The interference effect produced by two independent sources can be understood in terms of the detection process, owing to the inability of the detector to know from which of the two sources the photons come. Detection based on the Compton effect seems to be a powerful method for recording the interference between high-frequency coherent fields. It is shown that by taking advantage of the uncertainty over the photon momenta, the scattering probability for an electron in an interference fringe is very high when the electrons are not relativistic. When the fields have the same frequency in the laboratory system, relativistic electrons can "see" the interference only when the angles between the fields are very small. In general, relativistic electrons see interference when the fields are suitably shifted in frequency in the laboratory system.
The interference effect produced by two independent sources can be understood in terms of the detection process, owing to the inability of the detector to know from which of the two sources the photons come. Detection based on the Compton effect seems to be a powerful method for recording the interference between high-frequency coherent fields. It is shown that by taking advantage of the uncertainty over the photon momenta, the scattering probability for an electron in an interference fringe is very high when the electrons are not relativistic. When the fields have the same frequency in the laboratory system, relativistic electrons can "see" the interference only when the angles between the fields are very small. In general, relativistic electrons see interference when the fields are suitably shifted in frequency in the laboratory system.
In this paper, we bring the Zitterbewegung electron model and our photon model together to provide a classical explanation of the scattering of photons by electrons. We understand electron-photon interference (which is usually referred to as Compton scattering) as two electromagnetic oscillations interfering (classically) with each other. While developing the model, we offer some reflections on the Uncertainty Principle (Copenhagen interpretation of quantum mechanics). We conclude there is no need for it: God doesn’t play dice.
The Compton scattering is an elastic collision of the x-ray or gamma photons with free electrons (or loosely bound valence shell electrons). This scattering is demonstrated in Fig. 1. In this communication we are combining Heisenberg's uncertainty principle and the Compton scattering. Note, that some of the expressions (including their derivations) of this communication can be found in modern physics textbooks. Figure 1. Schematic representation of Compton scattering, in which an incoming photon scatters from an electron at rest. The electron of the rest mass m e has the rest energy of E r = m e c 2. The Compton scattered electron (hereinafter the Compton electron) posses a relativistic kinetic energy, the relativistic speed υ e and the linear momentum p e = m e υ e. Before scattering, let the photon moves along the positive x-axis having an energy E 0 = hν 0 , frequency ν 0 , wavelength λ 0 and linear momentum p 0 = hν 0 /c, where h (= 6.63 × 10-34 J s) is the Planck constant and c (= 2.99792×10 8 m s-1) is the speed of light. After scattering, the photon moves at an angle θ off the x-axis with an energy E = hν, frequency ν, wavelength λ and momentum p = hν/c. The conservation of linear momentum of the electron after the collision yields, p e 2 = p 0 2 + p 2-2p 0 pcosθ.
Interference effects produced by independent quantum sources are investigated, when the state of the field is not describable as a simple mixture of coherent states. The results of classical and quantum-mechanical calculations are compared. Whereas correlation effects are predicted both classically and quantum mechanically when the sources have random phases, there are important differences when the number of atoms is small. In particular, when each source consists of just one atom, the joint probability of detecting two photons at two different points in the receiving plane is found to vanish when the distance between them is an odd number of half fringes. Finally it is shown that when the number of atoms of each source is subject to Poisson fluctuations, one recovers the solution given by classical optics for thermal light, no matter how weak the sources may be on the average.
Chapter I The origins of quantum physics I The Compton effect — a strange dichotomy in the nature of electromagnetic radiation In a series of experiments conducted between 1919 and 1923, Arthur Holly Compton (Figure 1.1) investigated the scattering of monochromatic (single-wavelength) X-rays from graphite targets. He found that the radiation scattered at an angle 0 to the incident beam contained, in addition to radiation of the same wavelength as the incident radiation, a second component with a considerably longer wavelength. The existence of this second component in the scattered radiation could not be explained by the well-established theory of the scattering of electromagnetic waves by electrons. Compton considered instead the process illustrated in Figure 1.2, in which a particle of electromagnetic radiation, collides with a slow moving electron, which then recoils absorbing some of the X-ray particle’s energy. Treating the process as a collision between particles, and using only the (relativistic) conservation laws of energy and momentum, Compton was able to account for the effect completely. However, at the same time, in the same experiment, Compton was using interference effects, depending wholly on the wave model, in order to determine the wavelength of the scattered radiation. So here was an experiment which apparently required the simultaneous use of both the wave and particle models of electromagnetic radiation for the interpretation of the results! The existence of this strange dichotomy in the nature of electromagnetic radiation was just one indication of the need for a radical revision of views regarding the physical world.
Compton scattering is usually explained in terms of the relativistic mass and momentum. Here, a mathematically equivalent and simple non-relativistic interpretation shows that the Compton frequency shift is equal to the de Broglie frequency associated with the moving charged particle (e.g., an electron). In this work, the moving electron is considered as a particle and the electromagnetic energy associated with it is shown to be proportional to the de Broglie frequency. This energy is released when its motion is arrested, as for example on a diffraction screen, where it causes the observed interfernce patterns. Thus, electrons transport electromagnetic energy from a source to a sink.
The interference between quantum amplitude for two electrons, emitted from two source points, to be detected at two detection points, is a direct result of quantum exchange statistics. Such interference is observed in the coincidence probability, compared with that of statistically independent electrons, by computing the time correlation function from the arrival times of the electrons. When the two detectors are separated by a distance less than the coherence length, the coincidence probability is suppressed for electrons (antibunching) due to the Pauli principle, even though they do not interact with each other. However, electrons are charged particles. The Coulomb potential, which governs the scattering of one charged particle by another, is so long ranged. It is obvious that we must consider the Pauli principle and the Coulomb interactions simultaneously. This paper deals with basic experimental and theoretical investigations of the antibunching behavior of electrons in a free beam by considering the Pauli principle and the direct Coulomb interaction between two individual electrons. The experimentally found dependences are described in a model which considers the Coulomb scattering and theoretical values of correlation signals evaluated by analytical calculations agree with those determined by experiment. A study of the time correlation function from the arrival times of the electrons will lead to an understanding of the physical processes that take place in electron guns.