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 Despite an extensive search through his published papers and published and unpublished correspondence, I have found no indication that he ever thought really seriously about issues like those raised by Tait’s problem.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.
All this was changed by Einstein’s 1905 paper. Because of his quantum doubts, he distrusted explicit dynamical models. Within a few years a dualistic scheme appeared. Newton’s absolute space and time were replaced by space-time, but this was not the complete story. Actual physics emerged only with the statements about how rods and clocks behaved in space-time. This is where the scheme was dualistic. The behaviour of rods and clocks – and with it a theory of duration – never emerged organically from the structure of space-time, it was simply postulated. This is not to say the dualistic scheme is wrong in the statements it makes. Einstein’s theory is as secure as its foundations; there is no hint of failing there. However, insight into the nature of time and duration was lost.
For all that, general relativity does contain, hidden away in its mathematics (as I have already indicated), a theory of duration and the spatiotemporal framework. However, this did not come to light for many decades and even now is not properly appreciated. How this came about, and an account of the ‘hidden dynamical core’ of general relativity, are the subject of the next chapters.
It may help to end this chapter with a general remark on time. It is impossible to understand relativity if one thinks that time passes independently of the world. We come to that view only because change is so all-pervasive and so many different changes all seem to march in perfect step. Relativity is not about an abstract concept of time at alclass="underline" it is about physical devices called clocks. Once we grasp that, many difficulties fall away. If light did not travel so much faster than normal objects, we would observe relativistic effects directly and they would not strike us as strange. There is nothing inherently implausible in the idea that clocks travelling past us at high speed should be observed to go slower than the watch on our wrist. Motion of the clock might well alter the rate at which it ticks. After all, when we swim through water, we feel the way our body responds. If there were an aether, clocks could well be affected by their motion through it. What is difficult to grasp is how observers travelling with the moving clocks think our wristwatch is running slow, while we think just the same about their clocks (this apparent logical impossibility has been dealt with in Box 10). However, the important thing is to get away from the idea that time is something. Time does not exist. All that exists are things that change. What we call time is – in classical physics at least – simply a complex of rules that govern the change.
CHAPTER 9
Minkowski the Magician
THE NEW ARENA
Hermann Minkowski’s ideas have penetrated deep into the psyche of modern physicists. They find it hard to contemplate any alternative to his grand vision, presented in a famous lecture at Cologne on 21 September 1908. Its opening words, a magical incantation if ever there was one, are etched on their souls:
The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
The branch of knowledge that considers what exists is ontology. These three sentences changed the ontology of the world – for physicists at least.
For most physicists in the nineteenth century, space was the most fundamental thing. It persisted in time and constituted the deepest level in ontology. Space, in turn, was made up of points. They were the ground of being, conceived as identical, infinitesimal grains of sand close-packed in a block. Space was like glass. It was, of course, three-dimensional. However, alerted by Einstein’s work to how the relativity principle mixed up space and time, Minkowski commented that ‘Nobody has ever noticed a place except at a time, or a time except at a place.’ He had the idea that space and time belonged together in a far deeper sense than anyone had hitherto suspected. He fused them into space-time and called the points of this four-dimensional entity events. They became the new ground of being.
Such atoms of existence – the constituent events of space-time – are very different from the entities that I suggested in Part 2 as the true atoms of existence. The main aim of Part 3 is to show that space-time can be conceived of in two ways – as a collection of events, but also as an assemblage of extended configurations put together by the principle of best matching and the introduction of a ‘time spacing’ through a distinguished simplifier, as explained for the Newtonian case at the end of Chapter 7. However, reflecting the relativity of simultaneity, the assemblage has an additional remarkable property that gives rise to the main dilemma we face in trying to establish the true nature of time.
FROM THREE TO FOUR DIMENSIONS
In itself, the fusion of space and time was not such a radical step. It can be done for Newtonian space and time. To picture this, we must suppose that ordinary space has only two dimensions and not three. We can then imagine space as a blank card, and the bodies in space as marks on it. Any relative arrangement of these marks defines an instant of time.
The solution of Tait’s problem showed how relative configurations can, if their bodies obey Newton’s laws, be placed in absolute space at their positions at corresponding absolute times. If space is pictured as two-dimensional, absolute space is modelled not by a room but by a flat surface. The solution of Tait’s problem places each card on the surface in positions determined by the marks on the cards. In these positions, in which the centre of mass can be fixed at one point, any body moving inertially moves along a straight line on the surface.