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Many historical works on Einstein describe his approval of Mach?s philosophy and his effort to incorporate Mach?s Principle into his relativity theories. Einstein eventually abandoned Mach?s Principle but with some reservations. However, Mach?s Principle still persists and its presumed incompatibility with Einstein?s Relativity continues to be an obstacle for many in their attempts to understand Einstein?s theory. This essay intends to resolve the issue by showing that Einstein?s Special Relativity, in fact, is subject to Mach?s Principle and that the proof can be found in the relativistic velocities of atomic orbits.

At the present time the accepted cosmological picture is that of an infinite and expanding Universe based on Einstein's relativity. Cosmic redshifts are interpreted as galaxies receding from us with speeds that increase with distance, reaching velocities approaching c, the speed of light, and it is believed that we occupy the center of the expansion. Placing outselves at the center, and at relative rest, creates mathematical equations that are conceptually impossible. One can compare it to the difficulties our ancestors faced before Copernicus' time, trying to describe planetary orbits mathematically, with Earth at the center and at rest. The problem is solved by adopting Mach's Principle, which turns the picture around so that our frame of reference is moving with c relative to the rest of the Universe and the proof if found in the physics of atomic orbits, a domain where Einstein's relativistic mechanics fail.