The task of quantizing general relativity raises serious questions about the meaning of the present formulation and interpretation of quantum mechanics when applied to so fundamental a structure as the space-time geometry itself. This paper seeks to clarify the foundations of quantum mechanics. It presents a reformulation of quantum theory in a form believed suitable for application to general relativity. The aim is not to deny or contradict the conventional formulation of quantum theory, which has demonstrated its usefulness in an overwhelming variety of problems, but rather to supply a new, more general and complete formulation, from which the conventional interpretation can be deduced. The relationship of this new formulation to the older formulation is therefore that of a metatheory to a theory, that is, it is an underlying theory in which the nature and consistency, as well as the realm of applicability, of the older theory can be investigated and clarified.

"relative State" Formulation of Quantum Mechanics

Multiphoton interference reveals strictly nonclassical phenomena. Its applications range from fundamental tests of quantum mechanics to photonic quantum information processing, where a significant fraction of key experiments achieved so far comes from multiphoton state manipulation. The progress, both theoretical and experimental, of this rapidly advancing research is reviewed. The emphasis is given to the creation of photonic entanglement of various forms, tests of the completeness of quantum mechanics (in particular, violations of local realism), quantum information protocols for quantum communication (e.g., quantum teleportation, entanglement purification, and quantum repeater), and quantum computation with linear optics. The scope of the review is limited to ``few-photon'' phenomena involving measurements of discrete observables.

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Multiphoton entanglement and interferometry

Most working scientists hold fast to the concept of ‘realism’—a viewpoint according to which an external reality exists independent of observation. But quantum physics has shattered some of our cornerstone beliefs. According to Bell’s theorem, any theory that is based on the joint assumption of realism and locality (meaning that local events cannot be affected by actions in space-like separated regions) is at variance with certain quantum predictions. Experiments with entangled pairs of particles have amply confirmed these quantum predictions, thus rendering local realistic theories untenable. Maintaining realism as a fundamental concept would therefore necessitate the introduction of ‘spooky’ actions that defy locality. Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories. Our result suggests that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned. Most of us, most of the time, can get along in life and in science with a sturdy concept of what is 'real'. Generally speaking, an external reality exists independent of observation. But in the world of quantum physics, where individual events are predicted only in terms of probabilities, this will not do. According to Bell's theorem, any theory based on the joint assumption of realism and locality (meaning that local events cannot be affected by actions in space-like separated regions) is at variance with certain quantum predictions. Previous work with entangled pairs of particles has confirmed these quantum predictions, rendering local realistic theories untenable. Maintaining physical realism as a fundamental concept would therefore require the introduction of 'spooky' locality-defying actions. A new study combing experiment and theory now shows that a broad and rather reasonable class of such non-local realistic theories is incompatible with observed quantum correlations. This suggests that any future extension of quantum theory, if it is to agree with the experiments, must abandon certain features of realistic descriptions. Giving up the concept of locality is not sufficiently 'unreal'. According to Bell's theorem, any theory that is based on the joint assumption of realism and locality is at variance with certain quantum predictions. Here, theory and experiment agree that a class of such non-local realistic theories is incompatible with experimentally observable quantum correlations, suggesting that giving up the concept of locality is not sufficient to be consistent with quantum experiments, unless certain intuitive features of realism are abandoned.

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An experimental test of non-local realism

A droplet bouncing on a vertically vibrated bath can become coupled to the surface wave it generates. It thus becomes a "walker" moving at constant velocity on the interface. Here the motion of these walkers is investigated when they pass through one or two slits limiting the transverse extent of their wave. In both cases a given single walker seems randomly scattered. However, diffraction or interference patterns are recovered in the histogram of the deviations of many successive walkers. The similarities and differences of these results with those obtained with single particles at the quantum scale are discussed.

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Single-particle diffraction and interference at a macroscopic scale.

Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi-Rimini-Weber (GRW) model of spontaneous wavefunction collapse. The GRW model was proposed as a solution of the measurement problem of quantum mechanics and involves a stochastic and nonlinear modification of the Schrodinger equation. It deviates very little from the Schrodinger equation for microscopic systems but efficiently suppresses, for macroscopic systems, superpositions of macroscopically different states. As suggested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of space-time points, at which the collapses are centered. This set is random with distribution determined by the initial wavefunction. Our model is nonlocal and violates Bell’s inequality though it does not make use of a preferred slicing of space-time or any other sort of synchronization of spacelike separated points. Like the GRW model, it reproduces the quantum probabilities in all cases presently testable, though it entails deviations from the quantum formalism that are in principle testable. Our model works in Minkowski space-time as well as in (well-behaved) curved background space-times.

A Relativistic Version of the Ghirardi–Rimini–Weber Model

We re-examine the notion of the quantum potential introduced by the Broglie and Bohm and calculate its explicit form in the case of the two-slit interference experiment. We also calculate the ensemble of particle trajectories through the two slits. The results show clearly how the quantum potential produces the bunching of trajectories that is required to obtain the usual fringe intensity pattern. Hence we are able to account for the interference fringes while retaining the notion of a well-defined particle trajectory. The wider implications of the quantum potential particularly in regard to the quantum interconnectedness are discussed.

Quantum interference and the quantum potential

The time-dependent scattering of one-dimensional Gaussian wave packets of various energies incident on(1) a square potential barrier and(2) a square well is examined numerically, using the quantum potential introduced by Bohm. The time-dependent quantum potential is calculated in each case, and the results displayed on three-dimensional computer plots. The particle trajectories from different initial positions within the wave packet are also shown, giving a detailed description of reflection and tunneling in terms of individual processes. The wider implications of this analysis are also briefly considered.

A quantum potential description of one-dimensional time-dependent scattering from square barriers and square wells

What happens in a spin measurement

How late measurements of quantum trajectories can fool a detector

Spin superposition in neutron interferometry, spin measurement, and non–local Einstein-Podolsky-Rosen spin correlations can be understood in terms of well–defined individual particle trajectories with continuously variable spin vectors.

Chris Dewdney

Papers

Quantum interference and the quantum potential

A quantum potential description of one-dimensional time-dependent scattering from square barriers and square wells

What happens in a spin measurement

How late measurements of quantum trajectories can fool a detector

Spin and non-locality in quantum mechanics