Time dispersion in quantum mechanics

Abstract

In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables. This assumption is both untested and inconsistent with relativity. From dimensional analysis, we expect quantum effects along the time axis to be of order an attosecond. Such effects are not ruled out by current experiments. But they are large enough to be detected with current technology, if sufficiently specific predictions can be made. To supply such we use path integrals. The only change required is to generalize the usual three dimensional paths to four. We predict a large variety of testable effects. The principal effects are additional dispersion in time and full equivalence of the time/energy uncertainty principle to the space/momentum one. Additional effects include interference, diffraction, and entanglement in time. The usual ultraviolet divergences do not appear: they are suppressed by a combination of dispersion in time and entanglement in time. The approach here has no free parameters; it is therefore falsifiable. As it treats time and space with complete symmetry and does not suffer from the ultraviolet divergences, it may provide a useful starting point for attacks on quantum gravity.

Quantum Clock in the Projection Evolution Formalism

“…where c represents the possible degeneration of the spectrum. The transformation property (9) implies that it is sufficient to solve the eigenequation (10) b ≡ w b are independent of n. The distribution of ξ should have a pronounced maximum very close to zero. (In this work we assume ξ > 0 but the general condition is, that ξ ∈ R has a distribution around zero, asymmetric towards ξ > 0 values.…”

Time dispersion in quantum electrodynamics

“…In previous work we have looked at time dispersion in the single particle case [50] (paper A) and at the specific problems created in doing time-of-arrival measurements [51] (paper B). The investigation here extends this work to QED.…”

Time dispersion in quantum electrodynamics

“…In previous work we have looked at time dispersion in the single particle case [4] (paper A) and at the specific problems created in doing time-of-arrival measurements [5] (paper B). The investigation here extends this work to QED.…”

“…But consider the infinitesimal ı . We construct the Feynman diagrams by doing integrals in four momentum d 4 p over the propagators. The ı identifies one of these four integrals not as a normal but as a contour integral.…”