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by Katie Howard
In 1964,
Bell was proving that any quantum theory model, based or not on realism must violate the simple and unique property of locality. He concluded that if nature is governed by the predictions of quantum theory, the “locality principle” is simply wrong, and our world is nonlocal. It has also been proved that the nonlocality property as the main Bohmian mechanics is not a sign of its being on the wrong track, but quite the contrary.
As we know, the bohmian mechanics involves superluminal action-at-a-distance and thus violates the “locality principle” of relativity theory. This was considered, by the
Copenhagen camp, an indication that Bohmian mechanics was on the wrong track. The
Copenhagen view, in comparison, is indeed less local: It is nonlocal in cases that Bohmian mechanics can explain in a purely local way. (For example, for a particle in a quantum state that is a superposition of being in London and being in Tokyo, according to Copenhagenism there is no matter of fact about whether the particle actually is in London or in
Tokyo prior to the first attempt at detection—which presupposes a temporal ordering.) But it is also contradictory, vague and confusing enough for its adherents to claim it is completely local, and thus that nonlocality is a consequence of an attachment to realism. Therefore, so the argument goes, it was
Bell who finally proved realism wrong!
Bell, of course, emphatically rejected this incorrect interpretation of his nonlocality theorem. The crucial experiments violating Bell’s inequality and thus, according to
Bell’s theoretical analysis, demonstrating nonlocality have been performed many times since 1980 and have also led to significant improvements in experimental techniques. Some of these techniques have now become valuable for quantum cryptography and the first steps toward the construction of a quantum computer. These two fields are usually summarized under the keyword “quantum information,” and great hopes are expressed that quantum information will provide new insights into the nature of the quantum world. Despite considerable research efforts the relation between the quantum entanglement and non-locality is largely unexplored. Among the open questions is: Which quantum states of composite systems are entangled and which of those are non-local? Understanding this relation is not only of importance for fundamental research, but also in the context of quantum information processing. For certain tasks, such as quantum communication complexity problems, distillation of entanglement or device-independent quantum key distribution, entangled states are useful only to the extent that they exhibit nonlocal correlations. It is well-known that
Bell’s assumption of locality can be factored out into two conditions.
- Outcome independence: the outcome of the experiment at site A does not depend on the outcome of the experiment at site B.
- Parameter independence: the outcome of the experiment at site A does not depend on the choice of detector setting at site B.
The concept of locality prohibits any influences between events in space-like separated regions. Think of it in terms of Maxwell’s equations, where the electric and magnetic fields are plane waves travelling at a constant speed, which is the speed of light. If there is causality between two non-local events, the time delay must be larger than the time light takes to travel from the first to the second event.Leggett has proposed to consider theories that maintain the assumption of outcome independence, but drop the assumption of parameter independence. It is worth remarking at this point that the attribution of fundamental importance to this factorization of the locality assumption can easily be criticized. Whilst it is usual to describe the outcome at each site by ±1 this is an oversimplification. For example, if we are doing Stern-Gerlach measurements on electron spins then the actual outcome is a deflection of the path of the electron either up or down with respect to the orientation of the magnet. Thus, the outcome cannot be so easily separated from the orientation of the detector, as its full description depends on the orientation.Nevertheless, whatever one makes of the factorization, it is the case that one can construct toy models that reproduce the quantum predictions in
Bell experiments by dropping parameter independence. Therefore, it is worth considering what other reasonable constraints we can impose on theories when this assumption is dropped. Leggett’s assumption amounts to assuming that the hidden variable states in the theory can be divided into subensembles, in each of which the two photons have a definite polarization (which may however depend on the distant detector setting). The total ensemble corresponding to a quantum state is then a statistical average over such states. This is the class of theories that has been ruled out by the experiment.
The normal
Bell inequalities, combined with the known EPR experiments that agree with quantum mechanics, falsify “local realism”, i.e. the combination of assumptions that some values of physical quantities objectively exist before they’re measured - in contradiction with the postulates of quantum mechanics - and moreover they evolve according to local laws.
They are able to falsify this combined assumption because the (wrong) assumption implies, through
Bell’s proof, that the measured correlations must belong to a certain interval. But quantum mechanics predicts and experiments confirm that the actual correlations are often outside this interval. Quantum mechanics allows you to get much stronger correlations or anti-correlations than any hypothetical underlying local classical theory with hidden variables.
The sane conclusion is, of course, that we must finally do what all fully sane friends of Max Born did in 1926, take quantum mechanics seriously, and abandon “realism” (I don’t mean political realism which is good but quantum realism which is bad!): only probabilities may be predicted and it makes no sense to talk about the “real” values of observables of a quantum system before these values are measured. Only results of experiments have a physical meaning.
Nevertheless, some people still insist that it is plausible that “realism” holds and locality is what is violated. Relativity requires that the fundamental degrees of freedom - such as quantum fields - must evolve according to local and causal laws. This statement must be true with accuracy: it’s not only beautiful but it has been experimentally validated.
On the other hand, Zeilinger now argue that they have falsified a large class of “nonlocal realist” theories, too, because the measured correlations are higher even than what “nonlocal realist” theories allow. I don’t quite know how they can achieve such a goal. It is clearly a theoretical goal.
I think that every sane quantum physicist can predict the result of all these experiments and there can’t be any new surprises here: quantum mechanics works and physics behind all these experiments is controlled by the same simple laws that give clear predictions to every setup. On the other hand, they must be using some “improved” version of Bell’s theorem that also applies to some “nonlocal realist” theories, not only “local realist” theories as the original
Bell’s theorem. I don’t know what this hypothetical improved version of the theorem is.
Nevertheless, I endorse their position that the results of all these experiments make any attempt to preserve “realism” - i.e. to deny the probabilistic nature of quantum mechanics - highly contrived. The more you understand how these experiments work, the more you agree with us.Such models of physical realism, suggesting that the results of observations are consequence of the properties carried by physical systems, are called hidden-variable theories. The idea is that all measurement outcomes depend on pre-existing properties of objects that are independent of the measurement. The limitation of quantum theory then would be that we do not know all variables, they are hidden from us.
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