The value of Einstein’s mistakes

In his thoughtful and timely article, Steven Weinberg analyzes some of Einstein’s mistakes and notes some others. Another fundamental conceptual mistake is hidden in Einstein’s celebrated 1905 paper on relativity.

In a lengthy discussion in the first part of that paper, Einstein showed that the speed of light can be made constant by adopting a clock synchronization based on two-way light signals. With that synchronization, measurements of the one-way speed of light become logically circular, and Einstein later declared that the constancy of the speed of light was “neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make at my free discretion to arrive at a definition of simultaneity.” ¹

However, Einstein overlooked that the validity of Newton’s laws at low speeds in each reference frame permits the use of simple mechanical methods of synchronization, such as slow clock transport or sound signals. Einstein’s synchronization procedure with light signals is thus superfluous—it plays no fundamental role and is merely the most convenient of several possible synchronization procedures. Furthermore, if clocks are synchronized by slow clock transport or by some other mechanical procedure, then measurements of the one-way speed of light are not logically circular, and those measurements provide an unambiguous experimental test of the constancy of this speed. In fact, clock transport has been used in such experimental tests. ^2,3 Einstein should have considered the implications of alternative synchronization procedures for the conceptual foundations of relativity, and he should have recognized that the constancy of the speed of light had to be established by experiment, not by stipulation.