According to the modal interpretation, the standard mathematical framework of quantum mechanics specifies the physical magnitudes of a system, which have definite values. Probabilities are assigned to the possible values that these magnitudes may adopt. The interpretation is thus concerned with physical properties rather than with measurement results: it is a realistic interpretation. One of the notable achievements of this interpretation is that it dissolves the notorious measurement problem. The papers collected here, together with the introduction and concluding critical appraisal, (...) explain the various forms of the modal interpretation, survey its achievements, and discuss those problems that have yet to be solved. Audience: Philosophers of science, theoretical physicists, and graduate students in these disciplines. (shrink)

A proof is given, at a greater level of generality than previous 'no-go' theorems, of the impossibility of formulating a modal interpretation that exhibits 'serious' Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.

A number of arguments have been given to show that the modal interpretation of ordinary nonrelativistic quantum mechanics cannot be consistently extended to the relativistic setting. We find these arguments inconclusive. However, there is a prima facie reason to think that a tension exists between the modal interpretation and relativistic invariance; namely, the best candidate for a modal interpretation adapted to relativistic quantum field theory, a prescription due to Rob Clifton, comes out trivial when applied to a number of systems (...) of physical interest. However, it is far from clear whether this difficulty for the modal interpretation is traceable to relativistic invariance per se or to the infinite number of degrees of freedom involved. In any case, the proponents of the modal interpretation have work to do. (shrink)

Modal interpretations are hidden-variable, no-collapse interpretations of quantum mechanics that were designed to solve the measurement problem and reconcile this theory with relativity. Yet, as no-go theorems by Dickson and Clifton, Arntzenius and Myrvold demonstrate, current modal interpretations are incompatible with relativity. In the mainstream modal interpretations, properties of composite systems are generally unrelated to the properties of their subsystems. We propose holistic and relational interpretations of properties to explain this failure of property composition. Based on these interpretations, we consider (...) strategies for circumventing Myrvold's theorem, which are also effective against the other two theorems. (shrink)

This is the first of two papers responding to ‘recent’ commentary on various aspects of hyperplane dependence by several authors. In this paper I focus on the issues of the relations of HD to state reduction and unitary evolution. The authors who’s comments I address here are Maudlin and Myrvold. In the second paper of this set I focus on HD dynamical variables and localizable properties and measurements and address comments of de Koning, Halvorson, Clifton and Wallace. Each paper ends (...) with some reflections on the implications of HD for the ontology of Minkowski space-time. To set the stage for my responses, I begin this paper with some general position statements designed to correct what seem to be widespread and erroneous construals of some of my views. Two central points are argued for in this first paper. First, dynamical evolution occurs not only within foliations of Minkowski space-time. Rather the transition from the physical state of affairs on any one hyperplane to any other, whether the hyperplanes intersect or are parallel, is always an instance of dynamical evolution between them, generated by some active combination of boost-like transformations and/or time-like translations and/or state reductions and ‘reconstructions’. This point gives rise to a generalized conception of a history of dynamical evolution, allowing for the use of parameterized families of hyperplanes that multiply cover some portions of space-time. Nevertheless, and this is the second central point, for any two generalized histories, H and H’, the quantum states for a system on all the hyperplanes of H from the asymptotic past up to some hyperplane, h, determine the quantum states for the system on all the hyperplanes of H’ from the asymptotic past up to any hyperplane, h’, such that h’ lies to the past of all those state reduction regions that lie to the future of all hyperplanes of H that are ‘earlier’ than h. Consideration of these results should defuse concerns that have been voiced about the coherence and consistency of HD. A position closely related to the second point has already been argued for by Myrvold. (shrink)

The long established but infrequently discussed dependence of Lorentz boost generators on the presence and nature of interactions is reviewed in this tutorial note. The last third of the note presents a discussion of the covariant transformation and evolution equations for the non-conserved partial generators of the inhomogeneous Lorentz group for interacting subsystems.

Two of the main interpretative problems in quantum mechanics are the so-called measurement problem and the question of the compatibility of quantum mechanics with relativity theory. Modal interpretations of quantum mechanics were designed to solve both of these problems. They are no-collapse (typically) indeterministic interpretations of quantum mechanics that supplement the orthodox state description of physical systems by a set of possessed properties that is supposed to be rich enough to account for the classical-like behavior of macroscopic systems, but sufficiently (...) restricted so as to avoid the no-hidden-variables theorems. But, as recent no-go theorems suggest, current modal interpretations are incompatible with relativity. In this paper, we suggest a strategy for circumventing these theorems. We then show how this strategy could naturally be integrated in a relational version of the modal interpretation, where quantum-mechanical states assign relational rather than intrinsic properties. (shrink)

Jim Cushing emphasized that physical theory should tell us an intelligible and objective story about the world, and concluded that the Bohm theory is to be preferred over the Copenhagen interpretation. We argue here, however, that the Bohm theory is only one member of a wider class of interpretations that can be said to fulfill Cushing’s desiderata. We discuss how the pictures provided by these interpretations differ from the classical one. In particular, it seems that a rather drastic form of (...) perspectivalism is needed if accordance with special relativity is to be achieved. (shrink)