June 5, 2017
Simultaneity, Relativity, Timing, Speed of Light
Newton’s Mathematical Principles of Natural Philosophy provided the foundation of classical physics. This paper reviews several of his critical definitions, his three axioms, key corollaries, and concept of inertial frames. Newton’s first axiom or law requires the vector addition of velocities by Corollary I to translate the equation of motion of a constantly moving body from one inertial frame to another inertial frame. His relativity principle in Corollary V is often expanded to mean that any equation retains the same form in all inertial frames. This is true if the equations involve only Newtonian forces, but equations that specify velocity need to include the mutual velocity between moving inertial frames to fully transform the results between all reference frames. The speed of light parameter must correctly incorporate the mutual velocity between moving inertial frames. It is assumed the speed of light is a constant in all directions only in absolutely stationary, nongravitated reference frames, which is less restrictive than the assumption of universal speed of light in all inertial frames. A test is outlined with suggested equipment to measure the one-way speed of light simultaneously in three dimensions. Equations are provided to convert the results into the instantaneous directional velocity of the laboratory frame. It will take years to separate Earth’s different velocities and accelerations.