I would be surprised if anyone here pictured God as being above our northern hemisphere sky, although such images used to be commonplace in religious thought. We no longer attempt to locate God in space, but acknowledge God as Sovereign of space, not subject to it. The scientific discoveries of the seventeenth century helped to clarify our thinking about this.

But we all tend to locate God in time, imputing to the Sovereign of history the now as we perceive it. The discovery of relativity should help to clarify our thinking about this. In nonrelativistic Newtonian physics, the present divided all events into past and future. But relativity has no invariant concept of the present. According to relativity, a here-now divides events into three types: the past cone, the future cone, and the rest -- for which there is as yet no term in everyday language. (But when we begin seriously to explore the solar system and beyond, we shall be forced to coin a term. We shall be unable to converse with our explorers, and the concept of an objective or common present will disappear.)

The past is unalterable; no one seriously doubts that. What we do can affects the future; almost everyone believes this. But what about the rest -- the vast region of space-time that according to relativity is neither past nor future? Here physicists disagree. The consensus is that no signal can be sent into the rest, and the reasons for this are overwhelming. Such a possibility would lead directly to causality paradoxes implying the possibility of altering the past: an Arcturan whose here-now is neither in my past nor my future may have my here-now of last year in its rest of space-time, so if I could send it a birthday greeting from my here-now to its, nothing would preclude my receiving a thank you last year. But many physicists who struggle to understand the world -- not content merely to predict and manipulate it -- are reluctantly led to believe that what we do must affect what happens in the rest even if we can send no signals thereby. This is a fascinating domain where relativity and quantum theory meet -- the world of Bell's theorem and the Aspect experiments -- and I shall try to explain the problem by analogy with a game.

Every day I lunch at McDonald's and get a game card with three slots A, B, and C covered with a metallic film. I choose one slot and scrape off the film; I find either WIN or LOSE. Every day my friend plays the same game in another city. Over the years we have compiled statistics concerning one question: when does it happen that just one of us wins? We have observed that when we choose the same slot this always happens, and when we choose different slots this happens one fourth of the time in the long run. The question is: How does McDonald's prepare the game cards?

They have no way of knowing which slots we shall choose; we might choose the same slot, but then it always happens that just one of us wins; consequently, my card and my friend's card must always have opposite entries. Now there are two possibilities. My card may have all of its entries identical; then, since my friend's card is opposite, it must happen that just one of us wins. The other possibility is that one of my entries is the opposite of the others. There are six ways that I and my friend can choose different slots, and a simple counting of the possibilities shows that two out of these six -- or one third -- provide a win for just one of us. But we have observed that this happens only one fourth of the time. The only conclusion is that the game cards are not prepared in advance.

Precisely this situation occurs in the correlated polarization experiments of Alain Aspect and collaborators, experiments suggested by the discoveries of J. S. Bell. The game cards are photons, the slots are directions in which a polarization measurement can be performed, the WIN and LOSE are opposite polarizations. The conclusion both of quantum theory and of experiment is that the photon cannot carry with it a game card telling it how to respond to all of the polarization measurements that might be performed on it.

One delightful consequence is that one can say without exaggeration that indeterminism is no longer merely a philosophical speculation; it is established scientific fact. Einstein to the contrary, God plays dice with the universe.

But another consequence is grimmer. The beauty of the Aspect experiments is that the polarization measurements are performed so that no signal can be transmitted from one to the other -- each is neither in the past nor the future of the other, but in what I have called the rest. Most physicists are led to the conclusion that the choice of which polarization measurement to perform -- which slot on the game card to choose -- has a mysterious influence on the state of affairs at the place and time of the other measurement.

Let me dwell on this a bit longer, because it is deeply puzzling to everyone who thinks about it and is leading some to very strange beliefs about the nature of the world. No matter which slot I choose on the game card, my friend's chances of winning are unaffected. No signal is sent, no information is conveyed: my friend has no way of knowing which slot I choose until we compare notes later (at a here-now that lies in both of our future cones). But we have seen that the game cards are not prepared in advance. Are we not led inescapably to the conclusion that my choice of slot A affects the situation of my friend's card, forcing the corresponding entry to be opposite? Perhaps not, but before discussing that let me explain why this conclusion is disturbing. Since there is no invariant causal ordering of events that are in each other's rest of space-time, rather than say that my choice of a slot has caused a change in my friend's card, it is equally valid to say that the change in my friend's card has caused my choice of a slot; in fact, for some reference frames the change in the card occurs before my choice of a slot. This is a grim conclusion.

I am one of a very small minority who cling to the hope that an objective description of nature is possible in which the principle that only the future can be affected still holds. I think that the resolution of the problem may lie in thorough exploration of field-theoretic, as opposed to particle, descriptions of nature, and that it bears a strong resemblance to the snowflake problem. The snowflake problem is this: the inexhaustible variety of snowflakes makes it evident that chance plays a major role in their development, yet they always preserve hexagonal symmetry -- how does a portion of the snowflake growing at random on one side know to grow in precisely the same fashion as its partner all the way over on the other side? This is mysterious but not beyond understanding, and the understanding has to do with the study of the snowflake as a whole (a field-theoretic description). It would be beyond comprehension were the two portions of the snowflake disconnected (a particle description). But these are technical issues, which I am studying with my colleague Eric Carlen, and I think it best to put aside philosophical and religious beliefs in the day to day work of doing science.

Quantum theory produced a crisis in human thought unlike any previous scientific discovery, a crisis that, as John Bell has shown, is exacerbated by the findings of relativity. There are problems in the interpretation of quantum theory that simply refuse to go away. For a long time, it was thought that the phenomena of organic chemistry were governed by principles qualitatively different from those of inorganic chemistry. Vitalism, an early form of holism, was introduced, but then with the synthesis of urea understanding was achieved. It is my conviction that understanding in science always comes from reduction. What is at stake in the investigation of these questions is the very possibility of an objective description of nature.

Relativity and quantum theory taken together show that space, time, and chance are inextricably linked together. Where am I? In Princeton, at the Center of Theological Inquiry. What time is it? The morning of October 22, 1988, and time for me to stop talking. What will happen next? I don't know. This is reality as I perceive it; this is my here-now-uncertainty. But I am a creature, not the center of the universe and much less its Creator. Where is God? We no longer ask that. What is God's present? If we take relativity seriously, we must conclude that it is of a different order from my present, for other creatures have a present that is incomparable with mine. Does God know what will happen next? There are strong arguments from physics that any postulation of a knowledge of all possible future outcomes is contradictory, but I prefer a negative answer to this question on other grounds; I prefer to think of God as a risk taker, one who when creating the world chooses to make it alive. Preachers sometimes refer to chance as mere chance. But I believe that chance is a mighty archangel, by which I mean that it is a deep part of God's will, with immense power over our lives.

But I must confess to an inconsistency here. I began by pointing out that it is primitive to picture God in space. Relativity tells us that space and time are aspects of space-time, so it is primitive to picture God in time. And quantum theory tells us that space, time, and chance are part of space-time-chance, so it is primitive to picture God as subject to uncertainty. But those of us who hold to faith in the Incarnation are not put off by this; we know that even in the arena of space, time, and chance in which we struggle, our Redeemer lives.


Alain Aspect, Jean Dalibard, and Gérard Roger, Experimental test of Bell's inequalities using time-varying analyzers, Physical Review Letters 49, 1982, 1804--1807. -- Few experiments that confirmed what everyone already knew have caused as much excitement as this.

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, Cambridge, 1987. -- See especially the funny and deep article ``Bertlmann's socks and the nature of reality.''

N. D. Mermin, Bringing home the atomic world: quantum mysteries for anybody, American Journal of Physics 49, 1981, 940--943. -- My formulation in terms of game cards is based on this beautiful article.

Edward Nelson, Quantum Fluctuations, Princeton University Press, Princeton, 1985. -- A highly mathematical account of stochastic mechanics, an attempt at a realistic particle picture of nature.

Edward Nelson
Department of Mathematics
Princeton University