It is considered constraints imposed by the quantum mechanics on the measurement of the density of the electromagnetic energy. First, the energy of the electromagnetic wave and the volume (time) are bound with the Heisenberg uncertainty principle. It reduces from double to ordinary the relativistic effect for the density of the electromagnetic energy. Second, the frequency of photons and the number of photons are bound with the Heisenberg uncertainty principle. Then relativistic effects for the frequency of photons and for the number of photons are incompatible.It is considered constraints imposed by the quantum mechanics on the measurement of the density of the electromagnetic energy. First, the energy of the electromagnetic wave and the volume (time) are bound with the Heisenberg uncertainty principle. It reduces from double to ordinary the relativistic effect for the density of the electromagnetic energy. Second, the frequency of photons and the number of photons are bound with the Heisenberg uncertainty principle. Then relativistic effects for the frequency of photons and for the number of photons are incompatible.

arXiv:physics/0402022Feb 5, 20040 citations

Relativistic Quantum Mechanics

Günter Ludyk

Springer eBooksOct 25, 20170 citations

Energy operator for non-relativistic and relativistic quantum mechanics revisited

J. A. Sánchez-Monroy, John Morales, Eduardo Zambrano

Hamiltonian operators are gauge dependent. For overcome this difficulty we reexamined the effect of a gauge transformation on Schrödinger and Dirac equations. We show that the gauge invariance of the operator $H-i\hbar\frac{\partial}{\partial t}$ provides a way to find the energy operator from first principles. In particular, when the system has stationary states the energy operator can be identified without ambiguities for non-relativistic and relativistic quantum mechanics. Finally, we examine other approaches finding that in the case in which the electromagnetic field is time independent, the energy operator obtained here is the same as one recently proposed by Chen et al. [1].Hamiltonian operators are gauge dependent. For overcome this difficulty we reexamined the effect of a gauge transformation on Schrödinger and Dirac equations. We show that the gauge invariance of the operator $H-i\hbar\frac{\partial}{\partial t}$ provides a way to find the energy operator from first principles. In particular, when the system has stationary states the energy operator can be identified without ambiguities for non-relativistic and relativistic quantum mechanics. Finally, we examine other approaches finding that in the case in which the electromagnetic field is time independent, the energy operator obtained here is the same as one recently proposed by Chen et al. [1].

arXiv:1208.1425Aug 7, 20121 citation

Relativistic Quantum Mechanics

Zoltán Papp

Springer eBooksJan 1, 20260 citations

Relativistic Quantum Mechanics

Walter Greiner

Springer eBooksJan 1, 1990232 citations

A justification of the invariance of the speed of light by quantum theoretical considerations

Michael Cordin

phenomena can often be analysed in a visually clear way by thought experiments. In the present work a new thought experiment is analysed, which describes the emission of a photon by a special mechanism. The analysis leads to the finding, that there is a natural connection between the energy-time uncertainty and the Heisenberg position-momentum uncertainty principle. A deeper analysis of this thought experiment, especially with regard to a justification of the Doppler effect from the uncertainty principle, leads to the conclusion, that the speed of light is invariant. Therefore it seems reasonable to assume, that the origin of relativistic laws lies in non-relativistic quantum mechanics.phenomena can often be analysed in a visually clear way by thought experiments. In the present work a new thought experiment is analysed, which describes the emission of a photon by a special mechanism. The analysis leads to the finding, that there is a natural connection between the energy-time uncertainty and the Heisenberg position-momentum uncertainty principle. A deeper analysis of this thought experiment, especially with regard to a justification of the Doppler effect from the uncertainty principle, leads to the conclusion, that the speed of light is invariant. Therefore it seems reasonable to assume, that the origin of relativistic laws lies in non-relativistic quantum mechanics.

Scientific ReportsJan 13, 20210 citations

H-i\hbar\frac{\partial}{\partial t}

provides a way to find the energy operator from first principles. In particular, when the system has stationary states the energy operator can be identified without ambiguities for non-relativistic and relativistic quantum mechanics. Finally, we examine other approaches finding that in the case in which the electromagnetic field is time independent, the energy operator obtained here is the same as one recently proposed by Chen et al. [1].