# Time dispersion and quantum mechanics

## TL;DR

This paper proposes a symmetric treatment of time and space in quantum mechanics using path integrals, predicting testable effects like time dispersion and entanglement in time, with implications for quantum gravity research.

## Contribution

It introduces a generalized path integral approach that treats time as an observable, predicts measurable effects, and avoids ultraviolet divergences, offering new insights into quantum mechanics and gravity.

## Key findings

- Predicted time dispersion effects of order an attosecond.
- Established equivalence of time/energy and space/momentum uncertainty principles.
- Identified suppression of ultraviolet divergences through time entanglement.

## 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.