Mach’s Principle

Einstein’s introduction of Mach’s principle, shortly after the publication of the General Relativity Theory and his remarks of 1921 are considered, especially his prediction that “spectator matter” should alter the masses of nearby objects. Difficulties of implementing the principle in cosmological terms are mentioned. Sciama’s vector gravity theory is laid out, noting the role of the vector potential in the production of inertial reaction forces. From Sciama’s work it follows that “critical cosmic matter density” and cosmic scale spatial flatness with their concomitant condition that the total scalar gravitational potential \( \varphi \) is equal to the square of the speed of light is required if inertial reaction forces are solely due to gravity. The Wilkinson Microwave Anisotropy Probe results, which show space at cosmic scale to be flat, are mentioned in this connection. Carl Brans’ argument about the role of spectator matter and Ken Nordtvedt’s comments on gravitomagnetism are then discussed. Radiation reaction, gravity waves, and the instantaneity of inertial reaction forces are then investigated. The relationalist and physical interpretations of Mach’s principle are mentioned, and the chapter concludes with the statement of the Mach-Einstein-Sciama laws of inertia.