A Local-Ether Wave Equation Unifying
Quantum Mechanics, Electromagnetics, and Gravitation
Chapter 8 Interference of Matter Wave
Based on the local-ether wave equation for free particles, the dispersion of matter wave is revisited. From the dispersion relation, the angular frequency and the wavelength of the associated matter wave are derived, which correspond to the quantum energy and the momentum of the particle, respectively. 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 wave equation predicts an east-west directional anisotropy in mass and matter wavelength. As the phase variation of a particle beam is given by the propagation vector and the path length along the beam, a shift in either of these quantities then leads to a phase difference between two coherent beams. The derived phase-difference formulas consistently account for the matter-wave interference experiments demonstrating the Bragg reflection, the gravitational effect, and the Sagnac effect, in spite of the restriction on the reference frame. For electron wave, the effects of earth's rotation can be negligible and thus 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 wave equation leads to a terrestrial anisotropy due to earth's rotation in the Bragg angle in neutron diffraction. The predicted anisotropy then provides a means to test its validity.
This Chapter is based on:
C.C. Su, "Reinterpretation of the effects of earth's rotation and gravity on the neutron-interferometry experiment," Europhys. Lett., vol. 60, pp. 1-6, Oct. 2002.
C.C. Su, "Reinterpretation of matter-wave interference experiments based on the local-ether wave equation," http://arXiv.org/physics/0208085.
C.C. Su, "A quantum-mechanical origin of the mass-variation law," in Bull. Am. Phys. Soc., vol. 45, no. 2, p. 59, Apr. 2000.
A supplement to this Chapter:
C.C. Su, "A wave interpretation of the Compton effect as a further demonstration of the postulates of de Broglie," http://arXiv.org/physics/0506211.
Full texts of major papers contributing to this Chapter (in PDF)
(1) Bragg reflection and Sagnac effect,
(2) Neutron interferometry; and
(3) Compton effect