Based on the local-ether wave equation for free particle, the dispersion of matter wave is examined. From the dispersion relation, the angular frequency and wavelength of matter wave are derived. These formulas look like the postulates of de Broglie in conjunction with the Lorentz mass-variation law. However, the fundamental difference is that for terrestrial particles their speeds are referred specifically to a geocentric inertial frame and hence incorporate the speed due to earth's rotation. Thus the local-ether model predicts an east-west directional anisotropy both in mass and wavelength. Meanwhile, in spite of the restriction on reference frame, the local-ether model can account for the matter-wave interference experiments of the Bragg reflection and the Sagnac effect. For electron wave, the effects of earth's rotation are negligible and the derived Bragg angle is actually in accord with the Davisson-Germer experiment, as examined within the present precision. On the other hand, the local-ether model leads to a directional anisotropy in the Bragg angle in neutron diffraction. The predicted anisotropy due to earth's rotation then provide a means to test the local-ether wave equation.
Based on the local-ether wave equation for free particle, the dispersion of matter wave is examined. From the dispersion relation, the angular frequency and wavelength of matter wave are derived. These formulas look like the postulates of de Broglie in conjunction with the Lorentz mass-variation law. However, the fundamental difference is that for terrestrial particles their speeds are referred specifically to a geocentric inertial frame and hence incorporate the speed due to earth's rotation. Thus the local-ether model predicts an east-west directional anisotropy both in mass and wavelength. Meanwhile, in spite of the restriction on reference frame, the local-ether model can account for the matter-wave interference experiments of the Bragg reflection and the Sagnac effect. For electron wave, the effects of earth's rotation are negligible and the derived Bragg angle is actually in accord with the Davisson-Germer experiment, as examined within the present precision. On the other hand, the local-ether model leads to a directional anisotropy in the Bragg angle in neutron diffraction. The predicted anisotropy due to earth's rotation then provide a means to test the local-ether wave equation.
A wave equation complying with Galilean transformations is proposed for electromagnetic and matter waves. A fundamental feature entirely different from the principle of relativity is that the wave equation is referred specifically to the proposed local-ether frame. For electromagnetic wave, the local-ether wave equation accounts for a wide variety of experiments of propagation or interference. For matter wave, the wave equation leads to modifications of Schrodinger's equation which in turn lead to a unified quantum theory of electromagnetic and gravitational forces in conjunction with the identity of inertial and gravitational mass. Further, it leads to modifications of the Lorentz force law and of Maxwell's equations. Moreover, the wave equation leads to dispersion of matter wave, from which the speed-dependences in the mass of a particle and in the wavelength, angular frequency, and quantum energy of a matter wave are derived. The consequences of the wave equation are in accord with a wide variety of experiments which are commonly ascribed to the special relativity, the general relativity, the Lorentz mass-variation law, or to the de Broglie matter wavelength. Thereby, the local-ether wave equation unifies quantum mechanics, electromagnetics, and gravitation.
Recently, we have presented a local-ether wave equation incorporating a nature frequency and the electric scalar potential, from which the speed-dependences in the angular frequency and wavelength of matter wave, in the mass of particle, and in the energy of quantum states are derived. These relations look like the postulates of de Broglie and the Lorentz mass-variation law, except that the particle speed is referred specifically to a geocentric inertial frame and hence incorporates earth's rotation for earthbound particles. Further, the wave equation is extended by connecting the scalar potential to the augmentation operator which is associated with a velocity difference between involved particles. Then the electromagnetic force law is derived, which under some ordinary conditions reduces to the modified Lorentz force law. In this investigation, the interaction of atoms with electromagnetic radiation is explored. Then it is shown that the time evolution equation derived from the wave equation is substantially identical to Schrödinger's equation incorporating the vector potential, if the latter is observed in the atom frame and if the source generating the vector potential is electrically neutralized, as in common practice.
The theory of Quantum Electromagnetics presents a wave equation which is constructed, in compliance with Galilean transformations, for electromagnetic and matter waves. A fundamental feature entirely different from the principle of relativity is that the wave equation is referred specifically to the proposed local-ether frame. For electromagnetic wave, the local-ether wave equation accounts for a wide variety of experiments on propagation and interference. For matter wave, the wave equation leads to modifications of Schrodinger’s equation which in turn lead to a unified quantum theory of electromagnetic and gravitational forces in conjunction with the origin and the identity of inertial and gravitational mass. Further, it leads to modifications of the Lorentz force law and of Maxwell’s equations. Moreover, the wave equation leads to the dispersion of matter wave, from which the speed-dependence in the mass of a particle and in the wavelength, angular frequency, and quantum energy of a matter wave can be derived. The consequences of the wave equation are in accord with a wide variety of experiments that are commonly ascribed to the special relativity, the general relativity, the Lorentz mass-variation law, or to the de Broglie matter wave. Thereby, the local-ether wave equation unifies quantum mechanics, electromagnetics, and gravitation.
The phase shift of matter wave due to the Earth's rotation and gravity has been demonstrated in the neutron-interferometry experiments where the Bragg reflection of the neutron wave from crystals is used to form a closed path. In the literature, the rotation-induced phase shift is ascribed to an extra energy term associated with angular momentum in the Hamiltonian. In this investigation, based on a classical treatment of the collision of neutrons with the lattice planes, the modifications in the particle velocity due to the Earth's rotation as well as those due to gravity are calculated. Then, in conjunction with the relation between the particle velocity and the propagation vector of matter wave, it is shown that the corresponding phase shifts in matter wave are in accord with the interference experiments. Thereby, based on the velocity modification due to collision, a reinterpretation of the effects of the Earth's rotation and gravity on the neutron-wave interference is presented. Meanwhile, a null effect of the Earth's orbital motion is predicted.
The Compton effect is commonly cited as a demonstration of the particle feature of light, while the wave nature of matter has been proposed by de Broglie and demonstrated by Davisson and Germer with the Bragg diffraction of electron beams. In this investigation, we present an entirely different interpretation of the Compton effect based on the postulates of de Broglie and on an interaction between electromagnetic and matter waves. The speeds of interacting electrons in the Compton scattering are quite fast and its mechanism relies heavily on the mass variation. Thus, based on this wave interpretation, the Compton effect can be viewed as a further demonstration of the postulates of de Broglie for high-speed particles. In addition to the scattered wave, a direct radiation depending on the mass variation is predicted, which provides a means to test the wave interpretation.
Recently, we have presented the local-ether model of propagation of electromagnetic wave. This new classical model accounts for a wide variety of propagation phenomena, including the gravitational effects associated with the deflection of light by the Sun and the increment in interplanetary radar echo time, which are commonly ascribed to the general relativity. In this investigation, based on the local-ether model, a wave equation incorporating the gravitational potential, the electric scalar potential, and a natural frequency is proposed for the matter wave associated with a charged particle. The local-ether wave equation leads to a time evolution equation similar to Schrödinger's equation. Then both the gravitational and the electrostatic forces are derived in a quantum-mechanical approach. Furthermore, it is found that the gravitational mass and the inertial mass are identical to the natural frequency, aside from a common scaling factor. Thus the identity of gravitational and inertial mass is also derived from the local-ether wave equation.