Reinterpretation of Matter-Wave Interference Experiments Based on the Local-Ether Wave Equation

Abstract

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.