Time dispersion in quantum electrodynamics

Abstract

Quantum electrodynamics (QED) is often formulated in a way that appears fully relativistic. However since QED treats the three space dimensions as observables but time as a classical parameter, it is only partially relativistic. For instance, in the path integral formulation, the sum over paths includes paths that vary in space but not paths that vary in time. We apply covariance to extend QED to include time on the same basis as space. This implies dispersion in time, entanglement in time, full equivalence of the Heisenberg uncertainty principle (HUP) in time to the HUP in space, and so on. In the long time limit we recover standard QED. Further, entanglement in time has the welcome side effect of eliminating the ultraviolet divergences. We should see the effects at scales of attoseconds. With recent developments in attosecond physics and in quantum computing, these effects should now be visible. The results are therefore falsifiable. Since the promotion of time to an operator is done by a straightforward application of agreed and tested principles of quantum mechanics and relativity, falsification will have implications for those principles. Confirmation will have implications for attosecond physics, quantum computing and communications, and quantum gravity.