Accounting for mass variation in terms of velocity in quantum mechanics

Konstantin V. Kazakov

Ching-Chuan Su

By taking both the Doppler frequency shift for electromagnetic wave and the quantum energy variation of matter wave into consideration, a resonant-absorption condition based on the local-ether wave equation is presented to account for a variety of phenomena consistently, including the Ives-Stilwell experiment, the output frequency from ammonia masers, and the Mössbauer rotor experiment. It is found that in the resonant-absorption condition, the major term associated with the laboratory velocity is a dot-product term between this velocity and that of the emitting or absorbing atom. This term appears both in the Doppler frequency shift and the transition frequency variation and then cancels out. Thereby, the experimental results can be independent of the laboratory velocity and hence comply with Galilean relativity, despite the restriction that the involved velocities are referred specifically to the local-ether frame. However, by examining the resonant-absorption condition in the Mössbauer rotor experiment to a higher order, it is found that Galilean relativity breaks down.

Carlo Heissenberg, Augusto Sagnotti

Francesco R. Ruggeri

The idea of impulse, i.e. Change in momentum = Integral dt Force appears in Newtonian mechanics. Impulse is considered to be a physical observable, for example it may be linked to the damage done by a particle hitting a target. Impulse, however, only depends on momentum and so two particles with the same momentum, but different masses and velocities may cause the same damage i.e. represent the same physical observable. Momentum in nonrelativistic Newtonian mechanics is m v where m is rest mass and v velocity. Velocity requires a clock in order to measure it, yet two particles with the same momentum and different velocities are considered equivalent in terms of the damage done upon collision with a target i.e the physical impulse. Thus we suggest that time must formally disappear from mv, but this implies that rest mass must behave as t or dt. Furthermore, given Kinetic energy = .5mvv, it must behave as 1/dt. In other words, the reciprocal of kinetic energy behaves as a gradation of time. This is not a standard clock as the gradation is based on a specific kinetic energy and is different for another. In other words, two particles with the same p and different v, have different time gradations. This, however, is a quantum mechanical result. Thus we argue that quantum mechanics may be responsible for the idea of p yielding the same impulse hit for two different v. We further argue that these ideas may be extended to include rest mass with v=0 and to indicate that 1/p is linked to dx, a ruler gradation which is again a quantum mechanical result. Lastly, we argue that these ideas lead to the special relativistic result EE = ppcc + mmcccc and so argue that free particle quantum mechanics and special relativity are closely linked and that classical impulse follows from free particle quantum mechanics.

Bruce M. Bennett, Donald D. Hoffman, Chetan Prakash

Gustavo V. López

An extension of Shrödinger’s quantization on the space (x, p), where the Hamiltonian approach is needed, is made on the space (x, v) where the Hamiltonian approach is not needed at all. The purpose of this paper is to give a possible extension of the actual formulation of the Quantum Mechanics, and this is achieved through a function K(x, v, t) which takes the place of the Hamiltonian on the Shrödinger’s equation and has units of energy. This approach allows us to include the quantization of classical velocity depending problems (dissipative) and position depending mass variation problems. Some examples are given.