The End of Time: The Next Revolution in Physics

Interestingly, Max Born made his pioneering scattering calculations in the newly created wave mechanics by the second method. At that time Schrödinger had not even published his time-dependent equation. All the great early discoveries in wave mechanics, including Born’s statistical interpretation of the wave function (which he came to by mulling over his scattering calculations), were made before the supposedly more fundamental and ‘correct’ time-dependent equation had been found. I find this suggestive. It strengthens my belief that all the physics of the universe can be described by a timeless wave equation. In fact, Mott also used the stationary equation to obtain the alpha-particle tracks. That timeless equation can locate time capsules.

But ‘can’ is not ‘must’. The fact is that Mott used a special technique, always followed in such calculations, that mimics the wave-packet behaviour. The answer is to some extent simply assumed rather than truly derived and demonstrated. This can be done because the time-dependent and stationary Schrödinger equations have different structures, the latter having an extra freedom not present in the former. At each stage of his calculations, Mott systematically exploited this extra degree by making a definite kind of choice. This choice was not imposed by the mathematics but was made, probably instinctively, to match his temporal intuition. In fact, Mott’s solution is not a proper solution at all but a kind of bookkeeping record of how the real process would unfold in time. In addition, the condition corresponding to low entropy was also assumed rather than derived.

My conjecture seems to rest on a shaky basis. But there is more than one way of looking at this. The arguments for a timeless quantum universe are strong. The timelessness of the Wheeler-DeWitt equation, found by well-tried quantization methods, reflects the deepest structure of Einstein’s theory. Quite independently, we never observe anything other than time capsules – the entire observable universe is marked, at all epochs, by profound temporal asymmetry. If we trust the equation, our observations tell us the outcome of a mathematical calculation performed by the universe itself using that equation. For that is what the contingent universe must be: a solution of the equation. If what we observe – a profusion of time capsules – is a representative fact, then the equation does concentrate ψ on time capsules.

We can take Mott’s solution more seriously. Several points can be made. Situations in which part of a quantum system is in the semiclassical regime, so that Hamilton’s ‘light rays’ are present as latent or even incipient classical histories, are rather common and characteristic. The Heisenberg-Mott work then shows that such latent histories will become entangled with the remaining quantum variables, which must, in some way, reflect and carry information about those histories. What is not clear is whether the histories will exhibit a pronounced sense of direction – an arrow of time. That, above all, is put into the Mott solution by hand.

Also relevant is the mathematically somewhat suspect procedure known as successive approximation used to construct the Mott solution. There is no global arena in which the cloud chamber resides. Its atoms are effectively located in empty Euclidean space, and Mott could keep on adding approximations without worrying about their behaviour far from the cloud chamber. He was not constructing a genuine well-behaved solution, in which one must ensure the behaviour is right everywhere, especially at infinity. Instead, Mott used infinity as a kind of dustbin. This could not be done in a realistic situation, as I would now like to show.

A QUANTUM ORIGIN OF THE UNIVERSE?

When Planck made the first quantum discovery, he noted an interesting fact. The speed of light, Newton’s gravitational constant, and Planck’s constant clearly reflect fundamental properties of the world. From them it is possible to derive the characteristic mass length l_planck and time f_planck with approximate values

On atomic scales the Planck mass is huge, corresponding to about 10¹⁹ hydrogen atoms. In contrast, the Planck length and time are far smaller than anything physicists can currently measure.

Much of current cosmology is concerned with the ‘interface’ of quantum gravity and classical physics. The universe around us is described by general relativity. This classical treatment is said to be valid right back into the distant past, very close to the Big Bang. The quantum phase of cosmology is supposed to become important only at extraordinarily small scales, of the order of the Planck length, 10^–33 centimetres. Lights travel this distance in 10^–43 seconds, and it is argued that quantum gravity ‘comes into its own’ only in this almost incomprehensibly early epoch.