The End of Time: The Next Revolution in Physics

This had important consequences for the theory of time. Poincaré’s 1898 paper showed that it must answer two main questions: how simultaneity is to be defined, and what duration is. Associated with the second question is another, almost as important: what is a clock? Because of his approach, Einstein answered only the first question at a fundamental level. He gave at best only partial answers to the other two, and gave no explicit theories of either rods or clocks. Instead, he tacitly assumed the minimal properties they should possess. Otherwise, he relied to a very great extent on the relativity principle. It took him far. Few things in physics are more beautiful than the way he postulated the universal relativity principle and the one particular law of light propagation, and then deduced, from their combination, extraordinary properties of rods, clocks and time. If the premises were true, rods and clocks had to behave that way.

During his protracted creation of general relativity, Einstein used this trick several times. The strategy was always to avoid specific assumptions, and instead to seek principles. In this way he avoided ever having to address the physical working of rods and clocks: they were always treated separately as independent entities in both relativity theories. Their properties were not deduced from the inner structure of the theory, but were simply required to accord with the relativity principle. Einstein was well aware that this was ultimately unsatisfactory, and said so in a lecture delivered in 1923. He made similar comments again in 1948 in his Autobiographical Notes.

However, the tone of his comments does not suggest that he expected any great insight to spring from the rectification of this ‘sin’ (Einstein’s own expression). Only a ‘tidying up’ operation was needed. This gap in the theory of duration and clocks has still not been filled. I know of no study that addresses the question of what a clock is (and how crucially it depends on the determination of an inertial frame of reference) at the level of insight achieved in non-relativistic physics by James Thomson, Tait and Poincaré. Throughout relativity, both in its original, classical form and in the attempts to create a quantum form of it (which we come to in Part 5), clocks play a vital role, yet nobody really asks what they are. A distinguished relativist told me once that a clock is ‘a device that the National Bureau of Standards confirms keeps time to a good accuracy’. I felt that, as the theorist, he should be telling them, not the other way round.

The truth is that a chapter of physics somehow never got written. Despite his great admiration for Mach, Einstein was curiously insensitive to the issues highlighted by Mach and Poincaré. He did not directly address the nature and origin of the framework of dynamics. Despite an extensive search through his published papers and published and unpublished correspondence, I have found no indication that he ever thought really seriously about issues like those raised by Tait’s problem. This is rather surprising, since these were ‘hot topics’ during the very period in which Einstein created special relativity. He did not ask how the spatiotemporal framework (i.e. the framework of space and time used by physicists) arose; instead, he described the finished product and the processes that take place within the arena it creates.

In fact, Einstein and Hermann Minkowski, whose work will shortly be considered, brought about a marked change of emphasis in physics. To use an expression of John Wheeler, the ‘royal high road of physics’ from Galileo until Einstein was dynamics. Maxwell saw his own work as an extension of the principles developed by Galileo and Newton to new phenomena and to the field notion introduced by Faraday. At the same time, other scientists like Carl Neumann and Mach became aware of the need for new foundations of dynamics. In Poincaré’s writings of around 1900, one can see clear hints of how dynamics might have been developed further as the main stream of research. In particular, an explicit theory of the origin of the spatiotemporal framework might have emerged. That is more than evident from Poincaré’s 1898 paper on time and his 1902 comments, discussed in Chapter 5.