Note on an argument of W. Ochs against the ignorance interpretation of state in quantum mechanics

Jiří Souček

In the standard Quantum Mechanics (QM) there exists certain assumption (which I call the von Neuman axiom, see [1]) stating that an ensemble in the pure state is homogeneous. This means that all members of this ensemble are in the same individual state. Equivalently we can say that each pure state is an individual state (the term individual state means the state of an individual system). The von Neumann axiom is really hidden in QM: everyone who says “let us consider the system in the state ψ ” unconsciously uses this axiom. In this note I am going to show that the von Neumann axiom is false. This also means that the standard interpretation of the wave function as the state of the individual system is in general false. In the ontic/epistemic terminology this means that the ontic interpretation of the wave function cannot be true. There are four arguments for this statement (all these arguments are known): The classical argument The Bell inequality (BI) argument The Collapse argument The duplicity argument

Wilhelm Ochs

F.J. Duarte

This chapter examines the A. Einstein, B. Podolsky, and N. Rosen (EPR) argument and the opinion toward interpretational matters from various noted quantum physicists. The paradox of EPR can equally well be tested by polarization properties of pairs of photons. “When the momentum of a particle is known, its coordinate has no physical reality” is an essential component of the EPR argument. A useful pragmatic perspective on quantum mechanics is provided by N. G. Van Kampen. He argues that the difficulties in quantum mechanics only surface when one starts philosophizing: “this philosophizing has given rise to a number of ‘interpretations’, in which ψ is endowed with more physical significance than is needed”. There is a plethora of interpretations of quantum mechanics. Among the most prominent interpretations one finds are the Copenhagen interpretation and the many-worlds interpretation.

Dennis Dieks

Hanneke Janssen

This work is a critique of the program of "environment-induced decoherence" as advocated by Zurek, Zeh and Joos, among others. In particular, the alleged relevance of decoherence for a solution of the "measurement problem" is subjected to a detailed philosophical analysis. In the first chapter, an attempt is made to unravel what exactly this "measurement problem" amounts to for the decoherence theorists. The second chapter reviews the standard decoherence literature. The third chapter starts with a brief discussion of the philosophical implications of the decoherence program, followed by a non-standard reconstruction of the decoherence argument that aims to uncover some (mostly hidden) assumptions underlying the approach. It is argued that different subsets of these assumptions result in different versions of the decoherence argument. Next, these assumptions are investigated in more detail, and a number of open problems for the decoherence approach is formulated, in addition to the well-known "problem of outcomes". These problems concern the interpretational relevance of the preferred basis, the role and status of the ignorance interpretation of mixed states, imperfect decoherence and the role of the environment and the definition of subsystems. The fourth chapter addresses the question to what extent the embedding of decoherence in an Everett-like interpretational framework, such as Zurek's "existentional interpretation" and Wallace's structural-realistic version of the many-worlds interpretation, helps to resolve these problems. The main conclusions are formulated in the fifth chapter. Namely: 1) decoherence cannot address the "preferred-basis problem" without adding new interpretational axioms to the standard formalism, 2) the the locality principle (that says that the environment is the "irrelevant" part and should therefore be ignored) is not only problematic but also interpretationally superfluous, 3) the decoherence approach, when formulated in terms of the standard interpretation of quantum mechanics, is predicated on a solution of the "problem of outcomes" and thus cannot claim to account (even partially) for the latter, and 4) that the results of the decoherence program do not increase the plausibility of a realist interpretation of the quantum state.

F. Ghaboussi