Equation and test of possible delay time of Newton force

TL;DR

This paper explores a heuristic modification to Newton's law introducing a delay time, which could influence precise gravitational measurements and suggests re-evaluating experiments to test this hypothesis.

Contribution

It proposes a non-zero delay time in Newton's force law affecting non-gravitational accelerations, and discusses how existing experiments could confirm or constrain this delay.

Findings

Delay time of ~1ms may affect G measurements.

Re-evaluation of Cavendish experiments can test the delay hypothesis.

Modified experiments could establish upper limits on delay time.

Abstract

Recently, a simple heuristic modification of the Newton potential with a non-zero delay-time $\tau_G$ has been proposed. Our modification is largely suppressed for purely gravitational interactions, it becomes relevant under non-gravitational accelerations of the sources. We illustrate how the choice $\tau_G\sim1$ms may already influence the 5th digit of G determined by Cavendish experiments. Re-evaluation of old Cavendish experiments and implementing slightly modified new ones may confirm the proposal or, at least, put a stronger upper limit on $\tau_G$.