Significance of c /sqrt2 in relativistic physics

Abstract

In the description of 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 − V2/V2c), where V_c=c/\sqrt{2} is the critical speed. If the speed of relative motion exceeds Vc, there is a sign reversal with consequences that are contrary to Newtonian expectations.