The End of Time: The Next Revolution in Physics

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.