On the positive mass theorem in general relativity and Lorentz covariance of the Dirac wave equation in quantum mechanics

TL;DR

This paper challenges the positive mass theorem in general relativity by providing a counterexample and discusses the incompatibility of Lorentz covariance of the Dirac equation with Einstein's mass-energy equivalence.

Contribution

It demonstrates that the positive mass theorem's framework can be flawed and shows the incompatibility between Lorentz covariance of the Dirac equation and mass-energy equivalence.

Findings

Counterexample with a plane light wave shows no guaranteed total four-vector.

Lorentz covariance of Dirac equation conflicts with Einstein's mass-energy equivalence.

Theoretical flaws in the positive mass theorem framework.

Abstract

The positive mass theorem in general relativity states that in an asymptotically flat spacetime, if the momentum--energy tensor is divergence-free and satisfies a dominant energy condition, then a total momentum--energy four-vector can be formed, of which the energy component is nonnegative. In this paper, we take the wave four-tensor of a plane light wave in free space as a counterexample to show that there is no guarantee that a total four-vector can be formed. Thus the theoretical framework for the positive mass theorem is flawed. In addition, it is also shown as well that the Lorentz covariance of Dirac wave equation is not compatible with Einstein mass--energy equivalence.