Chapter 8. Other Local Deterministic Theories

Augusto Garuccio, P. Selleri

Augusto Garuccio, V. A. Rapisarda

Tim Maudlin

W. Michael Dickson

Review and preview In chapters 6 and 7, I described some links between locality and the treatment of probabilities in models of the EPR–Bohm experiment. From chapter 6, the main lesson was that, given the strict correlations of quantum mechanics, factorizability of the two-time probabilities is equivalent to two-time determinism. I also noted there that an adequate factorizable theory – one that avoids Bell's theorem – is possible only if λ-independence fails. In chapter 7, I argued that weak symmetry, local determination, and independent evolution together entail deterministic results and weak deterministic transitions. In chapter 8, I discussed the relationships among the locality conditions of chapter 6 and 7, Lorentz-invariance, and ‘metaphysical’ locality, especially local causality. I have by no means tried to give general answers to the questions raised there. Indeed, part of my thesis is that there is no general answer to be had. Nonetheless, one can use the results of chapters 6 and 7 to investigate the status of various interpretations. Most obviously, they can be used to evaluate whether a given theory is local: if a theory can be shown to violate one or more of the types of determinism entailed by the locality conditions of chapters 6 and 7, then that theory must be non-local in some sense.

P. J. E. Peebles

This chapter reviews measurement theory in quantum mechanics. The measurement prescription in quantum mechanics can be stated in a few lines and has found an enormous range of applications, in all of which it has proved to be consistent with logic and experimental tests. However, the implications seem so bizarre that people such as Albert Einstein and Eugene Wigner have argued that the theory cannot be physically complete as its stands. The chapter then extends the prescription to the case where the state vector is not known. It also discusses some of the “paradoxes” of quantum mechanics. Finally, the chapter presents Bell's theorem, which shows that there cannot be a local underlying deterministic theory for which quantum mechanics plays the role of a statistical approximation.

Gerard ’t Hooft

Even if the underlying deterministic model may be assumed to obey decent locality requirements, a systematic procedure to define a quantum Hilbert space starting from its ontological states, would in general lead to a quantum system without manifest locality at all. Instead, what we are really after is a procedure that generates a local, relativistic quantum field theory. In this chapter we describe a procedure that follows the construction of relativistic quantum field theory more closely. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.