Although considerable discussion about the completeness of quantum mechanics followed the publication in 1935 of the Gedanken experiment of Einstein, Podolsky, and Rosen (EPR), it was not until Bell's work, published in 3 965, that it was realized that the issue could be rigorously formulated and put to experimental test. An even more provocative demonstration of the incompatibility of quantum mechanics with local realism was recently discovered by Greenberger, Horne, and Zeilinger (GHZ) in a Gedanken experiment employing more than two particles.1 Typical of EPR experiments that have been proposed to date, one has a metastable system that decays into n particles.
Quantum physics violates the basic assumptions of local realism. Particles can be entangled with each other in ways that allow correlations stronger than possible in classical physics. This was first realized by Einstein, Podolsky and Rosen (EPR) in 1935 and led them to conclude that quantum theory was incomplete. It took about 30 years before J. S. Bell found observable consequences of this phenomenon by showing how entangled states violate inequalities for two-particle correlations derived purely from the assumption that the world obeys local realism. Violations of Bell inequalities were first observed experimentally in the Aspect experiment, which will be discussed below. Such experiments are technically challenging and care is needed to avoid any loopholes in the experimental setup that would still permit the description of the experiments by a local realistic theory. Bell inequalities describe violations of local realism on average, meaning that each individual experimental outcome could occur in a local realistic theory. It is the statistics of these outcomes that violates local realism. In contrast, another class of quantum states, so-called Greenberger–Horne–Zeilinger (GHZ) states, which contain three particles, can be shown to violate local realism in each measurement outcome. We will also discuss this class of states and experiments by Zeilinger's group, which demonstrated this type of violation of local realism for the first time. Our aim here is not to discuss the exact relations between quantum entanglement, non-locality and realism, and their physical and philosophical implications. While this is a highly interesting topic which attracts a lot of attention from researchers, such an exploration would go beyond the scope of this book.
The Einstein-Podolsky-Rosen (EPR) paradox gives an argument for the incompleteness of quantum mechanics based on the premises of local realism. A general view is that the argument is compromised, because EPR's premises are falsified by Greenberger-Horne-Zeilinger (GHZ) and Bell experiments. In this paper, we present an EPR argument based on premises not falsifiable by these experiments. We propose macroscopic EPR and GHZ experiments using spins
Sθ defined by two macroscopically distinct states. The analyzers that realize the unitary operations
Uθ determining the measurement settings
θ are devices that create macroscopic superposition states. For a system with two macroscopically distinct states available, macroscopic realism (MR) posits a predetermined outcome for a measurement
Sθ distinguishing between the states. Deterministic macroscopic realism (dMR) posits MR for the system prior to the interaction
Uθ. Weak macroscopic realism (wMR) posits MR for the system after
Uθ, at the time
tf (when the system is prepared for a final "pointer" measurement), the outcome of
Sθ not being changed by interactions that might occur at a remote system
B. The premise also posits that if the outcome for
SθA of a system
A can be predicted by a pointer measurement on a system
B defined after the interaction fixing the setting at
B, then the outcome for
SθA is determined at this time. The GHZ predictions negate dMR but are consistent with wMR. Yet, an EPR paradox arises based on wMR for the set-up proposed by Schrödinger, where one measures two complementary spins simultaneously, "one by direct, the other by indirect" measurement. We revisit the original EPR paradox and find similarly that an EPR argument can be based on a weak form of local realism not falsifiable by GHZ or Bell tests.
From a fundamental point of view we must acknowledge that, since about 1935, our conceptual understanding of quantum mechanics has not progressed so much. Really new ideas are few and far between – except of course the major line initiated by the contribution of Bell [6]. This is in big contrast with the rest of physics, where new theoretical and experimental discoveries in many fields have flourished, very often with the help of the tools of quantum mechanics. The fantastic evolution of the experimental techniques has completely changed the situation. At the beginning of quantum mechanics, the observation of the tracks of single particles in Wilson chambers [348] played the essential role in the introduction of the postulate of state vector reduction, but otherwise it was impossible to observe continuously a single electron, atom, or ion; the experiments that theorists were proposing in discussions on the principles of quantum measurement were therefore “thought experiments” (“Gedanken Experiment”), as for instance in the famous Solvay meetings [1, 21]. But nowadays, after almost of century of experimental progress, experiments that were then unthinkable have become a reality. A huge number of contemporary experiments involves the laws of quantum mechanics in general; several books would not be sufficient to describe all of them. Nevertheless, in the majority of experiments, what is really observed is the sum over a very large number of particles of one individual microscopic observable (sum of atomic dipoles for instance), which is accurately described by the average value of this observable.