Inertial mass = gravitational mass, what about momentum?

TL;DR

This paper challenges the assumption that inertial and gravitational energy-momentum tensors are identical, suggesting they may differ and impacting the validity of Einstein's equivalence principle.

Contribution

It reveals that the inertial and gravitational energy-momentum tensors may not coincide, proposing a way to experimentally verify their difference through electron beam measurements.

Findings

Inertial and gravitational momenta may differ.

Symmetric inertial energy-momentum tensor conflicts with energy-charge conservation.

Transverse flux measurement of spin-polarized electrons can test tensor differences.

Abstract

It has been tested precisely that the inertial and gravitational masses are equal. Here we reveal that the inertial and gravitational momenta may differ. More generally, the inertial and gravitational energy-momentum tensors may not coincide: Einstein's general relativity requires the gravitational energy-momentum tensor to be symmetric, but we show that a symmetric inertial energy-momentum tensor would ruin the concordance between conservations of quantized energy and charge. The nonsymmetric feature of the inertial energy-momentum tensor can be verified unambiguously by measuring the transverse flux of a collimated spin-polarized electron beam, and leads to a serious implication that the equivalence principle and Einstein's gravitational theory cannot be both exact.