atomic theory and the description of nature
The task of science is both to extend the range of our experience and to reduce it to order, and this task presents various aspects inseparably connected with each other.
Only by experience itself do we come to recognise those laws which grant us a comprehensive view of the diversity of phenomena.
As our knowledge becomes wider, we must always be prepared, therefore, to expect alterations in the points of view best suited for the ordering of our experience
In this connection, we must remember, above all, that as a matter of course, all new experience makes its appearance within the frame of our customary points of view and forms of perception.
The relative prominence accorded to the various aspects of scientific inquiry depends on the nature of the matter under investigation.
In physics, where our problem consists in the co-ordination of our experience of the external world, the question of the nature of our forms of perception will generally be less acute than it is in psychology where it is our own mental activity which is the object under investigation.
Yet occasionally just this “objectivity” of physical observations becomes particularly suited to emphasise the subjective character of all experience
There are many examples of this in the history of science.
I need only mention the great significance that the investigation of acoustical and optical phenomena, the physical media of our senses, has continually had in the development of psychological analysis.
As another example, we may notice the role which the elucidation of the laws of mechanics has played in the development of the general theory of knowledge
In the latest developments of physics, this fundamental feature of science has been particularly prominent.
The great extension of our experience in recent years has brought to light the insufficiency of our simple mechanical conceptions and, as a consequence, has shaken the foundation on which the customary interpretation of observations was based, thus throwing new light on old philosophical problems.
This is true not only of the revision of the foundations of the space-time mode of description brought about by the theory of relativity but also of the renewed discussion of the principle of causality which has emerged from the quantum theory.
The origin of the theory of relativity is closely bound up with the development of electromagnetic concepts, a development which, by extending the notion of force, has brought about such a profound transformation of the ideas underlying mechanics.
The recognition of the relative character of the phenomena of motion being dependent upon the observer had already played an essential part in the development of classical mechanics, where it served as an effective aid in the formulation of general mechanical laws.
For the time being, one succeeded in giving an apparently satisfactory treatment of the questions under discussion, both from a physical as well as from a philosophical point of view.
It was, in fact, first the recognition, brought about by the electro-magnetic theory, of the finite velocity of propagation of all actions of force which brought the matter to a climax
It is true that it was possible, on the basis of the electro-magnetic theory, to set up a causal mode of description which retained the fundamental mechanical laws of the conservation of energy and momentum, provided one ascribed energy and momentum to the fields of force themselves.
However, the conception of a universal ether, which was so useful in the development of the electromagnetic theory, appeared in this theory as an absolute frame of reference for the space-time description.
The unsatisfactory character of this conception, from a philosophical point of view, was strongly emphasized by the failure of all attempts to demonstrate the motion of the earth relative to this hypothetical universal ether, and this situation was not improved by the recognition that the failure of all such attempts was in complete agreement with the electromagnetic theory.
It was Einstein’s elucidation of the limitation which the finite velocity of propagation of all force effects, including those of radiation, imposes upon the possibilities of observation, and, therefore, upon the application of the space-time concepts, that first led us to a more liberal attitude towards these concepts, an attitude which found its most striking expression in the recognition of the relativity of the concept of simultaneity.
As we know, Einstein, adopting this attitude, succeeded in tracing significant new relationships also outside the domain to which the electromagnetic theory properly applies, and in his general theory of relativity, in which the effects of gravitation no longer occupy a special position among physical phenomena, he has approached, to a quite unexpected degree, the unity in the description of nature which is the ideal of the classical physical theories
The quantum theory arose out of the development of atomic conceptions, which, during the course of the last century, had increasingly provided a fruitful field for the application of mechanics and of the electromagnetic theory
In the years near the beginning of this century, however, the application of these theories to atomic problems was destined to reveal a hitherto unnoticed limita tion that its expression in Planck’s discovery of the so-called quantum of action, which imposes upon individual atomic processes an element of discontinuity quite foreign to the fundamental principles of classical physics, according to which all actions may vary in a continuous manner
The quantum of action has become increasingly indispensable in the ordering of our experi mental knowledge of the properties of atoms.
At the same time, however, we have been forced step by step to forego a al description of the behaviour of individual atoms in space and time, and to reckon with a free choice on the part of nature between various possibilities to which only probability considerations can be applied.
The endeavours to formulate general laws for these possibilities and probabilities by a suitably limited application of the concepts of the classical theories have led recently, after a series of phases in its development, to the creation of a rational quantum mechanics by means of which we are able to describe a very wide range of experience, and which may be regarded in every respect as a generalization of the classical physical theories.
In addition, we have gradually reached a complete understanding of the intimate connection between the renunciation of causality in the quantum-mechanical description and the limitation with regard to the possibility of distinguishing between phenomena and their observation, which is conditioned by the indivisibility of the quantum of action
The recognition of this situation implies an essential change in our attitude towards the principle of causality as well as towards the concept of observation.
In spite of many points in which they differ there is a profound inner similarity between the problems met with in the theory of relativity and those which are encountered in the quantum theory
in both cases we are concerned with the recognition of physical laws which lie outside the domain of our ordinary experience and which present difficulties to our accustomed forms of perception.
We learn that these forms of perception are idealizations, the suitability of which for reducing our ordinary sense impressions to order depends upon the practically infinite velocity of light and upon the smallness of the quantum of action.
In appraising this situation, however, we must not forget that, in spite of their limitation, we can by no means dispense with those forms of perception which colour our whole language and in terms of which all experience must ultimately be expressed.
It is just this state of affairs which primarily gives to the problems in question their general philo sophical interest.
While the finish given to our picture of the world by the theory of relativity has already been absorbed into the general scientific consciousness, this has scarcely occurred to the same extent with those as pects of the general problem of knowledge which have been elucidated by the quantum theory
When I was requested to write a paper the 1929 of the University of Copenhagen, I first intended to give, in the simplest possible form, an account of the new points of view brought about by the quantum theory, starting from an analysis of the elementary concepts on which our description of nature is founded
However, my occupation with other duties did not leave me sufficient time to complete such an account, the difficulty of which arose, not least, from the continuous development of the points of view in question.
Sensing difficulty, I gave up the idea of preparing a new exposition and was led to consider using instead a translation into Danish, made for this occasion, of some articles which, during recent years, I have published in foreign journals as contributions to the discussion of the problems of the quantum theory.
These articles belong to a series of lectures and papers in which, from time to time, I have attempted to give a coherent survey of the state of the atomic theory at the moment.
Some previous articles of this series form in some respects a background for the three articles which are reproduced here.
This is particularly true of a lecture entitled “The Structure of Atoms”, which was given in Stockholm in December 1922, and which was published at the time as a supplement of Nature
The articles here reproduced appear formally quite independent, however they are intimately connected with each other, in that they all discuss the latest phase in the development of the atomic theory, a phase in which the analysis of the fundamental concepts has become so prominent.
The fact that the articles follow the course of the development, and thus give an immediate impression of the gradual elucidation of the concepts, may perhaps help in some measure to make the subject more easily accessible to those readers who do not belong to the narrow circle of physicists.
In the following notes on the particular circumstances under which the articles appeared I have attempted, by the addition of some guiding remarks, to facilitate a general view of the contents and, as far as possible, to make up for such shortcomings of the exposition as might present difficulties to a wider circle of readers
The first article is an elaboration of a lecture delivered at the Scandinavian Mathematical Congress at Copenhagen in August 1925.
It gives in a condensed form a survey of the development of the quantum theory up to that time when a new phase was being ushered in by the paper of Heisenberg which is discussed at the close of the article.
The lecture deals with the application of the mechanical concepts within the atomic theory, and shows how the ordering of a vast amount of experimental data with the help of the quantum theory had prepared the way for the new development, which is characterized by the creation of rational quantum-mechanical methods.
Above all, the previous development had led to the recognition of the impossibility of carrying out coherent causal description of atomic phenomena.
A conscious resignation in this respect is already implied in the form, irrational from the point of view of the classical theories, of those postulates, mentioned in the article, upon which the author based his application of the quantum theory to the problem of atomic structure.
The fact that all changes in the state of an atom are described in agreement with the requirement of the indivisibility of the quantum of action, as individual processes by which the atom goes over from one so-called stationary state into another stationary state and for the occurrence of which only probability considerations can be made, must, on one hand, greatly limit the field of application of the classical theories.
On the other hand the necessity of making an extensive use, nevertheless of the classical concepts, upon which depends ultimately the interpretation of all experience, gave rise to the formulation of the so-called correspondence principle which expresses our endeavours to utilize all the classical concepts by giving them a suitable quantum-theoretical re-interpretation.
The detailed analysis of the experimental data from this point of view was, however destined to show more and more clearly that we did not then possess sufficiently adequate expedients for caring out a strict description based upon the correspondence principle
Owing to the special occasion on which the lecture was delivered, special emphasis has been placed in the article upon that employment of mathematical aids which is peculiar to theoretical physics.
The symbolical forms of expression of mathematics are here not merely indispensable tools for describing quantitative relationships, but they furnish at the same time an essential means for the elucidation of the general qualitative points of view.
The hope expressed at the conclusion of the article that mathematical analysis would again prove capable of assisting the physicist to surmount his difficulties has in the meantime been fulfilled beyond all expectations.
Not only was abstract algebra destined to play a decisive part in the formulation of Heisenberg’s quantum mechanics, as mentioned in the article, but the theory of differential equations-the most important of the expedients of classical physics was almost immediately afterwards to be extensively applied to atomic problems.
The point of departure for this application was the peculiar analogy between mechanics and optics upon which already Hamilton had based his important contribution to the development of the methods of classical mechanics.
The significance of this analogy for the quantum theory was first pointed out by de Broglie who in connection with Einstein’s well-known theory of light quanta, compared the motion of a particle with the propagation of wave systems.
As de Broglie pointed out, this comparison made it possible to give a simple geometrical meaning to the quantization rules, mentioned in the article, for the stationary states of the atoms.
By a further development of these considerations, Schrödinger succeeded in reducing the quantum-mechanical problem to the solution of a certain differential equation, the so-called Schrödinger wave equation, thus providing us with a method that has played a decisive rôle in the great development which the atomic theory has undergone in the last few years
The second article is an elaboration of a paper read before an international congress of physicists which took place at Como in September 1927 at the centenary of Volta’s death.
By this time the above-mentioned quantum-mechanical methods had reached a high degree of perfection and had demonstrated their fruitfulness in numerous applications
Yet, a divergence of opinion had arisen with regard to the physical interpretation of the methods, and this had led to much discussion.
Especially had the great success of Schrödinger’s wave mechanics revived the hopes of many physicists of being able to describe atomic phenomena along lines similar to those of classical physical theories without introducing irrationalities of the kind which had thus far been characteristic of the quantum theory.
In opposition to his view, it is maintained in the article that the fundamental postulate of the indivisibility of the quantum of action is itself, from the classical point of view, an irrational element which inevitably requires us to for a the causal mode of description and which, because of coupling between phenomena and their observation, forces us to adopt a new mode of description designated as complementary in the sense that any given application of classical concepts precludes the simultaneous use of other classical concepts which in a different connection are equally necessary for the elucidation of the phenomena.
It is pointed out that we immediately encounter this feature when considering the questions of the nature of light and of matter.
It had already been emphasized in the first article that, in our description of radiation phenomena, we are faced with a dilemma as regards the choice between the wave description of the electromagnetic theory and the corpuscular conception of the propagation of light in the theory of light quanta.
With regard to matter, the confirmation which, in the meantime, de Broglie’s wave ideas had received by the well-known experiments on the reflection of electrons by metal crystals placed us before a quite similar dilemma, since there can be no question of giving up the idea of the individuality of the elementary particles; for this individuality forms the secure foundation on which the whole of the recent development of the atomic theory depends
The main purpose of the article is to show that this feature of complementarity is essential for a consistent interpretation of the quantum-theoretical methods.
A very significant contribution to this discussion had been given shortly before by Heisenberg, who had pointed out the close connection between the limited applic ability of mechanical concepts and the fact that any measurement which aims at tracing the motions of the elementary particles introduces an unavoidable interference with the course of the phenomena and so in cludes an element of uncertainty which is determined by the magnitude of the quantum of action.
This indeterminacy exhibits, indeed, a peculiar complementary character which prevents the simultaneous use of space time concepts and the laws of conservation of energy and momentum, which is characteristic of the mechanical mode of description.
To understand why a causal description is impracticable, however, it is essential to remember, as shown in the article, that the magnitude of the disturbance caused by a measurement is always unknown, since the limitation in question applies to any use of mechanical concepts and, hence, applies to the agencies of observation as well as to the phenomena under investigation.
This very circumstance carries with it the fact that any observation takes place at the cost of the connection between the past and the future course of phenomena.
As already mentioned, the finite magnitude of the quantum of action prevents altogether a sharp distinction being made between a phenomenon and the agency by which it is observed, a distinction which underlies the customary concept of observation and therefore, forms the basis of the classical ideas of motion
With this in view, it is not surprising that the physical content of the quantum-mechanical methods is restricted to a formulation of statistical regularities in the relation ships between those results of measurement which characterize the various possible courses of the phenomena.
It is emphasized in the article that the symbolical garb of the methods in question closely corresponds to the fundamentally unvisualizable character of the problems concerned.
We come across a particularly characteristic example of the limitation imposed upon the possibility of applying mechanical ideas when we employ the concept of stationary states which, as mentioned above, even before the development of the quantum-mechanical methods, entered as an essential element in the application of the quantum theory to problems of atomic structure.
As shown in the article, any use of this concept excludes the possibility of tracing the motion of the individual particles within the atom.
We are here concerned with a characteristic complementarity analogous to that which we encounter when considering the questions of the nature of light and of matter.
As explained in detail the concept of stationary states may indeed be said to possess, within its field of application, just as much, or, if one prefers, just as little “reality” as the elementary particles themselves.
In each case we are concerned with expedients which enable us to express in a consistent manner essential aspects of the phenomena.
Besides when we use the concept of stationary states, the necessity in the quantum theory of paying attention to the delimitation of phenomena and, as emphasized already in the first paragraph of the article, of distinguishing strictly between closed and unclosed systems, is brought before us in a very instructive manner.
Hence, in the case of atoms, we come upon a particularly glaring failure of the causal mode of description when accounting for the occurrence of radiation processes.
While, when following the motions of free particles, we can visualize the lack of causality by considering our lack of simultaneous knowledge of the quantities entering into the classical mechanical description, the limited applicability of classical concepts is immediately evident in our account of the behaviour of atoms, since the description of the state of a single atom contains absolutely no element referring to the occurrence of transition processes, so that in this case we can scarcely avoid speaking of a choice between various possibilities on the part of the atom.
In connection with the question of the fundamental properties of the elementary particles, it may perhaps be of interest to call attention to a peculiar complementarity recently disclosed.
The fact that the experiments, which so far have been explained by ascribing a magnetic moment to electrons, have been given a natural interpretation by Dirac’s theory, briefly discussed in the last paragraph of the article, is, indeed, equivalent to saying that it is not possible to detect the magnetic moment of an electron by experiments based upon a direct observation of its motion.
The difference between free electrons and atoms, which we come upon here, is connected with the fact that measurements of the magnetic moment of atoms involve a renunciation, in accordance with the general conditions holding for the application of the concept of stationary states, of all attempts to trace the motion of the elementary particles
The important task, touched upon at the close of the article, of satisfying the general demand for relativity within the frame of the quantum theory, has not as yet carried out satisfactorily.
Indeed, the above mentioned theory of although a step forward in respect, has brought to light new difficulties.
The recognition of these, however, may lead to the development of new points of view with regard to the profound problems presented by the very existence of elementary particles.
While the present quantum-mechanical description depends upon a re-interpretation, based on the correspondence principle, of the classical electron theory, the classical theories offer no guide whatever to the understanding of the existence of the elementary particles themselves and of their specific mass and electrical charge.
We must, therefore, be prepared to find that further advance into this region will require a still more extensive renunciation of features which we are accustomed to demand of the space-time mode of description than the quantum theory attack on the atomic problem has required thus far, and we must be prepared to expect new surprises with regard to the applicability of the concepts of momentum and energy
The extensive use of mathematical symbols which is peculiar to the methods of quantum mechanics makes it difficult to give a true impression of the beauty and logical consistency of these methods without going into mathematical details.
Although in the preparation of this article I have endeavoured, as far as possible, to avoid the use of mathematical artifices, yet the purpose of the lecture, delivered before a group of physicists, to open a discussion on the present tendency in the development of the quantum theory, has made it necessary to go into details which will doubtless make it difficult for readers not somewhat acquainted beforehand with the subject.
However, I wish to point out that throughout the article the main emphasis has been placed upon that purely epistemological attitude which is particularly apparent in the first section and in the concluding remarks
In the third article, which is a contribution to a jubilee pamphlet published in June 1929 to celebrate the fiftieth anniversary of Planck’s doctorate, I have discussed in more detail the general philosophical aspects of the quantum theory.
Partly in view of the regret, so widely expressed, with regard to the renunciation of a strictly causal mode of description for atomic phenomena, the writer attempts to show that the difficulties concerning our forms of perception, which arise in the atomic theory because of the indivisibility of the quantum of action, may be considered as an instructive reminder of the general conditions underlying the creation of man’s concepts.
The impossibility of distinguishing in our customary way between physical phenomena and their observation places us, indeed, in a position quite similar to that which is so familiar in psychology where we are continually reminded of the difficulty of distinguishing between subject and object.
It may perhaps appear at first sight that such an attitude towards physics would leave room for a mysticism which is contrary to the spirit of natural science.
However, we can no more hope to attain to a clear understanding in physics facing the culties arising in the shaping of concepts in the use of the medium of expression than we
can in other fields of human inquiry.
Thus, according to the view of the author, it would be a misconception to believe that the difficulties of the atomic theory may be evaded by eventually replacing the concepts of classical physics by new conceptual forms.
Indeed, as already emphasized, the recognition of the limitation our forms of perception by no means implies that we can dispense with our customary ideas or their direct verbal expressions when reducing our sense impressions to order.
No more is it likely that the fundamental concepts of the classical theories will ever become superfluous for the description of physical experience.
The recognition of the indivisibility of the quantum of action, and the determination of its magnitude, not only depend on an analysis of measurements based on classical concepts, but it continues to be the application of these concepts alone that makes it possible to the symbolism of the quantum theory to the data of experience.
At the same time, however, we must bear in mind that the possibility of an unambiguous use of these fundamental concepts solely depends upon the self-consistency of the classical theories from which they are derived and that, therefore, the limits imposed upon the application of these concepts are naturally determined by the extent to which we may, in our account of the phenomena, disregard the element which is foreign to classical theories and symbolized by the quantum of action.
It is just this state of affairs that is so evident in the frequently discussed dilemma with regard to the properties of light and of matter.
Only in terms of the classical electromagnetic theory is it at all possible to give a tangible content to the question of the nature of light and of matter.
It is true that light quanta and matter waves are invaluable expedients in the formulation of the statistical laws governing such phenomena as the photo-electric effect and the interference of electron rays.
However, these phenomena belong, indeed, to a domain in which it is essential to take into account the quantum of action and where an unambiguous description is impossible.
The symbolical character, in this sense, of the artifices mentioned also becomes apparent in that an exhaustive description of the electromagnetic wave fields leaves no room for light quanta and in that in using the conception of matter waves, there is never any question of a complete description similar to that of the classical theories.
Indeed, as emphasized in the second article, the absolute value of the so-called phase of the waves never comes into consideration when interpreting the experimental results.
In this connection, it should also be emphasized that the term probability amplitude” for the amplitude functions of the matter waves is part of a mode of expression which, although often convenient, can, nevertheless, make no claim to possessing general validity.
As mentioned above, only with the help of classical ideas is it possible to ascribe an unambiguous meaning to the results of observation.
We shall, therefore, always beconcerned with applying probability considerations to the outcome of experiments which may be interpreted in terms of such conceptions.
Consequently, the use made of the symbolic expedients will in each individual case depend upon the particular circumstances pertaining to the experimental arrangement.
Now, what gives to the quantum-theoretical description its peculiar characteristic is just this, that in order to evade the quantum of action we must use separate experimental arrangements to obtain accurate measure ments of the different quantities, the simultaneous knowledge of which would be required for a complete description based upon the classical theories, and, further, that these experimental results cannot be supplemented by repeated measurements.
In fact, the indivisibility of the quantum of action demands that, when any individual result of measurement is interpreted in terms of classical conceptions, a certain amount of latitude be allowed in our account of the mutual action between the object and the means of observation.
This implies that a subsequent measurement to a certain degree deprives the information given by a previous measurement of its significance for predicting the future course of the phenomena
Obviously, these facts not only set a limit to the extent of the information obtainable by measurements, but they also set a limit to the meaning which we may attribute to such information.
We meet here in a new light the old truth that in our description of nature the purpose is not to disclose the real essence of the phenomena but only to track down, so far as it is possible, relations between the manifold aspects of our experience
It is against this background that we must judge the difficulties which we come upon if we attempt to give a correct impression of the content of the quantum theory and of its relation to the classical theories.
As already emphasized when discussing the second article, these questions can be fully elucidated only in terms of the mathematical symbolism which has made it possible to formulate the quantum theory as a rigorous re-interpretation, based upon the idea of correspondence, of the classical theories.
In view of the reciprocal symmetry peculiar to the use of the classical concepts in this symbolism, the writer in this article has preferred the term reciprocity to the word “complementarity used in the preceding article to denote the relation of mutual exclusion characteristic of the quantum theory with regard to the application of the various classical concepts and ideas.
Meanwhile, as the result of further discussion it has come to my notice that the former term may be misleading because the word “reciprocity” is frequently used in the classical theories with a quite different meaning.
The term complementarity which is already coming into use, may perhaps be more suited also to remind us of the fact that it is the combination of features which are united in the classical mode of description but appear separated in the quantum theory that ultimately allows us to consider the latter as a natural generalization of the classical physical theories.
Moreover, the purpose of such a technical term is to avoid, so far as possible, a repetition of the general argument as well as constantly to remind us of the difficulties which, as already mentioned, arise from the fact that all our ordinary verbal expressions bear the stamp of our customary forms of perception, from the point of view of which the existence of the quantum of action is an irrationality.
Indeed, in consequence of this state of affairs, even words like “to be” and “to know” lose their unambiguous meaning.
In this connection, an interesting example of ambiguity in our use of language is provided by the phrase used to express the failure of the causal mode of description, namely, that one speaks of a free choice on the part of nature.
Indeed, properly speaking, such a phrase requires the idea of an external chooser, the existence of which, however, is denied already by the use of the word nature.
We here come upon a fundamental feature in the general problem of knowledge, and we must realize that, by the very nature of the matter, we shall always have last recourse to a word picture, in which the words themselves are not further analyzed.
As emphasized in the article, we must, indeed, remember that the nature of our consciousness brings about a complementary reations in all domains of knowledge, between the analysis of a concept and its immediate application
The reference to certain psychological problems in the latter part of the article has a twofold purpose.
The analogies with some fundamental features of the quantum theory, exhibited by the laws of psychology, may not merely make it easier for us to adjust ourselves to the new situation in physics, but it is perhaps not too ambitious to hope that the lessons we have learned from the very much simpler physical problems will also prove of value in our endeavours to obtain a comprehensive survey of the more subtle psychological questions.
As stressed in the article, it is clear to the writer that for the time being we must be content with more or less appropriate analogies.
Yet it may well be that behind these analogies there lies not only a kinship with regard to the epistemological aspects, but that a more profound relationship is hidden behind the fundamental biological problems which are directly connected to both sides
Although it cannot yet be said that the quantum theory has contributed essentially to the elucidation of the latter problems, still there is much which indicates that we are concerned here with questions which closely approach the circle of ideas of the quantum theory.
Indeed, living organisms are first of all characterized by the sharp separation of the individuals from the outside world and their great ability to react to external stimuli.
It is very suggestive that this ability, at least so far as sight impressions are concerned, is developed to the utmost limit permitted by physics; for, as has often been remarked, only a few light quanta are needed to produce a visual sensation.
Nevertheless, it is obviously a quite open question whether the information we have acquired of the laws describing atomic phenomena provides us with a sufficient basis for tackling the problem of living organisms, or whether, hidden behind the riddle of life there lie yet unexplored aspects of epistemology.
Whatever the development in this domain may be, we have, as emphasized at the close of the article, every reason to rejoice that, within the relatively objective domain of physics, where emotional elements are so largely relegated to the background, we have encountered problems capable of reminding us anew of the general conditions underlying all human understanding, which from time immemorial, have attracted the attention of philosophers
Addendum (1931). The fourth article, which is an elaboration of a lecture delivered before the Scandinavian Meeting of Natural Scientists in 1929, is closely related to the other three articles, since it attempts to give a survey, against the same background, of the place of the atomic theory in the description of nature.
In particular, it was my desire to emphasize that, despite the great success attending the discovery of the building stones of a discovery depending on the application of classical concepts-the development of the atomic theory has, nevertheless, first of all given us a recognition of laws which cannot be included within the same formed by our accustomed modes of perception
As already indicated above, the lessons we have learned by the discovery of the quantum of action open up to us new prospects which may perhaps be of decisive importance, particularly in the discussion of the position of living organisms in our picture of the world
If, according to the ordinary usage, we speak of a machine as dead, this only means that we can give a description, sufficient for our purpose, of its working in terms of the conceptual forms of classical mechanics
However, in view of the present recognition of the insufficiency of classical concepts in the domain of atomic theory this criterion of the inanimate is no longer suit far as atomic phenomena are concerned.
Nevertheless, even the quantum mechanics may hardly depart sufficiently from the mode of description of classical characteristic capable of mastering the mechanics to be laws of life.
In this connection, however, we must remember that the investigation of the phenomena of life not only leads us, as emphasized in the article, into that domain of atomic theory where the usual idealization of a sharp distinction between phenomena and their observation breaks down, but that, in addition, there is set a fundamental limit to the analysis of the phenomena of life in terms of physical concepts, since the interference necessitated by an observation which would be as complete as possible from the point of view of the atomic theory would cause the death of the organism.
In other words: the strict application of those concepts which are adapted to our description of imanimate nature might stand in a relationship of exclusion to the consideration of the laws of phenomena of life
In exactly the same way as it is only possible on the basis of the fundamental complementarity between the applicability of the concept of atomic states and the coordination of the atomic particles in space and time to account, in a rational manner, for the characteristic stability of the properties of atoms, so might the peculiarity of the phenomena of life, and in particular the self stabilizing power of organisms, be inseparably connected with the fundamental impossibility of a detailed analysis of the physical conditions under which life takes place.
To put it briefly, one might perhaps say that quantum mechanics is concerned with the statistical behaviour of a given number of atoms under well-defined external conditions, while we are unable to define the state of a living being in terms of atomic measures in fact, owing to the metabolism of the organism, it is not even possible to ascertain what atoms actually belong to the living individual.
In this respect, the domain of the statistical quantum mechanics, which is based on the correspondence argument, occupies an intermediate position between the domain of applicability of the ideal of causal space-time mode of description and the domain of biology which is characterized by teleological arguments
Although, put in the above way, this idea concerns only the physical aspect of the problem, it may perhaps also be suited to form a background for the ordering of the psychical aspects of life.
As explained in the third article, and also touched upon above, the unavoidable influencing by introspection of all psychical experience, that is characterized by the feeling of volition, for the striking similarity to the conditions responsible for the failure of causality in the analysis of atomic phenomena
Above all, as indicated there, an essential refinement of interpretation, originally based on physical causality our of the psycho-physical parallelism ought to result from our taking into consideration the unpredictable modification of psychical experience produced by any attempt at an objective tracing of the accompanying physical processes in central nervous system.
With regard to this, however, it must not be forgotten that, in associating the psychical and physical aspects of existence, we are concerned with a special relationship of complementarity which it is not possible thoroughly to understand by one-sided application either of physical or of psychological laws.
In consideration of the general lessons we have learned from the atomic theory, it would also seem likely that only a renunciation in this respect will enable us to comprehend, in the sense explained more fully in the fourth article, that harmony which is experienced as free will and analyzed in terms of causality.
Atomic Theory and Mechanics (1925)
1. THE CLASSICAL THEORIES
The analysis of the equilibrium and the motion of bodies not only forms the the foundation of phsics, but for mathematical reasoning has also furnished a rich field, which has been exceedingly fertile for the development of pure mathematics