Julian Barbour - The End of Time - The Next Revolution in Physics

Newton imagined a bucket filled with water and suspended by a rope from the ceiling. The bucket is turned round many times, twisting the rope, and is then held still until the water settles. When the bucket is released, the rope unwinds, twisting the bucket. Initially the surface of the water remains flat, but slowly the motion of the bucket is transmitted to the water, which starts to spin, feels a centrifugal force and starts to rise up the side of the bucket. After a while, the water and bucket spin together without relative motion, and the water surface reaches its greatest curvature.

Newton asked what it was that caused the water’s surface to curve. Was it the water’s motion relative to the side of the bucket (Descartes’s claimed true philosophical motion relative to the immediately adjacent matter) or motion relative to absolute space? Surely the latter, since when the relative motion is greatest, at the start, there is no curvature of the water’s surface, but when the relative motion has stopped (and the water and bucket spin together) the curvature is greatest. This was Newton’s main argument for absolute space. It was strong and it ridiculed Descartes.

In Newton’s lifetime, his notion of absolute space, to which he gave such prominence, attracted strong criticism. If space were invisible, how could you say an object moves in a straight line through a space you cannot see? Newton never satisfactorily answered this question. Many people felt, as Descartes did, that motion must be relative to other matter, though not necessarily adjacent matter. Bishop Berkeley argued that, as in Copernican astronomy, motion must ultimately be relative to the distant stars, but he failed to get to grips with the problem that the stars too must be assumed to move in many different ways and thus could not define a single fixed framework, as Copernicus and Kepler had believed.

Newton’s most famous critic was the great German mathematician and philosopher Wilhelm Gottfried Leibniz, who had been involved in a very unpleasant dispute with Newton about which of them had first discovered the calculus, the revolutionary new form of mathematics that made so many things in science much easier, including the development of mechanics. In 1715, Leibniz began a famous correspondence on Newton’s ideas with Samuel Clarke, who was advised by Newton. The Leibniz-Clarke Correspondence has become a classic philosophy text. Many undergraduates study it, and philosophers of science often discuss it.

The exchange had an inconclusive outcome. It is generally agreed that Leibniz advanced effective philosophical arguments, but he never addressed the detailed issues in mechanics. Typically, he argued like this. Suppose that absolute space does exist and is like Newton claimed, with every point of space identical to every other. Now consider the dilemma God would have faced when he created the world. Since all places in absolute space are identical, God would face an impossible choice. Where would he put the matter? God, being supremely good and rational, must always have a genuine reason for doing something – Leibniz called this the ‘principle of sufficient reason’ (I have already appealed to this when I discussed brain function and consciousness, by requiring an observable effect to have an observable cause) – and because absolute space offered no distinguished locations, God would never be able to decide where to put the matter. Absolute time, on the assumption that it existed, presented the same difficulty. Newton had said that all its instants were identical. But then what reason could God have for deciding to create the world at some instant rather than another? Again, he would lack a sufficient reason. For reasons like these, not all of them so theological, Leibniz argued that absolute space and time could not exist.

A century and a half passed before the issue became a hot topic again. This raises an important issue: how could mechanics have dubious foundations and yet flourish? That it flourished nevertheless was due to fortunate circumstances that are very relevant to the theme of this book. First, although the stars do move, they are so far away that they provide an effectively rigid framework for defining motions as observed from the Earth. It was found that in this framework Newton’s laws do hold. It is hard to overestimate the importance of this fortunate effective fixity of the distant stars. It presented Newton with a wonderful backdrop and convenient framework. Had the astronomers been able to observe only the Sun, Moon and planets but not the stars (had they been obscured by interstellar dust), Newton could never have established his laws. Thus, scientists were able to accept Newton’s absolute space as the true foundation of mechanics, using the stars as a substitute for the real thing – that is, a true absolute frame of reference. They also found that Newton’s uniformly flowing time must march in step with the Earth’s rotation, since when that was used to measure time (in astronomical observations spanning centuries, and even millennia) Newton’s laws were found to hold. Once again, a substitute for the ‘real thing’ was at hand. One did not have to worry about the foundations. Fortunate circumstances like these are undoubtedly the reason why it is only recently that physicists have been forced to address the issue of the true nature of time.

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).