The problem of emission by an atom is treated according to Schroedinger’s rules. The translational motion of the atom as a whole is taken into account. The charge-current density vector is shown to be propagating with the velocity of light in the direction of the emitted quantum. Only unidirectional quanta can be emitted according to the theory. The reason is that the charge-current wave radiates infinitely more intensely if it travels with light velocity than otherwise.It is shown that Gordon’s treatment of the Compton effect involves an analogous phenomenon. It is suggested that Schroedinger’s equations designed for the conservation of energy and momentum work out better when the translational motion of the atom as a whole is considered.
The problem of emission by an atom is treated according to Schroedinger’s rules. The translational motion of the atom as a whole is taken into account. The charge-current density vector is shown to be propagating with the velocity of light in the direction of the emitted quantum. Only unidirectional quanta can be emitted according to the theory. The reason is that the charge-current wave radiates infinitely more intensely if it travels with light velocity than otherwise.It is shown that Gordon’s treatment of the Compton effect involves an analogous phenomenon. It is suggested that Schroedinger’s equations designed for the conservation of energy and momentum work out better when the translational motion of the atom as a whole is considered.
Theory of the Brownian motion of a Planck radiator in black body radiation.---In the case of a classical resonator it is shown that the motion takes place even though the emission and absorption is not unidirectional provided the radiation is not strictly monochromatic. This theory is then extended to the case of a quantized atom. Interference between the waves emitted by the atom and the surrounding radiation provides for the recoil actions without the assumption of unidirectional quanta. Statistically these have the same effect as Einstein's unidirectional quanta. This theory removes the contradiction postulated by Einstein between the Rubinowicz-Sommerfeld considerations and the requirements of classical Brownian motion. It leaves the wave-theory of light intact and is in agreement with Bohr's principle of correspondence.
Abstract The new quantum theory, based on the assumption that the dynamical variables do not obey the commutative law of multiplication, has by now been developed sufficiently to form a fairly complete theory of dynamics. One can treat mathematically the problem of any dynamical system composed of a number of particles with instantaneous forces acting between them, provided it is describable by a Hamiltonian function, and one can interpret the mathematics physically by a quite definite general method. On the other hand, hardly anything has been done up to the present on quantum electrodynamics. The questions of the correct treatment of a system in which the forces are propagated with the velocity of light instead of instantaneously, of the production of an electromagnetic field by a moving electron, and of the reaction of this field on the electron have not yet been touched. In addition, there is a serious difficulty in making the theory satisfy all the requirements of the restricted principle of relativity, since a Hamiltonian function can no longer be used. This relativity question is, of course, connected with the previous ones, and it will be impossible to answer any one question completely without at the same time answering them all. However, it appears to be possible to build up a fairly satisfactory theory of the emission of radiation and of the reaction of the radiation field on the emitting system on the basis of a kinematics and dynamics which are not strictly relativistic. This is the main object of the present paper. The theory is noil-relativistic only on account of the time being counted throughout as a c-number, instead of being treated symmetrically with the space co-ordinates. The relativity variation of mass with velocity is taken into account without difficulty. The underlying ideas of the theory are very simple. Consider an atom interacting with a field of radiation, which we may suppose for definiteness to be confined in an enclosure so as to have only a discrete set of degrees of freedom. Resolving the radiation into its Fourier components, we can consider the energy and phase of each of the components to be dynamical variables describing the radiation field. Thus if Er is the energy of a component labelled r and θr is the corresponding phase (defined as the time since the wave was in a standard phase), we can suppose each Er and θr to form a pair of canonically conjugate variables. In the absence of any interaction between the field and the atom, the whole system of field plus atom will be describable by the Hamiltonian H ═ ΣrEr + Ho equal to the total energy, Ho being the Hamiltonian for the atom alone, since the variables Er, θr obviously satisfy their canonical equations of motion Er ═ — ∂H/∂θr ═ 0, θr ═ ∂H/∂Er ═ 1.
The quantum theory of radiation, formulated in wave-mechanical language but in terms of running waves, is shown to lead under suitable conditions to the classical theory of emission by a particle as a first approximation. Non-relativistic mechanics is used, and the limitations of the method are brought out in terms of classical theory. The characteristic quantum phenomenon of the Compton effect requires that the Compton recoil shall exceed the spread in momentum of the particle, and so that the wave-packet shall greatly exceed in diameter the wave-length of the incident radiation; this condition is realizable on any scale of magnitude. For quasi-classical motion just the reverse is required; furthermore, if the motion is to last for a number of waveperiods, the wave-length must greatly exceed mch (m=massoftheparticle). The classical packet-motion arises from combinations between quantum-states of the particle-field system; this fact suggests that the photon is not a fundamental constituent of the field but only one possible aspect of its action. The infinite "zero-energy" associated apparently even with the lowest energy-state of the field implies no electromagnetic field intensities at any point. Whereas for problems on energy or momentum it is customary to represent an incident wave-train by a single typical quantum state, to obtain motional phenomena of classical type a more complete expression such as that given in the paper must be used. The physically empty field likewise corresponds to a mixture of quantum states but without correlation among their amplitudes.
It is shown that, assuming conservation of energy and momentum in individuai transitions, radiation must be regarded as propagated by linearly directed quanta. Evidence is brought forward in favour of the view that these quanta are spatially localised longitudinally as well as laterally. As these conclusions seem unavoidable, an attempt is made to see if there is any possibility of accounting for interference effects in terms of quants possessing periodic properties. The idea that a single quantum can produce interference effects is untenable. The conception of the phase of a quant is introduced, and it is supposed that atoms may absorb a quant in a given phase provided they are in a “state” corresponding to that phase. Considering radiation emanating from a point, it is shown that a tentative explanation of interference may be obtained if the quants have a constant phase at emission, and if they give atoms at any point an impulse towards the state corresponding to their phase at the point. According as these impulses reinforce or oppose each other, bright or dark parts of a fringe System are obtained. Practically the whole nomenclature and method of the wave theory may be taken over and applied to the quant phase field surrounding an emitting source. Essentially, on this view, an explanation of interference is sought in terms of different quants, and the dark and bright parte of a fringe system are to be explained, not in terms of different numbers of quante arriving at them, but in different phase relations of quante which do arrive. Quante are characterised by a magnetic and electric vector, whose magnitudes and directions define the state of polarisation and the phase. Electron orbite may also be regarded as characterised by two vectors in terms of which it seems as if the “state” may be specified. The relation between transition character and type of radiation emitted is finally considered and it is shown that the evidence so far available renders plausible an explanation of interference of the kind put forward. Much further experimental work, particularly in connection with the Stark and Zeeman effects, is, however, necessary, before sufficient precision can be given to the views put forward to make them satisfying. On the other hand, it seems premature to suppose that only a formal treatment is possible of the physical phenomena involved.
Abstract The new quantum mechanics could at first be used to answer questions concerning radiation only through analogies with the classical theory. In Heisenberg’s original matrix theory, for instance, it is assumed that the matrix elements of the polarisation of an atom determine the emission and absorption of radiation analogously to the Fourier components in the classical theory. In more recent theories a certain expression for the electric density obtained from the quantum mechanics is used to determine the emitted radiation by the same formulæ as in the classical theory. These methods give satisfactory results in many cases, but cannot even be applied to problems where the classical analogies are obscure or non-existent, such as resonance radiation and the breadths of spectral lines. A theory of radiation has been given by the author which rests on a more definite basis. It appears that one can treat a field of radiation as a dynamical system, whose interaction with an ordinary atomic system may be described by a Hamiltonian function. The dynamical variables specifying the field are the energies and phases of its various harmonic conrponents, each of which is effectively a simple harmonic oscillator. One must, of course, in the quantum theory take these variables to be q-numbers satisfying the proper quantum conditions. One finds then that the Hamiltonian for the interaction of the field with an atom is of the same form as that for the interaction of an assembly of light-quanta with the atom. There is thus a complete formal reconciliation between the wave and light-quantum points of view.
The photoelectric effect, the Compton effects, and now anticorrelation experiments have been claimed to prove that light consists of particles flying through a void. However the particle model is decisively falsified by the known wave qualities of electromagnetic radiation. Quantum Electrodynamics also uses spreading wave amplitudes; not flying particles. The evidence indicates that light is a wave and electrons are electromagnetic wave-structures that absorb and emit light in discrete wave-packets. These wave-quanta are emitted directionally and then spread in space in proportion to their wavelength. Their waves superposition with all other waves in space. In low intensity experiments, the waves that an electron in a photodetector absorbs come from the superpositioning of the source wave-quanta and background radiation. The importance of background radiation is evidenced by "dark counts". Treating electrons and the quanta they absorb and emit as particles when they are composed of waves is the source of all the paradoxes, unreality and confusion in Quantum Mechanics. The word "photon" should be replaced by "quantum" in the description of this particular electronic process. The conceptual model presented here explains the known phenomena without producing paradoxes and unifies quantum and classical electromagnetics.