It is assumed that objects exist, and the consequences and possible tests of these assumptions are examined. Various experiments on particle interactions are considered. (JFP)
The purpose of this lecture is to give a self-contained demonstration of a version of Bell's theorem and a discussion of the significance of the theorem and the experiments which it inspired. The lecture should be comprehensible to people who have had no previous acquaintance with the literature on Bell's theorem, but I hope that explicitness about premisses and consequences will make it useful even to those who are familiar with the literature. All versions of Bell's theorem are variations, and usually generalizations, of the pioneering paper of J. S. Bell of 1964, entitled “On the Einstein–Podolsky–Rosen Paradox.” All of them consider an ensemble of pairs of particles prepared in a uniform manner, so that statistical correlations may be expected between outcomes of tests performed on the particles of each pair. If each pair in the ensemble is characterized by the same quantum state φ, then the quantum mechanical predictions for correlations of the outcomes can in principle be calculated when the tests are specified. On the other hand, if it is assumed that the statistical behavior of the pairs is governed by a theory which satisfies certain independence conditions (always similar to the Parameter and Outcome Independence conditions stated below, though the exact details vary from version to version of Bell's theorem), then it is possible to derive a restriction upon the statistical correlations of the outcomes of tests upon the two particles.
This thesis addresses some of the consequences of giving quantum mechanics a realist interpretation. We consider three main topics: wave-particle duality, locality, and Lorentz invariance. First we show that classical particles alone or classical waves alone cannot explain all single particle quantum phenomena. Then we consider the possibility that a quantum particle is composed of a particle and a wave, both being taken to exist objectively. We are able to demonstrate the reality of empty waves (that is, waves without a particle) if we make three realist motivated assumptions. The main part of this thesis concerns locality. In 1964 Bell demonstrated that a local realist interpretation of quantum mechanics is not possible by deriving a set of inequalities that apply to two particle systems. More recently Greenberger, Home, and Zeilinger have demonstrated this for systems with more than two particles without the need for inequalities. We present a new way to derive Bell inequalities for two particles and show how this can be extended to systems with more than two particles. A number of proposals for experiments to test local realism are put forward. In particular, we show how it is possible to demonstrate the nonlocality of a single photon. A new demonstration of Bell's theorem is presented for two particles but without inequalities. A realizable quantum optical version is proposed and inequalities are proposed which would be required in a non-ideal experiment. Finally, the question of Lorentz invariance is considered. We define a condition for the existence of elements of reality and a condition for the Lorentz invariance of these elements of reality. Then we show that, by considering a particular gedanken experiment, we obtain a contradiction demonstrating that Lorentz-invariant realistic interpretations of quantum theory are not possible.
A broad class of theories, called "objective local theories," is defined, motivation for considering these theories is given, and experimental consequences of the class are investigated. An extension of previous analyses by Bell and by Clauser et al. shows that predictions of objective local theories and of quantum mechanics differ, and that an experimental test of the entire family of objective local theories can be performed. The experimental requirements are given. Objective local theories satisfying a plausible but experimentally untestable supplementary assumption are shown to be incompatible with existing experimental data.
This paper presents a conceptually simple account of the EPR argument and Bell’s theorem using entangled photon polarization experiments. It clarifies how quantum correlations arise from conditioning outcomes through fundamental properties of quantum entanglement that result in conditional probability structures rather than from superluminal influences or pre-existing particle properties. Building on this analysis, the paper explores the informational and philosophical consequences of Bell violations. Hidden-variable theories are shown to entail severe informational overhead by requiring microscopic labeling of otherwise indistinguishable particles, whereas quantum mechanics encodes structure economically through relational constraints on joint outcomes. A striking but rarely-emphasized feature of Bell-type experiments is that while traditionally the geometery of the apparatus used to carry out these experiments are aligned with each other, according to quantum mechanics the physical orientations of the apparatus have no physical meaning with respect to one another at the time of measurement. The geometry is defined only locally, relative to the laboratory in which the tests is set. The essay further argues that Bell’s theorem motivates a shift from object-centered classical realism toward a form of realism referred to as “Relational Realism” wherein correlations and informational structure are ontologically primary, while objects having individual properties are contextual and derivative. This perspective dissolves the traditional realism-versus-idealism dichotomy and situates quantum mechanics as a fundamentally relational theory of physical reality rather than an incomplete classical one.