Significance of c/sqrt(2) in Relativistic Physics

TL;DR

This paper explores the significance of the critical speed c/√2 in relativistic physics, showing how it affects the behavior of accelerated systems and gravitational fields, leading to sign reversals in relative motion.

Contribution

It introduces the concept of a critical speed c/√2 in relativistic motion, highlighting its effects on inertial and tidal accelerations in accelerated and gravitational systems.

Findings

Sign reversal in accelerations above c/√2

Critical speed influences relativistic motion behavior

Contrasts with Newtonian expectations

Abstract

In the description of \emph{relative} motion in accelerated systems and gravitational fields, inertial and tidal accelerations must be taken into account, respectively. These involve a critical speed that in the first approximation can be simply illustrated in the case of motion in one dimension. For one-dimensional motion, such first-order accelerations are multiplied by $(1-V^2/V_c^2)$, where $V_c=c/\sqrt{2}$ is the critical speed. If the speed of relative motion exceeds $V_c$, there is a sign reversal with consequences that are contrary to Newtonian expectations.