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

The situation is actually delicate and intriguing. Relativity absolutely prohibits the transmission of information faster than light. But, curiously, wave-function collapse does not transmit information. When information about particle 1 has been obtained by an experimentalist, he or she will know immediately what a distant experimentalist can learn about particle 2. But there is no way such information can be transmitted faster than light. There is no conflict with the rules of relativity, though many physicists are concerned that its ‘spirit’ is violated.

So far, we have considered only position measurements on a two-particle system. But we can also consider many other measurements, of momentum, for example. Given ψ in Q, we directly obtain predictions for positions. But Dirac’s transformation theory enables us to pass to the complementary momentum space, which gives direct predictions for momentum measurements. If the wave function is tightly entangled with respect to momentum, measuring the momentum of particle 1 would immediately tell us the momentum of particle 2. And this despite the fact that before any measurements are made there is considerable uncertainty about the momenta of the particles. However, what is certain is that they are entangled, or correlated. This brings us to the EPR paradox.

The nub of the Einstein-Podolsky-Rosen (EPR) paradox, formulated in 1935 by Einstein and collaborators Boris Podolsky and Nathan Rosen, is that two particles can be in a state in which they are perfectly correlated (entangled) as regards both their position and their momentum. The actual example of such a state that EPR found is rather unrealistic, but in 1952 David Bohm, an American theoretical physicist who later worked in London for many years, proposed a much more readily realized state using spin , the intrinsic angular momentum associated with quantum particles. Alain Aspect performed his experiments on such a system. What puzzled EPR about their state was that if the position of one particle was measured, the position of the other particle could be immediately established with certainty because of the perfect correlation. Since the second particle, being far away, could not be physically affected by the measurement, but it was known for certain where it would be found, EPR concluded that it must have had this definite property before the measurement on the first particle.

But, it could just as well have been decided to measure momentum. The measurement of one momentum will then instantaneously determine the other momentum with certainty. By the same argument as before, the particle must have possessed that momentum before the measurement on the first particle. Finally, the choice between momentum or position measurement is a matter of our whim, about which the second particle can know nothing. The only conclusion to draw is that the second particle must have possessed definite position and momentum before any measurements were made at all. However, according to the fundamental rules of quantum mechanics, as exemplified in the Heisenberg uncertainty principle, a quantum particle cannot possess definite momentum and position simultaneously. EPR concluded there must be something wrong – quantum mechanics must be incomplete.

Niels Bohr actually answered EPR quite easily, though not to everyone’s satisfaction. His essential point was that quantum mechanics predicts results made in a definite experimental context. We must not think that the two-particle system exists in its own right, with definite properties and independent of the rest of the world. To make position or momentum measurements, we must set up different instruments in the laboratory. Then the total system, consisting of the quantum system and the measuring system, is different in the two cases. Nature arranges for things to come out differently in the two cases. Nature is holistic: it is not for us to dictate what Nature is or does. Quantum mechanics is merely a set of rules that brings order into our observations. Einstein never found an answer to this extreme operationalism of Bohr, and remained deeply dissatisfied.

I feel sure that Bohr got closer to the truth than Einstein. However, Bohr too adopted a stance that I believe is ultimately untenable. He insisted that it was wrong to attempt to describe the instruments used in quantum experiments within the framework of quantum theory. The classical world of instruments, space and time must be presupposed if we are ever to talk about quantum experiments and communicate meaningfully with one another. Just as Schrödinger made his Kantian appeal to space and time as necessary forms of thought, Bohr made an equally Kantian appeal to macroscopic objects that behave classically. Without them, he argued, scientific discourse would be impossible. He is right in that, but in the final chapters I shall argue that it may be possible to achieve a quantum understanding of macroscopic instruments and their interaction with microscopic systems. Here it will help to consider why Einstein thought the way he did.

Referring to their demonstration that distant measurement on the first system, ‘which does not disturb the second in any way’, nevertheless seems to affect it drastically, EPR commented that ‘No reasonable definition of reality could be expected to permit this.’ These words show what is at stake – it is the atomistic picture of reality. Despite the sophistication of all his work, in both relativity and quantum mechanics, Einstein retained a naive atomistic philosophy. There are space and time, and distinct autonomous things moving in them. This is the picture of the world that underlies the EPR analysis. In 1949 Einstein said he believed in a ‘world of things existing as real objects’. This is his creed in seven words. But what are ‘real objects’?

To look at this question, we first accept that distinct identifiable particles can exist. Imagine three of them. There are two possible realities. In the Machian view, the properties of the system are exhausted by the masses of the particles and their separations, but the separations are mutual properties. Apart from the masses, the particles have no attributes that are exclusively their own. They – in the form of a triangle – are a single thing. In the Newtonian view, the particles exist in absolute space and time. These external elements lend the particles attributes – position, momentum, angular momentum – denied in the Machian view. The particles become three things. Absolute space and time are an essential part of atomism.

The lent properties are the building blocks of both classical and quantum mechanics. Classically, each particle has a unique set of them, defining the state of each particle at any instant. This is the ideal to which realists like Einstein aspire. The lent properties also occur in quantum mechanics. They are generally not the state itself, but superpositions of them are. If a quantum system is considered in isolation from the instruments used to study it, its basic elements still derive from a Newtonian ontology. This is what misled EPR into thinking they could outwit Bohr. Einstein’s defeat by Bohr is a clear hint that we shall only understand quantum mechanics when we comprehend Mach’s ‘overpowering unity of the All’.

Strong confirmation for quantum mechanics being holistic in a very deep sense was obtained in the 1960s, when John Bell, a British physicist from Belfast, achieved a significant sharpening of the EPR paradox. The essence of the original paradox is the existence of correlations between pairs of quantities – pairs of positions or pairs of momenta – that are always verified if one correlation or the other is tested. By itself, some degree of correlation between the two particles is not mysterious. The EPR-type correlated states are generally created from known uncorrelated states of two particles that are then allowed to interact. Even in classical physics, interaction under such circumstances is bound to lead to correlations. Bell posed a sharper question than EPR: is the extent of the quantum correlations compatible with the idea that, before any measurement is made, the system being considered already possesses all the definite properties that could be established by all the measurements that, when performed separately, always lead to a definite result?