5 Togetherness

Chapter 5

Togetherness

Einstein, through his explanation of the photoelectric effect, had been one of the grandfathers of quantum theory. However, he came to detest his grandchild. Like the vast majority of physicists, Einstein was deeply convinced of the reality of the physical world and trusted in the truthful reliability of science’s account of its nature. But he came to believe that this reality could only be guaranteed by the kind of naive objectivity that Newtonian thinking had assumed. In consequence, Einstein abhorred the cloudy fitfulness that Copenhagen orthodoxy assigned to the nature of the quantum world.

His first onslaught on modern quantum theory took the form of a series of highly ingenious thought experiments, each of which purported in some way to circumvent the limitations of the Heisenberg uncertainty principle. Einstein’s opponent in this contest was Niels Bohr, who each time succeeded in showing that a thorough-going application of quantum ideas to all aspects of the proposed experiment actually resulted in the uncertainty principle surviving unscathed. Eventually Einstein conceded defeat in this particular battle.

After licking his wounds for a while, Einstein returned to the fray, staking out a new ground for contention. With two younger collaborators, Boris Podolsky and Nathan Rosen, he showed that

there were some very peculiar, hitherto unnoticed, long-range implications for the quantum mechanical behaviour of two apparently well-separated particles. The issues are most easily explained in terms of a later development of what, bearing in mind its discoverers’ names, we may call EPR thinking. The argument was due to David Bohm and, although it is a little involved, it is well worth wrestling with.

Suppose two particles have spins s1 and s2 and it is known that the total spin is zero. This implies, of course, that s2 is −s1. Spin is a vector (that is, it has magnitude and direction – think of it as an arrow) and we have followed mathematical convention in using boldface type for vectorial quantities. A spin vector will, therefore, have three components measured along three chosen spatial directions, x, y, and z. If one were to measure the x component of s1 and get the answer s′ 1x, then the x component of s2 must be −s ′ 1x. If, on the other hand, one had measured the y component of s1, getting the answer s′ 1y, one would know that the y component of s2 would have to be −s ′ 1y. But quantum mechanics does not permit one to measure both the x and y components of spin simultaneously, because there is an uncertainty relation between them. Einstein argued that, while this might be the case according to orthodox quantum thinking, whatever happened to particle 1 could have no immediate effect upon the distant particle 2. In EPR thinking, the spatial separation of 1 and 2 implies the independence of what happens at 1 and what happens at 2. If that is so, and if one can choose to measure either the x or the y components of spin at 1 and get certain knowledge of the x or y components respectively of spin at 2, then Einstein claimed that particle 2 must actually have these definite values for its spin components, whether the measurements were actually made or not. This was something that conventional quantum theory denied, because, of course, the uncertainty relation between x and y spin components applied as much to particle 2 as to particle 1.

Einstein’s conclusion from this mildly complicated argument was

that there must be something incomplete in conventional quantum theory. It failed to account for what he believed must be definite values of spin components. Almost all his fellow physicists interpret things differently. In their view, neither s1 nor s2 have definite spin components until a measurement is actually made. Then, determining the x component of 1 forces the x component of 2 to take the opposite value. That is to say, the measurement at 1 also forces a collapse of the wavefunction at 2 onto the opposite value of the x spin component. If it had been the y component that had been measured at 1, then the collapse at 2 would have been onto the opposite y spin component. These two 2-states (known x component; known y component) are absolutely distinct from each other. Thus the majority view leads to the conclusion that measurement on 1 produces instantaneous change at 2, a change that depends precisely on exactly what is measured at 1. In other words, there is some counterintuitive togetherness-in-separation between 1 and 2; action at 1 produces immediate consequences for 2 and the consequences are different for different actions at 1. This is usually called the EPR effect. The terminology is somewhat ironic since Einstein himself refused to believe in such a long-range connection, regarding it as an influence that was too ‘spooky’ to be acceptable to a physicist. There the matter rested for a while.

The next step was taken by John Bell. He analysed what properties the 1–2 system would have if it were a genuinely separated system (as Einstein had supposed), with properties at 1 depending only on what happened locally at 1 and properties at 2 depending only on what happened locally at 2. Bell showed that if this strict locality were the case, there would be certain relations between measurable quantities (they are now called the Bell inequalities) that quantum mechanics predicted would be violated in certain circumstances. This was a very significant step forward, moving the argument on from the realm of thought experiments into the empirically accessible realm of what could actually be investigated in the laboratory. The experiments were not easy to do but eventually, in the early 1980s, Alain Aspect and his collaborators were able to

carry out a skilfully instrumented investigation that vindicated the predictions of quantum theory and negated the possibility of a purely local theory of the kind that Einstein had espoused. It had become clear that there is an irreducible degree of non-locality present in the physical world. Quantum entities that have interacted with each other remain mutually entangled, however far they may eventually separate spatially. It seems that nature fights back against a relentless reductionism. Even the subatomic world cannot be treated purely atomistically.

The EPR effect’s implication of deep-seated relationality present in the fundamental structure of the physical world is a discovery that physical thinking and metaphysical reflection have still to come to terms with in fully elucidating all its consequences. As part of that continuing process of assimilation, it is necessary to be as clear as possible about what is the character of the entanglement that EPR implies. One must acknowledge that a true case of action at a distance is involved, and not merely some gain in additional knowledge. Putting it in learned language, the EPR effect is ontological and not simply epistemological. Increase in knowledge at a distance is in no way problematic or surprising. Suppose an urn contains two balls, one white, the other black. You and I both put in our hands and remove one of the balls in our closed fists. You then go a mile down the road, open your fist and find that you have the white ball. Immediately you know I must have the black one. The only thing that has changed in this episode is your state of knowledge. I always had the black ball, you always had the white ball, but now you have become aware that this is so. In the EPR effect, by contrast, what happens at 1 changes what is the case at 2. It is as if, were you to find that you had a red ball in your hand, I would have to have a blue ball in mine, but if you found a green ball, I would have to have a yellow ball and, previous to your looking, neither of us had balls of determinate colours.

An alert reader may query all this talk about instantaneous change. Does not special relativity prohibit something at 1 having any effect

at 2 until there has been time for the transmission of an influence moving with at most the velocity of light? Not quite. What relativity actually prohibits is the instantaneous transmission of information, of a kind that would permit the immediate synchronization of a clock at 2 with a clock at 1. It turns out that the EPR kind of entanglement does not permit the conveyance of messages of that kind. The reason is that its togetherness-in-separation takes the form of correlations between what is happening at 1 and what is happening at 2 and no message can be read out of these correlations without knowledge of what is happening at both ends. It is as if a singer at 1 was singing a random series of notes and a singer at 2 was also singing a random series of notes and only if one were able to hear them both together would one realize that the two singers were in some kind of harmony with each other. Realizing this is so warns us against embracing the kind of ‘quantum hype’ argument that incorrectly asserts that EPR ‘proves’ that telepathy is possible.