The experimental violation of mathematical relations known as Bell's inequalities sounded the death-knell of Einstein's idea of 'local realism' in quantum mechanics. But which concept, locality or realism, is the problem?
The development of quantum mechanics early in the twentieth century obliged physicists to change radically the concepts they used to describe the world. The main ingredient of the first quantum revolution, wave–particle duality, has led to inventions such as the transistor and the laser that are at the root of the information society. Thanks to ideas developed by Albert Einstein and John S. Bell, another essential quantum ingredient, entanglement, is now leading us through the conceptual beginnings of a second quantum revolution — this time based on quantum information1,2.
In contrast to wave–particle duality, which is a one-particle quantum feature, entanglement involves at least two particles. In entangled states such as those discovered by Einstein, Podolsky and Rosen (EPR)3, quantum mechanics predicts strong correlations between measurements on two systems that have previously interacted but which are separated at the time of the measurement (Box 1). To interpret these correlations, Einstein said, one must accept the concept of local realism. This principle states that results of measurements on a system localized in space-time are fully determined by properties carried along by that system (its physical reality) and cannot be instantaneously influenced by a distant event (locality).
But after Bell's discovery that local realism entailed a limit on the correlations — a limit he expressed in his celebrated inequalities4 — a series of ever more ideal experiments (ref. 5 and references therein) has led us to abandon the concept. It is then natural to raise the question of whether one should drop locality — which equates to the impossibility of any influence travelling faster than light — or rather drop the notion of physical reality.
There is no logical answer to that question: one can choose to abandon either concept, or even both. Tony Leggett has explored6 one of these possibilities by considering a particular class of physically plausible theories that abandon locality, but maintain realism. He found these theories to be incompatible with quantum mechanics, and expressed the disagreement by new inequalities6. As there was no experimental result available to test Leggett's inequalities, a new type of measurement was necessary.
In experiments detailed on page 871 of this issue7, Gröblacher et al. have carried out such measurements. They modified an experiment previously used to test Bell's inequalities through measurements on two photons (Box 1) by changing the original linear polarization measurement into an elliptical polarization measurement. This is readily done by inserting a quarter-wave plate in front of a standard (linear) polarizer. From an experimental point of view, however, the new test is more demanding, and requires almost ideal optical elements and a high signal-to-noise ratio. Thanks to their high-efficiency source of entangled photons, the authors meet these requirements, and find a significant violation of the generalized Leggett's inequalities that they have established. Following Leggett, they conclude by questioning realism rather than locality — at variance with the often-heard statement that “quantum mechanics is non-local”.
Interesting as this conclusion is, it remains a matter of personal preference, not of logical deduction. The violation of Bell's inequalities implied that realism and locality are not simultaneously tenable. Violation of Leggett's inequalities implies only that realism and a certain type of non-locality are incompatible: there are other types of non-local models that are not addressed by either Leggett's inequalities or the experiment.
Consider, for instance, the experiment pictured in Box 1, and assume that a measurement is performed first on photon ν1. This measurement gives either a result of +1 or −1; immediately after one of the two results is obtained, the quantum description of ν2, which had not been favouring any precise polarization before the measurement on ν1, collapses into a state of polarization identical to the one found for photon ν1, from which one can readily derive the usual quantum-mechanical EPR correlations. If we take this description — based on standard quantum-mechanical calculations — as a model, it cannot be rejected by any experiment that is in agreement with quantum mechanics, including the more complex elliptical polarization measurements performed by Gröblacher et al.7.
This model is clearly non-local in the relativistic sense, as we must invoke a particular frame of reference to give a sense to the statements that measurement on ν1 happens first, and that its result immediately affects the state of ν2. Can we say that the model is realist? In a sense yes, as we can qualify the individual polarization of each photon at each step. I must admit, however, that I am not comfortable with the notion of a physical reality that is instantaneously modified by something happening far away — not to speak of the problems related to breaking down explicit relativistic covariance8. In many of Einstein's writings9, the notion of a physical reality describing completely the state of a system localized in space-time is clearly linked to the relativistic impossibility that this physical reality be instantaneously modified by a faraway event. To quote Einstein10, the necessity of completing quantum mechanics in a local–realist way could be escaped “only by either assuming that the measurement of S1 (telepathically) changes the real situation of S2 or by denying independent real situations to things which are spatially separated from each other. Both alternatives appear to me entirely unacceptable.”
Nobody knows what Einstein would have thought had he known of the violation of Bell's and Leggett's inequalities. I tend to accept the kind of non-local image sketched above as useful to stimulate my imagination, although I am aware that it implies renouncing the kind of realism I would have liked. The conclusion one draws is more a question of taste than logic, and one can argue that such a discussion is irrelevant to science. But I rather share the view that such debates, and accompanying experiments such as those of Gröblacher et al.7, allow us to look deeper into the great mysteries of quantum mechanics. That, it is to be hoped, can contribute to transforming the second quantum revolution from the present stage of basic research to a fully fledged technological revolution.
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International Journal of Theoretical Physics (2009)