I WOULD like to present before you certain aspects of modern physics and draw your attention to the profound changes in the principle of scientific explanation of natural phenomena brought about by quantum theory. The last fifty years have recorded remarkable discoveries. These discoveries have their repercussions in the realm of ideas. Fifty years ago the belief in causality and determination was absolute. Today physicists have gained knowledge but faith. To understand properly the significance of such a profound change it will be necessary to discuss briefly how it all came about. Classical physics had begun with the study of astronomy. Physicists had taken the equations of celestial mechanics as their model of a universal law. Since matter had resolved into a conglomeration of particles, the ideal scheme was to explain all phenomena in terms of their motions and interactions. It was only necessary to set up a proper set of equations and to take account of all possible mutual interactions. If the mass, position, and velocity of all the particles were known at any instant, these equations would theoretically enable the physicist to predict the position and motion of every particle at any other subsequent moment.
The phenomena of light did not at first fit into this simple scheme. With the discovery of the electron as a universal constituent of matter, the electromagnetic theory of Maxwell was converted into an electronic theory by Lorentz. To the dynamical laws were added the electromagnetic equations and the two together apparently gave an exact and ideal formulation of the laws of causality. It was more or less a matter of faith to maintain that if it were possible for us to obtain all the necessary data by delicate observations, universal laws would enable us to follow each individual molecule in this intricate labyrinth and we should find in each case an exact fulfilment of the laws and agreement with observation. The above in brief forms an expression of faith of a classical physicist. We see that it involves as necessary consequences, belief in continuity, in the possibility of space-time description of all changes and in the existence of universal laws independent of observers which inexorably determine the course of the future and the fate of the material world for all times.
II
The development of the quantum theory has raised fundamental issues. Facts have been discovered which demonstrate the breakdown of the fundamental equations which justified our belief in determinism. A critical examination of the way in which physical measurements are made has shown the impossibility of measuring accurately all the quantities necessary for a space-time description of the motion of the corpuscles.
Experiments reveal either the corpuscular or the wave nature of the photon or the electron according to the circumstances of the case and present us with an apparently impossible task of fusing two contradictory characters into one sensible image. mage. The only solution suggested has been a renunciation of the space-time representation of atomic phenomena and with it our belief in causality and determinism.
Let me briefly recapitulate the facts. In 1900 Planck discovered the quantum of action while studying the conditions of equilibrium between matter and the radiation field. Apparently, the interchange of energy took place in discrete units whose magnitude depended on hand on the frequency of the radiation emitted or absorbed by matter. Photo-electric emission had similar disquieting features. Einstein, therefore, suggested a discrete structure of the radiation field in which energy existed in quanta instead of being continuously distributed in space as required by the wave theory. This light quantum, however, is not the old light- corpuscle of Newton. The rich experimental materials supporting the wave theory preclude that possibility altogether. Moreover, the fundamental relation, Eh, and p= hk, connect the energy and momentum of the photon with the frequency and the vector wave number k, making a direct reference to an idealised plane wave so foreign to the old idea of a corpuscle. Soon afterwards Böhr postulated the existence of radiationless stationary states of atoms and showed how it led to a simple explanation of the atomic spectra. The extreme simplicity of the proposed structure and its striking sue- cess in correlating a multitude of experimental facts at once revealed the inadequacy of the ordinary laws of mechanics and electro-dyna-mics in explaining the remarkable stability of the atoms.
The new ideas found application in different branches of physics. Discontinuous quantum processes furnished solutions to many Suitably modified, the theory furnished a reasonable explanation of the periodic classification of elements and the thermal behaviour of substances at low temperatures. There was, however, one striking feature. It was apparently discovered which demonstrates the breakdown of the fundamental equations which justified our belief in determinism. A critical examination of the way in which physical measurements are made has shown the impossibility of measuring accurately all the quantities necessary for a space-time description of the motion of the corpuscles.
Experiments reveal either the corpuscular or the wave nature of the photon or the electron according to the circumstances of the case and present us with an apparently impossible task of fusing two contradictory characters into one sensible image. mage. The only solution suggested has been a renunciation of the space-time representation of atomic phenomena and with it our belief in causality and determinism.
Let me briefly recapitulate the facts. In 1900 Planck discovered the quantum of action while studying the conditions of equilibrium between matter and the radiation field. Apparently, interchange of energy took place in discrete units whose magnitude depended on hand the frequency of the radiation emitted or absorbed by matter. Photo-electric emission had similar disquieting features. Einstein, therefore, suggested a discrete structure of the radiation field in which energy existed in quanta instead of being continuously distributed in space as required by the wave theory. This light quantum, however, is not the old light- corpuscle of Newton. The rich experimental materials supporting the wave theory preclude that possibility altogether. Moreover, the fundamental relation, Eh, and p= hk, connecting energy and momentum of the photon with the frequency and the vector wave number k, makes a direct reference to the idealised plane wave so foreign to the old idea of a corpuscle. Soon afterwards Böhr postulated the existence of radiationless stationary states of atoms and showed how it led to a simple explanation of the atomic spectra. The extreme simplicity of the proposed structure and its striking sue- cess in correlating a multitude of experimental facts at once revealed the inadequacy of the ordinary laws of mechanics and electro-dynamics in explaining the remarkable stability of the atoms. The new ideas found application in different branches of physics. Discontinuous quantum processes furnished solutions to many Suitably modified, the theory furnished a reasonable explanation of the periodic classification of elements and the thermal behaviour of substances at low temperatures. There was, however, one striking feature. It was thrown when a certain die is cast a large number of times and arrives at a statistical law which will tell us how many times out of a thousand it will fall on a certain side. But if we can take into account the exact location of its centre of gravity, all the circumstances of the throw. the initial velocity, the resistance of the table and the air and every other peculiarity that may affect it, there can be no question of chance, because each time we can reckon where the die will stop and know in what position it will rest. It is the assertion of the im- possibility of even conceiving such elementary determining laws for the atomic system that is disconcerting to the classical physicist.
Von Neumann has analysed the statistical interpretation of the quantum mechanical laws and claims to have demonstrated that the results of the quantum theory cannot be regarded as obtainable from exact causal laws by a process of averaging. He asserts definitely that a causal explanation of quantum mechanics is not possible without an essential modification or sacrifice of some parts of the existing theory, Böhr has recently analysed the situation and asserted that we cannot hope any future development of the theory will ever allow a return to a description of the atomic phenomena more conformable to the ideal of causality. He points out the importance of the searching analysis of the theory of observation made by Heisenberg, whereby he has arrived at his famous principle of indeterminacy. According to it, it is never possible for us to determine the simultaneous values of momentum and positional co-ordinates of any system with an accuracy greater than what is compatible with the inequality
This natural limitation does not affect the physics of bodies of finite size but makes space-time descriptions of corpuscles and photons impossible. When we proceed to study the behaviour of the elementary particles, our instruments of measurement have an essential influence on the final results. We have also to concede that the contributions of the instrument and the object, are not separately computable from the results as they are interpreted- ed in a classical way with the usual ideas of co-ordinate and momentum accepting ng thereby a lack of control of all action and reaction of object and instrument due to quantum effects. It is in this imperative necessity of describing all our knowledge with the usual classical ideas, that Böhr seeks an explanation of the apparently irreconcilable behaviour of corpuscles and radiation in different experiments. For example, if we set our experiments in such a fashion as to determine accurately the space-time co-ordinates, the same arrangement cannot be simultaneously used to calculate the energy-momentum relations accurately; when our arrangements have pushed the accuracy of determining the positional co-ordinates to its utmost limit, the results evidently will be capable only of a corpuscular representation. If, on the other hand, our aim is to determine momentum and energy with the utmost accuracy, the necessary apparatus will not allow us any determination of positional coordinates and the results we obtain can be understood only in terms of the imagery of wave motion. The apparently contradictory nature of our conclusions is to be explained by the fact, that every measurement has an individual character of its own. The quantum theory does not allow us to separate rigorously the contribution of the object and the instrument and as such the sum total of our knowledge gained in individual cases cannot be synthesised to give a consistent picture of the object of our study which enables us to predict with certainty its behaviour in any particular situation. We are thus doomed to have only statistical laws for these elementary particles and any further development is not likely to affect these general conclusions.
It is clear that a complete acceptance of all the above conclusions would mean a complete break with the ancient accepted principles of scientific explanation. Causality and the universal laws are to be thrown simultaneously overboard. These assertions are so revolutionary that, no wonder, they have forced physicists to opposing camps. There are some whe look upon causality as an indispensable post late for all scientific activities. The inability to apply it consistently because of the limitations of the present state of human knowledge would not justify a total denial of its existence. Granted that physics has outgrown the stage of a mechanistic formulation of the principle, they assert that it is now the task of tests to seek a better formulation. Others of the opposing camp look upon old determinism as an inhuman conception, not only because it sets up an impossible ideal, but also as it forces man to a fatalistic attitude which regards humanity as inanimate automata in the hands on an iron law of causation. For them, the new theory has humanised physics. The quantum statistical conception of determinism nestles closer to reality and substitutes a graspable truth for an inaccessible ideal. The theory has brought hope and inspired activity. It constitutes a tremendous step towards the understanding of nature. The features of the present theory may not all be familiar but use will remove the initial prejudice. We are not to impose our reason and philosophy on nature. Our philosophy and our logic evolve and adjust themselves more and more to reality.
In spite of the striking success of the new theory, its provisional character is often frankly admitted. The field theory is as yet in an unsatisfactory state. In spite of strong optimism, difficulties do not gradually dissolve and disappear. They are relegated to a lumber room, whence the menace of an ultimate divergence of all solutions neutralises much of the convincing force of imposing mathematical symbols. Nor is the problem of matter and radiation solved by the theory of complementary characters. Also, we hear already of the limitations of the new theory encountered in its application to nuclear problems. The quantum theory is frankly utilitarian in its outlook; but is the ideal of a universal theory completely overthrown by the penetrating criticism of the nature of physical measurements?
Böhr has stressed the unique character of all physical measurements. We try to synthesise their results and we get probabilities to reckon with instead of certainties. But how does the formalism 2mi d He emerge as a certain law? The wider the generalisation, the less becomes the content. A universal law would be totally devoid of it. It may nevertheless unfold unsuspected harmonies in the realm of concept. More than ever now, physics does need such a generalisation to bring order in its domain of ideas.
