Are There Quantum Jumps? Part I The British Society for the Philosophy of Science Are There Quantum Jumps? Part I Author(s): E. Schrödinger Source: The British Journal for the Philosophy of Science, Vol. 3, No. 10 (Aug., 1952), pp. 109-123 Published by: Oxford University Press on behalf of The British Society for the Philosophy of Science Stable URL: http://www.jstor.org/stable/685552 . Accessed: 07/04/2013 17:23 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . Oxford University Press and The British Society for the Philosophy of Science are collaborating with JSTOR to digitize, preserve and extend access to The British Journal for the Philosophy of Science. http://www.jstor.org This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/action/showPublisher?publisherCode=oup http://www.jstor.org/action/showPublisher?publisherCode=bsps http://www.jstor.org/stable/685552?origin=JSTOR-pdf http://www.jstor.org/page/info/about/policies/terms.jsp http://www.jstor.org/page/info/about/policies/terms.jsp The British Journal for the Philosophy of Science VOLUME III AUGUST, 1952 No. Io ARE THERE QUANTUM JUMPS? PART I* E. SCHRODINGER . cominciai a credere, che uno, che lascia un'opinione imbevuta col latte, e seguita da infiniti, per venire in un' altra da pochissimi seguita, e negata da tutte le scuole, e che veramente sembra un paradosso grandissimo, bisognasse per necessitY, che fusse mosso, per non dir forzato, da ragioni pid efficaci.' Galileo, Dialogue on the Two Greatest World Systems, 2nd Day. I The Cultural Background PHYSICAL science, which aims not only at devising fascinating new experiments, but at obtaining a rational understanding of the results of observations, incurs at present, so I believe, the grave danger ot getting severed from its historical background. The innovations of thought in the last 50 years, great and momentous and unavoidable as they were, are usually overrated compared with those of the pre- ceding century; and the disproportionate foreshortening by time- perspective, of previous achievements on which all our enlighten- ment in modern times depends, reaches a disconcerting degree accord- ing as earlier and earlier centuries are considered. Along with this disregard for historical linkage there is a tendency to forget that all science is bound up with human culture in general, and that scientific findings, even those which at the moment appear the most advanced and esoteric and difficult to grasp, are meaningless outside their cultural context. A theoretical science, unaware that those of its constructs considered relevant and momentous are destined eventually to be * Received 28. iv. 52 H IO9 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp E. SCHRODINGER framed in concepts and words that have a grip on the educated com- munity and become part and parcel of the general world picture- a theoretical science, I say, where this is forgotten, and where the initiated continue musing to each other in terms that are, at best, understood by a small group of close fellow travellers, will necessarily be cut off from the rest of cultural mankind; in the long run it is bound to atrophy and ossify, however virulently esoteric chat may continue within its joyfully isolated groups of experts. This has happened before in similar circumstances. Benjanun Farrington puts it admirably in his Greek Science,1 vol. 2, p. 173 : 'Perhaps the most decisive defeat of the scientific spirit in antiquity had been the loss of the sense of history. History is the most funda- mental science, for there is no human knowledge which cannot lose its scientific character when men forget the conditions under which it originated, the questions which it answered, and the functions it was created to serve. A great part of the mysticism and superstition of educated men consists of knowledge which has broken loose from its historical moorings.' The disregard for historical connectedness, nay the pride of embarking on new ways of thought, of production and of action, the keen endeavour of shaking off, as it were, the indebtedness to our predecessors, are no doubt a general trend of our time. In the fine arts we notice strong currents quite obviously informed by this vein; we witness its results in modern painting, sculpture, architecture, music and poetry. There are many who look upon this as a new buoyant rise, while others regard it as a flaring up that inaugurates decay. It is not here the place to dwell on this question, and my personal views on it might interest nobody. But I may say that whenever this trend enters science, it ought to be opposed. There obviously is a certain danger of its intruding into science in general, which is not an isolated enterprise of the human spirit, but grows on the same historic soil as the others and participates in the mood of the age. There is, however, so I believe, no other nearly so blatant example of this happening as the theories of physical science in our time. I believe that we are here facing a development which is the precise counterpart of that in the fine arts alluded to above. The most appropriate expression to use for it is one borrowed from the history of poetry : G6ngorism. It refers to the poetry of the Spaniard Luis de G6ngora (156I-I627), very fine poems, by the way, 1 Pelican Books, London, 1949 IIO This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp ARE THERE QUANTUM JUMPS? especially the early ones. Yet also his later poems (to which the term more particularly refers) are well sounding and they all make sense. But he uses all his acuity and skill on making it as difficult as possible to the reader to unravel the sense, so that even natives of Castile use extended commentaries to grasp the meaning safely. One ought not, I think, to say that if, in this, physics is following a general trend of our time, we must not oppose it. Though we are entirely the product of historical development, yet it is we who make its continuation and not history that drags us along a predestined trail. It depends entirely on us, on our stopping to think and acting according to reason, whether there will be decay or a new rise after the crisis. This is what Bertrand Russell in recent years has not tired to inculcate with regard to much more momentous questions than the fate of theoretical physics. However, here we shall be concerned with the latter. My friend and scientific colleague Professor Hans Thirring, in his book Homo Sapiens,' in which he conducts an elaborate and very creditable campaign against War, and for Universal Peace, incidentally opines that in antiquity everybody except a few men of genius considered the earth to be a flat disk. Professor E. P. Wigner, in an article on ' The Limits of Science ' 2 is in doubt whether to date the ' birthyear' of chemistry around 1780 (Lavoisier) or at 18o8 (Dalton's law). Physics, he says, is somewhat older, since Newton's Principia became available in 1687. He grants that 'Archimedes discovered laws of physics around 2S50 B.C. but his discoveries can hardly be called the real beginning of physics.' I must not take up space by refuting these strange views, but refer the reader to Professor Benjamin Farrington's two excellent Pelican books on Greek Science. Still I would mention that among the 'insignificant' discoveries of that period was the inference, drawn (probably by Archimedes) from the heliocentric system of Aristarchus, that the fixed stars must be at least at a distance of, in our units, about two light years ; and the further conclusion that from there the sun would appear as a faint star, and therefore, inversely, many of those stars must equal and even exceed the sun in size--or luminosity, as we would call it today. Of course scientific knowledge takes some time to get a grip on the cultured community. Charles Darwin tells us in the Voyage of a Naturalist of the sensation he caused in 1833 among the 1 Wien, 1948 2 Proc. Am. Philosoph. Soc. 1950, 94, 422 III This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp E. SCHRODINGER 'educated' society in Argentine by telling them that the earth is a sphere. This knowledge was then more than 2,300 years old. What has all this to do with quantum jumps ? I have been trying to produce a mood that makes one wonder what parts of con- temporary science will still be of interest to others than historians 2,000 years hence. There have been ingenious constructs of the human mind that gave an exceedingly accurate description of observed facts and have yet lost all interest except to historians. I am thinking of the theory of epicycles. I confess to the heretical view that their modern counterpart in physical theory are the quantum j umps. Or rather these correspond to the circles which the sun, the moon and the stars were thought to describe around the earth in 24 hours after earlier and better knowledge had been condemned. I am reminded of epicycles of various orders when I am told of the hierarchy of virtual quantum transitions. But let these rude remarks not deter you. We shall now come to grips with the subject proper. 2 The Discontinuous States as Proper Modes Max Planck's essential step in 1900, amounted, as we say now, to laying the foundation of quantum theory; it was his discovery, by abstract thought, of a discontinuity where it was least expected, namely in the exchange of energy between an elementary material system (atom or molecule) and the radiation of light and heat. He was at first very reluctant to draw the much more incisive conclusion that each atom or molecule had only to choose between a discrete set of 'states'; that it could normally only harbour certain discrete amounts of energy, sharply defined and characteristic of its nature; that it would normally find itself on one of these ' energy levels' (as the modern expression runs)-except when it changes over more or less abruptly from one to another, radiating its surplus energy to the surrounding, or absorbing the required amount from there, as the case may be. Planck was even more hesitant to adopt the view that radiation itself be divided up into portions or light-quanta or 'photons,' to use the present terminology. In all this his hesitance had good reasons. Yet only a few years later (1905) Einstein advanced the hypothesis of light-quanta, clinching it with irresistible arguments; and in 1913 Niels Bohr, by taking the discrete states of the atoms seriously and extending Planck's assumptions in two directions with great ingenuity, but irrefutable consistency, could explain quantita- II2 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp ARE THERE QUANTUM JUMPS? tively some of the atomic line spectra, which are all patently discrete, and which had in their entirety formed a great conundrum up to then : Bohr's theory turned them into the ultimate and irrevocable direct evidence, that the discrete states are a genuine and real fact. Bohr's theory held the ground for about a dozen of years, scoring a grand series of so marvellous and genuine successes, that we may well claim excuses for having shut our eyes to its one great deficiency: while describing minutely the so-called 'stationary' states which the atom had normally, i.e. in the comparatively uninteresting periods when nothing happens, the theory was silent about the periods of transition or 'quantum jumps' (as one then began to call them). Since intermediary states had to remain disallowed, one could not but regard the transition as instantaneous ; but on the other hand, the radiating of a coherent wave train of 3 or 4 feet length, as it can be observed in an interferometer, would use up just about the average interval between two transitions, leaving the atom no time to 'be' in those stationary states, the only ones of which the theory gave a description. This difficulty was overcome by quantum mechanics, more especially by wave mechanics, which furnished a new description of the states; this was precisely what was still missing in the earliest version of the new theory which had preceded wave mechanics by about one year. The previously admitted discontinuity was not abandoned, but it shifted from the states to something else, which is most easily grasped by the simile of a vibrating string or drumhead or metal plate, or of a bell that is tolling. If such a body is struck, it is set vibrating, that is to say it is slightly deformed and then runs in rapid succession through a continuous series of slight deformations again and again. There is, of course, an infinite variety of ways of striking a given body, say a bell, by a hard or soft, sharp or blunt instrument, at different points or at several points at a time. This produces an infinite variety of initial deformations and accordingly a truly infinite variety of shapes of the ensuing vibration: the rapid 'succession of cinema pictures,' so we might call it, which describes the vibration following on a particular initial deformation is infinitely manifold. But in every case, however complicated the actual motion is, it can be mathematically analysed as being the superposition of a discrete series of comparatively simple 'proper vibrations,' each of which goes on with a quite definite frequency. This discrete series of frequencies depends on the shape and on the material of the body, its density and elastic properties. It can be computed from the theory of elasticity, 113 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp E. SCHRODINGER from which the existence and the discreteness of proper modes and proper frequencies, and the fact that any possible vibration of that body can be analysed into a superposition of them, are very easily deduced quite generally, i.e. for an elastic body of any shape whatsoever. The achievement of wave mechanics was, that it found a general model picture in which the 'stationary' states of Bohr's theory take the rble of proper vibrations, and their discrete 'energy levels' the rble of the proper frequencies of these proper vibrations ; and all this follows from the new theory, once it is accepted, as simply and neatly as in the theory of elastic bodies, which we mentioned as a simile. Moreover, the radiated frequencies, observed in the line spectra, are in the new model, equal to the differences of the proper frequencies; and this is easily understood, when two of them are acting simultaneously, on simple assumptions about the nature of the vibrating 'something.' 3 The Alleged Energy Balance-a Resonance Phenomenon But to me the following point has always seemed the most relevant, and it is the one I wish to stress here, because it has been almost obliterated-if words mean something, and if certain words now in general use are taken to mean what they say. The principle of super- position not only bridges the gaps between the 'stationary' states, and allows, nay compels us, to admit intermediate states without removing the discreteness of the 'energy levels' (because they have become proper frequencies); but it completely does away with the prerogative of the stationary states. The epithet stationary has become obsolete. Nobody who would get acquainted with wave mechanics without knowing its predecessor (the Planck-Einstein-Bohr-theory) would be inclined to think that a wave-mechanical system has a pre- dilection for being affected by only one of its proper modes at a time. Yet this is implied by the continued use of the words 'energy levels,' C transitions,' ' transition probabilities.' The perseverance in this way of thinking is understandable, because the great and genuine successes of the idea of energy parcels has made it an ingrained habit to regard the product of Planck's constant h and a frequency as a bundle of energy, lost by one system and gained by another. How else should one understand the exact dove-tailing in the great 'double-entry' book-keeping in nature ? I maintain that it can in all cases be understood as a resonance pheno- 114 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp ARE THERE QUANTUM JUMPS? menon. One ought at least to try, and look upon atomic frequencies just as frequencies and drop the idea of energy-parcels. I submit that the word 'energy' is at present used with two entirely different meanings, macroscopic and microscopic. Macroscopic energy is a ' quantity-concept ' (Quantitatsgr6sse). Microscopic energy meaning hv) is a ' quality-concept' or 'intensity-concept' (Intensititsgr6sse) ; it is quite proper to speak of high-grade and low-grade energy according to the value of the frequency v. True, the macroscopic energy is, strangely enough, obtained by a certain weighted summation over the frequencies, and in this relation the constant h is operative. But this does not necessarily entail that in every single case of micro- scopic interaction a whole portion hv of macroscopic energy is ex- changed. I believe one is allowed to regard microscopic interaction as a continuous phenomenon without losing either the precious results of Planck and Einstein on the equilibrium of (macroscopic) energy between radiation and matter, or any other understanding of pheno- mena that the parcel-theory affords. The one thing which one has to accept and which is the inalien- able consequence of the wave-equation as it is used in every problem, under the most various forms, is this : that the interaction between two microscopic physical systems is controlled by a peculiar law of resonance. This law requires that the diference of two proper fre- quencies of the one system be equal to the difference of two proper frequencies of the other: V1 - V1 = V2 V2() The interaction is appropriately described as a gradual change of the amplitudes of the four proper vibrations in question. People have kept to the habit of multiplying this equation by h and saying it means, that the first system (index I) has dropped from the energy level hV1 to the level hvx', the balance being transferred to the second system, enabling it to rise from hy2 to hV2'. This interpretation is obsolete. There is nothing to recommend it, and it bars the understanding of what is actually going on. It obstinately refuses to take stock of the principle of superposition, which enables us to envisage simultaneous gradual changes of any and all amplitudes without surrendering the essential discontinuity, if any, namely that of the frequencies. To be accurate we must add, that the condition of resonance, equation (I), may include three or more interacting systems. It may for example read V - V' = v2' - v2 + v3' -v3 .. (2) IIs5 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp E. SCHRODINGER Moreover we may adopt the view that the two or more interacting systems are regarded as one system. One is t;ien inclined to write equations (i) and (2), respectively, as follows V1 +v2 V12+ V2 .. . ( v1 + •V ~ V 1 V1 2 + V21 ,. . . . (2') and to state the resonance condition thus : the interaction is restricted to constituent vibrations of the same frequency. This is a familiar state of affairs, of old. Unfamiliar is the tacit admission that frequencies are additive, when two or more systems are considered as forming one system. It is an inevitable consequence of wave mechanics. Is it so very repugnant to common sense ? If I smoke 25 cigarettes per day, and my wife smokes Io, and my daughter 12-is not the family consumption 47 per day-on the average ? 4 A Typical Experiment Jokes aside, I wish to consider some typical experiments that ostensibly force the energy parcel view upon us, and I wish to show that this is an illusion. A beam of cathode rays of uniform velocity, which can be gradually increased, is passed through sodium vapour. Behind the vessel containing the vapour the beam passes an electric field which deflects it and tells us the velocity of the particles after the passage. At the same time a spectrometer inspects the light, if any, emitted by the vapour. For small initial velocity nothing happens : no light, no change of velocity in the cathode beam. But when the initial velocity is increased beyond a sharply defined limit, two things happen. The vapour begins to glow, radiating the frequency of the first line of the 'principal series'; and the beam of cathode rays emerging from the vapour is split into two by the deflecting electric field, one indicating the initial velocity unchanged, and another slow one has 'lost an amount of energy' equal to the frequency of the said spectral line multiplied by Planck's constant h. If the velocity is further increased the story repeats itself when the incident cathode ray energy increases beyond the 'energy level' that is responsible for the second line (or rather the 'level-difference' in question); this line appears and a third beam of cathode rays with correspondingly reduced speed occurs; and so on. This was, and still is, regarded as blatant evidence of the energy parcel view. But it is just as easily understood from the resonance point of view. A cathode ray of particles with uniform velocity is a mono- 116 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp ARE THERE QUANTUM JUMPS? chromatic beam of de Broglie waves. Only when its frequency (vl) surpasses the frequency difference (v2' - v2) between the lowest (v2) and the second (v2') proper frequencies of the sodium atom is there a de Broglie frequency v,' > o that fulfils the resonance demand, equation (I). Then the vibration v,' appears in the de Broglie wave and v2,' among the atoms which begin to glow with frequency v2' -V2, since Maxwell's 'electromagnetic vacuum' is prepared for resonance with anything. The splitting of the cathode ray beam in the deviating electric field, after passing the vapour, is accounted for by de Broglie's wave equation. An electric field has for de Broglie waves an 'index of refraction' that depends on their frequency (' dispersion') and has a gradient in the direction of the field (which thus acts as an 'inhomogeneous medium'). Any further events that might happen, for instance a transfer of some of the 'energy quanta' h(v2' - v2) from the sodium atoms to other gas molecules by 'impacts of the second kind,' are just as easily understood as resonance phenomena, provided only one keeps to the wave picture throughout and for all particles involved. Many similar cases of apparent transfer of energy-parcels can be reduced to resonance-for instance photochemical action. The pattern is always the same: you may either take equations like (I) or (2) as they stand (resonance), or multiply them by h and think they express an energy balance of every single micro-transition. In the preceding example one point is of particular interest. One is able by an external agent (the electric field) to separate in space the two or more frequencies which have arisen in the cathode ray by the inter- action ; for they behave differently towards this agent and the different behaviour is completely understood from de Broglie's wave equation ; one thus obtains two or more beams of homogeneous frequency (or velocity). It is extremely valuable that there are simple cases of this kind in which the separation into two 'phases' has nothing enigmatic ; it is an immediate consequence of the principles laid down in L. de Broglie's earliest work on material waves. I say, this is fortunate; for there is a vast domain of phenomena in which the separation in space either takes place in the natural conditions of observation, or can easily be brought about by simple appliances; but it is not as easily explained on first principles. This might dishearten one in accepting the view of gradually changing amplitudes, that I put forward here; for the separation into different phases that produces itself before our eyes seems to confirm the belief that a discontinuous 117 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp E. SCHRODINGER abrupt and complete transition occurs in every single microscopic interaction. 5 Chemistry, Photochemistry, and the Photoelectric Effect The vast amount of phenomena I am alluding to is in the first place ordinary chemistry. Two or more constituents, mixed in a solution or in a gaseous phase, begin to react with each other, under the influence of light or otherwise; the portions that have reacted and have formed a new chemical compound may separate them- selves almost entirely from the rest and form a new phase, say because the product is almost insoluble in the liquid, or (in the case of a gaseous mixture) by its being a liquid or solid with a low vapour pressure at the temperature in question. Almost any chemical reaction may serve as an example, but let us take a slow one to facilitate speech and thought. If a suitable mixture of hydrogen gas (H2) and oxygen gas (02) is illuminated by ultraviolet light, the following slow reaction is induced 2H2 + 02 - 2H20 (3) As the concentration of water vapour (H20) increases, part of it separates off into liquid droplets. The actual process is not as simple as the balance (3) indicates, it is a chain reaction. But we need pay no attention to this, and contemplate only the initial state and the end-product. Wave- mechanically the gaseous mixture is represented by a vibration of the combined system, and, by the way, not by one proper vibration since there is anyhow the vast variety of translational and rotational modes, and, of course, the electronic modes. The gaseous compound, H20, is represented by an entirely different vibration of the same system. The modes composing it, absent at first, are gradually chiming in as the reaction proceeds. But then there is a third group of vibrations representing the liquid H20; they gradually build up where they are facilitated by dust nuclei, and are observed as droplets. It is, of course, deplorable that wave mechanics does not allow us to follow this observed process analytically, while, in the now current inter- pretation, ample information is forthcoming about a host of experi- ments that nobody has ever been or ever will be able to perform (for instance we are told, what is the probability of our finding at a definite spot inside a given hydrogen atom an electron, if we look for one). But there is no reason to suspect that the separation of phases is funda- mentally different from the spectroscopic resolution of a beam of II8 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp ARE THERE QUANTUM JUMPS? light or of cathode rays into its monochromatic constituents. One need not be afraid that the formation of spatial boundaries, separating coherent regions of chemically or physically distinct properties, cannot possibly be controlled by the wave equation, but must necessarily be accounted for by the picturesque pageantry of individual molecules swallowing or re-spewing whole energy parcels, being disrupted and re-combined, until they eventually go to form one or two molecules of a new type. I deem the latter simply wrong ; it is not in accordance with our present state of knowledge, whose further progress is hampered if these easy pictures, that are in common use, are taken literally. And we are encouraged to take them literally not only by text-books and popular essays but also by the language used in very high-browed technical treatises. By this I will not deny that this imagery is a very useful, nay indispensable, conceptual shorthand in chemical research. One cannot see how to avoid it when, for example, a complicated chain reaction is to be unravelled. And, of course, the chemical equation for describing a reaction will never be ousted, though it ostensibly describes the single micro-event and is wrong in this. It is an instance of the famous 'as if.' It is not the first instance of this kind in the relation of chemistry and physics. The chemist used the valency stroke for building models of complicated molecules. It represented very real facts of observation. For a long time the physicist could not afford any explanation of the mechanism of the chemical bond. Then, in brief succession, two were given: there is a heteropolar bond (Kossel, 1916) and a homopolar bond (London-Heitler, 1926). The discoveries were illuminating to the chemist, indeed they removed some difficulties caused by interpreting the valency strokes too naively. But, of course, the valency strokes were retained as an extremely convenient shorthand. They could be retained because they were based on carefully pondered observation. As one of the simplest photochemical reactions we may regard the photoelectric effect, which was one of the main incentives for Einstein in 1905 to launch the hypothesis of light quanta. When a metal plate is illuminated by light of sufficiently high frequency, electrons emerge from it forthwith with an energy corresponding to this frequency. There is no time delay, even when the intensity of the incident light is so weak that according to the electron theory of H. A. Lorentz, which was at the time in full swing, an electron would need half an hour to be sped up to the velocity in question. This was-and, 119 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp E. SCHRODINGER I am afraid, still is-regarded as convincing evidence of the instan- taneous transfer of whole quanta of energy from the light to the electron. I understand the present orthodox interpretation to be as follows. The incident light beam produces at once in each of tens of thousands of electrons an exceedingly small probability of taking within the next split second a leap into a state of higher translational energy; a correspondingly small fraction of those tens of thousands do so and emerge from the metal, and that is why the game starts without delay. But according to wave mechanics, as put forward by de Broglie and myself and generally accepted, the interpretation does produce without delay electronic wave trains of the higher frequency that we observe emerging from the metal. (For to observe the frequency of an electron or its velocity means the same thing.) After this has been recognised, is the probability scheme any longer needed ? Has the idea of the mysterious sudden leaps of single electrons not become gratituitous ? Is it expedient ? The waves are there anyhow, and we are not at a loss to prove it. We need only put a tube of crystal powder in the way of the emerging beam and produce an interference pattern of the type first achieved by G. P. Thomson (it might not be as beautiful as Thomson's, but it would vouch for the waves all the same). 6 Single Interaction Processes between Micro-Systems (' Collisions') There are besides chemistry several other domains of theoretical investigation in which the simplifying scheme of individual con- stituent micro-systems on sharp energy levels, with abrupt transitions between them, affords a very convenient shorthand. Nearly all thermodynamical considerations are greatly facilitated by adopting this scheme in speech and thought, which makes very little difference, if any, in the results. This constitutes a certain danger. In the inseparable union of speech and thought the primacy, rather para- doxically, rests with speech. When we hear the same words again and again pronounced with authority, we are apt to forget that they were originally meant as an abbreviation; we are induced to believe that they describe a reality. If the simplified scheme of sharp energy states and abrupt transi- tions between them was workable throughout in all instances (which 120 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp ARE THERE QUANTUM JUMPS? I do not think is the case), one would have to try and cast it into a consistent theory. At the moment no such theory exists and I can see no prospect of obtaining one, nor any inducement to try, for the reason just mentioned in parenthesis. At present the scheme is inconsistent, not only because of the mystery the transitions continue to present from their first appearance in the theories of Planck (1goo) and Bohr (1913), but also for another reason, intimately connected with the former. In application to two individual micro-systems which interact, it is not at all clear which are the pure energy levels distinguished, to which the scheme shall apply. The choice rests with the mathematical technique. The usual procedure is as follows. The total energy (which enters the mathematical analysis as the 'operator' of the wave equation) is regarded as made up of three additive parts ; the two main contributions are said to pertain to the single systems and are said to control their behaviours, respectively, if they did not interact ; the third is said to be their energy (or' operator ') of interaction. But this partition is rather artificial, at any rate whilst the interaction takes place. It is largely guided by the requirement that the main parts should be comparatively simple and easy to deal with analytically, the whole complication of the problem being shoved into the interaction, which is called a perturbation and dealt with by methods of approximation. Even so, it is hardly ever amenable to a true solution (albeit an approximate one) ; one has to content oneself with finding out what happens in a small interval of time. One computes the very small changes of amplitudes that occur during this short interval; and one is pleased to call the time-rate of change the probability of transition. By calling it so one expresses the belief that after the interaction has taken place and the two systems have separated again each of them will find itself in a pure sharp energy state. The computation does not give this result. The computation tells us, that in either system a host of pure energy-states will be super- posed-with a certain dependence between the partial amplitudes in the one system and those in the other. But one chooses to interpret this result as meaning that there will be complete exchange between only one pair of proper modes, one of the many for which the resonance condition holds. One might say, why not, if this interpretation works and if it is consistent ? I maintain that it is inconsistent. The reason is the following. Assume each of the two systems found itself in a pure energy state, when they were isolated, before the interaction started. 121 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp E. SCHRODINGER Now let the interaction set in ; take it to be very weak. It is certainly legitimate to adopt the attitude that we are now faced with one system ; nay, this is the fundamentally correct attitude to take; the splitting of the wave-operator (' energy ') into two private parts plus a part depicting the interaction is only a mathematical artifice. But however weak the interaction be, it has the immediate consequence that the combined system is now very far from any one of its pure energy states. This is not the result of a very strong mutual physical influence. It obtains prior to any physical change. It results from a slight dis- tuning of the proper modes by the perturbation. What were clear 'one tone' proper modes in the isolated systems no longer are in the combined 'dis-tuned' systems-not nearly. You have to re-shuffle them and combine (superpose them) in your mind in an intriguing fashion to find the proper modes of the combined system. I say 'in your mind '-there is, of course, no immediate physical re-shuffling ; you just state that your combined system is very far from finding itself in one of its proper modes. And that is the very reason why, as time goes on, anything will happen at all, and why, in fact, even a weak interaction, given time, will produce substantial changes of the amplitudes. For it is a simple elementary and universally recognised statement of wave mechanics that an isolated system that vibrates exactly in one of its proper modes undergoes no change whatsoever. This has, by the way, a consequence worth mentioning. When we spoke just before of a weak interaction setting in between the previously isolated systems, the reader may very naturally have pictured to himself the two systems being first at great distance and then approaching each other and getting in contact. I avoided this description on purpose, because it would flatly contradict the assump- tion that the isolated systems were in pure energy states. If so they cannot be said to approach each other. To think of atoms and molecules in pure energy states, moving hither and thither, colliding and rebounding contradicts the fundamental concepts of the theory. Where anything happens, we are not facing pure energy states. So obviously we never are. Let me return for a moment to our two micro-systems in weak interaction or, as I prefer to say, to a system consisting of two parts in slight coupling. The state of affairs is simply this : if this system as a whole settled down in one of its exact proper modes, this would not be a state which the current view interprets as indicating a definite partition of the total energy between the two parts-not nearly; 122 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp ARE THERE QUANTUM JUMPS? I mean to say, it is not a question of slight fluctuation or uncertainty, but of many widely different partitions. If you abolished the coupling at this moment, the now isolated parts would vibrate, each of them, in a superposition of widely different proper modes. Summarising: the current view, which privileges the 'sharp energy states,' is self-contradictory, anyhow in the language it uses (what people mean, when they say something else than they mean, is difficult to guess). We found it self-contradictory in that it cannot be maintained for both the whole and the parts ; we are left to choose and to apply the privilege the way it is most convenient. We found a minor inconsistency in the apparently innocent statement that two systems (both of sharply defined energy) approach each other and collide. This seems a little less obnoxious, because it can be evaded by saying : Oh well, we do not mean really quite sharp. Some may consider this point a rather gratuitous nagging. I wonder whether in actual collision problems it is entirely irrelevant. (The concluding part of this article will be published in November.) NOTE Professor Michael Polanyi drew my attention to a mistake. My description of the Franck-Hertz experiment in the first paragraph of Section 4 is, to put it mildly, oversimplified. The cathode ray beam is appreciably scattered in the vapour. The two or more electronic frequencies that emerge could therefore hardly be separated by the simple transversal field method. But any two of them can be separated by a potential barrier which the one can penetrate, while the other is turned back, being totally reflected. Since this is also com- pletely understood by de Broglie's wave equation, the main argument is not impaired. E. S. School of Theoretical Physics Dublin Institute for Advanced Studies 64-66 Merrion Square, Dublin 123 This content downloaded from 128.103.149.52 on Sun, 7 Apr 2013 17:23:30 PM All use subject to JSTOR Terms and Conditions http://www.jstor.org/page/info/about/policies/terms.jsp Article Contents p. 109 p. 110 p. 111 p. 112 p. 113 p. 114 p. 115 p. 116 p. 117 p. 118 p. 119 p. 120 p. 121 p. 122 p. 123 Issue Table of Contents The British Journal for the Philosophy of Science, Vol. 3, No. 10 (Aug., 1952), pp. i-iv+109-216 Front Matter [pp. i-iv] Are There Quantum Jumps? Part I [pp. 109-123] The Nature of Philosophical Problems and Their Roots in Science [pp. 124-156] Hans Selye and a Unitary Conception of Disease [pp. 157-168] The Scientific Basis of Leonardo da Vinci's Theory of Perspective [pp. 169-185] Notes and Comments The Principle of Methodological Individualism [pp. 186-189] The Mechanical Chess-Player [pp. 189-191] Mind-like Behaviour in Artefacts and the Concept of Mind [pp. 191-193] Science and Literary Criticism [pp. 194-196] Reviews Review: Mathematical Logic [pp. 197-200] Review: untitled [p. 200] Review: untitled [pp. 201-202] Review: untitled [pp. 202-204] Review: untitled [pp. 204-207] Review: untitled [pp. 207-210] Review: untitled [pp. 210-211] Recent Publications on the Philosophy of Science [pp. 212-215] Back Matter [pp. 216-216]