Quantum theory

“ The very nature of the quantum theory thus forces us to regard the space-time co-ordination and the claim of causality, the union of which characterises the classical theories, as complementary but exclusive features of the description, symbolising the idealisation of observation and definition respectively. ”

“ The other paths which the quantum-theory permits are occupied, until we get to a considerable distance from the nucleus, whereas in hydrogen they are vacant. Paths that have large [Pg 107] quantum numbers, though possible in theory, cannot occur in practice, at any rate in the laboratory, because they are so large that they would cause the electron to get into the region of other atoms. In certain nebulæ, where matter is almost inconceivably tenuous, the spectrum shows that electrons can travel round hydrogen nuclei in orbits whose total quantum number is as large as 30. ”

“ The assumption is, that whatever vibration takes place in the atom is to be attributed to the vibratory locomotion of some bit of material, detachable from the remainder. The difficulty with the quantum theory is that, on this hypothesis, we have to picture the atom as providing a limited number of definite grooves, which are the sole tracks along which vibration can take place, whereas the classical scientific picture provides none of these grooves. The quantum theory wants trolley-cars with a limited number of routes, and the scientific picture provides horses galloping over prairies. ”

“ The postulates of the quantum theory. The quantum theory in the form in which it has been applied to the problems of atomic structure rests upon two postulates which have a direct bearing on the difficulties mentioned above. According to the first postulate there are certain states in which the atom can exist without emitting radiation, although the particles are supposed to have an accelerated motion relative to one another. ”

“ According to the quantum theory, just the impossibility of neglecting the interaction with the agency of measurement means that every observation introduces a new uncontrollable element. Indeed, it follows from the above considerations that the measurement of the positional co-ordinates of a particle is accompanied not only by a finite change in the dynamical variables, but also the fixation of its position means a complete rupture in the causal description of its dynamical behaviour, while the determination of its momentum always implies a gap in the knowledge of its spatial propagation. ”

“ The fact that the symbolical quantum theory methods ascribe a particular phase to each stationary state the value of which depends upon the previous history of the atom, would for the first moment seem to contradict the very idea of stationary states. As soon as we are really concerned with a time problem, however, the consideration of a strictly closed system is excluded. ”

“ Just as the relativity theory has taught us that the convenience of distinguishing sharply between space and time rests solely on the smallness of the velocities ordinarily met with compared to the velocity of light, we learn from the quantum theory that the appropriateness of our usual causal space-time description depends entirely upon the small value of the quantum of action as compared to the actions involved in ordinary sense perceptions. ”

“ In the quantum theory we meet this difficulty at once in the question of the inevitability of the feature of irrationality characterising the quantum postulate. I hope, however, that the idea of complementarity is suited to characterise the situation, which bears a deep-going analogy to the general difficulty in the formation of human ideas, inherent in the distinction between subject and object. ”

“ Thus, in quantum theory, there is no reason why we should not be willing to accept as an [Pg 47] ultimate the fundamental fact that when an electron jumps radiation is emitted, provided always that we can give independent meaning in terms of operations to the jumping of an electron. If there is no experiment suggesting other and intermediate phenomena, we ought to be able to rest intellectually satisfied with this. ”

“ Experiment has isolated what are believed to be units of action, which at least in many phenomena behave as indivisible atoms called quanta; but the theory, as at present developed, does not permit us to represent the quantum of action by the number 1. The quantum is a very minute fraction of the absolute unit. ”

“ In the second the atom uses the small fraction of a quantum offered to it to buy a ticket in a sweepstake in which the prizes are whole quanta; some of the atoms will win whole quanta which they can absorb, and it is these winning atoms in our retina which tell us of the existence of Sirius.
The collection-box explanation is not tenable. As Jeans once said, not only does the quantum theory forbid us to kill two birds with one stone; it will not even let us kill one bird with two stones. ”

“ But he did early and important work on that other gigantic 20th century scientific achievement, the quantum theory. [10] In one of his papers, published first in Zurich, Switzerland, in 1916, Einstein showed that controlled emission of light energy could be obtained from an atom under certain conditions. When an atom or molecule has somehow had its energy level raised, the release of this stored energy could be stimulated by subjecting the atom or molecule to a small “shot” of electromagnetic radiation of the proper frequency. ”

“ We attack the problem of atomic constitution by asking the question: "How may an atom be formed by the successive capture and binding of the electrons one by one in the field of force surrounding the nucleus?"
Before attempting to answer this question it will first be necessary to consider in more detail what the quantum theory teaches us about the general character of the binding process. We have already seen how the hydrogen spectrum gives us definite information about the course of this process of binding the electron by the nucleus. ”

“ One would not be surprised if in the reconstruction of the scheme of physics which the quantum theory is now pressing on us, secondary law becomes the basis and primary law is discarded. In the reconstructed world nothing is impossible though many things are improbable. ”

“ Could we pick out one atom in Einstein’s brain and say that if it had made the wrong quantum jump there would have been a corresponding flaw in the theory of relativity? Having regard to the physical influences of temperature and promiscuous collision it is impossible to maintain this. It seems that we must attribute to the mind power not only to decide the behaviour of atoms individually but to affect systematically large groups—in fact to tamper with the odds on atomic behaviour. This has always been one of the most dubious points in the theory of the interaction of mind and matter. ”

“ If atomicity depends on laws inherent in nature, it seems at first difficult to understand why it should relate to matter especially; since matter is not of any great account in the analytical scheme, and owes its importance to irrelevant considerations introduced by the mind. It has appeared, however, that atomicity is by no means confined to matter and electricity; the quantum, which plays so great a part in recent physics, is apparently an atom of action. ”

“ A greater and really serious danger is threatening from the side of the quantum theory, for the existence of amounts of energy that remain concentrated in small spaces during their propagation, to which several phenomena seem to point, is in absolute contradiction to Maxwell's equations. ”

“ At present we can notice the contrast that the laws which we now [Pg 246] recognise as man-made are characterised by continuity, whereas the laws to which the mind as yet lays no claim are characterised by atomicity. The quantum theory with its avoidance of fractions and insistence on integral units seems foreign to any scheme which we should be likely subconsciously to have imposed as a frame for natural phenomena. Perhaps our final conclusion as to the world of physics will resemble Kronecker’s view of pure mathematics. ”

“ Hitherto we have only regarded certain general features of the quantum problem. The situation implies, however, that the main stress has to be laid on the formulation of the laws governing the interaction between the objects which we symbolise by the abstractions of isolated particles and radiation. ”

“ We meet the same difficulties when we try to explain in detail the characteristic effect of external forces upon the spectrum of hydrogen. A foundation for further advances in this field has been made in recent years through a development of the quantum theory, which allows a fixation of the stationary states not only in the case of simple periodic systems, but also for certain classes of non-periodic systems. These are the conditionally periodic systems whose equations of motion can be solved by a "separation of the variables." ”

“ It is remarkable that it is in line with the trend of modern science. Eddington has pointed out that there is a certain finite number which is fundamental in the universe, namely the number of electrons. According to the quantum theory, it would seem that the number of possible arrangements of electrons may well also be finite, since they cannot move in all possible orbits, but only in such as make the action in one complete revolution conform to the quantum principle. ”

“ On the whole, it would scarcely seem justifiable, in the case of the interaction problem, to demand a visualisation by means of ordinary space-time pictures. In fact, all our knowledge concerning the internal properties of atoms is derived from experiments on their radiation or collision reactions, such that the interpretation of experimental facts ultimately depends on the abstractions of radiation in free space, and free material particles. Hence, our whole space-time view of physical phenomena, as well as the definition of energy and momentum, depends ultimately upon these abstractions. ”

“ If the electromagnetic waves, as has been assumed, are distributed evenly over the field of radiation, it is not easy to understand why they give energy to some atoms and not to others, and why the selected ones always—with a given frequency—acquire a definite energy quantum, independent of the intensity of the radiation. For small intensities of the incident radiation, the atom, in order to acquire the proper quantum, must absorb energy from a greater part of the field of radiation (or for a longer time) than for large intensities. ”

“ It may be questioned whether the difficulty still exists when the quantum theory is stated in the form which it takes in Sommerfeld’s work. We no longer have little parcels of energy; what we have is a property of periodic processes. It would not be accurate to state this property in the form: the total action throughout a complete period of any periodic process is or an exact multiple of . ”

“ Indeed, the proper vibrations of the Schrödinger wave equation have been found to furnish a representation of the stationary states of an atom meeting all requirements. The energy of each state is connected with the corresponding period of vibration according to the general quantum relation (1) . Furthermore, the number of nodes in the various characteristic vibrations gives a simple interpretation to the concept of quantum number which was already known from the older methods, but at first did not seem to appear in the matrix formulation. ”

“ Similarly, the superposition of two characteristic solutions corresponds to a continuous vibrating distribution of electrical charge, which on classical electrodynamics would give rise to an emission of radiation, illustrating instructively the consequences of the quantum postulate and the correspondence requirement regarding the transition process between two stationary states formulated in matrix mechanics. ”

“ In connexion with the complementary nature of the quantum theoretical description, we must, as already mentioned, constantly keep the possibilities of definition as well as of observation before the mind. For the discussion of just this question the method of wave mechanics developed by Schrödinger has, as we shall see, proved of great help. It permits a general application of the principle of superposition also in the problem of interaction, thus offering an immediate connexion with the above considerations concerning radiation and free particles. ”

“ It would seem that what the light-waves were really bearing within reach of each atom was not a millionth of a quantum but a millionth chance of securing a whole quantum. The wave-theory of light pictures and describes something evenly distributed over the whole wave-front which has usually been identified with energy. Owing to well-established phenomena such as interference and diffraction it seems impossible to deny this uniformity, but we must give it another interpretation; it is a uniform chance of energy. ”

“ By radiation absorption and scattering energy is shuffled among the different receptacles in matter and aether, but only a whole quantum passes at each step. It was in fact this definiteness of thermodynamical equilibrium which first put Prof. Max Planck on the track of the quantum; and the magnitude of was first calculated by analysis of the observed composition of the radiation in the final state of randomness. Progress of the theory in its adolescent stage was largely due to Einstein so far as concerns the general principles and to Bohr as regards its connection with atomic structure. ”

“ It may, however, be stated that, if we restrict ourselves to a definite atom, the rule will hold that, among a series of orbits with the same auxiliary quantum number but different principal quantum numbers, that orbit in which the electron attains a greater distance from the nucleus has the higher number. ”