The person who above all brought the issue of foundations back to the fore was the Austrian physicist Ernst Mach, whose brilliant studies in the nineteenth century of supersonic projectiles and their sonic boom are the reason why the Mach numbers are named after him. Mach was interested in many subjects, especially the nature and methods of science. His philosophical standpoint had points in common with Bishop Berkeley, but even more with the ideas of the great eighteenth-century Scottish empiricist David Hume. Mach insisted that science must deal with genuinely observable things, and this made him deeply suspicious of the concepts of invisible absolute space and time. In 1883 he published a famous history of mechanics containing a trenchant and celebrated critique of these concepts. One suggestion he made was particularly influential.
It arose as a curious consequence of the covert way Newton had attacked Descartes. Considering Newton’s bucket argument, Mach concluded that, if motion is relative, it was ridiculous to suppose that the thin wall of the bucket was of any relevance. Mach had no idea that Newton was attacking Descartes’s notion of the one true philosophical motion, just as Newton had not seen that Descartes had invented it only to avoid the wrath of the Inquisition. Newton had used the bucket argument to show that relative motion could not generate centrifugal force, but Mach argued that the relative motions that count are the ones relative to the bulk of the matter in the universe, not the puny bucket. And where is the bulk of the matter in the universe? In the stars.
This led Mach to the revolutionary suggestion that it is not space but all the matter in the universe, exerting a genuine physical effect, that creates centrifugal force. Since this is just a manifestation of inertial motion, which Newton claimed took place in absolute space, Mach’s proposal boiled down to the idea that the law of inertia is indeed, as Bishop Berkeley believed, a motion relative to the stars, not space. Mach’s important novelty was that there must be proper physical laws that govern the way distant matter controls the motions around us. Each body in the universe must be exerting an effect that depends on its mass and distance. The law of inertia will turn out to be a motion relative to some average of all the masses in the universe. For this basic idea, Einstein coined the expression Mach’s principle, by which it is now universally known (though attempts at precise definition vary quite widely).
Mach’s idea suggests that the Newtonian way of thinking about the workings of the universe, which is still deep-rooted, is fundamentally wrong. The Newtonian scheme describes an ‘atomized’ universe. The most fundamental thing is the containing framework of space and time: that exists before anything else. Matter exists as atoms, tiny unchanging masses that move in space and time, which govern their motion. Except when close enough to interact, the atoms move with complete indifference to one another, each following a straight and lonely path through the infinite reaches of absolute space. The Machian idea takes the power from space and time and gives it to the actual contents of the universe, which all dance in their motions relative to one another. It is an organic, holistic view that knits the universe together. Very characteristic is this remark of Mach in his The Science of Mechanics (pp.287-8):
Nature does not begin with elements, as we are obliged to begin with them. It is certainly fortunate for us that we can, from time to time, turn aside our eyes from the overpowering unity of the All and allow them to rest on individual details. But we should not omit, ultimately to complete and correct our views by a thorough consideration of the things which for the time being we have left out of consideration.
Mach himself made only tentative suggestions for a new relative mechanics, but his remarks caught the imagination of many people, above all Einstein, who said that Hume and Mach were the philosophers who had influenced him most deeply. Einstein spent many years trying to create a theory that would embody Mach’s principle, and initially believed that he had succeeded in his general theory of relativity. That is why he gave it that name. However, after a few years he came to have doubts. Eventually he concluded that Mach’s idea had been made obsolete by developments in physics, especially the theory of electro-magnetism developed by Faraday and Maxwell, which had introduced new concepts not present in Newton’s scheme.
Throughout the twentieth century, physicists and philosophers discussed Mach’s principle at great length, without coming to any conclusion. It is my belief that the problem lies in Einstein’s highly original but indirect approach. Mach had not made a really clear proposal, and Einstein never really stopped and asked himself just what should be achieved by Mach’s principle. I shall consider this in Part 3, but I need to anticipate a small part of the story in order to justify Part 2. Einstein’s theory is rather complicated and achieves several things at once. It is not easy to separate the parts and see the ‘Machian’ structure. In my opinion, general relativity is actually as Machian as it could be. What is more, it is the Machian structure that has such dramatic consequences when one tries to reconcile the theory with quantum mechanics. If, as I believe, the quantum universe is timeless, it is so because of the Machian structure of general relativity. To explain the core issues, I need a simplified model that captures the essentials. This Part 2 will provide. It will also provide a direct link between the great early debate about the foundations of mechanics and the present crisis of quantum cosmology. Two key issues are still the same: what is motion, and what is time? It will also enable me to explain the main work in physics with which I have been involved, and make it easier for you to see why I have come to doubt the existence of time.
Science advances in curious ways, and scientists are often curiously unconcerned with foundations. Descartes was one of the greatest philosophers, yet in that first book in 1632 he never gave a moment’s thought to the definition of motion. We are so used to living on the solid Earth that it seems unproblematic to say that a body moves in a straight line. If the Inquisition had not condemned Galileo, Descartes would never have argued for the relativity of motion. But for the inconsistency of his system, Newton would not have made an issue out of absolute space and time. He would not have devised the bucket argument, Mach might never have had his novel idea, and Einstein would not have been inspired to his greatest creation.
Had the Inquisition condemned Galileo a few months later, Descartes would have published his ideas in their original form – and general relativity might never have been found.
AN ALTERNATIVE ARENA
I would like to say a bit more about my own personal development, which as the book progresses will help you to understand why I am so deeply convinced of the need to have a new concept of time. In the very first days after my trip to the Bavarian Alps, while thinking hard about time, I came across Mach’s book. Like so many others, I was captivated by his idea about inertia. His comments on time also encouraged me greatly: ‘It is utterly beyond our power’, he said, ‘to measure the changes of things by time. Quite the contrary, time is an abstraction, at which we arrive by means of the changes of things.’ This was just the conclusion I had reached. A year or so later, after I had decided to study the foundations of physics, I started to read the papers Einstein had written when he was creating general relativity. Comparing them with what Mach had written, I came to the conclusion that Einstein had simply not set about the problem in the right way: he had not attacked it directly. It seemed to me necessary to go back to first principles.