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

An intriguing way to achieve this was suggested by Baierlein, Sharp and Wheeler’s paper in 1962 and its enigmatic hint that ‘time’ was somehow carried within space. This was taken literally, especially since it seemed to solve another problem of quantum acrobatics. In real acrobatics, not only location but also timing is of the essence. Nobody knew how to do quantum mechanics without an independent time external to the quantum degrees of freedom. But such a time appeared to have gone missing in gravity. Instead of time and two true degrees of freedom, there appeared to be no time but three degrees of freedom; these, moreover, were suspect. The count was all too suggestive – and many people came to the same conclusion: there is a time, but it is hidden in the three degrees of freedom.

According to this insight, the basic framework of quantum mechanics could be preserved, but the time it so urgently needed would be taken from the ‘world’ to which it was to be applied. Putting it in very figurative terms, one-third of space would become time, while the remaining two-thirds would become two true quantum degrees of freedom. Because time was to be extracted from space, from within the very thing that changes, the time that was to be found was called intrinsic time . The notion of intrinsic time was – and is – a breathtaking idea. But there was a price to be paid, and there was also a closely related problem to be overcome: which third of space is to be time?

The problem was that no clear choice could be made. Any and all 3-spaces can appear in the relations that summarize so beautifully the true essence of general relativity. What is more, any choice would ultimately amount to the introduction of distinguished coordinates on space-time. But this would run counter to the whole spirit of relativity theory, the essence of which was seen to be the complete equivalence of all coordinates. So if a choice were made, the price would be the loss of this equivalence. The price and the problem are one and the same. They presented the quantum theoreticians with a head-on collision between the basic principles of their two most fundamental theories – the need for a definite time in quantum mechanics and the denial of a definite time in general relativity. At an international meeting on quantum gravity held at Oxford in 1980, Karel Kuchař, concluding his review of the subject, stated that the problem of ‘quantum geometrodynamics is not a technical one, but a conceptual one. It consists in the diametrically opposite ways in which relativity and quantum mechanics view the concept of time ’. I have added the italics. I was there to hear the talk, and Kuchaf’s comment made a deep impression on me.

The search for the third of space that would become time has been like The Hunting of the Snark , Lewis Carroll’s mythical beast that no one could find. Since the idea of intrinsic time was first clearly formulated about thirty-five years ago, the beast has not been found. Karel has done more than anyone else to try to track it down. If he cannot find it, I feel that comes quite close to a non-existence proof. My own belief is that the idea is based on an incorrect notion of time. It is a mythical beast invoked in vain to solve a titanic struggle. It does not surprise me that a special time has not been found lurking in the tapestry of space-time. All I see in that tapestry are change and differences – and the differences are measured democratically. The idea of a special intrinsic time to be extracted out of space, or out of any part of space-time or its contents, violates the democratic theory of emphemeris time that lies at the heart of general relativity.

If we look at the Newtonian parallel of the notion, it seems strange. In a world of three particles, it is like saying that one of the sides of the triangle they form is time while the other two are true degrees of freedom. Such an attempt to find time breaks up the unity of the universe. No astronomer observing a triple-star system would begin to think like that. The key property of astronomical ephemeris time is that all change contributes to the measure of duration. There has to be a different way to think about time.

I believe it was found, perhaps unintentionally, by Bryce DeWitt in 1967. John Wheeler had strongly urged him to find the fundamental equation of quantum gravity. It was Wheeler’s high priority to find the Schrödinger equation of geometrodynamics. What the theory of intrinsic time should yield is a time-dependent Schrödinger equation that – in figurative language – evolves a wave function for ‘two-thirds of space’ with respect to a ‘time’ constituted by the remaining ‘one-third of space’. Balking at the invidious task of selecting which third should be ‘time’, DeWitt fell back on a very general formalism developed fifteen years earlier by Dirac that made it possible to avoid having to make a choice.

Dirac’s method makes it possible to treat all parts of space on an equal footing, and simply defers to later the problem of time. DeWitt used Dirac’s method to write the fascinating equation that, as Kuchaf noted, he himself calls ‘that damned equation’, John Wheeler usually calls the ‘Einstein-Schrödinger equation’ and everyone else calls the ‘Wheeler-DeWitt equation’. But what is this equation, and what does it tell us about the nature of time?

The most direct and naive interpretation is that it is a stationary Schrödinger equation for one fixed value (zero) of the energy of the universe. This, if true, is remarkable, for the Wheeler-DeWitt equation must, by its nature, be the fundamental equation of the universe. I pointed out in the discussion of the structure of molecules that the ‘ball-and-strut’ models are only approximations to the quantum description, being merely the most probable configurations. The Wheeler-DeWitt equation is telling us, in its most direct interpretation, that the universe in its entirety is like some huge molecule in a stationary state and that the different possible configurations of this ‘monster molecule’ are the Instants of time . Quantum cosmology becomes the ultimate extension of the theory of atomic structure, and simultaneously subsumes time.

We can go on to ask what this tells us about time. The implications are as profound as they can be. Time does not exist. There is just the furniture of the world that we call instants of time. Something as final as this should not be seen as unexpected. I see it as the only simple and plausible outcome of the epic struggle between the basic principles of quantum mechanics and general relativity. For the one – in its standard form at least – needs a definite time, but the other denies it. How can theories with such diametrically opposed claims coexist peacefully? They are like children squabbling over a toy called time. Isn’t the most effective way to resolve such squabbles to remove the toy? We have already seen that there is a well-defined sense in which classical general relativity is timeless. That is, I believe, the deepest truth that can be read from its magical tapestry. The question then is whether we can understand quantum mechanics and the existence of history without time. That is what the rest of the book is about.

History and Quantum Cosmology(p. 240) More details on the Leibnizian idea that the actual universe is more varied than any other conceivable universe are given in Smolin (1991), Barbour and Smolin (1992), and Barbour (1994b). The quotation from T. S. Eliot is in Eliot (1964). My book is Barbour (1989).

‘That Damned Equation’(p. 247) Technical note: In connection with Chapter 11, it is interesting that the form of the Wheeler-DeWitt equation is independent of the signature of space-time.