Determinism in Classical and Quanta1 Physics

by J.M. Jauch

I( Concepts which have been proved to be useful in ordering things easily acquire such authority over us that we forget their human origin and accept them as invariable."

Albert Einstein

1. Introduction

The quotation from Einstein is doubly significant with respect to the concept of determinism, because this concept is precisely one of those which has acquired such authority over the thinking of scientists that even Einstein could not tear himself away from the belief that the ultimate process laws of physics must be deterministic, and that for that very reason quantum mechanics, as we know it today with its probabi- listic interpretation, cannot possibly furnish a complete description of reality.

It was that same Einstein who, much later in life, in a letter to Max Born, wrote: "I can't believe that God plays dice". That is why Eins- tein in his later years withdrew almost completely from active partici- pation in the development of quantum physics.

The problem of determinism (also inaccurately called causality) is at the very heart of the controversy that has plagued quantum physics from the Solvay Congress in 1927 until the present, without seemingly having come nearer to a solution.

I t seems therefore appropriate to examine this notion somewhat

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more critically than is customary. In this lecture, I shall do that from a physicist's point of view. I propose to trace its historical origins, to examine the reason for its adoption and its hold on scientific thought, to show some of its relationships to other concepts such as "reality", the Yarrow of time", the problem of "induction" and the notion of the "process law" in modern science. Finally I will review its effect on present-day attempts in the search for more fundamental and determin- istic alternatives to quantum mechanics.

2. 'The Notion of Scientific Determinism

Philosophers have identified at least three different notions of determinism, which may be classed as epistemic, causal, and ontic determinism.

The first concerns statements such as : From the knowledge of the present state of a physical system I can deduce some properties of a future state.

The second affirms that the state of the present determines that of the future (and the past) by a universal process law.

The third merely affirms existence of the world in the future from that of the present.

I shall speak here about determinism in only a limited, technica1 sense, which coincides approximately with the second of these three meanings. It is the kind of determinism which corresponds to the naive physicist's understanding of this idea. However in some discussions, essentially with reference to quantum theory, the first and second of these meanings of determinism are occasionally used simultaneously, and this has occasionally led to confusion.

Even within this limited idea of determinism there are so many ambiguities that a critical analysis of this concept will no doubt reveal a considerable area of doubt as to its exact meaning.

It might be appropriate to begin our attempt at definition with the chief proponent of determinism, Pierre Simon Laplace (1749-1827). In the introduction to his Thkohe analytique des Probabilitks, published in 1812, we find the following classic statement :

"Let us imagine an Intelligence which would know at a given instant of time all forces acting in nature and the position of all things of which the world consists. Let us assume, further, that this

Determinism in Classical and Quanta1 Physics 15

Intelligence would be capable of subjecting all these data to mathe- matical analysis. Then it would derive a result that would embrace in one and the same formula the motion of the largest bodies in the universe and of the lightest atoms. Nothing would be uncertain for this Intelligence. The past and the future would be present to its eyes.” 1

What is so striking about this statement is its utterly hypothetical character. Nevertheless, it would be rash to dismiss it therefore as essentially without scientific value. On the contrary, such a statement is meant to be a program and a motivation for research in a particular direction (as is clearly manifest from the text which follows it). Essen- tially it says to the scientist of the future: If you see events happening without apparent cause, this means that the causes are only hidden, and it is useful and promising to try to uncover them.

The second remarkable point about Laplace’s definition is its clear recognition that determinism obliterates the distinction between future and past. Indeed if one takes i t literally, the future as well as the past are contained in the present and the distinction between something that is going to happen and something that has happened is relegated to a prescientific anthropomorphism. In other words, the distinction is a kind of illusion.

These problems are of course not new. St Augustin and Calvin had the same difficulties with their doctrines of predestination which fol- lowed with merciless logic from the omniscient God, just as it follows from Laplace’s “Superior Intelligence”.

But Laplace is not concerned with the problem of reconciling com- mon sense with the consequences of his hypothesis, something that challenged the minds of the most subtle and angelic doctors of theology for many centuries. He merely refuses to take an interest in those consequences.

It is not surprising that subsequent physicists stayed clear of such extreme formulations of determinism, and many preferred an unsym- metrical formulation such as :

“By determinism we understand the belief that the future of the whole universe, or of an isolated part of it, is determined in terms of a complete description of its present condition” (Bridgman). * While in this definition Bridgman attempted to describe determinism

with objectivity, the following is a more pragmatic criterion:

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"An occurrence is causally determined if it can be predicted with certainty" (Planck). 3

Bertrand Russell is even more careful to hide the anthropomorphic

"A causal law is any law which, if true, makes it possible, given a certain number of events, to infer something about one or more other events" (Russell).

Notice how studiously Russel avoids here any reference to the past or to the future, and also avoids identifying the observer or his know- ledge. I t would indeed be hard to find any fault in this formulation, except for the difficulty in making precise the notion of event. Russell thought here of classical physics but we shall encounter the difficulty again in quanta1 physics where this point becomes much more important.

These samples may suffice to delineate the subject matter and to give us a sufficiently vivid picture of the concept under discussion.

One thing is certain : The whole of 19th century physics was perme- ated with this concept. It formed the background and general frame- work into which every scientist of standing and reputation would try to organize his scientific concepts. Only the advent of quantum theory breached the solid wall of the advancing science, a breach that shows no signs of healing, one which, on the contrary, shows signs of being a major mutation leading to an entirely different scientific philosophy.

Before I come to this part of my lecture, I want to inject here some historical remarks.

part of this kind of definition by telling us :

3. History of Determinism

Although determinism is particularly characteristic of the physics of the 19th century, it has a long and interesting history in the course of which it underwent various modifications. As far as I can discover, the first explicit formulation of a deterministic evolution process is due to the Greek atomists. I t was Leucippus who is supposed to have written:

"Naught happens from nothing but everything from a ground and of necessity. "

Aristotle found this to be nonsense and he reproached the atomists with overlooking entirely the conditions under which events come to pass. While he would thus recognise the lawfulness of natural proc-

Determinism in Classical and Quanta1 Physics 17

esses, that is, the transformation of the possible to the actual, he would not deny the occurrence of chance and its irreducible reality. How could it be otherwise in Aristotle’s physics since the actual is unique, hence determined, while the possible is undetermined and therefore subject to chance?

For Aristotle it was quasi-self-evident that we can learn something new from tomorrow but not from yesterday.

In spite of this balanced attitude of the Philosopher there is always a streak of determinism in the Greek scientific tradition. In the poetic tradition this is clearly visible in the Greek tragedy with its portrayal of the inexorable fate of man that no manner of will can evade. Thus for the Greek poets the ends are determined while the means are still open to chance.

Even such convinced atomists as Epicurus and Lucretius could not admit the unmitigated determinism of the early atomists and they added to their doctrine that peculiar element of atomic theory, so beautifully explained in Lucretius’ De Rerum Natura as the irregular sideways swerving of the atoms in their regular movements.

In the Middle Ages the Greek atomic theory was virtually unknown since it was considered a corollary of a dangerous, heathen form of atheism. This was no doubt Lucretius’ fault since it was he who under- lined the ideological purpose of his form of atomism: viz., to free man from the burden of superstitions (which for him was a euphemism for religion).

However two other philosophical traditions influenced medieval thought in the direction of determinism: One was the philosophy of stoicism and the other was fatalism in both its Moslem and Christian forms (St Augustin).

Most philosophers, theologians and scientists who thought about these questions were aware of the enormous difficulties which deter- minism brought into the philosophy of man and his fate. How is it possible to reconcile free will, responsibility, guilt and merit, communi- cation, meaning and evolution with a deterministic philosophy? The most incredible contrivances were invented to accomplish it.

Descartes with his Mind and Matter assumes a parallel deterministic evolution of both entities which are supposed to correspond to each other like two clocks keeping the same time to produce the illusion of a meaningful interaction. Leibniz even had infinitely many entities with the uncanny property that they would evolve parallel and create an illusion of correspondence.

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And the theologians, both Christian and Moslem, racked their brains as to how they could possibly reconcile the evil in the world with the all-knowing and benevolent God who knew it all beforehand and thus let come to pass whatever misery we find in this sad world of ours, without of course being responsible for it.

No wonder that Voltaire had an easy time satirizing Leibniz’ ”best of all possible worlds” with his Cadide .

With the advent of modern mechanics, that is, with Galilei and Newton, determinism took on a new aspect which we might describe as scientific determinism.

The most important change that characterizes the 18th century science was the removal of the final causes. The universe and the physical systems sufficiently detached from the rest of the world came to be represented by clocks, and it is perhaps no coincidence that this century also marks the beginning of the watch industry.

With the 19th century, the new element of power was added, per- fectly symbolized by the steam engine. Determinism became reinforced as a paradigm of scientific explanation because it corresponded to the notion of science as a source of power.

It was only with the advent of the 20th century that scientific deter- minism reached a crisis while at the same time power has become a source of profond anxiety for men.

4. The Disintregration of Determinism

Most of the time the philosophy of science follows the history of science. The problem of causality and determinism is a notable excep- tion to this rule. In fact, the most important analysis of causality in science was first made by Davi,d Hume in his chief philosophical work, the 7reatise of Human Nature which he wrote at the age of 25.

In this epoch-making work Hume criticizes the principle of causality as used by the scholastics, Descartes and others, by pointing out that the relation of cause and effect is not, as they believed, a necessary and logical connection. H m e on the contrary shows that causal connections between different events can be inferred only from experience and not from reasoning and reflection.

Hume’s doctrine of causation produced a shock in the history of philosophy whose reverberations are still felt today. Kant tells us that it was Hume who awakened him from his “dogmatic slumber”, partic-

Determinism in Classical and Quanta1 Physics 19

ularly by his criticism of the principle of causality. He invented for this purpose his celebrated synthetic a priori propositions, which include all propositions learned from experience. A synthetic a priori propo- sition is one which may be discovered only through experience but once known is recognized as having a basis other than experience. With this ingenious invention Kant was able not only to save causality but as he says:

"I venture to assert that there is not a single metaphysical pro- blem which has not been solved, or for the solution of which the key at least has not been supplied."

Surely, Kant did not suffer from excessive modesty! On the side of physics the first shadow on the simple-minded deter-

minism of Laplace was cast by the discovery of the kinetic theory of gases and statistical mechanics. The thermodynamic variables, with which we describe the behavior of highly complex system such as a finite volume of a gas, satisfy perfectly deterministic laws such as the equations of state and the invariable approach to equilibrium. Yet these laws are known to be only apparently deterministic since, if they were not, they would contradict the more fundamental laws of mechanics. Boltzmann was perhaps the first to emphasize the essentially statistical character of these laws, and it was Einstein in one of his first important publications who showed the relationship of statistical fluctuations, which are the inevitable consequences of Boltzmann's interpretation, to Brownian movmen t .

Although determinism was saved by this development, at least in principle, there appeared on the horizon a very important new possi- bility. If statistical laws can behave nearly deterministically for systems with large degrees of freedom, could it not be true that all physical process laws, even the most fundamental ones, are perhaps only statis- tical laws and that they appear deterministic only because we cannot, with the usual observations, discern the fluctuations?

As far as I know there are at least two distinguished scientists who asked themselves this question and who answered it affirmatively. One is Charles S. Peirce, the American philosopher and mathematician, and the other is F. Exner, successor to Boltzmann as professor of physics at the University of Vienna.

He influenced both J. Dewey and W. James. He also invented mathematical logic and semantics. Yet his unconventional life and sharp criticisms pre-

Peirce is the founder of pragmatism in America.

20 J. M. Jauch

vented his having an academic career and he ended his life in poverty in the little town of Milford, Pennsylvania.

One of his main scientific theses was the denial of determinism and its replacement by a new scientific principle which he called variescence. The reason which he gives for rejecting determinism is that if the universe were governed by immutable laws there could be no progres~.~

While Peirce was obviously influenced by Darwinism, Exner was under the influence of Boltzmann. He published a book in 1919 the principal thesis of which was that the fundamental elementary processes are essentially statistical. a It contains the following passage:

“Let us not forget that the principle of causality and the need for causality have been suggested to us exclusively by experiences with macroscopic phenomena and that a transference of the principle to microscopic phenomena, viz., the assumption that every individual occurrence can be strictly causally determined, has no longer any justification based on experience.”

Exner was Schrodinger’s teacher and the latter gave an exposition of this thesis in his inaugural lecture in Zurich in 1922. His distinguished audience was so critical of this view that he dared not publish his lecture, as he related in an autobiographical note, until seven years later- after determinism had been replaced by a probability law in the then newly-established quantum mechanics.

5 . Determinism in Quanta1 Physics

The last remark brings us to the great scientific mutation which culminated in the discovery of quantum mechanics. I t brought with it a fundamental change in the attitude of the physicists towards deter- minism. The interpretation of the mathematical formalism of quantum mechanics by Born, which is now almost universally accepted by the physicists, precludes the possibility of precise predictions of the elemen- tary processes associated with Planck’s quantum of action. This fact leads to considerable epistemological difficulties which even now form the subject of many controversies.

Before describing some of these difficulties I want to remark, how- ever, that the statistical properties of microevents is an empirical fact which does not depend on any theory or any particular interpretation of a theory. However, quantum mechanics together with its interpreta-

Determinism in Classical ana Quanta1 Physics 21

tion permit exact statements about the probability of the occurrence of events, and many of these statements can be and have been verified to a high degree of accuracy. In order to illustrate this point I want to discuss here an extremely simple but rather typical example.

Suppose that we have a source of monochromatic light of such low intensity that we can make observations on individual photons. Suppose that we let such a stream of photons fall on two Polaroid plates with their axes of polarization at an angle of 45'.

Fig. 1. Direction of the axes of polarization of two Polaroid plates.

The photons which fall on the first plate will be randomly polarized, but when they have traversed it they will all be linearly polarized along the direction of the axis of the first plate. When they arrive at the second each individual photon behaves in a random manner. About half of them will penetrate the second plate and reappear on the other side with their state of linear polarization in the new direction. The other half will be absorbed.

For an individual photon the outcome at the second plate is uncer- tain. This is an empirical fact, quite independent of and prior to any theory of quanta1 phenomena.

Faced with this empirical situation one can take essentially either of two different attitudes:

a) While maintaining a belief in strict determinism, one can con- tinue the search for causal relationships between the behavior of the ,photon, or

b) One can consider this (and similar) experiences as evidence of the breakdown of strict determinism.

Most physicists today have accepted the second version, but an

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important minority, among them some of the founders of quantum theory, has maintained the first. The difficulty with the first version is on two levels: the empirical and the logical.

Empirically, any attempt to find observable properties of photons which could be correlated with the seemingly erratic behavior of the photons at the second plate have failed. These hypothetical properties, if they exist at all, must therefore be quasi-unobservable and they are for this reason usually referred to as hidden variables.

Logically, there exist various Uproofs” that hidden variables are incompatible with the rest of quantum mechanics as we know it today. The interpretation of such proofs is not to be taken to mean that hidden variables are logically impossible and that their existence can be dis- proved by mathematical reasoning. There are available plenty of examples of hidden variable theories. None of these theories is possible within the limits of empirical data without giving these variables quite anomalous properties, very different from the classical properties which they are supposed to represent.

This, of course, is not a sufficient reason to rule them out and, finally, the only convincing evidence for or against such theories will eventually have to come from carefully designed experiments to test deviations from the quantum theoritical predictions for certain observ- able effects.

Fortunately, during recent years, such experiments have been per- formed. The results have been in contradiction with the proposed hid- den variable theories.

Thus, as of today, we may cautiously conclude that, if determinism is to be maintained also in microphysics by means of hidden variables, then these variables must have far more subtle properties than anyone has yet been able to invent. The obvious theories of this sort just do not work.

6 . Review of the Case for Determinism

The foregoing exposition permits us to draw some tentative con- clusions as to the present state of determinism in the formulation of physical theories.

I. Most philosophers of science today would seem to agree that there is no logical necessity for assuming a deterministic process law for

Determinism in Classical and Quanta1 Physics 23

evolution. In fact, the problem of determinism is closely related to that of induction. Therefore, even if, within one particular theory, evolution is deterministic, there is no logical necessity that nature will behave in accordance with this theory tomorrow.

11. Observation of phenomena will never permit a conclusive decision in favor of determinism. Such observations are always statistical in character even in the domain of classical physics, and they are therefore not suited for establishing determinism.

111. It is true that in classical physics there is a large collection of phenomena which are described to a very high degree of accuracy with a deterministic theory. Such theories are based on two foun- dations: a) The notion of the pure state, wich refers to an idealized physical

b) The notion of the deterministic evolution of such states.

IV. In quanta1 physics, and more precisely in quantum mechanics determinism cannot be incorporated into the theoretical structure. While it is possible to maintain a deterministic evolution of the pure states (Schrodinger equation), the interpretation of the formalism leads to predictions which are necessarily statistical in nature. This reflects perfectly the actual statistical behavior of microsystems as they are observed experimentally.

W e come therefore to the conclusion that determinism, far from being logically necessary or empirically established even in the classical domain, is actually very dificult to maintain in microphysics.

situation,

7. Problems for the Future

The rejection of determinism as a scientific paradigm has some important consequences which lead to serious and possibly important problems for the future.

One of these problems is the problem of measurement. This problem may be briefly stated as follows : How is it possible to establish objective and unambiguous facts, which are the basis of any theoretical description of nature, in a world where all equipment, even that used for the measurement itself, is governed by probability laws?

A second closely related problem is this: How can we understand

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the nearly deterministic behavior of certain large objects? In other words, why is a deterministic theory a relatively good approximation in a large part of physics?

Finally, in my opinion, one of the most significant complexes of problems of the future is the understanding of the behavior of large systems with a high degree of organization. The simplest systems of this kind are encountered in statistical physics where the establishment of long-range order and symmetry lead to the phenomena of phase transition. But much more important and infinitely more complex are biological and social systems where the structural and functional organi- zation becomes the dominating feature and leads to evolutionary behav- ior where determinism is singularly inadequate.

I, for one, am convinced that the reduction of such a system to the evolutionary behavior of component systems is likely to reveal only one of two complementary sides of the whole and that we must be prepared to accept complementary descriptions as the basic ingredients of any science which is relevant to society.

REFERENCES

P. S. LAPLACE, Thkorie anulytique des Probabilitds, in Oeuvres compl2tes. (Paris: Gauthier-Villars, 1878-1912). P. BRIDGMAN, 7 h e Logic o f Modern Physics. (New York: Macmillan, 1949), p. 209. M. PLANCK, Scientific Autobiography and Other Papers. (New York: Philosophical Library, 1949. B. RUSSELL, €I uman Knowledge, Its Scope and Its Limits. (New York: Simon and Schuster, 1948). CHARLES S. PEIRCE, Selected Writings, Edited by P.P. Wiener. (New York: Double- day, 1958). F. EXNER, Vorlesun en iiber die Physikalischen Grundlagen der Naturwissen- schaften. (Vienna: ficutickc, 1919). E. SCHR~DINGER, Natunuiss. 17, 9 (1929).

J.M. Jauch Department of Theoretical Physics University of Geneva Switzerland

Dialectics Vol. 27, No 1 (1975)

Determinism in Classical and Quanta1 Physics 25

DISCUSSION

MERCIER: I have several questions that I would like to ask. 1) How do you reconcile Laplace’s all-knowing being with his an-

swer tc? Napoleon that he has no need for God as a hypothesis in his system?

JAUCH: I cannot reconcile the two statements and I doubt whether Laplace could have done it.

MERCIER: (2) You did not quote Pascal in your historical survey, yet Pascal was the founder of the probability calculus and it seems to me that if Kant had read Pascal it would have been very useful for the philosophy of causality.

JAUCH: Pascal certainly played a very important role in the calculus of probability although it would be too much to say that he was “the founder”. But my intention was not to give a history of this calculus but to mention some of the highlights in the history of determinism.

MERCIER: (3) In a paper on determinisms published in the Festschrift for Lande, as well as in other, earlier, publications, I made a plea for not using the term “determinism” to refer exclusively to what is known as Laplacean determinism; and so, a plea for not speaking of indeter- minism to refer to a basic aspect of quantum theory. For quantum mechanics allows for predictions which have been experimentally veri- fied in cross-section determinations (I use the word prediction pur- posely), whereas relativity theory does not all,ow for such predictions in principle. I strongly feel that the word “indeterminism” is to be very much avoided in this kind of discussion.

JAUCH: I thank you for reminding me of this terminological subtlety.

DRIESCHNER: If I understand you correctly, you stated that any deter- ministic theory that would lead to the same results quantum mechanics leads to, would not be of real interest to you. This seems rather strange to me, because many people, following Einstein, are puzzled by precisely that indeterminism that is typically characteristic of the Copenhagen interpretation of quantum mechanics. They would like to overcome just this “weakness” of contemporary quantum theory. How, then, can you say that any such attempt would not be of real interest to you? Don’t you think that the current discussions of the various interpreta- tions of quantum mechanics are meaningful discussions?

JAUCH: You ask two questions. Let me answer the first one in the following manner:

Any attempt, even if successful, to render the results of quantum mechanics in a deterministic conceptual frame remains of a very limited

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interest as long as no measurable prediction can be made which differ in the two theories. As long as their predictions remain identical for all possible or imaginable measurable effects the preference for one or the other theory is rooted in ideological prejudices which by and in themselves are not important for a scientific theory.

As to the second question I would say that the current discussions of the various interpretations of quantum mechanics are meaningful, and in fact very important, because they may eventually lead to a better understanding of the epistemology of science and the possible extensions or generalizations of the theory to cover as yet unknown physical laws.

VON WEIZSACKER (commenting on Jauch’s reply to a question by Drieschner, touching on three topics) :

(1) Hidden variable theories will not lead to a successful theory that could replace quantum mechanics as we know it today.

JAUCH: Although my inner conviction leans for many reasons in the same direction as yours, I would not quite dare to make such a categor- ical assertion.

VON WEIZSACKER: (2) Bohr, while he was right in the controversy, never really understood Einstein’s deepest concern.

JAUCH: I have many times felt, when contemplating the controversy between these great men of science, that they were both going past each other as if they were moving on two different lanes with only a contact

1. Their disagreements were on philosophical matters, which the conceptual background and the undefinable categories of thinking such as reality, truth, determinism and complementarity. How- ever, they did not disagree on many of the matters which could be subjected to experimental tests.

2. Both, Einstein and Bohr, have developed during their lifetime and they represent in the deepest sense complementary attitudes both of which are essential in the process of communication between nature and man.

VON WEIZSACKER: (3) I reiterate the view I expressed earlier that it is inherently impossible to go beyond quantum mechanics and its Copen- hagen interpretation.

JAUCH: I know that this view is held by many people who have lived in the tradition of the Copenhagen interpretation. Although I strongly sympathize with this interpretation (or perhaps with the general spirit of it) I would think views such as expressed in von Weizslcker’s state- ment are rather audacious. I would prefer to be more cautious.

at infinity. Yet one must not overlook the P ollowing two points: