Physics and Philosophy by Heisenberg (1958)

Foreword by FS Northrop

There is a general awareness that contemporary physics has brought about an important revision in man’s conception of the universe and his relation to it.  The suggestion has been made that this revision pierces to the basis of man’s fate and freedom, affecting even his conception of his capacity to control his own destiny.  In no portion of physics does this suggestion show itself more pointedly than in the principle of indeterminacy of quantum mechanics.  The author of this book is the discoverer of this principle.  In fact, it usually bears his name.  Hence, no one is more competent to pass judgment on what it means than he.

In his previous book, The Physical Principles of the Quantum Theory (1930), Heisenberg gave an exposition of the theoretical interpretation, experimental meaning and mathematical apparatus of quantum mechanics for professional physicists.  Here he pursues this and other physical theories with respect to their philosophical implications and some of their likely social consequences for the layman.  More specifically, he attempts here to raise and suggest answers to three questions: (1) What do the experimentally verified theories of contemporary physics affirm?  (2) How do they permit or require man to think of himself in relation to his universe?  (3) How is this new way or thinking, which is the creation of the modem West, going to affect other parts of the world?

The third of these questions is dealt with briefly by Heisenberg at the beginning and end of this inquiry.  The brevity of his remarks should not lead the reader to pass lightly over their import.  As he notes, whether we like it or not, modem ways are going to alter and in part destroy traditional customs and values.  It is frequently assumed by native leaders of nonWestern societies, and also often by their Western advisers, that the problem of introducing modem scientific instruments and ways into Asia, the Middle East and Africa is merely that of giving the native people their political independence and then providing them with the funds and the practical instruments.  This facile assumption overlooks several things.  First, the instruments of modem science derive from its theory and require a comprehension of that theory for their correct manufacture or effective use.  Second, this theory in turn rests on philosophical, as well as physical, assumptions.  When comprehended, these philosophical assumptions generate a personal and social mentality and behavior quite different from, and at points incompatible with, the family, caste and tribally centered mentality and values of the native Asian, Middle Eastern or African people.  In short, one cannot bring in the instruments of modern physics without sooner or later introducing its philosophical mentality, and this mentality, as it captures the scientifically trained youth, upsets the old familial and tribal moral loyalties.  If unnecessary emotional conflict and social demoralization are not to result, it is important that the youth understand what is happening to them.  This means that they must see their experience as the coming together of two different philosophical mentalities, that of their traditional culture and that of the new physics.  Hence, the importance for everyone of understanding the philosophy of the new physics.

But it may be asked, Isn’t physics quite independent of philosophy?  Hasn’t modem physics become effective only by dropping philosophy?  Clearly, Heisenberg answers both of these questions in the negative.  Why is this the case?  Newton left the impression that there were no assumptions in his physics which were not necessitated by the experimental data.  This occurred when he suggested that he made no hypotheses and that he had deduced his basic concepts and laws from the experimental findings.  Were this conception of the relation between the physicist’s experimental observations and his theory correct, Newton’s theory would never have required modifica­tion, nor could it ever have implied consequences which experiment does not confirm.  Being implied by the facts, it would be as indubitable and final as they are.

In 1887, however, an experiment performed by Michelson and Morley revealed a fact which should not exist were the theoretical assumptions of Newton the whole truth.  This made it evident that the relation between the physicist’s experimental facts and his theoretical assumptions is quite other than what Newton had led many modem physicists to suppose.  When, some ten years later, experiments on radiation from black bodies enforced an additional reconstruction in Newton’s way of thinking about his subject matter, this conclusion became inescapable.  Expressed positively, this means that the theory of physics is neither a mere description of experimental facts nor something deducible from such a description; instead, as Einstein has emphasized, the physical scientist only arrives at his theory by speculative means.  The deduction in his method runs not from facts to the assumptions of the theory but from the assumed theory to the facts and the experimental data.  Consequently, theories have to be proposed speculatively and pursued deductively with respect to their many consequences so that they can be put to indirect experimental tests.  In short, any theory of physics makes more physical and philosophical assumptions than the facts alone give or imply.  For this reason, any theory is sub­ject to further modification and reconstruction with the advent of new evidence that is incompatible, after the manner of the results of the Michelson-Morley experiment, with its basic assumptions.

These assumptions, moreover, are philosophical in character.  They may be ontological, ie. referring to the subject matter of scientific knowledge which is independent of its relation to the perceiver; or they may be epistemological, ie. referring to the relation of the scientist as experimenter and knower to the subject matter which he knows.  Einstein’s special and general theories of relativity modify the philosophy of modem physics in the first of these two respects by radically altering the philosophical theory of space and time and their relation to matter.  Quantum mechanics, especially its Heisenberg principle of indeterminacy, has been notable for the change it has brought in the physicist’s epistemological theory of the relation of the experimenter to the object of his scientific knowledge.  Perhaps the most novel and important thesis of this book is its author’s contention that quantum mechanics has brought the concept of potentiality back into physical science.  This makes quantum theory as important for ontology as for epistemology.  At this point, Heisenberg’s philosophy of physics has an element in common with that of Whitehead.

It is because of this introduction of potentiality into the subject matter of physics, as distinct from the epistemological predicament of physicists, that Einstein objected to quantum mechanics.  He expressed this objection by saying: “God does not play dice.” The point of this statement is that the game of dice rests on the laws of chance, and Einstein believed that the latter concept finds its scientific meaning solely in the epistemological limitations of the finite knowing mind in its relation to the omnicomplete object of scientific knowledge and, hence, is misapplied when referred ontologically to that object itself.  The object being per se all complete and in this sense omniscient, after the manner of God, the concept of chance or of probability is inappropriate for any scientific description of it.

This book is important because it contains Heisenberg’s answer to this criticism of his principle of indeterminacy and of quantum theory by Einstein and by others.  In understanding this answer two things must be kept in mind: (1) The aforementioned relation between the data of experimental physics and the concepts of its theory.  (2) The difference between the role of the concept of probability in (a) Newton’s mechanics and Einstein’s theory of relativity and in (b) quantum mechanics.  Upon (1), Einstein and Heisenberg, and rela­tivistic mechanics and quantum mechanics, are in agreement.

It is only with respect to (2) that they differ.  Yet the reason for Heisenberg’s and the quantum physicist’s difference from Einstein on (2) depends in considerable part on (1) which Einstein admits.  (1) affirms that the experimental data of physics do not imply its theoretical concepts.  From this it follows that the object of scientific knowledge is never known directly by observation or experimentation, but is only known by speculatively proposed theoretic construction or axiomatic postulation, tested only indirectly and experimentally via its deduced consequences.  To with the same initial conditions must be repeated many times, and the values of position or momentum, which may be different in each observation, must similarly be found to be distributed according to the predicted probability distribution.  In short, the crucial difference between quantum mechanics and Einstein’s or Newton’s mechanics centers in the definition of a mechanical system at any moment of time, and this difference is that quantum mechanics introduces the concept of probability into its definition of state and the mechanics of Newton and Einstein does not.

This does not mean that probability had no place in Newton’s or Einstein’s mechanics.  Its place was, however, solely in the theory of errors by means of which the accuracy of the Yes or No verification or nonconfirmation of the prediction of the theory was determined.  Hence, the concept of probability and chance was restricted to the epistemological relation of the scientist in the verification of what he knows; it did not enter into the theoretical statement of what he knows.  Thus, Einstein’s dictum that “God does not play dice” was satisfied in his two theories of relativity and in Newton’s mechanics.

Is there any way of deciding between Einstein’s contention and that of Heisenberg and other quantum theorists?  Many answers have been given to this question.  Some physicists and philosophers, emphasizing operational definitions, have argued that, since all physical theories, even classical ones, entail human error and uncertainties, there is nothing to be decided between Einstein and the quantum theorists.  This, however, is (a) to overlook the presence of axiomatically constructed, constitutive theoretic definitions as well as theory-of-errors, operational definitions in scientific method and (b) to suppose that the concept of probability and the even more complex uncertainty find the object of scientific knowledge we must go, therefore, to its theoretical assumptions.

When we do this for (a) Newton’s or Einstein’s mechanics and for (b) quantum mechanics, we discover that the concept of probability or chance enters into the definition of the state of a physical system, and, in this sense, into its subject matter, in quantum mechanics, but does not do so in Newton’s mechanics or Einstein’s theory of relativity.  This undoubtedly is what Heisenberg means when he writes in this book that quantum theory has brought the concept of potentiality back into physical science.  It is also, without question, what Einstein has in mind when he objects to quantum theory.

Put more concretely, this difference between quantum mechanics and previous physical theories may be expressed as follows: In Newton’s and Einstein’s theory, the state of any isolated mechanical system at a given moment of time is given precisely when only numbers specifying the position and momentum of each mass in the system are empirically determined at that moment of time; no numbers referring to a probability are present.  In quantum mechanics the interpretation of an observation of a system is a rather complicated procedure.  The observation may consist in a single reading, the accuracy of which has to be discussed, or it may comprise a complicated set of data, such as the photograph of the water droplets in a cloud chamber; in any case, the result can be stated only in terms of a probability distribution concerning, for instance, the position or momentum of the particles of the system.  The theory then predicts the probability distribution for a future time.  The theory is not experimentally verified when that future state arrives if merely the momentum or position numbers in a particular observation lie within the predicted range.  The same experiment relation enter into quantum mechanics only in the operational-definitional sense.  Heisenberg shows that the latter supposition is false.

Other scientists and philosophers, going to the opposite extreme, have argued that, merely because there is uncertainty in predicting certain phenomena, this constitutes no argument whatever for the thesis that these phenomena are not completely determined.  This argument combines the statical problem of defining the state’ of a mechanical system at a given time with the dynamical or causal problem of predicting changes in the state of the system through time.  But the concept of probability in quantum theory enters only into its statics, ie. its theoretical definition of state.  The reader will find it wise, therefore, to keep distinct these two components, ie. the statical theoretical definition-of-state component and the dynamic, or causal, theoretical change-of-state-through-time component.  With respect to the former, the concept of probability and the attendant uncertainty enter theoretically and in principle; they do not refer merely to the operational and epistemological uncertainties and errors, arising from the finiteness of, and inaccuracies in, human behavior, that are common to any scientific theory and any experimentation whatsoever.

But, why, it may be asked, should the concept of probability be introduced into the theoretic definition of the state of a mechanical system at any statical moment in principle?  In making such a theoretical construct by axiomatic postulation, do not Heisenberg and quantum theoreticians generally beg the question at issue between themselves and Einstein?  This book makes it clear that the answer to these questions is as follows: The reason for the procedure of quantum mechanics is thesis (1) above, which Einstein himself also accepts.

Thesis (1) is that we know the object of scientific knowledge only by the speculative means of axiomatic theoretic construction or postulation; Newton’s suggestion that the physicist can deduce our theoretical concepts from the experimental data being false.  It follows that there is no a priori or empirical meaning for affirming that the object of scientific knowledge, or, more specifically, the state of a mechanical system at a given time t1, must be defined in a particular way.  The sole criterion is, which set of theoretic assumptions concerning the subject matter of mechanics when pursued to their deduced experimental consequences is confirmed by the experimental data?

Now, it happens that when we theoretically and in principle define the state of a mechanical system for subatomic phenomena in terms solely of numbers referring to position and momentum, as Einstein would have us do, and deduce the consequences for radiation from black bodies, this theoretical assumption concerning the state of a mechanical system and the subject matter of atomic physics is shown to be false by experimental evidence.  The experimental facts simply are not what the theory calls for.  When, however, the traditional theory is modified with the introduction of Planck’s constant and the addition in principle of the second set of numbers referring to the probability that the attached position-momentum numbers will be found, from which the uncertainty principle follows, the experimental data confirm the new theoretical concepts and principles.  In short, the situation in quantum mechanics with respect to experiments on black-body radiation is identical with that faced by Einstein with respect to the Michelson-Morley experiment.  In both cases, only by introducing the new theoretical assumption in principle is physical theory brought into accord with the experimental facts.  Thus, to assert that, notwithstanding quantum mechanics, the positions and momenta of subatomic masses are “really” sharply located in space and time as designated by one pair of numbers only and, hence, completely deterministic causally, as Einstein and the aforementioned philosophers of science would have one do, is to affirm a theory concerning the subject matter of physical knowledge which experiments on black-body radiation have shown to be false in the sense that a deductive experimental consequence of this theory is not confined.

It does not follow, of course, that some new theory compatible with the foregoing experimental facts might not be discovered in which the concept of probability does not enter in principle into its definition of state.  Professor Norbert Wiener, for example, believes that he has clues to the direction such a theory might take.  It would, however, have to reject a definition of state in terms of the four space-time dimensions of Einstein’s theory and would, therefore, be incompatible with Einstein’s thesis on other grounds.  Certainly, one cannot rule out such a possibility.  Nevertheless, until such an alternative theory is presented, anyone, who does not claim to possess some a priori or private source of information concerning what the object of scientific knowledge must be, has no alternative but to accept the definition of state of quantum theory and to affirm with the author of this book that it restores the concept of potentiality to the object of modern scientific knowledge.  Experiments on black-body radiation require one to conclude that God plays dice.

What of the status of causality and determinism in quantum mechanics?  Probably the interest of the layman and the humanist in this book depends most on its answer to this question.  If this answer is to be understood, the reader must pay particular attention to Heisenberg’s description of (a) the aforementioned definition of state by recourse to the concept of probability and (b) the Schrödinger time-equation.  The reader must also make sure, and this is the most difficult task of all, that the meaning of the words “causality” and “determinism” in his mind when he asks the above question is identical with the meaning these words have in Heisenberg’s mind when he specifies the answer.  Otherwise, Heisenberg will be answering a different question from the one the reader is asking and a complete misunderstanding upon the reader’s part will occur.

The situation is further complicated by the fact that modem physics permits the concept of causality to have two different, scientifically precise meanings, the one stronger than the other, and there is no agreement among physicists about which one of these two meanings the word “causality” is to be used to designate.  Hence, some physicists and philosophers of science use the word to designate the stronger of the two meanings.  There is evidence, at times at least, that this is Professor Heisenberg’s usage in this book.  Other physicists and philosophers, including the writer of this Introduction, use the word “causality” to designate the weaker of the two meanings and the word “determinism” to designate the stronger meaning.  When the former usage is followed, the words “causality” and “determinism” become synonymous.  When the second usage is followed, every deterministic system is a causal system, but not every causal system is deterministic.

Great confusion has entered into previous discussion of this topic because frequently neither the person who asks the question nor the physicist who has answered it has been careful to specify in either question or answer whether he is using the word “causality” in its weaker or in its stronger modem scientific meaning.  If one asks “Does causality hold in quantum mechanics?” not specifying whether one is asking about causality in its stronger or in its weaker sense, one then gets apparently contradictory answers from equally competent physicists.  One physicist, taking the word “causality” in its stronger sense, quite correctly answers “No.” The other physicist, taking “causality” in its weaker sense, equally correctly answers “Yes.” Naturally, the impression has arisen that quantum mechanics is not specific about what the answer is.  Nevertheless, this impression is erroneous.  The answer of quantum mechanics becomes unequivocal the moment one makes the question and the answer unambiguous by specifying which meaning of “causality” one is talking about.  It is important, therefore, to become clear about different possible meanings of the word “causality.” Let us begin with the layman’s commonsense usage of the word “cause” and then move to the more exact meanings in modern physics, considering the meaning in Aristotle’s physics on the way.

One may say “The stone hit the window and caused the glass to break.” In this use of “causality” it is thought of as a relation between objects, ie. between the stone and the windowpane.  The scientist expresses the same thing in a different way.  He describes the foregoing set of events in terms of the state of the stone and the windowpane at the earlier time t1 when the stone and the windowpane were separated and the state of this same system of two objects at the later time e when the stone and the windowpane collided.  Consequently, whereas the layman tends to think of causality as a relation between objects, the scientist thinks of it as a relation between different states of the same object or the same system of objects at different times.   This is why, in order to determine what quantum mechanics says about causality, one must pay attention to two things: (1) The state-function which defines the state of any physical system at any specific time t.  (2) The Schrödinger time-equation which relates the state of the physical system at the earlier time t1 to its different state at any specifiable later time t2.  What Heisenberg says about (1) and (2) must, therefore, be read with meticulous care.

It will help to understand what quantum mechanics says about the relation between the states of a given physical object, or system of physical objects, at different times if we consider the possible properties that this relation might have.  The weakest possible case would be that of mere temporal succession with no necessary connection whatever and with not even a probability, however small, that the specifiable initial state will be followed in time by a specifiable future state.  Hume gives us reasons for believing that the relation between the sensed states of im­mediately sensed natural phenomena is of this character. Certainly, as he pointed out, one does not sense any relation of necessary connection.  Nor does one directly sense probability.  All that sensation gives us with respect to the successive states of any phenomenon is the mere relation of temporal succession.

This point is of great importance.  It means that one can arrive at a causal theory in any science or in commonsense knowledge, or even at a probability theory, of the relation between the successive states of any object or system, only by speculative means and axiomatically constructed, deductively formulated scientific and philosophical theory which is tested not directly against the sensed and experimental data but only indirectly by way of its deductive consequences.

A second possibility with respect to the character of the relation between the states of any physical system at different times is that the relation is a necessary one, but that one can know what this necessary connection is only by knowing the future state.  The latter knowledge of the future state may be obtained either by waiting until it arrives or by having seen the future or final state of similar systems in the past.  When such is the case, causality is teleological.  Changes of the system with time are determined by the final state or goal of the system.  The physical system which is an acorn in the earlier state e and an oak tree in the later state e is an example.  The connection between these two states seems to be a necessary one.  Acorns never change into maple trees or into elephants.  They change only into oaks.  Yet, given the properties of this physical system in the acorn state of the earlier time t1, no scientist has as yet been able to deduce the properties of the oak tree which the system will have at the later time t2.  Aristotelian physics affirmed that all causal relations are teleological.

Another possibility is that the relation between the states of any object, or any system of objects, at different times is a relation of necessary connection such that, given knowledge of the initial state of the system, assuming isolation, its future state can be deduced.  Stated in more technical mathematical language, this means that there exists an indirectly verified, axiomatically constructed theory whose postulates (1) specify a state-function, the independent variables of which completely define the state of the system at any specific instant of time, and (2) provide a time-equation relating the numerical empirical values of the independent variables of this function at any earlier time t1 to their numerical empirical values at any specific later time e in such a way that by introducing the operationally determined e set of numbers into the time-equation the future e numbers can be deduced by merely solving the equation.  When this is the case, the temporal relation between states is said to exemplify mechanical causation.

It is to be noted that this definition of mechanical causality leaves open the question of what independent variables are required to define the state of the system at any given time.  Hence, at least two possibilities arise: (a) the concept of probability may be used to define the state of the system or (b) it may not be so used.  When (b) is the case no independent variables referring to probabilities appear in the state-function and the stronger type of mechanical causality is present.  When (a) is the case independent variables referring to probabilities, as well as to other properties such as position and momentum, appear in the state-function and only the weaker type of mechanical causation occurs.  If the reader keeps these two meanings of mechanical causation in mind and makes sure which meaning Heisenberg is referring to in any particular sentence of this book, he should be able to get its answer to the question concerning the status of causality in modem physics.

What of determinism?  Again, there is no agreed-upon convention among physicists and philosophers of science about how this word is.  to be used.  It is in accord with the commonsense usage to identify it with the strongest possible causality.  Let us, then, use the word “determinism” to denote only the stronger type of mechanical causation.  Then I believe the careful reader of this book will get the following answer to his question: In Newtonian, Relativistic and quantum mechanics, mechanical, rather than teleological, causality holds.  This is why quantum physics is called quantum mechanics, rather than quantum teleologies.  But, whereas causality in Newton’s and Einstein’s physics is of the stronger type and, hence, both mechanical and deterministic, in quantum mechanics it is of the weaker causal type and, hence, mechanical but not deterministic.  From the latter fact it follows that if anywhere in this book Heisenberg uses the words “mechanical causality” in their stronger, deterministic meaning and the question be asked “Does mechanical causation in this stronger meaning hold in quantum mechanics?” then the answer has to be “No.”

The situation is even more complicated, as the reader will find, than even these introductory distinctions between the different types of causation indicate.  It is to be hoped, however, that this focusing of attention upon these different meanings will enable the reader to find his way through this exceptionally important book more easily than would otherwise be the case.   These distinctions should suffice, also, to enable one to grasp the tremendous philosophical significance of the introduction of the weaker type of mechanical causation into modern physics, which has occurred in quantum mechanics.  Its significance consists in reconciling the concept of objective, and in this sense ontological, potentiality of Aristotelian physics with the concept of mechanical causation of modern physics.

It would be an error, therefore, if the reader, from Heisenberg’s emphasis upon the presence in quantum mechanics of something analogous to Aristotle’s concept of potentiality, concluded that contemporary physics has taken us back to Aristotle’s physics and ontology.  It would be an equal error conversely to conclude, because mechanical causation in its weaker meaning still holds in quantum mechanics, that all is the same now in modern physics with respect to its causality and ontology as was the case before quantum mechanics came into being.  What has occurred is that in quantum theory contemporary man has moved on beyond the classical medieval and the modem world to a new physics and philosophy which combines consistently some of the basic causal and ontological assumptions of each.  Here, let it be recalled, we use the word “ontological” to denote any experimentally verified concept of scientific theory which refers to the object of scientific knowledge rather than merely to the epistemological relation of the scientist as knower to the object which he knows. Such an experimentally verified philosophical synthesis of ontological potentiality with ontological mechanical causality, in the weaker meaning of the latter concept, occurred when physicists found it impossible to account theoretically for the Compton effect and the results of experiment on black-body radiation unless they extended the concept of probability from its Newtonian and Relativistic merely epistemological, theory-of-errors role in specifying when their theory is or is not experimentally confirmed to the ontological role, specified in principle in the theory’s postulates, of characterizing the object of scientific knowledge itself.

Need one wonder that Heisenberg went through the subjective emotional experiences described in this book before he became reconciled to the necessity, imposed by both experimental and mathematical considerations, of modifying the philosophical and scientific beliefs of both medieval and modem man in so deep-going a manner.  Those interested in a firsthand description of the human spirit in one of its most creative moments will want to read this book because of this factor alone.  The courage which it took to make this step away from the unqualified determinism of classical modem physics may be appreciated if one recalls that even such a daring, creative spirit as Einstein balked.  He could not allow God to play dice; there could not be potentiality in the object of scientific knowledge, as the weaker form of mechanical causality in quantum mechanics allows.

Before one concludes, however, that God has become a complete gambler and that potentiality is in all objects, certain limitations which quantum mechanics places on the application of its weaker form of mechanical causation must be noted.  To appreciate these qualifications the reader must note what this book says about (1) the Compton effect, (2) Planck’s constant h, and (3) the uncertainty principle which is defined in terms of Planck’s constant.

This constant h is a number referring to the quantum of action of any object or system of objects.  This quantum, which extends atomicity from matter and electricity to light and even to energy itself, is very small.  When the quantum numbers of the system being observed are small, as is the case with subatomic phenomena, then the uncertainty specified by the Heisenberg uncertainty principle of the positions and momenta of the masses of the system becomes significant.  Then, also, the probability numbers associated with the position-momentum numbers in the state-function become significant.  When, however, the quantum numbers of the system are large, then the quantitative amount of uncertainty specified by the Heisenberg principle becomes insignificant and the probability numbers in the state-function can be neglected.  Such is the case with gross commonsense objects.  At this point quantum mechanics with its basically weaker type of causality gives rise, as a special case of itself, to Newtonian and relativistic mechanics with their stronger type of causality and determinism.  Consequently, for human beings considered merely as gross commonsense objects the stronger type of causality holds and, hence, determinism reigns also.

Nevertheless, subatomic phenomena are scientifically significant in man.  To this extent, at least, the causality governing him is of the weaker type, and he embodies both mechanical fate and potentiality.  There are scientific reasons for believing that this occurs even in heredity.  Any reader who wants to pursue this topic beyond the pages of this book should turn to What Is Life?  by Professor Erwin Schrödinger, the physicist after whom the time-equation in quantum mechanics is named.  Undoubtedly, potentiality and the weaker form of causality hold also for countless other characteristics of human beings, particularly for those cortical neural phenomena in man that are the epistemic correlates of directly introspected human ideas and purposes.

If the latter possibility is the case, the solution of a baffling scientific, philosophical and even moral problem may be at hand.  This problem is: How is the mechanical causation, even in its weaker form, of quantum mechanics to be reconciled with the teleological causation patently present in the moral, political and legal purposes of man and in the teleological causal determination of his bodily behavior, in part at least, by these purposes?  In short, how is the philosophy of physics expounded in this book by Heisenberg to be reconciled with moral, political and legal science and philosophy?

It may help the reader to appreciate why this book must be mastered before these larger questions can be correctly understood or effectively answered if very brief reference is made here to some articles which relate its theory of physical causation to the wider relation between mechanism and teleology in the humanities and the social sciences.  The relevant articles are (a) by Professors Rosenblueth, Wiener and Bigelow in the journal of The Philosophy of Science for January, 1943; (b) by Doctors McCulloch and Pitts in The Bulletin of Mathematical Biophysics, Volume 5, 1943, and Volume 9, 1947; and (c) ‘Chapter XIX of Ideological Differences and World Order, edited by the writer of this Introduction and published by the Yale University.  University Press, Cambridge; Macmillan Company, New York; 1946.

If read after this book, (a) will show how teleological causality arises as a special case of the mechanical causality described by Heisenberg here.  Similarly, (b) will provide a physical theory of the neurological correlates of introspected ideas, expressed in terms of the teleological mechanical causality of (a), thereby giving an explanation of how ideas can have a causally significant effect on the behavior of men.  Likewise, (c) will show how the ideas and purposes of moral, political and legal man relate, by way of (b) and (a), to the theory of physical potentiality and mechanical causality so thoroughly described by Heisenberg in this book.

It remains to call attention to what Professor Heisenberg says about Bohr’s principle of complementary.  This principle plays a great role in the interpretation of quantum theory by “the Copenhagen School” to which Bohr and Heisenberg belong.  Some students of quantum mechanics, such as Margenau in his book The Nature of Physical Reality,* are inclined to the conclusion that quantum mechanics requires merely its definition of state, its Schrödinger time-equation and those other of its mathematical postulates which suffice to ensure, as noted above, that Relativistic and Newtonian mechanics come out of quantum mechanics as one of its special cases.  According to the latter thesis, the principle of complementary arises from the failure to keep the stronger and weaker form of mechanical causality continuously in mind, with the resultant attribution of the stronger form to those portions of quantum mechanics where only the weaker form is involved.  When this happens, the principle of complementary has to be introduced to avoid contradiction.  If, however, one avoids the foregoing practice, the principle of complementary becomes, if not unnecessary, at least of a form such that one avoids the danger, noted by Margenau and appreciated by Bohr, of giving pseudo solutions to physical and philosophical problems by playing fast and loose with the law of contradiction, in the name of the principle of complementary.

By its use the qualifications that had to be put on both the particle-picture commonsense language of atomic physics and its commonsense wave-picture language were brought together.  But once having formulated the result with axiomatically constructed mathematical exactitude, any further use of it is merely a superficial convenience when, leaving aside the exact and essential mathematical assumptions of quantum mechanics, one indulges in the commonsense language and images of waves and particles.  It has been necessary to go into the different interpretations of the principle of complementary in order to enable the reader to pass an informed judgment concerning what Heisenberg says in this book about the commonsense and Cartesian concepts of material and mental substances.  This is the case because his conclusion concerning Descartes results from his generalization of the principle of complementary beyond physics, first, to the relation between commonsense biological concepts and mathematical physical concepts and, second, to the body-mind problem.  The result of this generalization is that the Cartesian theory of mental substances comes off very much better in this book, as does the concept of substance generally, than is the case in any other book on the philosophy of contemporary physics which this writer knows.  Whitehead, for example, concluded that contemporary science and philosophy find no place for, and have no need of, the concept of substance.  Neutral monists such as Lord Russell and logical positivists such as Professor Carnap agree.

Generally speaking, Heisenberg argues that there is no compelling reason to throwaway any of the commonsense concepts of either biology or mathematical physics, after one knows the refined concepts that lead to the complete clarification of the problems in atomic physics.  Because the latter clarification is complete, it is relevant only to a very limited range of problems within science and cannot enable us to avoid using many concepts at other places that would not stand critical analysis of the type carried out in quantum theory.  Since the ideal of complete clarification cannot be achieved—and it is important that we should not be deceived about this point one may indulge in the usage of commonsense concepts if it is done with sufficient care and caution.  In this respect, certainly, complementary is a very useful scientific concept.

In any event, two things seem clear and make what Heisenberg says on these matters exceedingly important.  First, the principle of complementary and the present validity of the Cartesian and commonsense concepts of body and mind stand and fall together.  Second, it may be that both these notions are merely convenient stepladders which should now be, or must eventually be, thrown away.  Even so, in the case of the theory of mind at least, the stepladder will have to remain until by its use we find the more linguistically exact and empirically satis­factory theory that will permit us to throw the Cartesian language away.  To be sure, piecemeal theories of mind which do not appeal to the notion of substance now exist, but none of their authors, unless it be Whitehead, has shown how the language of this piecemeal theory can be brought into commensurate and compatible relationship with the scientific language of the other facts of human knowledge.  It is likely, therefore, that anyone, whether he be a professional physicist or philosopher or the lay reader, who may think he knows better than Heisenberg on these important matters, runs the grave risk of supposing he has a scientific theory of mind in its relation to body, when in fact this is not the case.

Up to this point we have directed attention, with but two exceptions, to what the philosophy of contemporary physics has to say about the object of scientific knowledge qua object, independent of its relation to the scientist as knower.  In short, we have been concerned with its ontology.  This philosophy also has its epistemological component.  This component falls into three parts: (1) The relation between (a) the directly observed data given to the physicist as inductive knower in his observations or his experiments and (b) the speculatively proposed, indirectly verified, axiomatically constructed postulates of his theory.  The latter term (b) defines the objects of scientific knowledge qua object and, hence, gives the ontology.  The relation between (a) and (b) defines one factor in the epistemology.  (2) The role of the concept of probability in the theory of errors, by means of which the physicist defines the criterion for judging how far his experimental findings can depart, due to errors of human experimentation, from the deduced consequences of the postulates of the theory and still be regarded as confirming the theory.  (3) The effect of the experiment being performed upon the object being known.  What Heisenberg says about the first and second of these three epistemological factors in contemporary physics has already been emphasized in this Introduction.  It remains to direct the reader’s attention to what he says about item (3).

In modern physical theory, previous to quantum mechanics, (3) played no role whatever.  Hence, the epistemology of modern physics was then completely specified by (1) and (2) alone.  In quantum mechanics, however, (3) (as well as (1) and (2)) becomes very important.  The very act of observing alters the object being observed when its quantum numbers are small.  From this fact Heisenberg draws a very important conclusion concerning the relation between the object, the observing physicist, and the rest of the universe.  This conclusion can be appreciated if attention is directed to the following key points.  It may be recalled that in some of the definitions of mechanical causality given earlier in this Introduction, the qualifying words “for an isolated system” were added; elsewhere it was implicit.  This qualifying condition can be satisfied in principle in Newtonian and Relativistic mechanics, and also in practice by making more and more careful observations and refinements in one’s experimental instruments.  The introduction of the concept of probability into the definition of state of the object of scientific knowledge in quantum mechanics rules out, however, in principle, and not merely in practice due to the imperfections of human observation and instruments, the satisfying of the condition that the object of the physicist’s knowledge is an isolated system.  Heisenberg shows also that the including of the experimental apparatus and even of the eye of the observing scientist in the physical system which is the object of the knower’s knowledge does not help, since, if quantum mechanics be correct, the states of all objects have to be defined in principle by recourse to the concept of probability.  Consequently, only if the whole universe is included in the object of scientific knowledge can the qualifying condition “for an isolated system” be satisfied for even the weaker form of mechanical causation.  Clearly, the philosophy of contemporary physics is shown by this book to be as novel in its epistemology as it is in its ontology.  Indeed, it is from the originality of its ontology-the consistent unification of potentiality and mechanical causality in its weaker form-that the novelty of its epistemology arises.

Unquestionably, one other thing is clear.  An analysis of the specific experimentally verified theories of modern physics with respect to what they say about the object of human knowledge and its relation to the human knower exhibits a very rich and complex ontological and epistemological philosophy which is an essential part of the scientific theory and method itself.  Hence, physics is neither epistemologically nor ontologically neutral.  Deny anyone of the epistemological assumptions of the physicist’s theory and there is no scientific method for testing whether what the theory says about the physical object is true, in the sense of being empirically confirmed.  Deny anyone of the ontological assumptions and there is not enough content in the axiomatically constructed mathematical postulates of the physicist’s theory to permit the deduction of the experimental facts which it is introduced to predict, co-ordinate consistently and explain.  Hence, to the extent that experimental physicists assure US that their theory of contemporary physics is indirectly and experimentally verified, they ipso facto assure us that its rich and complex ontological and epistemological philosophy is verified also.

When such empirically verified philosophy of the true in the natural sciences is identified with the criterion of the good and the just in the humanities and the social sciences, one has natural-law ethics and jurisprudence.  In other words, one has a scientifically meaningful cognitive criterion and method for judging both the verbal, personal and social norms of the positive law and the living ethos embodied in the customs, habits and traditional cultural institutions of the de facto peoples and cultures of the world.  It is the coming together of this new philosophy of physics with the respective philosophies of culture of mankind that is the major event in today’s and tomorrows world.  At this point, the philosophy of physics in this book and its important reference to the social consequences of physics come together.

The chapters of this book have been read as Gifford Lectures at the University of St.  Andrews during the winter term 1955-56.  According to the will of their founder the Gifford Lectures should “freely discuss all questions about man’s conceptions of God or the Infinite, their origin, nature, and truth, whether he can have any such conceptions, whether God is under any or what limitations and so on.” The lectures of Heisenberg do not attempt to reach these most general and most difficult problems.

But they try to go far beyond the limited scope of a special science into the wide field of those general human problems that have been raised by the enormous recent development and the far-reaching practical applications of natural science.

—FS Northrop, Stirling Professor of Philosophy and Law, Yale University (1958)

Chapter 1An Old and a New Tradition

When one speaks today of modem physics, the first thought is of atomic weapons.  Everybody realizes the enormous influence of these weapons on the political structure of our present world and is willing to admit that the influence of physics on the general situation is greater than it ever has been before.  But is the political aspect of modem physics really the most important one?  When the world has adjusted itself in its political structure to the new technical possibilities, what then will remain of the influence of modem physics?

To answer these questions, one has to remember that every tool carries with it the spirit by which it has been created.  Since every nation and every political group has to be interested in the new weapons in some way irrespective of the location and of the cultural tradition of this group, the spirit of modem physics will penetrate into the minds of many people and will connect itself in different ways with the older traditions.  What will be the outcome of this impact of a special branch of modem science on different powerful old traditions?  In those parts of the world in which modem science has been developed the primary interest has been directed for a long time toward practical activity, industry and engineering combined with a rational analysis of the outer and inner conditions for such activity.  Such people will find it rather easy to cope with the new ideas since they have had time for a slow and gradual adjustment to the modern scientific methods of thinking.  In other parts of the world these ideas would be confronted with the religious and philosophical foundations of the native culture.  Since it is true that the results of modern physics do touch such fundamental concepts as reality, space and time, the confrontation may lead to entirely new developments which cannot yet be foreseen.  One characteristic feature of this meeting between modern science and the older methods of thinking will be its complete internationality.  In this exchange of thoughts the one side, the old tradition, will be different in the different parts of the world, but the other side will be the same everywhere and therefore the results of this exchange will be spread over all areas in which the discussions take place.

For such reasons it may not be an unimportant task to try to discuss these ideas of modern physics in a not too technical language, to study their philosophical consequences, and to compare them with some of the older traditions.  The best way to enter into the problems of modern physics may be by a historical description of the development of quantum theory.  It is true that quantum theory is only a small sector of atomic physics and atomic physics again is only a very small sector of modern science.  Still it is in quantum theory that the most fundamental changes with respect to the concept of reality have taken place, and in quantum theory in its final form the new ideas of atomic physics are concentrated and crystallized.  The enormous and extremely complicated experimental equipment needed for research in nuclear physics shows another very impressive aspect of this part of modern science.  But with regard to the experimental technique nuclear physics represents the extreme extension of a method of research which has determined the growth of modern science ever since Huygens or Volta or Faraday.  In a similar sense the discouraging mathematical complication of some parts of quantum theory may be said to represent the extreme consequence of the methods of Newton or Gauss or Maxwell.  But the change in the concept of reality manifesting itself in quantum theory is not simply a continuation of the past; it seems to be a real break in the structure of modern science.  Therefore, the first of the following chapters will be devoted to the study of the historical development of quantum theory.

Chapter 2—The History of Quantum Theory

The origin of quantum theory is connected with a well-known phenomenon, which did not belong to the central parts of atomic physics.  Any piece of matter when it is heated starts to glow, gets red hot and white hot at higher temperatures.  The color does not depend much on the surface of the material, and for a black body it depends solely on the temperature.  Therefore, the radiation emitted by such a black body at high temperatures is a suitable object for physical research; it is a simple phenomenon that should find a simple explanation in terms of the known laws for radiation and heat.  The attempt made at the end of the nineteenth century by Lord Rayleigh and Jeans failed, however, and revealed serious difficulties.  It would not be possible to describe these difficulties here in simple terms.  It must be sufficient to state that the application of the known laws did not lead to sensible results.  When Planck entered this line of research in 1895 he tried to turn the problem from radiation to the radiating atom.  This turning did not remove any of the difficulties inherent in the problem, but it simplified the interpretation of the empirical facts.  It was just at this time, during the summer of 1900, that Curlbaum and Rubens in Berlin had made very accurate new measurements of the spectrum of so heat radiation.  When Planck heard of these results he tried to represent them by simple mathematical formulas which looked plausible from his research on the general connection between heat and radiation.  One day Planck and Rubens met for tea in Planck’s home and compared Rubens’ latest results with a new formula suggested by Planck.  The comparison showed a complete agreement.  This was the discovery of Planck’s law of heat radiation.

It was at the same time the beginning of intense theoretical work for Planck.  What was the correct physical interpretation of the new formula?  Since Planck could, from his earlier work, translate his formula easily into a statement about the radiating atom (the so-called oscillator), he must soon have found that his formula looked as if the oscillator could only contain discrete quanta of energy—a result that was so different from anything known in classical physics that he certainly must have refused to believe it in the beginning.  But in a period of most intensive work during the summer of 1900 he finally convinced himself that there was no way of escaping from this conclusion.  It was told by Planck’s son that his father spoke to him about his new ideas on a long walk through the Grunewald, the wood in the suburbs of Berlin.  On this walk he explained that he felt he had possibly made a discovery of the first rank, comparable perhaps only to the discoveries of Newton.  So Planck must have realized at this time that his formula had touched the foundations of our description of nature, and that these foundations would one day start to move from their traditional present location toward a new and as yet unknown position of stability.  Planck, who was conservative in his whole outlook, did not like this consequence at all, but he published his quantum hypothesis in December of 1900.

The idea that energy could be emitted or absorbed only in discrete energy quanta was so new that it could not be fitted into the traditional framework of physics.  An attempt by Planck to reconcile his new hypothesis with the older laws of radiation failed in the essential points.  It took five years until the next step could be made in the new direction.

This time it was the young Albert Einstein, a revolutionary genius among the physicists, who was not afraid to go further away from the old concepts.  There were two problems in which he could make use of the new ideas.  One was the so-called photoelectric effect, the emission of electrons from metals under the influence of light.  The experiments, especially those of Lenard, had shown that the energy of the emitted electrons did not depend on the intensity of the light, but only on its color or, more precisely, on its frequency.  This could not be understood on the basis of the traditional theory of radiation.  Einstein could explain the observations by interpreting Planck’s hypothesis as saying that light consists of quanta of energy traveling through space.  The energy of one light quantum should, in agreement with Planck’s assumptions, be equal to the frequency of the light multiplied by Planck’s constant.

The other problem was the specific heat of solid bodies.  The traditional theory led to values for the specific heat which fitted the observations at higher temperatures but disagreed with them at low ones.  Again Einstein was able to show that one could understand this behavior by applying the quantum hypothesis to the elastic vibrations of the atoms in the solid body.  These two results marked a very important advance, since they revealed the presence of Planck’s quantum of action-as his constant is called among the physicists-in several phenomena, which had nothing immediately to do with heat radiation.  They revealed at the same time the deeply revolutionary character of the new hypothesis, since the first of them led to a description of light completely different from the traditional wave picture.  Light could either be interpreted as consisting of electromagnetic waves, according to Maxwell’s theory, or as consisting of light quanta, energy packets traveling through space with high velocity.  But could it be both?  Einstein knew, of course, that the well-known phenomena of diffraction and interference could be explained only on the basis of the wave picture.  He was not able to dispute the complete contradiction between this wave picture and the idea of the light quanta; nor did he even attempt to remove the inconsistency of this interpretation.  He simply took the contradiction as something which would probably be understood only much later.

In the meantime the experiments of Becquerel, Curie and Rutherford had led to some clarification concerning the structure of the atom.  In 1911 Rutherford’s observations on the interaction of a-rays penetrating through matter resulted in his famous atomic model.  The atom is pictured as consisting of a nucleus, which is positively charged and contains nearly the total mass of the atom, and electrons, which circle around the nucleus like the planets circle around the sun.  The chemical bond between atoms of different elements is explained as an interaction between the outer electrons of the neighboring atoms; it has not directly to do with the atomic nucleus.  The nucleus determines the chemical behavior of the atom through its charge which in turn fixes the number of electrons in the neutral atom.  Initially this model of the atom could not explain the most characteristic feature of the atom, its enormous stability.  No planetary system following the laws of Newton’s mechanics would ever go back to its original configuration after a collision with another such system.  But an atom of the element carbon, for instance, will still remain a carbon atom after any collision or interaction in chemical binding.

The explanation for this unusual stability was given by Bohr in 1913, through the application of Planck’s quantum hypothesis.  If the atom can change its energy only by discrete energy quanta, this must mean that the atom can exist only in discrete stationary states, the lowest of which is the normal state of the atom.  Therefore, after any kind of interaction the atom will finally always fall back into its normal state.

By this application of quantum theory to the atomic model, Bohr could not only explain the stability of the atom but also, in some simple cases, give a theoretical interpretation of the line spectra emitted by the atoms after the excitation through electric discharge or heat.  His theory rested upon a combination of classical mechanics for the motion of the electrons with quantum conditions, which were imposed upon the classical motions for defining the discrete stationary states of the system.  A consistent mathematical formulation for those conditions was later given by Sommerfeld.  Bohr was well aware of the fact that the quantum conditions spoil in some way the consistency of Newtonian mechanics.  In the simple case of the hydrogen atom one could calculate from Bohr’s theory the frequencies of the light emitted by the atom, and the agreement with the observations was perfect.  Yet these frequencies were different from the orbital frequencies and their harmonics of the electrons circling around the nucleus, and this fact showed at once that the theory was still full of contradictions.  But it contained an essential part of the truth.  It did explain qualitatively the chemical behavior of the atoms and their line spectra; the existence of the discrete stationary states was verified by the experiments of Franck and Hertz, Stern and Gerlach.

Bohr’s theory had opened up a new line of research.  The great amount of experimental material collected by spectroscopy through several decades was now available for information about the strange quantum laws governing the motions of the electrons in the atom.  The many experiments of chemistry could be used for the same purpose.  It was from this time on that the physicists learned to ask the right questions; and asking the right question is frequently more than halfway to the solution of the problem.

What were these questions?  Practically all of them had to do with the strange apparent contradictions between the results of different experiments.  How could it be that the same radiation that produces interference patterns, and therefore must consist of waves, also produces the photoelectric effect, and therefore must consist of moving particles?  How could it be that the frequency of the orbital motion of the electron in the atom does not show up in the frequency of the emitted radiation?  Does this mean that there is no orbital motion?  But if the idea of orbital motion should in incorrect, what happens to the electrons inside the atom?  One can see the electrons move through a cloud chamber, and sometimes they are knocked out of an atom; why should they not also move within the atom?  It is true that they might be at rest in the normal state of the atom, the state of lowest energy.  But there are many states of higher energy, where the electronic shell has an angular momentum.  There the electrons cannot possibly be at rest.  One could add a number of similar examples.  Again and again one found that the attempt to describe atomic events in the traditional terms of physics led to contradictions.

Gradually, during the early twenties, the physicists became accustomed to these difficulties, they acquired a certain vague knowledge about where trouble would occur, and they learned to avoid contradictions.  They knew which description of an atomic event would be the correct one for the special experiment under discussion.  This was not sufficient to form a consistent general picture of what happens in a quantum process, but it changed the minds of the physicists in such a way that they somehow got into the spirit of quantum theory.  Therefore, even some time before one had a consistent formulation of quantum theory one knew more or less what would be the result of any experiment.

One frequently discussed what one called ideal experiments.  Such experiments were designed to answer a very critical question irrespective of whether or not they could actually be carried-out.  Of course it was important that it should be possible in principle to carry out the experiment, but the technique might be extremely complicated.  These ideal experiments could be very useful in clarifying certain problems.  If there was no agreement among the physicists about the result of such an ideal experiment, it was frequently possible to find a similar but simpler experiment that could be carried out, so that the experimental answer contributed essentially to the clarification of quantum theory.

The strangest experience of those years was that the paradoxes of quantum theory did not disappear during this process of clarification; on the contrary, they became even more marked and more exciting.  There was, for instance, the experiment of Compton on the scattering of X-rays.  From earlier experiments on the interference of scattered light there could be no doubt that scattering takes place essentially in the following way: The incident light wave makes an electron in the beam vibrate in the frequency of the wave; the oscillating electron then emits a spherical wave with the same frequency and thereby produces the scattered light.  However, Compton found in 1923 that the frequency of scattered X-rays was different from the frequency of the incident X-ray.  This change of frequency could be formally understood by assuming that scattering is to be described as collision of a light quantum with an electron.  The energy of the light quantum is changed during the collision; and since the frequency times Planck’s constant should be the energy of the light quantum, the frequency also should be changed.  But what happens in this interpretation of the light wave?  The two experiments-one on the interference of scattered light and the other on the change of frequency of the scattered light-seemed to contradict each other without any possibility of compromise.

By this time many physicists were convinced that these apparent contradictions belonged to the intrinsic structure of atomic physics.  Therefore, in 1924 de Broglie in France tried to extend the dualism between wave description and particle description to the elementary particles of matter, primarily to the electrons.  He showed that a certain matter wave could “correspond” to a moving electron, just as a light wave corresponds to a moving light quantum.  It was not clear at the time what the word “correspond” meant in this connection.  But de Broglie suggested that the quantum condition in Bohr’s theory should be interpreted as a statement about the matter waves.  A wave circling around a nucleus can for geometrical reasons only be a stationary wave; and the perimeter of the orbit must be an integer multiple of the wave length.  In this way de Broglie’s idea connected the quantum condition, which always had been a foreign element in the mechanics of the electrons, with the dualism between waves and particles.

In Bohr’s theory the discrepancy between the calculated orbital frequency of the electrons and the frequency of the emitted radiation had to be interpreted as a limitation to the concept of the electronic orbit.  This concept had been somewhat doubtful from the beginning.  For the higher orbits, however, the electrons should move at a large distance from the nucleus just as they do when one sees them moving through a cloud chamber.  There one should speak about electronic orbits.  It was therefore very satisfactory that for these higher orbits the frequencies of the emitted radiation approach the orbital frequency and its higher harmonics.  Also Bohr had already suggested in his early papers that the intensities of the emitted spectral lines approach the intensities of the corresponding harmonics.  This principle of correspondence had proved very useful for the approximative calculation of the intensities of spectral lines.  In this way one had the impression that Bohr’s theory gave a qualitative but not a quantitative description of what happens inside the atom; that some new feature of the behavior of matter was qualitatively expressed by the quantum conditions, which in turn were connected with the dualism between waves and particles.

The precise mathematical formulation of quantum theory finally emerged from two different developments.  The one started from Bohr’s principle of correspondence.  One had to give up the concept of the electronic orbit but still had to maintain it in the limit of high quantum numbers, i.e., for the large orbits.  In this latter case the emitted radiation, by means of its frequencies and intensities, gives a picture of the electronic orbit; it represents what the mathematicians call a Fourier expansion of the orbit.  The idea suggested itself that one should write down the mechanical laws not as equations for the positions and velocities of the electrons but as equations for the frequencies and amplitudes of their Fourier expansion.  Starting from such equations and changing them very little one could hope to come to relations for those quantities which correspond to the frequencies and intensities of the emitted radiation, even for the small orbits and the ground state of the atom.  This plan could actually be carried out; in the summer of 1925 it led to a mathematical formalism called matrix mechanics or, more generally, quantum mechanics.  The equations of motion in Newtonian mechanics were replaced by similar equations between matrices; it was a strange experience to find that many of the old results of Newtonian mechanics, like conservation of energy, etc, could be derived also in the new scheme.  Later the investigations of Born, Jordan and Dirac showed that the matrices representing position and momentum of the electron do not commute.  This latter fact demonstrated clearly the essential difference between quantum mechanics and classical mechanics.

The other development followed de Broglie’s idea of matter waves.  Schrödinger tried to set up a wave equation for de Broglie’s stationary waves around the nucleus.  Early in 1926 he succeeded in deriving the energy values of the stationary states of the hydrogen atom as “Eigenvalues” of his wave equation and could give a more general prescription for transforming a given set of classical equations of motion into a corresponding Wave equation in a space of many dimensions.  Later he was able to prove that his formalism of wave mechanics was mathematically equivalent to the earlier formalism of quantum mechanics. Thus one finally had a consistent mathematical formalism, which could be defined in two equivalent ways starting either from relations between matrices or from wave equations.  This formalism gave the correct energy values for the hydrogen atom; it took less than one year to show that it was also successful for the helium atom and the more complicated problems of the heavier atoms.  But in what sense did the new formalism describe the atom?  The paradoxes of the dualism between wave picture and particle picture were not solved; they were hidden somehow in the mathematical scheme.

A first and very interesting step toward a real understanding of quantum theory was taken by Bohr, Kramers and Slater in 1924.  These authors tried to solve the apparent contradiction between the wave picture and the particle picture by the concept of the probability wave.  The electromagnetic waves were interpreted not as “real” waves but as probability waves, the intensity of which determines in every point the probability for the absorption (or induced emission) of a light quantum by an atom at this point.  This idea led to the conclusion that the laws of conservation of energy and momentum need not be true for the single event, that they are only statistical laws and are true only in the statistical average.  This conclusion was not correct, however, and the connections between the wave aspect and the particle aspect of radiation were still more complicated.

But the paper of Bohr, Kramers and Slater revealed one essential feature of the correct interpretation of quantum theory.  This concept of the probability wave was something entirely new in theoretical physics since Newton.  Probability in mathematics or in statistical mechanics means a statement about our degree of knowledge of the actual situation.  In throwing dice we do not know the fine details of the motion of our hands which determine the fall of the dice and therefore we say that the probability for throwing a special number is just one in six.  The probability wave of Bohr, Kramers, Slater, however, meant more than that; it meant a tendency for something.  It was a quantitative version of the old concept of “potentia” in Aristotelian philosophy.  It introduced something standing in the middle between the idea of an event and the actual event, a strange kind of physical reality just in the middle between possibility and reality.

Later when the mathematical framework of quantum theory was fixed, Born took up this idea of the probability wave and gave a clear definition of the mathematical quantity in the formalism, which was to be interpreted as the probability wave.  It was not a three-dimensional wave like elastic or radio waves, but a wave in the many-dimensional configuration space, and therefore a rather abstract mathematical quantity.

Even at this time, in the summer of 1926, it was not clear in every case how the mathematical formalism should be used to describe a given experimental situation.  One knew how to describe the stationary states of an atom, but one did not know how to describe a much simpler event-as for instance an electron moving through a cloud chamber.

When Schrödinger in that summer had shown that his formalism of wave mechanics was mathematically equivalent to quantum mechanics he tried for some time to abandon the idea of quanta and “quantum jumps” altogether and to replace the electrons in the atoms simply by his three-dimensional matter waves. He was inspired to this attempt by his result, that the energy levels of the hydrogen atom in his theory seemed to be simply the eigenfrequencies of the stationary matter waves.  Therefore, he thought it was a mistake to call them energies; they were just frequencies.  But in the discussions which took place in the autumn of 1926 in Copenhagen between Bohr and Schrödinger and the Copenhagen group of physicists it soon became apparent that such an interpretation would not even be sufficient to explain Planck’s formula of heat radiation.

During the months following these discussions an intensive study of all questions concerning the interpretation of quantum theory in Copenhagen finally led to a complete and, as many physicists believe, satisfactory clarification of the situation.  But it was not a solution which one could easily accept.  I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighboring park I repeated to myself again and again the question: Can nature possibly be as absurd as it seemed to us in these atomic experiments?

The final solution was approached in two different ways.  The one was a turning around of the question.  Instead of asking: How can one in the known mathematical scheme express a given experimental situation?  the other question was put: Is it true, perhaps, that only such experimental situations can arise in nature as can be expressed in the mathematical formalism?  The assumption that this was actually true led to limitations in the use of those concepts that had been the basis of classical physics since Newton.  One could speak of the position and of the velocity of an electron as in Newtonian mechanics and one could observe and measure these quantities.  But one could not fix both quantities simultaneously with an arbitrarily high accuracy.  Actually the product of these two inaccuracies turned out to be not less than Planck’s constant divided by the mass of the particle.  Similar relations could be formulated for other experimental situations.  They are usually called relations of uncertainty or principle of indeterminacy.  One had learned that the old concepts fit nature only inaccurately.

The other way of approach was Bohr’s concept of complementary.  Schrödinger had described the atom as a system not of a nucleus and electrons but of a nucleus and matter waves.  This picture of the matter waves certainly also contained an element of truth.  Bohr considered the two pictures-particle picture and wave picture-as two complementary descriptions of the same reality.  Any of these descriptions can be only partially true, there must be limitations to the use of the particle concept as well as of the wave concept, else one could not avoid contradictions.  If one takes into account those limitations which can be expressed by the uncertainty relations, the contradictions disappear.

In this way since the spring of 1927 one has had a consistent interpretation of quantum theory, which is frequently called the “Copenhagen interpretation.” This interpretation received its crucial test in the autumn of 1927 at the Solvay conference in Brussels.  Those experiments which had always led to the worst paradoxes were again and again discussed in all details, especially by Einstein.  New ideal experiments were invented to trace any possible inconsistency of the theory, but the theory was shown to be consistent and seemed to fit the experiments as far as one could see.

The details of this Copenhagen interpretation will be the subject of the next chapter.  It should be emphasized at this point that it has taken more than a quarter of a century to get from the first idea of the existence of energy quanta to a real understanding of the quantum theoretical laws.  This indicates the great change that had to take place in the fundamental concepts concerning reality before one could understand the new situation.

Chapter 3—The Copenhagen Interpretation

The Copenhagen interpretation of quantum theory starts from a paradox.  Any experiment in physics, whether it refers to the phenomena of daily life or to atomic events, is to be described in the terms of classical physics.  The concepts of classical physics form the language by which we describe the arrangement of our experiments and state the results.  We cannot and should not replace these concepts by any others.  Still the application of these concepts is limited by the relations of uncertainty.  We must keep in mind this limited range of applicability of the classical concepts while using them, but we cannot and should not try to improve them.

For a better understanding of this paradox it is useful to compare the procedure for the theoretical interpretation of an experiment in classical physics and in quantum theory.  In Newton’s mechanics, for instance, we may start by measuring the position and the velocity of the planet whose motion we are going to study.  The result of the observation is translated into mathematics by deriving numbers for the coordinates and the momenta of the planet from the observation.  Then the equations of motion are used to derive from these values of the coordinates and momenta at a given time the values of these coordinates or any other properties of the system at a later time, and in this way the astronomer can predict the properties of the system at a later time.  He can, for instance, predict the exact time for an eclipse of the moon.

In quantum theory the procedure is slightly different.  We could for instance be interested in the motion of an electron through a cloud chamber and could determine by some kind of observation the initial position and velocity of the electron.  But this determination will not be accurate; it will at least contain the inaccuracies following from the uncertainty relations and will probably contain still larger errors due to the difficulty of the experiment.  It is the first of these inaccuracies which allows us to translate the result of the observation into the mathematical scheme of quantum theory.  A probability function is written down which represents the experimental situation at the time of the measurement, including even the possible errors of the measurement.

This probability function represents a mixture of two things, partly a fact and partly our knowledge of a fact.  It represents a fact in so far as it assigns at the initial time the probability unity (ie. complete certainty) to the initial situation: the electron moving with the observed velocity at the observed position; “observed” means observed within the accuracy of the experiment.  It represents our knowledge in so far as another observer could perhaps know the position of the electron more accurately.  The error in the experiment doesat least to some extent-not represent a property of the electron but a deficiency in our knowledge of the electron.  Also this deficiency of knowledge is expressed in the probability function.

In classical physics one should in a careful investigation also consider the error of the observation.  As a result one would get a probability distribution for the initial values of the coordinates and velocities and therefore something very similar to the probability function in quantum mechanics.  Only the necessary uncertainty due to the uncertainty relations is lacking in classical physics.

When the probability function in quantum theory has been determined at the initial time from the observation, one can from the laws of quantum theory calculate the probability function at any later time and can thereby determine the probability for a measurement giving a specified value of the measured quantity.  We can, for instance, predict the probability for finding the electron at a later time at a given point in the cloud chamber.  It should be emphasized, however, that the probability function does not in itself represent a course of events in the course of time.  It represents a tendency for events and our knowledge of events.  The probability function can be connected with reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system.  Only then does the probability function allow us to calculate the probable result of the new measurement.  The result of the measurement again will be stated in terms of classical physics.

Therefore, the theoretical interpretation of an experiment requires three distinct steps: (1) the translation of the initial experimental situation into a probability function; (2) the following up of this function in the course of time; (3) the statement of a new measurement to be made of the system, the result of which can then be calculated from the probability function.  For the first step the fulfillment of the uncertainty relations is a necessary condition.  The second step cannot be described in terms of the classical concepts; there is no description of what happens to the system between the initial observation and the next measurement.  It is only in the third step that we change over again from the “possible” to the “actual.”

Let us illustrate these three steps in a simple ideal experiment.  It has been said that the atom consists of a nucleus and electrons moving around the nucleus; it has also been stated that the concept of an electronic orbit is doubtful.  One could argue that it should at least in principle be possible to observe the electron in its orbit.  One should simply look at the atom through a microscope of a very high resolving power, then one would see the electron moving in its orbit.  Such a high resolving power could to be sure not be obtained by a microscope using ordinary light, since the inaccuracy of the measurement of the position can never be smaller than the wavelength of the light.  But a microscope using alpha-rays with a wavelength smaller than the size of the atom would do.  Such a microscope has not yet been constructed but that should not prevent us from discussing the ideal experiment.

Is the first step, the translation of the result of the observation into a probability function, possible?  It is possible only if the uncertainty relation is fulfilled after the observation.  The position of the electron will be known with an accuracy given by the wavelength of the alpha-ray.  The electron may have been practically at rest before the observation.  But in the act of observation at least one light quantum of the alpha-ray must have passed the microscope and must first have been deflected by the electron.  Therefore, the electron has been pushed by the light quantum, it has changed its momentum and its velocity, and one can show that the uncertainty of this change is just big enough to guarantee the validity of the uncertainty relations.  Therefore, there is no difficulty with the first step.

At the same time one can easily see that there is no way of observing the orbit of the electron around the nucleus.  The second step shows a wave pocket moving not around the nucleus but away from the atom, because the first light quantum will have knocked the electron out from the atom.  The momentum of light quantum of the alpha-ray is much bigger than the original momentum of the electron if the wavelength of the alpha-ray is much smaller than the size of the atom.  Therefore, the first light quantum is sufficient to knock the electron out of the atom and one can never observe more than one point in the orbit of the electron; therefore, there is no orbit in the ordinary sense.  The next observation-the third step-will show the electron on its path from the atom.  Quite generally there is no way of describing what happens between two consecutive observations.  It is of course tempting to say that the electron must have been somewhere between the two observations and that therefore the electron must have described some kind of path or orbit even if it may be impossible to know which path.  This would be a reasonable argument in classical physics.  But in quantum theory it would be a misuse of the language which, as we will see later, cannot be justified.  We can leave it open for the moment, whether this warning is a statement about the way in which we should talk about atomic events or a statement about the events themselves, whether it refers to epistemology or to ontology.  In any case we have to be very cautious about the wording of any statement concerning the behavior of atomic particles.

Actually we need not speak of particles at all.  For many experiments it is more convenient to speak of matter waves; for instance, of stationary matter waves around the atomic nucleus.  Such a description would directly contradict the other description if one does not pay attention to the limitations given by the uncertainty relations.  Through the limitations the contradiction is avoided.  The use of “matter waves” is convenient, for example, when dealing with the radiation emitted by the atom.  By means of its frequencies and intensities the radiation gives information about the oscillating charge distribution in the atom, and there the wave picture comes much nearer to the truth than the particle picture.  Therefore, Bohr advocated the use of both pictures, which he called “complementary” to each other.  The two pictures are of course mutually exclusive because a certain thing cannot at the same time be a particle (ie. substance confined to a very small volume) and a wave (ie. a field spread out over a large space), but the two complement each other.  By playing with both pictures, by going from the one picture to the other and back again, we finally get the right impression of the strange kind of reality behind our atomic experiments.  Bohr uses the concept of “complementary” at several places in the interpretation of quantum theory.  The knowledge of the position of a particle is complementary to the knowledge of its velocity or momentum.  If we know the one with high accuracy we cannot know the other with high accuracy; still we must know both for determining the behavior of the system.  The space-time description of the atomic events is complementary to their deterministic description.  The probability function obeys an equation of motion as the coordinates did in Newtonian mechanics; its change in the course of time is completely determined by the quantum mechanical equation, but it does not allow a descrip­tion in space and time.  The observation, on the other hand, enforces the description in space and time but breaks the determined continuity of the probability function by changing our knowledge of the system.

Generally the dualism between two different descriptions of the same reality is no longer a difficulty since we know from the mathematical formulation of the theory that contradictions cannot arise.  The dualism between the two complementary pictures-waves and particles-is also clearly brought out in the flexibility of the mathematical scheme.  The formalism is normally written to resemble Newtonian mechanics, with equations of motion for the coordinates and the momenta of the particles.  But by a simple transformation it can be rewritten to resemble a wave equation for an ordinary three-dimensional matter wave. Therefore, this possibility of playing with different complementary pictures has its analogy in the different transformations of the mathematical scheme; it does not lead to any difficulties in the Copenhagen interpretation of quantum theory.

A real difficulty in the understanding of this interpretation arises, however, when one asks the famous question: But what happens “really” in an atomic event?  It has been said before that the mechanism and the results of an observation can always be stated in terms of the classical concepts.  But what one deduces from an observation is a probability function, a mathematical expression that combines statements about possibilities or tendencies with statements about our knowledge of facts.  So we cannot completely objectify the result of an observation, we cannot describe what “happens” between this observation and the next.  This looks as if we had introduced an element of subjectivism into the theory, as if we meant to say: what happens depends on our way of observing it or on the fact that we observe it.  Before discussing this problem of subjectivism it is necessary to explain quite clearly why one would get into hopeless difficulties if one tried to describe what happens between two consecutive observations.

For this purpose it is convenient to discuss the following ideal experiment: We assume that a small source of monochromatic light radiates toward a black screen with two small holes in it.  The diameter of the holes may be not much bigger than the wavelength of the light, but their distance will be very much bigger.  At some distance behind the screen a photographic plate registers the incident light.  If one describes this experiment in terms of the wave picture, one says that the primary wave penetrates through the two holes; there will be secondary spherical waves starting from the holes that interfere with one another, and the interference will produce a pattern of varying intensity on the photographic plate.

The blackening of the photographic plate is a quantum process, a chemical reaction produced by single light quanta.  Therefore, it must also be possible to describe the experiment in terms of light quanta.  If it would be permissible to say what happens to the single light quantum between its emission from the light source and its absorption in the photographic plate, one could argue as follows: The single light quantum can come through the first hole or through the second one.  If it goes through the first hole and is scattered there, its probability for being absorbed at a certain point of the photographic plate cannot depend upon whether the second hole is closed or open.  The probability distribution on the plate will be the same as if only the first hole was open.  If the experiment is repeated many times and one takes together all cases in which the light quantum has gone through the first hole, the blackening of the plate due to these cases will correspond to this probability distribution.  If one considers only those light quanta that go through the second hole, the blackening should correspond to a probability distribution derived from the assumption that only the second hole is open.  The total blackening, therefore, should just be the sum of the blackenings in the two cases; in other words, there should be I no interference pattern.  But we know this is not correct, and I the experiment will show the interference pattern.  Therefore, the statement that any light quantum must have gone either through I the first or through the second hole is problematic and leads to contradictions.  This example shows clearly that the concept of the probability function does not allow a description of what happens between two observations.  Any attempt to find such a description would lead to contradictions; this must mean that the term “happens” is restricted to the observation.

Now, this is a very strange result, since it seems to indicate that the observation plays a decisive role in the event and that the reality varies, depending upon whether we observe it or not.  To make this point clearer we have to analyze the process of I observation more closely.  To begin with, it is important to remember that in natural science we are not interested in the universe as a whole, including ourselves, but we direct our attention to some part of the universe and make that the object of our studies.  In atomic physics this part is usually a very small object, an atomic particle or a group of such particles, sometimes much larger-the size does not matter; but it is important that a large part of the I universe, including ourselves, does not belong to the object.

Now, the theoretical interpretation of an experiment starts with the two steps that have been discussed.  In the first step we have to describe the arrangement of the experiment, eventually combined with a first observation, in terms of classical physics and translate this description into a probability function.  Thisprobability function follows the laws of quantum theory, and its change in the course of time, which is continuous, can be calculated from the initial conditions; this is the second step.  The probability function combines objective and subjective elements.  It contains statements about possibilities or better tendencies (“potentia” in Aristotelian philosophy), and these statements are completely objective, they do not depend on any observer; and it contains statements about our knowledge of the system, which of course are subjective in so far as they may be different for different observers.  In ideal cases the subjective element in the probability function may be practically negligible as compared with the objective one.  The physicists then speak of a “pure case.”

When we now come to the next observation, the result of which should be predicted from the theory, it is very important to realize that our object has to be in contact with the other part of the world, namely, the experimental arrangement, the measuring rod, etc., before or at least at the moment of observation.  This means that the equation of motion for the probability function does now contain the influence of the interaction with the measuring device.  This influence introduces a new element of uncertainty, since the measuring device is necessarily described in the terms of classical physics; such a description contains all the uncertainties concerning the microscopic structure of the device which we know from thermodynamics, and since the device is connected with the rest of the world, it contains in fact the uncertainties of the microscopic structure of the whole world.  These uncertainties may be called objective in so far as they are simply a consequence of the description in the terms of classical physics and do not depend on any observer.  They may be called subjective in so far as they refer to our incomplete knowledge of the world.

After this interaction has taken place, the probability function contains the objective element of tendency and the subjective element of incomplete knowledge, even if it has been a “pure case” before.  It is for this reason that the result of the observation cannot generally be predicted with certainty; what can be predicted is the probability of a certain result of the observation, and this statement about the probability can be checked by repeating the experiment many times.  The probability function does, unlike the common procedure in Newtonian mechanics, not describe a certain event but, at least during the process of observation, a whole ensemble of possible events.  The observation itself changes the probability function discontinuously; it selects of all possible events the actual one that has taken place.  Since through the observation our knowledge of the system has changed discontinuously, its mathematical representation also has undergone the discontinuous change and we speak of a “quantum jump.” When the old adage “Natura non facit saltus” is used as a basis for criticism of quantum theory, we can reply that certainly our knowledge can change suddenly and that this fact justifies the use of the term “quantum jump.”

Therefore, the transition from the “possible” to the “actual” takes place during the act of observation.  If we want to describe what happens in an atomic event, we have to realize that the word “happens” can apply only to the observation, not to the state of affairs between two observations.  It applies to the physical, not the psychical act of observation, and we may say that the transition from the “possible” to the “actual” takes place as soon as the interaction of the object with the measuring device, and thereby with the rest of the world, has come into play; it is not connected with the act of registration of the result by the mind of the observer.  The discontinuous change in the probability function, however, takes place with the act of registration, because it is the discontinuous change of our knowledge in the instant of registration that has its image in the discontinuous change of the probability function.

To what extent, then, have we finally come to an objective description of the world, especially of the atomic world?  In classical physics science started from the belief-or should one say from the illusion?-that we could describe the world or at least parts of the world without any reference to ourselves.  This is actually possible to a large extent.  We know that the city of London exists whether we see it or not.  It may be said that classical physics is just that idealization in which we can speak about parts of the world without any reference to ourselves.  Its success has led to the general ideal of an objective description of the world.  Objectivity has become the first criterion for the value of any scientific result.  Does the Copenhagen interpretation of quantum theory still comply with this ideal?  One may perhaps say that quantum theory corresponds to this ideal as far as possible.  Certainly quantum theory does not contain genuine subjective features, it does not introduce the mind of the physicist as a part of the atomic event.  But it starts from the division of the world into the “object” and the rest of the world, and from the fact that at least for the rest of the world we use the classical concepts in our description.  This division is arbitrary and historically a direct consequence of our scientific method; the use of the classical concepts is finally a consequence of the general human way of thinking.  But this is already a reference to ourselves and in so far our description is not completely objective.

It has been stated in the beginning that the Copenhagen interpretation of quantum theory starts with a paradox.  It starts from the fact that we describe our experiments in the terms of classical physics and at the same time from the knowledge that these concepts do not fit nature accurately.  The tension between these two starting points is the root of the statistical character of quantum theory.  Therefore, it has sometimes been suggested that one should depart from the classical concepts altogether and that a radical change in the concepts used for describing the experiments might possibly lead back to a nonstatical, completely objective description of nature.  This suggestion, however, rests upon a misunderstanding.  The concepts of classical physics are just a refinement of the concepts of daily life and are an essential part of the language which forms the basis of all natural science.  Our actual situation in science is such that we do use the classical concepts for the description of the experiments, and it was the problem of quantum theory to find theoretical interpretation of the experiments on this basis.  There is no use in discussing what could be done if we were other beings than we are.  At this point we have to realize, as von Weizsacker has put it, that “Nature is earlier than man, but man is earlier than natural science.” The first part of the sentence justifies classical physics, with its ideal of complete objectivity.  The second part tells us why we cannot escape the paradox of quantum theory, namely, the necessity of using the classical concepts.

We have to add some comments on the actual procedure in the quantum-theoretical interpretation of atomic events.  It has been said that we always start with a division of the world into an object, which we are going to study, and the rest of the world, and that this division is to some extent arbitrary.  It should indeed not make any difference in the final result if we, for example, add some part of the measuring device or the whole device to the object and apply the laws of quantum theory to this more complicated object.  It can be shown that such an alteration of the theoretical treatment would not alter the predictions concerning a given experiment.  This follows mathematically from the fact that the laws of quantum theory are for the phenomena in which Planck’s constant can be considered as a very small quantity, approximately identical with the classical laws.  But it would be a mistake to believe that this application of the quantum-theoretical laws to the measuring device could help to avoid the fundamental paradox of quantum theory.  The measuring device deserves this name only if it is in close contact with the rest of the world, if there is an interaction between the device and the observer.  Therefore, the uncertainty with respect to the microscopic behavior of the world will enter into the quantum-theoretical system here just as well as in the first interpretation.  If the measuring device would be isolated from the rest of the world, it would be neither a measuring device nor could it be described in the terms of classical physics at all.

With regard to this situation Bohr has emphasized that it is more realistic to state that the division into the object and the rest of the world is not arbitrary.  Our actual situation in research work in atomic physics is usually this: we wish to understand a certain phenomenon, we wish to recognize how this phenomenon follows from the general laws of nature.  Therefore, that part of matter or radiation which takes part in the phenomenon is the natural object in the theoretical treatment and should be separated in this respect from the tools used to study the phenomenon.  This again emphasizes a subjective element in the description of atomic events, since the measuring device has been constructed by the observer, and we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning.  Our scientific work in physics consists in asking questions about nature in the language that we possess and trying to get an answer from experiment by the means that are at our disposal.  In this way quantum theory reminds us, as Bohr has put it, of the old wisdom that when searching for harmony in life one must never forget that in the drama of existence we are ourselves both players and spectators.  It is understandable that in our scientific relation to nature our own activity becomes very important when we have to deal with parts of nature into which we can penetrate only by using the most elaborate tools.

Chapter 10Language and Reality

Throughout the history of science new discoveries and new ideas have always caused scientific disputes, have led to polemical publications criticizing the new ideas, and such criticism has often been helpful in their development; but these controversies have never before reached that degree of violence which they attained after the discovery of the theory of relativity and in a lesser degree after quantum theory.  In both cases the scientific problems have finally become connected with political issues; and some scientists have taken recourse to political methods to carry their views through.  This violent reaction on the recent development of modern physics can only be understood when one realizes that here the foundations of physics have started moving; and that this motion has caused the feeling that the ground would be cut from science.  At the same time it probably means that one has not yet found the correct language with which to speak about the new situation and that the incorrect statements published here and there in the enthusiasm about the new discoveries have caused all kinds of misunderstanding.  This is indeed a fundamental problem.  The improved experimental technique of our time brings into the scope of science new aspects of nature which cannot be described in terms of the common concepts.  But in what language, then, should they be described?  The first language that emerges from the process of scientific clarification is in theoretical physics usually a mathematical language, the mathematical scheme, which allows one to predict the results of experiments.  The physicist may be satisfied when he has the mathematical scheme and knows how to use it for the interpretation of the experiments.  But he has to speak about his results also to nonphysicists who will not be satisfied unless some explanation is given in plain language, understandable to anybody.  Even for the physicist the description in plain language will be a criterion of the degree of understanding that has been reached.  To what extent is such a description at all possible?  Can one speak about the atom itself?  This is a problem of language as much as of physics, and therefore some remarks are necessary concerning language in general and scientific language specifically.

Language was formed during the prehistoric age among the human race as a means for communication and as a basis for thinking.  We know little about the various steps in its formation; but language now contains a great number of concepts which are a suitable tool for more or less unambiguous communication about events in daily life.  These concepts are acquired gradually without critical analysis by using the language, and after having used a word sufficiently often we think that we more or less know what it means.  It is of course a well-known fact that the words are not so clearly defined as they seem to be at first sight and that they have only a limited range of applicability.  For instance, we can speak about a piece of iron or a piece of wood, but we cannot speak about a piece of water.  The word “piece” does not apply to liquid substances.  Or, to mention another ex­ample: In discussions about the limitations of concepts, Bohr likes to tell the following story: “A little boy goes into a grocer’s shop with a penny in his hand and asks—Could I have a penny’s worth of mixed sweets?  The grocer takes two sweets and hands them to the boy saying: ‘Here you have two sweets. You can do the mixing yourself.’ “ A more serious example of the problematic relation between words and concepts is the fact that the words “red” and “green” are used even by people who are colorblind, though the ranges of applicability of these terms must be quite different for them from what they are for other people.

This intrinsic uncertainty of the meaning of words was of course recognized very early and has brought about the need for definitions, or—as the word “definition” says—for the setting of boundaries that determine where the word is to be used and where not.  But definitions can be given only with the help of other concepts, and so one will finally have to rely on some concepts that are taken as they are, unanalyzed and undefined.  In Greek philosophy the problem of the concepts in language has been a major theme since Socrates, whose life was—if we can follow Plato’s artistic representation in his dialogues—a continuous discussion about the content of the concepts in language and about the limitations in modes of expression.  In order to obtain a solid basis for scientific thinking, Aristotle in his logic started to analyze the forms of language, the formal structure of conclusions and deductions independent of their content.  In this way he reached a degree of abstraction and precision that had been unknown up to that time in Greek philosophy and he thereby contributed immensely to the clarification, to the establishment of order in our methods of thought.  He actually created the basis for the scientific language.

On the other hand, this logical analysis of language again involves the danger of an oversimplification.  In logic the attention is drawn to very special structures, unambiguous connec­tions between premises and deductions, simple patterns of reasoning, and all the other structures of language are neglected. These other structures may arise from associations between certain meanings of words; for instance, a secondary meaning of a word which passes only vaguely through the mind when the word is heard may contribute essentially to the content of a sentence.  The fact that every word may cause many only half-conscious movements in our mind can be used to represent some part of reality in the language much more clearly than by the use of the logical patterns.  Therefore, the poets have often objected to this emphasis in language and in thinking on the logical pattern, which-if I interpret their opinions correctly—can make language less suitable for its purpose.  We may recall for instance the words in Goethe’s Faust which Mephistopheles speaks to the young student:

Waste not your time, so fast it flies;

Method will teach you time to win;

Hence, my young friend, I would advise,

With college logic to begin.

Then will your mind be so well braced,

In Spanish boots so tightly laced,

That on twill circumspectly creep,

Thought’s beaten track securely keep,

Nor will it, ignis-fatuus like,

Into the path of error strike.

Then many a day they’ll teach you how

The mind’s spontaneous acts, till now

As eating and as drinking free,

Require a process;—one, two, three!

In truth the subtle web of thought

Is like the weaver’s fabric wrought,

One treadle moves a thousand lines,

Swift dart the shuttles to and fro,

Unseen the threads unnumbered flow,

A thousand knots one stroke combines.

Then forward steps your sage to show,

And prove to you it must be so;

The first being so, and so the second.

The third and fourth deduced we see;

And if there were no first and second,

Nor third nor fourth would ever be.

This, scholars of all countries prize,

Yet among themselves no weavers rise.

Who would describe and study aught alive,

Seeks first the living spirit thence to drive:

Then are the lifeless fragments in his hand,

There only fails, alas I—the spirit—band.

This passage contains an admirable description of the structure of language and of the narrowness of the simple logical patterns.  On the other hand, science must be based upon language as the only means of communication and there, where the problem of unambiguity is of greatest importance, the logical patterns must play their role.  The characteristic difficulty at this point may be described in the following way.  In natural science we try to derive the particular from the general, to understand the par­ticular phenomenon as caused by simple general laws.  The general laws when formulated in the language can contain only a few simple concepts—else the law would not be simple and general.  From these concepts are derived an infinite variety of possible phenomena, not only qualitatively but with complete precision with respect to every detail.  It is obvious that the concepts of ordinary language, inaccurate and only vaguely defined as they are, could never allow such derivations.  When a chain of conclusions follows from given premises, the number of possible links in the chain depends on the precision of the premises.  Therefore, the concepts of the general laws must in natural science be defined with complete precision, and this can be achieved only by means of mathematical abstraction.  In other sciences the situation may be somewhat similar in so far as rather precise definitions are also required; for instance, in law.  But here the number of links in the chain of conclusions need not be very great, complete precision is not needed, and rather precise definitions in terms of ordinary language are sufficient.

In theoretical physics we try to understand groups of phenomena by introducing mathematical symbols that can be correlated with facts, namely, with the results of measurements.  For the symbols we use names that visualize their correlation with the measurement.  Thus the symbols are attached to the language. Then the symbols are interconnected by a rigorous system of definitions and axioms, and finally the natural laws are expressed as equations between the symbols.  The infinite variety of solutions of these equations then corresponds to the infinite variety of particular phenomena that are possible in this part of nature.  In this way the mathematical scheme represents the group of phenomena so far as the correlation between the symbols and the measurements goes.  It is this correlation which permits the expression of natural laws in the terms of common language, since our experiments consisting of actions and observations can always be described in ordinary language.

Still in the process of expansion of scientific knowledge the language also expands; new terms are introduced and the old ones are applied in a wider field or differently from ordinary language.  Terms such as energy, electricity and entropy are obvious examples.  In this way we develop a scientific language which may be called a natural extension of ordinary language adapted to the added fields of scientific knowledge.  During the past century a number of new concepts have been introduced in physics, and in some cases it has taken considerable time before the scientists have really grown accustomed to their use.  The term electromagnetic field, for instance, which was to some extent already present in Faraday’s work and which later formed the basis of Maxwell’s theory, was not easily accepted by the physicists, who directed their attention primarily to the mechanical motion of matter.  The introduction of the concept really involved a change in scientific ideas as well, and such changes are not easily accomplished.

Still, all the concepts introduced up to the end of the last century formed a perfectly consistent set applicable to a wide field of experience, and, together with the former concepts, formed a language which not only the scientists but also the technicians and engineers could successfully apply in their work.  To the underlying fundamental ideas of this language belonged the assumptions that the order of events in time is entirely independent of their order in space, that Euclidean geometry is valid in real space, and that the events “happen” in space and time independently of whether they are observed or not.  It was not denied that every observation had some influence on the phenomenon to be observed but it was generally assumed that by doing the experiments cautiously this influence could be made arbitrarily small.  This seemed in fact a necessary condition for the ideal of objectivity which was considered as the basis of all natural science.

Into this rather peaceful state of physics broke quantum theory and the theory of special relativity as a sudden, at first slow and then gradually increasing, movement in the foundations of natural science.  The first violent discussions developed around the problems of space and time raised by the theory of relativity.  How should one speak about the new situation?  Should one consider the Lorentz contraction of moving bodies as a real contraction or only as an apparent contraction?  Should one say that the structure of space and time was really different from what it had been assumed to be or should one only say that the experimental results could be connected mathematically in a way corresponding to this new structure, while space and time, being the universal and necessary mode in which things appear to us, remain what they had always been?  The real problem behind these many controversies was the fact that no language existed in which one could speak consistently about the new situation.  The ordinary language was based upon the old concepts of space and time and this language offered the only unambiguous means of communication about the setting up and the results of the measurements.  Yet the experiments showed that the old concepts could not be applied everywhere.

The obvious starting point for the interpretation of the theory of relativity was therefore the fact that in the limiting.  case of small velocities (small compared with the velocity of light) the new theory was practically identical with the old one.  Therefore, in this part of the theory it was obvious in which way the mathematical symbols had to be correlated with the measurements and with the terms of ordinary language; actually it was only through this correlation that the Lorentz transformation had been found.  There was no ambiguity about the meaning of the words and the symbols in this region.  In fact this correlation was already sufficient for the application of the theory to the whole field of experimental research connected with the problem of relativity.  Therefore, the controversial questions about the “real” or the “apparent” Lorentz contraction, or about the definition of the word “simultaneous” etc., did not concern the facts but rather the language.

With regard to the language, on the other hand, one has gradually recognized that one should perhaps not insist too much on certain principles.  It is always difficult to find general convincing criteria for which terms should be used in the language and how they should be used.  One should simply wait for the development of the language, which adjusts itself after some time to the new situation.  Actually in the theory of special relativity this adjustment has already taken place to a large extent during the past fifty years.  The distinction between “real” and “apparent” contraction, for instance, has simply disappeared.  The word “simultaneous” is used in line with the definition given by Einstein, while for the wider definition discussed in an earlier chapter the term “at a space-like distance” is commonly used, etc.

In the theory of general relativity the idea of a non-Euclidean geometry in real space was strongly contradicted by some philosophers who pointed out that our whole method of setting up the experiments already presupposed Euclidean geometry.  In fact if a mechanic tries to prepare a perfectly plane surface, he can do it in the following way.  He first prepares three surfaces of, roughly, the same size which are, roughly, plane.  Then he tries to bring any two of the three surfaces into contact by putting them against each other in different relative positions.  The degree to which this contact is possible on the whole surface is a measure of the degree of accuracy with which the surfaces can be called “plane.” He will be satisfied with his three surfaces only if the contact between any two of them is complete everywhere.  If this happens one can prove mathematically that Euclidean geometry holds on the three surfaces.  In this way, it was argued, Euclidean geometry is just made correct by our own measures.

From the point of view of general relativity, of course, one can answer that this argument proves the validity of Euclidean geometry only in small dimensions, in the dimensions of our experimental equipment.  The accuracy with which it holds in this region is so high that the above process for getting plane surfaces can always be carried out.  The extremely slight deviations from Euclidean geometry which still exist in this region will not be realized since the surfaces are made of material which is not strictly rigid but allows for very small deformations and since the concept of “contact” cannot be defined with complete precision.  For surfaces on a cosmic scale the process that has been described would just not work; but this is not a problem of experimental physics.

Again, the obvious starting point for the physical interpretation of the mathematical scheme in general relativity is the fact that the geometry is very nearly Euclidean in small dimensions; the theory approaches the classical theory in this region.  Therefore, here the correlation between the mathematical symbols and the measurements and the concepts in ordinary language is unambiguous.  Still, one can speak about a non-Euclidean geometry in large dimensions.  In fact a long time before the theory of general relativity had even been developed the possibility of a non-Euclidean geometry in real space seems to have been con­sidered by the mathematicians, especially by Gauss in Göttingen.  When he carried out very accurate geodetic measurements on a triangle formed by three mountains—the Brocken in the Harz Mountains, the Inselberg in Thuringia, and the Hohenhagen near Göttingen—he is said to have checked very carefully whether the sum of the three angles was actually equal to 180 degrees; and that he considered a difference which would prove deviations from Euclidean geometry as being possible.  Actually he did not find any deviations within his accuracy of measurement.  In the theory of general relativity the language by which we describe the general laws actually now follows the scientific language of the mathematicians, and for the description of the experiments themselves we can use the ordinary concepts, since Euclidean geometry is valid with sufficient accuracy in small dimensions.

The most difficult problem, however, concerning the use of the language arises in quantum theory.  Here we have at first no simple guide for correlating the mathematical symbols with concepts of ordinary language; and the only thing we know from the start is the fact that our common concepts cannot be applied to the structure of the atoms.  Again the obvious starting point for the physical interpretation of the formalism seems to be the fact that the mathematical scheme of quantum mechanics approaches that of classical mechanics in dimensions which are large as compared to the size of the atoms.  But even this statement must be made with some reservations.  Even in large dimensions there are many solutions of the quantum-theoretical equations to which no analogous solutions can be found in classical physics.  In these solutions the phenomenon of the interference of probabilities would show up, as was discussed in the earlier chapters; it does not exist in classical physics.  Therefore, even in the limit of large dimensions the correlation between the mathematical symbols, the measurements, and the ordinary concepts is by no means trivial.  In order to get to such an unambiguous correlation one must take another feature of the problem into account.  It must be observed that the system which is treated by the methods of quantum mechanics is in fact a part of a much bigger system (eventually the whole world); it is interacting with this bigger system; and one must add that the microscopic properties of the bigger system are (at least to a large extent) unknown.  This statement is undoubtedly a correct description of the actual situation.  Since the system could not be the object of measurements and of theoretical investigations, it would in fact not belong to the world of phenomena if it had no interactions with such a bigger system of which the observer is a part.  The interaction with the bigger system with its undefined microscopic properties then introduces a new statistical element into the description-both the quantum-theoretical and the classical one-of the system under consideration.  In the limiting case of the large dimensions this statistical element destroys the effects of the “interference of probabilities” in such a manner that now the quantum-mechanical scheme really approaches the classical one in the limit.  Therefore, at this point the correlation between the mathematical symbols of quantum theory and the concepts of ordinary language is unambiguous, and this correlation suffices for the interpretation of the experiments.  The remaining problems again concern the language rather than the facts, since it belongs to the concept “fact” that it can be described in ordinary language.

But the problems of language here are really serious.  We wish to speak in some way about the structure of the atoms and not only about the “facts”—the latter being, for instance, the black spots on a photographic plate or the water droplets in a cloud chamber.  But we cannot speak about the atoms in ordinary language.  The analysis can now be carried further in two entirely different ways.  We can either ask which language concerning the atoms has actually developed among the physicists in the thirty years that have elapsed since the formulation of quantum mechanics.  Or we can describe the attempts for defining a precise scientific language that corresponds to the mathematical scheme.

In answer to the first question one may say that the concept of complementary introduced by Bohr into the interpretation of quantum theory has encouraged the physicists to use an ambiguous rather than an unambiguous language, to use the classical concepts in a somewhat vague manner in conformity with the principle of uncertainty, to apply alternatively different classical concepts which would lead to contradictions if used simultaneously.  In this way one speaks about electronic orbits, about matter waves and charge density, about energy and momentum, etc., always conscious of the fact that these concepts have only a very limited range of applicability.  When this vague and unsystematic use of the language leads into difficulties, the physicist has to withdraw into the mathematical scheme and its unambiguous correlation with the experimental facts.

This use of the language is in many ways quite satisfactory, since it reminds us of a similar use of the language in daily life or in poetry.  We realize that the situation of complementary is not confined to the atomic world alone; we meet it when we reflect about a decision and the motives for our decision or when we have the choice between enjoying music and analyzing its structure.  On the other hand, when the classical concepts are used in this manner, they always retain a certain vagueness, they acquire in their relation to “reality” only the same statistical significance as the concepts of classical thermodynamics in its statistical interpretation.  Therefore, a short discussion of these statistical concepts of thermodynamics may be useful.

The concept temperature in classical thermodynamics seems to describe an objective feature of reality, an objective property of matter.  In daily life it is quite easy to define with the help of a thermometer what we mean by stating that a piece of matter has a certain temperature.  But when we try to define what the temperature of an atom could mean we are, even in classical physics, in a much more difficult position.  Actually we cannot correlate this concept “temperature of the atom” with a well-defined property of the atom but have to connect it at least partly with our insufficient knowledge of it.  We can correlate the value of the temperature with certain statistical expectations about the properties of the atom, but it seems rather doubtful whether an expectation should be called objective.  The concept “temperature of the atom” is not much better defined than the concept “mixing” in the story about the boy who bought mixed sweets.

In a similar way in quantum theory all the classical concepts are, when applied to the atom, just as well and just as little defined as the “temperature of the atom;” they are correlated with statistical expectations; only in rare cases may the expectation become the equivalent of certainty.  Again, as in classical thermodynamics, it is difficult to call the expectation objective.  One might perhaps call it an objective tendency or possibility, a “potentia” in the sense of Aristotelian philosophy.  In fact, I believe that the language actually used by physicists when they speak about atomic events produces in their minds similar notions as the concept “potentia.” So the physicists have gradually become accustomed to considering the electronic orbits, for example, not as reality but rather as a kind of “potentia.” The language has already adjusted itself, at least to some extent, to this true situation.  But it is not a precise language in which one could use the normal logical patterns; it is a language that produces pictures in our mind, but together with them the notion that the pictures have only a vague connection with reality, that they represent only a tendency toward reality.

The vagueness of this language in use among the physicists has therefore led to attempts to define a different precise language which follows definite logical patterns in complete conformity with the mathematical scheme of quantum theory.  The result of these attempts by Birkhoff and Neumann and more recently by Weizsacker can be stated by saying that the mathematical scheme of quantum theory can be interpreted as an extension or modification of classical logic.  It is especially one fundamental principle of classical logic which seems to require a modification.  In classical logic it is assumed that, if a statement has any meaning at all, either the statement or the negation of the statement must be correct.  Of “here is a table” or “here is not a table,” either the first or the second statement must be correct.  Tertium non datur, a third possibility does not exist.  It may be that we do not know whether the statement or its negation is correct; but in “reality” one of the two is correct.

In quantum theory this law tertium non datur is to be modified.  Against any modification of this fundamental principle one can of course at once argue that the principle is assumed in common language and that we have to speak at least about our eventual modification of logic in the natural language.  Therefore, it would be a self-contradiction to describe in natural language a logical scheme that does not apply to natural language.  There, however, Weizsacker points out that one may distinguish various levels of language.  One level refers to the objects-for instance, to the atoms or the electrons.  A second level refers to statements about objects.  A third level may refer to statements about statements about objects, etc.  It would then be possible to have different logical patterns at the different levels.  It is true that finally we have to go back to the natural language and thereby to the classical logical patterns.  But Weizsacker suggests that classical logic may be in a similar manner a priori to quantum logic, as classical physics is to quantum theory.  Classical logic would then be contained as a kind of limiting case in quantum logic, but the latter would constitute the more general logical pattern.

The possible modification of the classical logical pattern shall, then, first refer to the level concerning the objects.  Let us consider an atom moving in a closed box which is divided by a wall into two equal parts.  The wall may have a very small hole so that the atom can go through.  Then the atom can, according to classical logic, be either in the left half of the box or in the right half.  There is no third possibility: “tertium non datur.” In quantum theory, however, we have to admit—if we use the words “atom” and “box” at all—that there are other possibilities which are in a strange way mixtures of the two former possibilities. This is necessary for explaining the results of our experiments.  We could, for instance, observe light that has been scattered by the atom.  We could perform three experiments—first the atom is (for instance, by closing the hole in the wall) confined to the left half of the box, and the intensity distribution of the scattered light is measured; then it is confined to the right half and again the scattered light is measured; and finally the atom can move freely in the whole box and again the intensity distribution of the scattered light is measured.  If the atom would always be in either the left half or the right half of the box, the final intensity distribution should be a mixture (according to the fraction of time spent by the atom in each of the two parts) of the two former intensity distributions.  But this is in general not true experimentally.  The real intensity distribution is modified by the “interference of probabilities”; this has been discussed before.

In order to cope with this situation Weizsacker has introduced the concept “degree of truth.” For any simple statement in an alternative like “The atom is in the left (or in the right) half of the box” a complex number is defined as a measure for its “degree of truth.” If the number is one, it means that the statement is true; if the number is zero, it means that it is false.  But other values are possible.  The absolute square of the complex number gives the probability for the statement’s being true; the sum of the two probabilities referring to the two parts in the alternative (either left or right in our case) must be unity.  But each pair of complex numbers referring to the two parts of the alternative represents, according to Weizsacker’s definitions, a “statement” which is certainly true if the numbers have just these values; the two numbers, for instance, are sufficient for determining the intensity distribution of scattered light in our experiment.  If one allows the use of the term “statement” in this way one can introduce the term “complementary” by the following definition—Each statement that is not identical with either of the two alternative statements—in our case with the statements: “the atom is in the left half” or “the atom is in the right half of the box”—is called complementary to these statements.  For each complementary statement the question whether the atom is left or right is not decided.  But the term “not decided is by no means equivalent to the term “not known.“  “Not known” would mean that the atom is “really” left or right, only we do not know where it is.  But “not decided” indicates a different situation, expressible only by a complementary statement.

This general logical pattern, the details of which cannot be described here, corresponds precisely to the mathematical formalism of quantum theory.  It forms the basis of a precise language that can be used to describe the structure of the atom.  But the application of such a language raises a number of difficult problems of which we shall discuss only two here: the relation between the different “levels” of language and the consequences for the underlying ontology.  In classical logic the relation between the different levels of language is a one-to-one correspondence.  The two statements, “The atom is in the left half” and “It is true that the atom is in the left half,” belong logically to different levels.  In classical logic these statements are completely equivalent, for instance, they are either both true or both false.  It is not possible that the one is true and the other false.  But in the logical pattern of complementary this relation is more complicated.  The correctness or incorrectness of the first statement still implies the correctness or incorrectness of the second statement.  But the incorrectness of the second statement does not imply the incorrectness of the first statement.  If the second statement is incorrect, it may be undecided whether the atom is in the left half; the atom need not necessarily be in the right half.  There is still complete equivalence between the two levels of language with respect to the correctness of a statement, but not with respect to the incorrectness.  From this connection one can understand the persistence of the classical laws in quantum theory: wherever a definite result can be derived in a given experiment by the application of the classical laws the result will also follow from quantum theory, and it will hold experimentally.

The final aim of Weizsacker’s attempt is to apply the modified logical patterns also in the higher levels of language, but these questions cannot be discussed here.  The other problem concerns the ontology that underlies the modified logical patterns.  If the pair of complex numbers represents a “statement” in the sense just described, there should exist a “state” or a “situation” in nature in which the statement is correct.  We will use the word “state” in this connection. The “states” corresponding to complementary statements are then called “coexistent states” by Weizsacker.  This term “coexistent” describes the situation correctly; it would in fact be difficult to call them “different states,” since every state contains to some extent also the other “coexistent states.” This concept of “state” would then form a first definition concerning the ontology of quantum theory.  One sees at once that this use of the word “state,” especially the term “coexistent state,” is so different from the usual materialistic ontology that one may doubt whether one is using a convenient terminology.  On the other hand, if one considers the word “state” as describing some potentiality rather than a reality—one may even simply replace the term “state” by the term “potentiality”—then the concept of “coexistent potentialities” is quite plausible, since one potentiality may involve or overlap other potentialities.

All these difficult definitions and distinctions can be avoided if one confines the language to the description of facts, ie. experimental results.  However, if one wishes to speak about the atomic particles themselves one must either use the mathematical scheme as the only supplement to natural language or one must combine it with a language that makes use of a modified logic or of no well-defined logic at all.  In the experiments about atomic events we have to do with things and facts, with phenomena that are just as real as any phenomena in daily life.  But the atoms or the elementary particles themselves are not as real; they form a world of potentialities or possibilities rather than one of things or facts.

The philosophical implications of modern physics have been discussed in the foregoing chapters in order to show that this most modern part of science touches very old trends of thought at many points, that it approaches some of the very old problems from a new direction.  It is probably true quite generally that in the history of human thinking the most fruitful developments frequency take place at those points where two different lines of thought meet.  These lines may have their roots in quite different parts of human culture, in different times or different cultural environments or different religious traditions; hence if they actually meet, that is, if they are at least so much related to each other that a real interaction can take place, then one may hope that new and interesting developments will follow.  Atomic physics as a part of modem science does actually penetrate in our time into very different cultural traditions.  It is not only taught in Europe and the Western countries, where it.  belongs to the traditional activity in the natural sciences, but it is also studied in the Far East, in countries like Japan and China and India.

Chapter 11—The Role of Modern Physics

The philosophical implications of modern physics have been discussed in the foregoing chapters in order to show that this most modern part of science touches very old trends of thought at many points, that it approaches some of the very old problems from a new direction.  It is probably true quite generally that in the history of human thinking the most fruitful developments frequency take place at those points where two different lines of thought meet.  These lines may have their roots in quite different parts of human culture, in different times or different cultural environments or different religious traditions; hence if they actually meet, that is, if they are at least so much related to each other that a real interaction can take place, then one may hope that new and interesting developments will follow.  Atomic physics as a part of modem science does actually penetrate in our time into very different cultural traditions.  It is not only taught in Europe and the Western countries, where it belongs to the traditional activity in the natural sciences, but it is also studied in the Far East, in countries like Japan and China and India, with their quite different cultural background, and in Russia, where a new way of thinking has been established in our time; a new way related both to specific scientific developments of the Europe of the nineteenth century and to other entirely different traditions from Russia itself.  It can certainly not be the purpose of the following discussion to make predictions about the probable result of the encounter between the ideas of modern physics and the older traditions.  But it may be possible to define the points from which the interaction between the different ideas may begin.

In considering this process of expansion of modern physics it would certainly not be possible to separate it from the general expansion of natural science, of industry and engineering, of medicine, etc., that is, quite generally of modern civilization in all parts of the world.  Modern physics is just one link in a long chain of events that started from the work of Bacon, Galileo and Kepler and from the practical application of natural science in the seventeenth and eighteenth centuries.  The connection between natural science and technical science has from the beginning been that of mutual assistance: The progress in technical science, the improvement of the tools, the invention of new technical devices have provided the basis for more, and more accurate, empirical knowledge of nature; and the progress in the understanding of nature and finally the mathematical formulation of natural laws have opened the way to new applications of this knowledge in technical science.  For instance, the invention of the telescope enabled the astronomers to measure the motion of the stars more accurately than before; thereby a considerable progress in astronomy and in mechanics was made possible.  On the other hand, precise knowledge of the mechanical laws was of the greatest value for the improvement of mechanical tools, for the construction of engines, etc.  The great expansion of this combination of natural and technical science started when one had succeeded in putting some of the forces of nature at the disposal of man.  The energy stored up in coal, for instance, could then perform some of the work which formerly had to be done by man himself.  The industries growing out of these new possibilities could first be considered as a natural continuation and expansion of the older trades; at many points the work of the machines still resembled the older handicraft and the work in the chemical factories could be considered as a continuation of the work in the dyehouses and the pharmacies of the older times.  But later entirely new branches of industry developed which had no counterpart in the older trades; for instance, electrical engineering.  The penetration of science into the more remote parts of nature enabled the engineers to use forces of nature which in former periods had scarcely been known; and the accurate knowledge of these forces in terms of a mathematical formulation of the laws governing them formed a solid basis for the construction of all kinds of machinery.

The enormous success of this combination of natural and technical science led to a strong preponderance of those nations or states or communities in which this kind of human activity flourished, and as a natural consequence this activity had to be taken up even by those nations which by tradition would not have been inclined toward natural and technical sciences.  The modern means of communication and of traffic finally completed this process of expansion of technical civilization.  Undoubtedly the process has fundamentally changed the conditions of life on our earth; and whether one approves of it or not, whether one calls it progress or danger, one must realize that it has gone far beyond any control through human forces.  One may rather consider it as a biological process on the largest scale whereby the structures active in the human organism encroach on larger parts of matter and transform it into a state suited for the increasing human population.

Modern physics belongs to the most recent parts of this development, and its unfortunately most visible result, the invention of nuclear weapons, has shown the essence of this development in the sharpest possible light.  On the one hand, it has demonstrated most clearly that the changes brought about by the combination of natural and technical sciences cannot be looked at only from the optimistic viewpoint; it has at least partly justified the views of those who had always warned against the dangers of such radical transmutation of our natural conditions of life.  On the other hand, it has compelled even those nations or individuals who tried to keep apart from these dangers to pay the strongest attention to the new development, since obviously political power in the sense of military power rests upon the possession of atomic weapons.  It can certainly not be the task of this volume to discuss extensively the political implications of nuclear physics.  But at least a few words may be said about these problems because they always come first into the minds of people when atomic physics is mentioned.

It is obvious that the invention of the new weapons, especially of the thermonuclear weapons, has fundamentally changed the political structure of the world.  Not only has the concept of independent nations or states undergone a decisive change, since any nation which is not in possession of such weapons must depend in some way on those very few nations that do produce these arms in large quantity; but also the attempt of warfare on a large scale by means of such weapons has become practically an absurd kind of suicide.  Hence one frequently hears the optimistic view that therefore war has become obsolete, that it will not happen again.  This view, unfortunately, is a much too optimistic oversimplification.  On the contrary, the absurdity of warfare by means of thermonuclear weapons may, in a first approximation, act as an incentive for war on a small scale.  Any nation or political group which is convinced of its historical or moral right to enforce some change of the present situation will feel that the use of conventional arms for this purpose will not involve any great risks; they will assume that the other side will certainly not have recourse to the nuclear weapons, since the other side being historically and morally wrong in this issue will not take the chance of war on a large scale.  This situation would in turn induce the other nations to state that in case of small wars inflicted upon them by aggressors, they would actually have recourse to the nuclear weapons, and thus the danger obviously remains.  It may quite well be that in about twenty or thirty years from now the world will have undergone so great changes that the danger of warfare on a large scale, of the application of all technical resources for the annihilation of the opponent, will have greatly diminished or disappeared.  But the way to this new state will be full of the greatest dangers.  We must as in all former times, realize that what looks historically or morally right to the one side may look wrong to the other side.  The continuation of the status quo may not always be the correct solution; it may, on the contrary, be most important to find peaceful means of adjustments to new situations, and it may in many cases be extremely difficult to find any just decision at all.  Therefore, it is probably not too pessimistic to say that the Great War can be avoided only if all the different political groups are ready to renounce some of their apparently most obvious rights—in view of the fact that the question of right or wrong may look essentially different from the other side.  This is certainly not a new point of view; it is in fact only an application of that human attitude which has been taught through many centuries by some of the great religions.

The invention of nuclear weapons has also raised entirely new problems for science and scientists.  The political influence of science has become very much stronger than it was before World War II, and this fact has burdened the scientist, especially the atomic physicist, with a double responsibility.  He can either take an active part in the administration of the country in connection with the importance of science for the community; then he will eventually have to face the responsibility for decisions of enormous weight which go far beyond the small circle of research and university work to which he was wont.  Or he may voluntarily withdraw from any participation in political decisions; then he will still be responsible for wrong decisions which he could possibly have prevented had he not preferred the quiet life of the scientist.  Obviously it is the duty of the scientists to inform their governments in detail about the unprecedented destruction that would follow from a war with thermonuclear weapons.  Beyond that, scientists are frequently requested to participate in solemn resolutions in favor of world peace; but considering this latter demand I must confess that I have never been able to see any point in declarations of this kind.  Such resolutions may seem a welcome proof of goodwill; but anyone who speaks in favor of peace without stating precisely the conditions of this peace must at once be suspected of speaking only about that kind of peace in which he and his group thrive best-which of course would be completely worthless.  Any honest declaration for peace must be an enumeration of the sacrifices one is prepared to make for its preservation.  But as a rule the scientists have no authority to make statements of this kind.

At the same time the scientist can do his best to promote international co-operation in his own field.  The great importance that many governments attach to research in nuclear physics nowadays and the fact that the level of scientific work is still very different in different countries favors international cooperation in this work.  Young scientists of many different countries may gather in research institutions in which a strong activity in the field of modern physics is going on and the common work on difficult scientific problems will foster mutual understanding.  In one case, that of the Geneva organization, it has even been possible to reach an agreement between a number of different nations for building a common laboratory and for constructing by a combined effort the expensive experimental equipment for research in nuclear physics.  This kind of cooperation will certainly help to establish a common attitude toward the problems of science—common even beyond the purely scientific problems among the younger generation of scientists.  Of course one does not know beforehand what will grow out of the seeds that have been sown in this way when the scientists return into their old environments and again take part in their own cultural traditions.  But one can scarcely doubt that the exchange of ideas between young scientists of different countries and between the different generations in every country will help to approach without too much tension that new state of affairs in which a balance is reached between the older traditional forces and the inevitable necessities of modern life.  It is especially one feature of science which makes it more than anything else suited for establishing the first strong connection between different cultural traditions.  This is the fact that the ultimate decisions about the value of a special scientific work, about what is correct or wrong in the work, do not depend on any human authority.  It may sometimes take many years before one knows the solution of a problem, before one can distinguish between truth and error; but finally the questions will be decided, and the decisions are made not by any group of scientists but by nature itself. Therefore, scientific ideas spread among those who are interested in science in an entirely different way from the propagation of political ideas.

While political ideas may gain a convincing influence among great masses of people just because they correspond or seem to correspond to the prevailing interests of the people, scientific ideas will spread only because they are true.  There are objective and final criteria assuring the correctness of a scientific statement.  All that has here been said about international cooperation and exchange of ideas would of course be equally true for any part of modem science; it is by no means confined to atomic physics.  In this respect modem physics is just one of the many branches of science, and even if its technical applications-the arms and the peaceful use of atomic energy-attach a special weight to this branch, there would be no reason for considering international co-operation in this field as far more important than in any other field.  But we have now to discuss again those features of modem physics which are essentially different from the previous development of natural science, and we have for this purpose once more to go back to the European history of this development that was brought about by the combination of natural and technical sciences.

It has frequently been discussed among the historians whether the rise of natural science after the sixteenth century was in any way a natural consequence of earlier trends in human thinking.  It may be argued that certain trends in Christian philosophy led to a very abstract concept of God, that they put God so far above the world that one began to consider the world without at the same time also seeing God in the world.  The Cartesian partition may be called a final step in this development.  Or one may point out that all the theological controversies of the sixteenth century produced a general discontent about problems that could not really be settled by reason and were exposed to the political struggles of the time; that this discontent favored interest in problems which were entirely separated from the theological disputes.  Or one may simply refer to the enormous activity, the new spirit that had come into the European societies through the Renaissance.  In any case during this period a new authority appeared which was completely independent of Christian religion or philosophy or of the Church, the authority of experience, of the empirical fact.  One may trace this authority back into older philosophical trends, for instance, into the philosophy of Ockham and Duns Scotus, but it became a vital force of human activity only from the sixteenth century onward.  Galileo did not only think about the mechanical motions, the pendulum and the falling stone; he tried out by experiments, quantitatively, how these motions took place.  This new activity was in its beginning certainly not meant as a deviation from the traditional Christian religion.  On the contrary, one spoke of two kinds of revelation of God.  The one was written in the Bible and the other was to be found in the book of nature.  The Holy Scripture has been written by man and is therefore subject to error, while nature is the immediate expression of God’s intentions.

However, the emphasis on experience was connected with a slow and gradual change in the aspect of reality.  While in the Middle Ages what we nowadays call the symbolic meaning of a thing was in some way its primary reality, the aspect of reality changed toward what we can perceive with our senses.  What we can see and touch became primarily real.  And this new concept of reality could be connected with a new activity: we can experiment and see how things really are.  It was easily seen that this new attitude meant the departure of the human mind into an immense field of new possibilities, and it can be well understood that the Church saw in the new movement the dangers rather than the hopes.  The famous trial of Galileo in connection with his views on the Copernican system marked the beginning of a struggle that went on for more than a century.  In this controversy the representatives of natural science could argue that experience offers an undisputable truth, that it cannot be left to any human authority to decide about what really happens in nature, and that this decision is made by nature or in this sense by God.  The representatives of the traditional religion, on the other hand, could argue that by paying too much attention to the material world, to what we perceive with our senses, we lose the connection with the essential values of human life, with just that part of reality which is beyond the material world.  These two arguments do not meet, and therefore the problem could not be settled by any kind of agreement or decision.

In the meantime natural science proceeded to get a clearer and wider picture of the material world.  In physics this picture was to be described by means of those concepts which we nowadays call the concepts of classical physics.  The world consisted of things in space and time, the things consist of matter, and matter can produce and can be acted upon by forces.  The events follow from the interplay between matter and forces; every event is the result and the cause of other events.  At the same time the human attitude toward nature changed from a contemplative one to the pragmatic one.  One was not so much interested in nature as it is; one rather asked what one could do with it.  Therefore, natural science turned into technical science; every advancement of knowledge was connected with the question as to what practical use could be derived from it.  This was true not only in physics; in chemistry and biology the attitude was essentially the same, and the success of the new methods in medicine or in agriculture contributed essentially to the propagation of the new tendencies.

In this way, finally, the nineteenth century developed an extremely rigid frame for natural science which formed not only science but also the general outlook of great masses of people.  This frame was supported by the fundamental concepts of classical physics, space, time, matter and causality; the concept of reality applied to the things or events that we could perceive by our senses or that could be observed by means of the refined tools that technical science had provided.  Matter was the primary reality.  The progress of science was pictured as a crusade of conquest into the material world.  Utility was the watchword of the time.

On the other hand, this frame was so narrow and rigid that it was difficult to find a place in it for many concepts of our language that had always belonged to its very substance, for instance, the concepts of mind, of the human soul or of life.  Mind could be introduced into the general picture only as a kind of mirror of the material world; and when one studied the properties of this mirror in the science of psychology, the scientists were always tempted—if I may carry the comparison further-to pay more attention to its mechanical than to its optical properties.  Even there one tried to apply the concepts of classical physics, primarily that of causality.  In the same way life was to be explained as a physical and chemical process, governed by natural laws, completely determined by causality.  Darwin’s concept of evolution provided ample evidence for this interpretation.  It was especially difficult to find in this framework room for those parts of reality that had been the object of the traditional religion and seemed now more or less only imaginary.  Therefore, in those European countries in which one was wont to follow the ideas up to their extreme consequences, an open hostility of science toward religion developed, and even in the other countries there was an increasing tendency toward indifference toward such questions; only the ethical values of the Christian religion were excepted from this trend, at least for the time being.  Confidence in the scientific method and in rational thinking replaced all other safeguards of the human mind.

Coming back now to the contributions of modern physics, one may say that the most important change brought about by its results consists in the dissolution of this rigid frame of concepts of the nineteenth century.  Of course many attempts had been made before to get away from this rigid frame which seemed obviously too narrow for an understanding of the essential parts of reality.  But it had not been possible to see what could be wrong with the fundamental concepts like matter, space, time and causality that had been so extremely successful in the history of science.  Only experimental research itself, carried out with all the refined equipment that technical science could offer, and its mathematical interpretation, provided the basis for a critical analysis—or, one may say, enforced the critical analysis—of these concepts, and finally resulted in the dissolution of the rigid frame.

This dissolution took place in two distinct stages.  The first was the discovery, through the theory of relativity, that even such fundamental concepts as space and time could be changed and in fact must be changed on account of new experience.  This change did not concern the somewhat vague concepts of space and time in natural language; but it did concern their precise formulation in the scientific language of Newtonian mechanics, which had erroneously been accepted as final.  The second stage was the discussion of the concept of matter enforced by the experimental results concerning the atomic structure.  The idea of the reality of matter had probably been the strongest part in that rigid frame of concepts of the nineteenth century, and this idea had at least to be modified in connection with the new ex­perience.  Again the concepts so far as they belonged to the natural language remained untouched.  There was no difficulty in speaking about matter or about facts or about reality when one had to describe the atomic experiments and their results.  But the scientific extrapolation of these concepts into the smallest parts of matter could not be done in the simple way suggested by classical physics, though it had erroneously determined the general outlook on the problem of matter.

These new results had first of all to be considered a serious warning against the somewhat forced application of scientific concepts in domains where they did not belong.  The application of the concepts of classical physics, eg, in chemistry, had been a mistake.  Therefore, one will nowadays be less inclined to assume that the concepts of physics, even those of quantum theory, can certainly be applied everywhere in biology or other sciences.  We will, on the contrary, try to keep the doors open for the entrance of new concepts even in those parts of science where the older concepts have been very useful for the understanding of the phenomena.  Especially at those points where the application of the older concepts seems somewhat forced or appears not quite adequate to the problem we will try to avoid any rash conclusions.

Furthermore, one of the most important features of the development and the analysis of modem physics is the experience that the concepts of natural language, vaguely defined as they are, seem to be more stable in the expansion of knowledge than the precise terms of scientific language, derived as an idealization from only limited groups of phenomena.  This is in fact not surprising since the concepts of natural language are formed by the immediate connection with reality; they represent reality.  It is true that they are not very well defined and may therefore also undergo changes in the course of the centuries, just as reality itself did, but they never lose the immediate connection with reality.  On the other hand, the scientific concepts are idealizations; they are derived from experience obtained by refined experimental tools, and are precisely defined through axioms and definitions.  Only through these precise definitions is it possible to connect the concepts with a mathematical scheme and to derive mathematically the infinite variety of possible phenomena in this field.  But through this process of idealization and precise definition the immediate connection with reality is lost.  The concepts still correspond very closely to reality in that part of nature which had been the object of the research.  But the correspondence may be lost in other parts containing other groups of phenomena.

Keeping in mind the intrinsic stability of the concepts of natural language in the process of scientific development, one sees that—after the experience of modem physics—our attitude toward concepts like mind or the human soul or life or God will be different from that of the nineteenth century, because these concepts belong to the natural language and have therefore immediate connection with reality.  It is true that we will also realize that these concepts are not well defined in the scientific sense and that their application may lead to various contradic­tions, for the time being we may have to take the concepts, unanalyzed as they are; but still we know that they touch reality.  It may be useful in this connection to remember that even in the most precise part of science, in mathematics, we cannot avoid using concepts that involve contradictions.  For instance, it is well known that the concept of infinity leads to contradictions that have been analyzed, but it would be practically impossible to construct the main parts of mathematics without this concept.

The general trend of human thinking in the nineteenth century had been toward an increasing confidence in the scientific method and in precise rational terms, and had led to a general skepticism with regard to those concepts of natural language which do not fit into the closed frame of scientific thought—for instance, those of religion.  Modem physics has in many ways increased this skepticism; but it has, at the same time turned it against the overestimation of precise scientific concepts, against a too-optimistic view on progress in general, and finally against skepticism itself.  The skepticism against precise scientific concepts does not mean that there should be a definite limitation for the application of rational thinking.  On the contrary, one may say that the human ability to understand may be in a certain sense unlimited.  But the existing scientific concepts cover always only a very limited part of reality, and the other part that has not yet been understood is infinite.  Whenever we proceed from the known into the unknown we may hope to understand, but we may have to learn at the same time a new meaning of the word “understanding.” We know that any understanding must be based finally upon the natural language because it is only there that we can be certain to touch reality, and hence we must be skeptical about any skepticism with regard to this natural language and its essential concepts.  Therefore, we may use these concepts as they have been used at all times.  In this way modern physics has perhaps opened the door to a wider outlook on the relation between the human mind and reality.

This modern science, then, penetrates in our time into other parts of the world where the cultural tradition has been entirely different from the European civilization.  There the impact of this new activity in natural and technical science must make itself felt even more strongly than in Europe, since changes in the conditions of life that have taken two or three centuries in Europe will take place there within a few decades.  One should expect that in many places this new activity must appear as a decline of the older culture, as a ruthless and barbarian attitude, that upsets the sensitive balance on which all human happiness rests.  Such consequences cannot be avoided; they must be taken as one aspect of our time.  But even there the openness of modern physics may help to some extent to reconcile the older traditions with the new trends of thought.  For instance, the great scientific contribution in theoretical physics that has come from Japan since the last war may be an indication for a certain relationship between philosophical ideas in the tradition of the Far East and the philosophical substance of quantum theory.  It may be easier to adapt oneself to the quantum-theoretical concept of reality when one has not gone through the naive materialistic way of thinking that still prevailed in Europe in the first decades of this century.

Of course such remarks should not be misunderstood as an underestimation of the damage that may be done or has been done to old cultural traditions by the impact of technical progress.  But since this whole development has for a long time passed far beyond any control by human forces, we have to accept it as one of the most essential features of our time and must try to connect it as much as possible with the human values that have been the aim of the older cultural and religious traditions.  It may be allowed at this point to quote a story from the Hasidic religion: There was an old rabbi, a priest famous for his wisdom, to whom all people came for advice.  A man visited him in despair over all the changes that went on around him, deploring all the harm done by so-called technical progress.  “Isn’t all this technical nuisance completely worthless,” he exclaimed “if one considers the real values of life?” “This may be so,” the rabbi replied, “but if one has the right attitude one can learn from everything.” “No,” the visitor rejoined, “from such foolish things as railway or telephone or telegraph one can learn nothing whatsoever.” But the rabbi answered, “You are wrong.  From the railway you can learn that you may by being one instant late miss everything.  From the telegraph you can learn that every word counts.  And from the telephone you can learn that what we say here can be heard there.” The visitor understood what the rabbi meant and went away.

Finally, modern science penetrates into those large areas of our present world in which new doctrines were established only a few decades ago as foundations for new and powerful societies.  There modern science is confronted both with the content of the doctrines, which go back to European philosophical ideas of the nineteenth century (Hegel and Marx), and with the phenomenon of uncompromising belief.  Since modern physics must playa great role in these countries because of its practical applicability, it can scarcely be avoided that the narrowness of the doctrines is felt by those who have really understood modern physicsand its philosophical meaning.  Therefore, at this point an interaction between science and the general trend of thought may take place.  Of course the influence of science should not be overrated; but it might be that the openness of modern science could make it easier even for larger groups of people to see that the doctrines are possibly not so important for the society as had been assumed before.  In this way the influence of modern science may favor an attitude of tolerance and thereby may prove valuable.

On the other hand, the phenomenon of uncompromising belief carries much more weight than some special philosophical notions of the nineteenth century. We cannot close our eyes to the fact that the great majority of the people can scarcely have any well-founded judgment concerning the correctness of certain important general ideas or doctrines.  Therefore, the word “belief” can for this majority not mean “perceiving the truth of something” but can only be understood as “taking this as the basis for life.” One can easily understand that this second kind of belief is much firmer, is much more fixed than the first one, that it can persist even against immediate contradicting experience and can therefore not be shaken by added scientific knowledge.  The history of the past two decades has shown by many examples that this second kind of belief can sometimes be upheld to a point where it seems completely absurd, and that it then ends only with the death of the believer.  Science and history can teach us that this kind of belief may become a great danger for those who share it.  But such knowledge is of no avail, since one cannot see how it could be avoided, and therefore such belief has always belonged to the great forces in human history. From the scientific tradition of the nineteenth century one would of course be inclined to hope that all belief should be based on a rational analysis of every argument, on careful deliberation; and that this other kind of belief, in which some real or apparent truth is simply taken as the basis for life, should not exist. It is true that cautious deliberation based on purely rational argu­ments can save us from many errors and dangers, since it allows readjustment to new situations, and this may be a necessary condition for life.  But remembering our experience in modem physics it is easy to see that there must always be a fundamental complementary between deliberation and decision.  In the practical decisions of life it will scarcely ever be possible to go through all the arguments in favor of or against one possible decision, and one will therefore always have to act on insufficient evidence.  The decision finally takes place by pushing away all the arguments—both those that have been understood and others that might come up through further deliberation-and by cutting off all further pondering.  The decision may be the result of deliberation, but it is at the same time complementary to deliberation; it excludes deliberation.  Even the most important decisions in life must always contain this inevitable element of irrationality.  The decision itself is necessary, since there must be something to rely upon, some principle to guide our actions.  Without such a firm stand our own actions would lose all force.  Therefore, it cannot be avoided that some real or apparent truth form the basis of life; and this fact should be acknowledged with regard to those groups of people whose basis is different from our own.

Coming now to a conclusion from all that has been said about modem science, one may perhaps state that modem physics is just one, but a very characteristic, part of a general historical process that tends toward a unification and a widening of our present world.  This process would in itself lead to a diminution of those cultural and political tensions that create the great danger of our time.  But it is accompanied by another process which acts in the opposite direction.  The fact that great masses of people become conscious of this process of unification leads to an instigation of all forces in the existing cultural communities that try to ensure for their traditional values the largest possible role in the final state of unification.  Thereby the tensions increase and the two competing processes are so closely linked with each other that every intensification of the unifying process-for instance, by means of new technical progress-intensifies also the struggle for influence in the final state, and thereby adds to the instability of the transient state.  Modern physics plays perhaps only a small role in this dangerous process of unification.  But it helps at two very decisive points to guide the development into a calmer kind of evolution.  First, it shows that the use of arms in the process would be disastrous and, second, through its openness for all kinds of concepts it raises the hope that in the final state of unification many different cultural traditions may live together and may combine different human endeavors into a new kind of balance between thought and deed, between activity and meditation.