Online research in philosophy

Bohmian mechanics is an alternative interpretation of quantum mechanics. We outline the main characteristics of its non-relativistic formulation. Most notably it does provide a simple solution to the infamous measurement problem of quantum mechanics. Presumably the most common objection against Bohmian mechanics is based on its non-locality and its apparent conflict with relativity and quantum field theory. However, several models for a quantum field theoretical generalization do exist. We give a non-technical account of some of these models.

The paper introduces what is deemed as the general epistemological problem of measurement: what characterizes measurement with respect to generic evaluation? It also analyzes the fundamental positions that have been maintained about this issue, thus presenting some sketches for a conceptual history of measurement. This characterization, in which three distinct standpoints are recognized, corresponding to a metaphysical, an anti-metaphysical, and relativistic period, allows us to introduce and briefly discuss some general issues on the current epistemological status of measurement science.

The integration of recent work on decoherence into a so-called modal interpretation offers a promising new approach to the measurement problem in quantum mechanics. In this paper I explain and develop this approach in the context of the interactive interpretation presented in Healey (1989). I begin by questioning a number of assumptions which are standardly made in setting up the measurement problem, and I conclude that no satisfactory solution can afford to ignore the influence of the environment. Further, I argue that there are good reasons to believe that on a modal interpretation environmental interactions rapidly ensure that a quantummechanically describable apparatus indeed records a definite result following a measurement interaction.

Everett's relative-state formulation of quantum mechanics is an attempt to solve the measurement problem by dropping the collapse dynamics from the standard von Neumann-Dirac theory of quantum mechanics. The main problem with Everett's theory is that it is not at all clear how it is supposed to work. In particular, while it is clear that he wanted to explain why we get determinate measurement results in the context of his theory, it is unclear how he intended to do this. There have been many attempts to reconstruct Everett's no-collapse theory in order to account for the apparent determinateness of measurement outcomes. These attempts have led to such formulations of quantum mechanics as the many-worlds, many-minds, many-histories, and relative-fact theories. Each of these captures part of what Everett claimed for his theory, but each also encounters problems.

This paper is concerned with the possibility and nature of relativistic hidden-variable formulations of quantum mechanics. Both ad hoc teleological constructions of spacetime maps and frame-dependent constructions of spacetime maps are considered. While frame-dependent constructions are clearly preferable, they provide neither mechanical nor causal explanations for local quantum events. Rather, the hiddenvariable dynamics used in such constructions is just a rule that helps to characterize the set of all possible spacetime maps. But while having neither mechanical nor causal explanations of the values of quantummechanical measurement records is a significant cost, it may simply prove too much to ask for such explanations in relativistic quantum mechanics.

Everett demonstrates the appearance of collapse, within the context of the unitary linear dynamics. However, he does not state clearly how observers are to have determinate measurement records, hence 50 years of debate. This, however, is inherent. He defines the observer as the record of observations, which, naturally, is the record of correlations established with the physical environment. As in Rovelli's Relational Quantum Mechanics, the correlations record is the sole determinant of the effective physical environment, here the quantum mechanical frame of reference: due to multiple realisation of the functional identity of the observer, the physical environment is a simultaneity of all the physical environments in which it is instantiated, a 'universe superposition', in which only the environment correlated with the observer by observations is determinate. This effects a discrete and idiosyncratic physical environment for each version of an observer, in which determinate measurement records are recorded. Quantum mechanics is on this view fully relational, demonstrated as not only viable but necessary by Rovelli & Laudisa. The quantum mechanical frame of reference is Everett's 'Relative State', and on Tegmark's 'inside view', the time evolution follows the standard von Neumann-Dirac formulation. Thus observers get precisely the measurement records predicted by the standard formulation, but since objectively there is only the appearance of collapse, there is neither a measurement problem nor a disparity with relativity. The linear dynamics and the collapse dynamics are directly experienced, as the passage of time and the making of observations, respectively.

In order to judge whether a theory is empirically adequate one must have epistemic access to reliable records of past measurement results that can be compared against the predictions of the theory. Some formulations of quantum mechanics fail to satisfy this condition. The standard theory without the collapse postulate is an example. Bell's reading of Everett's relative-state formulation is another. Furthermore, there are formulations of quantum mechanics that only satisfy this condition for a special class of observers, formulations whose empirical adequacy could only be judged by an observer who records her measurement results in a special way. Bohm's theory is an example. It is possible to formulate hidden-variable theories that do not suffer from such a restriction, but these encounter other problems.

Philosophical debate on the measurement problem of quantum mechanics has, for the most part, been confined to the non-relativistic version of the theory. Quantizing quantum field theory, or making quantum mechanics relativistic, yields a conceptual framework capable of dealing with the creation and annihilation of an indefinite number of particles in interaction with fields, i.e. quantum systems with an infinite number of degrees of freedom. I show that a solution to the standard measurement problem is available if we exploit the properties of the infinite quantum models available in this broader conceptual framework.

A field-theoretic version of Wigner’s friend (1961) illustrates how the quantum measurement problem arises for field theory. Similarly, considering spacelike separate measurements of entangled fields by observers akin to Wigner’s friend shows the sense in which relativistic constraints make the measurement problem particularly difficult to resolve in the context of a relativistic field theory. We will consider proposals by Wigner (1961), Bloch (1967), Helwig and Kraus (1970), and Bell (1984) for resolving the measurement problem for quantum field theory. We will conclude by considering the possibility of giving up rich dynamical explanation in the context of a many-maps formulation of relativistic quantum field theory.

Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum field theory (AQFT) provides a rigorous framework within which to analyse entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations on an experimenter's ability to perform operations on a field in one spacetime region that can disentangle its state from the state of the field in other spacelike-separated regions. These limitations show just how deeply entrenched entanglement is in relativistic quantum field theory, and yield a fresh perspective on the ways in which the theory differs conceptually from both standard non-relativistic quantum theory and classical relativistic field theory.