem. For he shows that the mathematics of quantum theory, which has yielded such manifold confirmed predictions, is incompatible with the idea of mutually independent contemporaries. And in the thirteen years since 1964 no one has shown how to rid the quantum mathematics of this implication and yet retain its utility.

It should be said that Bell somewhat confused the issue by employing the notion of hidden variables, perhaps to save determinism, but Stapp has shown that this feature can be eliminated and the theorem still derived.

We have then physical as well as philosophical reasons to dismiss the idea of mutually independent events. The science that produced the idea has also eliminated it. The alternative is not to suppose that contemporary, spatially separated events are mutually influential. In that case a decision here would have to take account of a decision there that would have had to take account of a decision here taking account of the one there, and so on in endless proliferation and confusion. Or else one would have to say there was, at a given moment, but a single decision for the cosmos, as though the universe were but a series of acts of God. This is the monistic nightmare in which all localized action is lost and nothing definite can be said without saying everything else, which is impossible. This was why, after for some years defending (against Whitehead) an interdependence view of contemporaneity in order to avoid the paradox of purely external relations, I came to accept the relativistic view, paradoxical as it also seemed. But now with Bell and Stapp things are different. Events at place A and those at place B cannot be independent. Not that they must be interdependent. But either an influence goes from A to B or from B to A. The analogue in formal logic is that of P and Q being neither equivalent nor simply independent, though we do not know which is the entailing and which the entailed proposition.

The idea of interaction or biconditioning does seem a requirement of common sense and experience. Thus in dialogue each person influences the other. Yes, but persons, and individual things generally, are not single events, ultimate units of the world’s plurality, or final terms for spatial or temporal relations. Rather they are sequential series, families, of events. The veto upon mutually interactive events is compatible with mutually interactive careers or event sequences. "Interaction," and symmetry generally, is shorthand. Thus I now may influence you as at a later moment, and you as you were a moment ago may influence me as I am now. These relationships require three terms, three events, not just two. Between the ultimate units of analysis, the single events, there is only one-way influence, but several such asymmetrical relations may for convenience be summed up as interactions between individuals. The truth that talk about individuals is shorthand was seen by Buddhists long ago. How many philosophers today are pre-Buddhist in this respect! Also prescientific, for all modern science relates events to events, in the last analysis, not things to things.

The relativity scheme of space-time remains intact as a way of picturing ordinary, nonquantum relations between persons or things and even as a way of picturing relations between single events so far as these relations consist only of influences of the kind dealt with in ordinary life, such as those used to move macroscopic bodies, or to send messages. The influence of events at A upon events at B or of events at B upon those at A is shown to be mathematically necessary, but the mere knowledge that some such influence exists does not allow us to predict what a change at A will do in any single case to things at B. We do not even know which way the influence will go, but only that there must be one. Moreover, the effect disappears when averages are made over physical ensembles. Thus the veto on messages sent faster than the speed of light still stands.

It follows from the foregoing that for many practical purposes the idea of mutually independent contemporaries retains its significance. If some remote planet is inhabited by rational beings, we cannot plan any definite action upon those beings or in our lifetime exchange messages with them. This is all to the good. It is enough to have to concern ourselves with people on the other side of this our planet without having to think of the weal or woe, or the intentions, of those on remote planets in quite other solar systems. Altogether there is as much interaction and as much independence as we have need of.

In the foregoing I have been leaning heavily on the work of the physicist Henry P. Stapp. He holds a "revised Whiteheadian" theory according to which all single events, creative acts, or decisions" (he shares Whitehead’s fondness for this word in its most generalized or nonanthropomorphic meaning, which does not entail conscious choice) belong to one well-ordered series, each event being a necessary condition for all and only those coming "after" it in the series. The interaction of two things or persons consists in each having some of its events in this sense before and some after one or more of the other’s events. Each event is necessary condition for every, but sufficient condition for no, following event. (It is sufficient condition for there being some subsequent event and for its type of probability, but not for its definite character.) If values of the variable x denote events in my career and values of the variable y events in my neighbor’s career, then as we interact there are in the well-ordered or ultimate series (on which, according to Stapp, all events fall) some instances of x both before and after instances of y. No single instance of x would both condition or come before and be conditioned by or come after the same instance of y. Causality would be wholly noncircular.

The net effect, as Stapp notes, is a great gain in coherence for the process view of reality, which was gravely compromised by taking relativity as the last word on the structure of space-time.

This change also simplifies, if it does not first make possible, the influence upon the world that Whitehead attributes to divine decisions. They only need be inserted between successive events in the ultimate series. Only those who know the troubles process philosophers have had in trying to insert divine influences into the World of mutually independent contemporaries know what a relief this doctrine affords (1, 2, 6). One possibility I thought of years ago in wrestling with this problem was a one-dimensional series similar to the one that Stapp postulates, but, since neither common sense (nor past philosophy) nor the physics I then knew about seemed to give any support for the idea, I could not quite believe it.

With all its complexities and subtleties, the process view as now revised is, in basic essentials, the simplest and most straightforward cosmology ever conceived that is compatible with what we now know about nature. The only way to refute this assertion is to point to another cosmology that is superior in these respects. To do this will prove harder than to find grounds for complaint about this or that feature of White-head’s writings. Stapp’s writing, some of it not yet published, seems a model of clarity and very different in various ways from Whitehead’s, yet it preserves what on the basic level most matters in the Whiteheadian vision.

Metaphysics, the irrelevance of which has been so widely declared, is showing itself relevant indeed. We stand, one may surmise, before a new era in speculative philosophy. Bell’s discovery is philosophically as revolutionary as Heisenberg’s. That so many years could pass before it was much noticed seems surprising. Perhaps the needless entanglement with the sterile idea of hidden variables is the reason for the neglect. In any case, as many such cases show, the world is always busy as well as prejudiced. However, philosophy can hardly abstain much longer from considering Stapp’s startling idea, derived from Whitehead with help from Bell, that the four dimensions of space-time are our way of picturing relations obtaining, in terms of various types of influence, among instances of creative becoming whose well-ordered series of conditions and conditioned fall upon a single ultimate dimension. This dimension is far more like an ultimate time than an ultimate space, since it has a radical directionality, each member conditioning (when all types of influence are taken into account) all those coming "after" and none of those coming "before" it. It is time’s one-way dependence, not space’s symmetrical dependence or interdependence, that is the clue to reality in general or as such. Taken absolutely, space is, as so many philosophers have suspected, an illusion. (A Kantian might view this as at least a partial vindication of the formidable Koenigsberger.)

This result is only what formal logic should have led us to expect. For the relation upon which all reasoning depends is neither mutual conditioning (equivalence) nor complete independence but the normally one-way entailment or simple conditioning. This point is almost childishly simple. But it is profound, for by it alone can we reconcile the indispensable contrasting ideas of order and freedom, persistence and novelty, necessity and contingency, past and future, being and creative becoming, security and adventure, the satisfyingly predictable and the thrillingly unforeseeable, as in scientific discoveries or in all the best music. "Order" is significant only because, as Whitehead bluntly says, disorder is as real as order. The past can be "closed" only because the future is open. Asymmetry, not symmetry, is king.

Realities are neither simply outside each other, as flume, Russell, and other extreme pluralists have held, nor simply inside each other, as Fa Tsang in ancient China and Royce and Blanshard in recent times have stated, but cumulatively inside their successors as new realities which have essential reference to their predecessors are endlessly created. Causality is merely the way in which each instance of freedom takes into account the previous instances, as each of our experiences refers back through memory to our own past and through perception to the world’s past. Freedom is influenced by its own previous acts and by nothing else whatever. Even divine influence can only be the Eminent form of freedom whose decisions also must be in the ultimate series. Thus Berdyaev’s idea of a "divine time" can be given a meaning. For it is only divine "prehension," as the Eminent form of memory and perception, that can adequately preserve what has come to be and thus render it truly closed and forever definite thereafter. Atheistic systems will have to do with some less complete and positive account of how the past influences the present.

Every great scientist, like every great philosopher, sees some things rightly and some wrongly. Thus, granted Stapp’s interpretation of Bell’s discovery, though Einstein was wrong in refusing to give up classical determinism, he was right in rejecting absolute simultaneity. Two unit events at strictly the same locus in the ultimate succession must have the same conditions and probably consequences and be indistinguishable. And what could assign them the same locus in ordinary time? If they are interdependent, their distinguishability is lost; and if they are entirely independent, what could enable them to form parts of one unambiguously present state of nature?

It was also sound to look for a finite upper limit to velocity. An actual world cannot be all possible worlds, and any world order consists in excluding some logically possible sorts of happenings. Thus Epicurus was right in contradicting Democritus’s idea that atoms exist in all conceivable sizes. To be actual is to exclude some possibilities. This applies to actual laws, say those characterizing our "cosmic epoch," as well as to instances coming under the laws. It is quantum theory that has at last brought science to admit the contingency that qualifies every instance of becoming. The new indeterminacy is piecemeal contingency. Not only could there be other laws, but also, even granted the laws and the actual causal conditions, each new actuality could have been otherwise than it has been. Einstein, who was somewhat in love with necessity, inclined to view it as the very meaning of order and rationality. Rather, order or rationality is a mixture of "necessity and chance," as Epicurus shrewdly divined. "P entails q" is significant only because it is possible and common in such cases for q not to entail p.

In fairness we should perhaps agree with Pauli (against Born) that Einstein’s main objection, and a more cogent one, to quantum theory was not the statistical aspect, to which he was a major contributor, but to the subjectivism sometimes derived from it, the view that nature is merely certain correlations (statistical or not) among our perceptions. This for Einstein made the theory an incomplete description of the order of nature, which can hardly obtain as only an order of human perceptions. Yet it is widely agreed that, as now formulated, quantum theory gives us a mathematical model, not of an independent reality, but of our perceptions of reality. Einstein (also, I think, Schroedinger and Popper) has expressed dissatisfaction with this limitation. Heisenberg seems not wholly consistent on the issue. Stapp desiderates a mathematical model of what is going on in nature at large, but he concedes that we do not yet have such a model. In his view the present theory is merely "pragmatic." According to the revised Whiteheadian theory, the desired model should refer to items on the ultimate series, the members of which may be conceived abstractly as decisions or partly free events, subject only to statistical regularities. Our momentary human experiences are paradigmatic examples of such events, but they have no ontological priority.

Experiencing as creative of its own novel unity is the absolute principle, and it includes the persistence of the already created. Causality is merely, as Whitehead so nicely put it, the necessity that each new actuality must "house" its actual world, i.e., its past. I have shown elsewhere that the partial predictability of the future is a logical consequence of this postulate (4; cf. also 3). It is the real solution to Hume’s problem about causality, provided we take past to refer to the order in which actualities come to exist, rather than only to the "temporal" order as it appears in relativity physics or is accessible to detailed human discernment. We can believe in an order of creation without necessarily supposing that observing animals such as we are have unlimited capacity to know that order. Obviously we cannot know just how it feels to be a butterfly, or even a chimpanzee, or for that matter our own wife or husband. So why should we complain because there is some mystery for us about the order in which actualities become actual?

Whitehead makes one remark that might seem to imply a potential objection to the new principle. He says that the mutual independence of contemporaries constitutes their freedom. Without this independence, what happens anywhere would immediately condition what happens anywhere else. However, this would be fatal to freedom only if the sole alternative to mutual independence were mutual dependence. And this is not a necessary, if it is even a possible, interpretation of Bell’s result. What happens here now may condition what happens somewhere else without measurable temporal lapse, although what happens at the somewhere else does not condition what happens here and now. In that case what happens here is entirely free so far as the other happening is concerned, and the other happening, though conditioned by what happens here, still retains its freedom since, by the process conception of conditioning, no set of conditions can be fully determinative of the resulting actuality. I think Whitehead was subtly misled by the symmetry that distinguishes space from time, a symmetry that, we now appear to know, holds only with respect to certain forces, those communicated not over the speed of light and constituting interaction only as shorthand description of a tissue of one-way actions between unit events.

We seem to have in this situation one more example of the truth that symmetry is invariably partial or in some sense artificial. The mutual externality that has often been taken to distinguish matter from mind, the spatial from the merely temporal, like so many other supposedly absolute distinctions between physical and mental process turns out to be an illusion, if taken without qualification. And the mutual interaction that has often been proposed as the way to avoid that illusion is revealed as an opposite exaggeration.

Not symmetry, asymmetry is king, the one-way dependence of creativity in each instance on its antecedent instances.


The modified Whiteheadian view has in common with the unmodified doctrine that, in either case, substance and spatiality (Kant’s third category of reciprocity) reduce to Kant’s first category of cause-effect, which in process terms is the same as prehendable-prehending. Against the unmodified view I see two objections.

(1) There is Bradley’s argument that (mutually) external relations imply a relation between the terms and the relation, generating a regress. (With the externality holding of one term only, there is, as Bradley failed to note, no regress, for the internally related term, simply in being itself, has relation to the other term.)

(2) There is the difficulty of seeing how the divine Consequent Nature can be compatible with the idea of its taking light years for spatially separated events to be together as data of one prehension. To meet this difficulty one may (with Whitehead and Ford) view God as an actual entity" or (with me) as a society, in either view not without what may appear as troublesome paradoxes.

For the two reasons stated I must hope that the Stapp modification proves acceptable, odd as it may seem to our human imaginations. Whichever way further study takes opinion, it is, I hold, a great advantage of process philosophy that it faces only one basic problem where tradition saw three. The basic problem is that of one-way dependence, or in the Buddhist phrase, whatever this or that Buddhist meant by it, "dependent origination." Substantiality (or social order) and spatiality are but complications in the essential business of prehensive supersession, A prehending B which prehended C, etc. Substances, societies, are especially intimate sequences of actualities prehending a common characteristic from predecessors; spatiality is only the at least partly symmetrical case: either (the unmodified view)

A) Mutual inheritance between sufficiently near or enduring societies, otherwise mutual non-inheritance, and

B) Mutual non-inheritance between actual entities; or (Stapp)

A) As above, except as qualified by

B’) One-way inheritance of a special, subtle kind between pairs of actual entities; otherwise non inheritance, as in (B).

Thus on both theories a single principle does triple work. When a physicist or mathematician achieves such sweeping integration of concepts under one concept, people get excited. Philosophers, for one reason or another, often seem not to care. Physicists now say what Whitehead said rather long ago: nature consists in the last analysis of "events, not things." Physicists as such can hardly be expected to see also that causal inheritance is prehensive. But when psychologists seriously turn their attention to the question of comparative psychology and the general problem of mind in nature, then they and the physicists (and perhaps even most of the philosophers) may come to see it.



1. Paul Fitzgerald, "Relativity Physics and the God of Process Philosophy," Process Studies 2/4 (Winter, 1972), 251-73.

2. Lewis S. Ford, "Is Process Theism Compatible with Relativity Theory?" Journal of Religion 48/2 (April, 1968), 124-35.

3. Charles Hartshorne, "The Meaning of ‘Is going to be’," Mind 74/293 (January, 1965), 115-29.

4. Charles Hartshorne, "Creativity and the Deductive Logic of Causality," Review of Metaphysics 27/1 (September, 1973), 62-74.

5. Charles Hartshorne, "The Neglect of Relative Predicates in Modern Philosophy," American Philosophical Quarterly 14/4 (October, 1977).

6. John T. Wilcox, "A Question from Physics for Certain Theists," Journal of Religion 41/4 (October, 1961), 293-300.



1 I am deeply indebted to Henry P. Stapp for his lucid explanations (partly in conversations) of the essentials of Bell’s theorem and for his revision of the Whiteheadian cosmology to render it compatible with Bell’s result. For the relevant literature see the references given in Stapp’s essay above, particularly 1, 9,10, and 7, sections iii, x, and especially appendix B on p. 1318.