Non-locality II: Dynamical models of the EPR–Bohm experiment

KENNETH H. SCHATIEN

W. Michael Dickson

We now have under our belts several interpretations of quantum mechanics, each requiring, or anyhow advocating, some understanding of quantum probabilities. In the next two chapters, I will consider some connections among various interpretations of quantum probabilities and non-locality. I do so in the context of the well-known EPR–Bohm experiment, though it is worth emphasizing at the start that non-locality is very likely the rule rather than the exception for quantum-mechanical systems. Entanglement of systems occurs not only in the confines of a laboratory, but also in the course of quite typical interactions among quantum-mechanical systems. Nonetheless, the EPR-Bohm experiment shines a bright light on the phenomenon of non-locality, and is therefore the most useful context in which to explore the relation between probability and non-locality. In this chapter, I consider models of the EPR–Bohm experiment that deliver probabilities for the various outcomes given the initial state of the pair of particles. In the next chapter, I consider fully dynamical models, i.e., ones that provide a dynamics for the complete state of the pair of particles as well as probabilities for various outcomes based on these complete states. The EPR–Bohm experiment The EPR–Bohm experiment is well known, but some observations about it are important for later.

Dipankar Home, M. A. B. Whitaker

Satoshi Uchiyama

Measuring processes of a single spin-1/2 object and of a pair of spin-1/2 objects in the EPR-Bohm state are modeled by systems of differential equations. These models are based on mainly the following two ideas: (i) as a result of the interaction with a measuring apparatus, the state of the object, changes and approaches an attractor, in which the object possesses the measured value in the phase space of states of objects; (ii) a quantum-mechanical state corresponds to an ensemble of states in the corresponding attractor in the phase space. The latter model is a local model with hidden variables of the EPR-Bohm gedanken experiment. Although there is no dynamical interaction between the pair of spin-1/2 objects, the model reproduces approximately the quantum-mechanical correlations by using coincidence counting. Hence the Bell inequality is violated. This result supports the idea that the coincidence counting is the source of the apparent nonlocality in the EPR-Bohm gedankenexperiment.

M. A. B. Whitaker, J.G. Dennison

智 内山

Measuring processes of a single spin-1/2 object and of a pair of spin-1/2 objects in the EPR-Bohm state are modeled by systems of differential equations. These models are based on mainly the following two ideas: (i) as a result of the interaction with a measuring apparatus, the state of the object, changes and approaches an attractor, in which the object possesses the measured value in the phase space of states of objects; (ii) a quantum-mechanical state corresponds to an ensemble of states in the corresponding attractor in the phase space. The latter model is a local model with hidden variables of the EPR-Bohm gedanken experiment. Although there is no dynamical interaction between the pair of spin-1/2 objects, the model reproduces approximately the quantum-mechanical correlations by using coincidence counting. Hence the Bell inequality is violated. This result supports the idea that the coincidence counting is the source of the apparent nonlocality in the EPR-Bohm gedankenexperiment.