Quantum Theory and Determinism L. Vaidman Raymond and Beverly Sackler School of Physics and Astronomy Tel-Aviv University, Tel-Aviv 69978, Israel Historically, appearance of the quantum theory led to a prevailing view that Nature is indeter- ministic. The arguments for the indeterminism and proposals for indeterministic and deterministic approaches are reviewed. These include collapse theories, Bohmian Mechanics and the many-worlds interpretation. It is argued that ontic interpretations of the quantum wave function provide simpler and clearer physical explanation and that the many-worlds interpretation is the most attractive since it provides a deterministic and local theory for our physical Universe explaining the illusion of randomness and nonlocality in the world we experience. I. INTRODUCTION be a deterministic theory. Last year I made a revision of the entry which was refereed. One of the comments of the Quantum theory and determinism usually do not go referee was: \Why I consider the fact that MWI is a de- together. A natural combination is quantum theory and terministic theory a reason for believing it?" I thought randomness. Indeed, when in the end of 19th century it is obvious: a theory which cannot predict what will physics seemed to be close to provide a very good de- happen next given all information that exist now, clearly terministic explanation of all observed phenomena, Lord is not as good as a theory which can. Kelvin identified \two clouds" on \the beauty and clear- It seems that in the end of the 19th century a ref- ness of the dynamical theory". One of this \clouds" eree would not ask such a question. The dominant view was the quantum theory which brought a consensus that then was that physics, consisted of Newton's mechanics there is randomness in physics. Recently we even \cer- and Maxwell's electrodynamics, is a deterministic theory tify" randomness using quantum experiments [1]. which is very close to provide a complete explanation of I do not think that there is anything wrong with these Nature. Most scientists accepted a gedanken possibility experiments. They create numbers which we can safely of existence of \Laplacean Demon" [3]: consider \random" for various cryptographic tasks. But I We may regard the present state of the Uni- feel that we should not give up the idea that the Universe verse as the effect of its past and the cause of is governed by a deterministic law. Quantum theory is its future. An intellect which at a certain mo- correct, but determinism is correct too. I will argue that ment would know all forces that set nature in the quantum theory of the wave function of the Universe motion, and all positions of all items of which is a very successful deterministic theory fully consistent nature is composed, if this intellect were also with our experimental evidence. However, it requires ac- vast enough to submit these data to analy- cepting that the world we experience is only part of the sis, it would embrace in a single formula the reality and there are numerous parallel worlds. The ex- movements of the greatest bodies of the Uni- istence of parallel worlds allows us to have a clear deter- verse and those of the tiniest atom; for such ministic and local physical theory. an intellect nothing would be uncertain and Before presenting this view I review how quantum the- the future just like the past would be present ory led to believe that Nature is random. I give a critical before its eyes. review of attempts to construct theories with randomness (Laplace, 1814) underlying quantum theory. I discuss modifications of the standard formalism suggesting physical mechanisms The idea of determinism has ancient roots [4]: for collapse. Then I turn to options for deterministic the- ories by discussing Bohmian mechanics and its variations, Nothing occurs at random, but everything for in particular a many Bohmian worlds proposal. Finally, I a reason and by necessity. present the many-worlds interpretation and explain how (Leucippus, 440 BCE) one can deal with its most serious difficulty, the issue of Obvious tensions with the idea of a free will of a man probability. or of a God led many philosophers to analyze this ques- tion. Probably the most clear and radical position was expressed by Spinoza [5]: II. DETERMINISM In nature there is nothing contingent, but all In my entry on the Many-Worlds Interpretation things have been determined from the neces- (MWI) [2] I wrote that we should prefer the MWI relative sity of the divine nature to exist and produce to some other interpretations because it removes random- an effect in a certain way. ness from quantum mechanics and thus allows physics to (Spinoza, 1677) 2 Spinoza slightly preceded Leibniz who forcefully defended law of causality), he wrote, is a \heuristic the Principle of Sufficient Reason [6]: principle, a signpost and in my opinion the most valuable signpost we possess, to guide Everything proceeds mathematically ... if us through the motley disorder of events and someone could have a sufficient insight into to indicate the direction in which scientific in- the inner parts of things, and in addition had quiry should proceed in order to attain fruit- remembrance and intelligence enough to con- ful results [Plank, 1932]" sider all the circumstances and take them into (Earman, 1986) account, he would be a prophet and see the future in the present as in a mirror. I do not see a \failure to find deterministic laws of physics". All physical laws I studied, except for the col- (Leibniz, 1680) lapse of the wave function which has many other prop- Hundred years ago Russell mentioned similar views, but erties which suggest to rejected it, are deterministic. I already had some doubts [7]: think that the prevailing view of indeterminism in the last century is an accidental mistake of the evolution of Sci- The law of causation, according to which ence, similar to ether hypothesis rejected hundred years later events can theoretically be predicted by ago. means of earlier events, has often been held to be a priori, a necessity of thought, a cate- gory without which science would not be pos- III. PROBABILISTIC THEORIES sible. These claims seem to me excessive. In certain directions the law has been verified Laplace, the symbol of determinism in physics is also empirically, and in other directions there is the founder of probability calculus [9]. He denied that no positive evidence against it. But science there is an objective probability. The foundation of the can use it where it has been found to be true, probability theory is a realistic and deterministic theory without being forced into any assumption as with agents which are ignorant about some of the ontol- to its truth in other fields. We cannot, there- ogy. fore, feel any a priori certainty that causation The interpretation of probability is still a very contro- must apply to human volitions. versial subject. The leading role in it plays de Finetti (Russel, 1914) who also forcefully claims that there is no such thing as probability. It is only an effective concept of an ignorant It was quantum theory which completely changed the agent [10]: general attitude. But the founders of quantum me- My thesis, paradoxically, and a little chanics did not give up the idea of determinism easily. provocatively, but nonetheless genuinely, is Schr¨odinger,Plank, and notably Einstein with his famous simply this: dictum: \God does not play dice", were standing against PROBABILITY DOES NOT EXIST indeterminism. Earman, a contemporary philosopher The abandonment of superstitious beliefs who spent probably more effort on the issue of deter- about the existence of the Phlogiston, the minism than anyone else, writes [8]: Cosmic Ether, Absolute Space and Time, . ... while there is no a priori guarantee that . or Fairies and Witches was an essential step the laws of the ideal theory of physics will along the road to scientific thinking. Proba- be deterministic, the history of physics shows bility, too, if regarded as something endowed that determinism is taken to be what might with some kind of objective existence, is no be termed a `defeasible methodological im- less a misleading misconception, an illusory perative': start by assuming that determin- attempt to exteriorize or materialize our true ism is true; if the candidate laws discovered so probabilistic beliefs. far are not deterministic, then presume that (de Finetti, 1970) there are other laws to be discovered, or that The program of presenting quantum theory as an ob- the ones so far discovered are only approx- jective probability theory cannot use classical probabil- imations to the correct laws; only after long ity theory since it assumes underlying definite values un- and repeated failure may we entertain the hy- known to some agents. These definite values can be con- pothesis that the failure to find deterministic sidered as \hidden variables". There are many limita- laws does not represent a lack of imagination tions of the type of possible hidden variables, so it was ac- or diligence on our part but reflects the fact knowledged that probability theory underlying quantum that Nature is non-deterministic. An expres- theory cannot be a classical probability theory [11, 12]. sion of this sentiment can be found in the Spekkens, who introduced a toy model which serves as an work of Max Planck, one of the founders of important test bed for many attempts in this direction, quantum physics: determinism (a.k.a. the understands it well [13]: 3 It is important to bear in mind that one can- option. If I shall see that my option, the MWI, fails, I not derive quantum theory from the toy the- might turn to studying the operator algebra seriously.