The End of Time: The Next Revolution in Physics

Within the purely classical theory, the origin of the mismatch is clear: it is the criss-cross best-matching construction of space-time that I illustrated with the help of Tristan and Isolde. However, the discrepancy between the quantum expectations of well-behaved massless particles with two polarizations and the intricate interstreaming reality of relativity rapidly became the central dilemma of quantum gravity. Forty years on, it has still not yet been resolved to everyone’s satisfaction – it is that intractable. This is perhaps not surprising, for the issue at stake is the fabric of the world. Does it exist in something like that great invisible framework that took possession of Newton’s imagination, or is the world self-supporting? Do we swim in nothing? Nobody has yet been able to make quantum theory function without a framework. In fact, many people do not realize that the framework is a potential problem – Dirac’s transformation theory is in truth the story of acrobatics in a framework, and for physicists nurtured on Dirac’s The Principles of Quantum Mechanics the acrobatics is quantum theory. Acrobatics must be precise – if the trapeze is not where it should be, death can result. Such are the exigencies that led the early researchers to posit a graviton with just two true degrees of freedom.

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.