The covariant Klein-Gordon equation requires twice the boundary conditions of the Schrödinger equation and does not have an accepted single-particle interpretation. Instead of interpreting its solution as a probability wave determined by an initial boundary condition, this paper considers the possibility that the solutions are determined by both an initial and a final boundary condition. By constructing an invariant joint probability distribution from the size of the solution space, it is shown that the usual measurement probabilities can nearly be recovered (...) in the non-relativistic limit, provided that neither boundary constrains the energy to a precision near ℏ/t 0 (where t 0 is the time duration between the boundary conditions). Otherwise, deviations from standard quantum mechanics are predicted. (shrink)

Presents a guide to the basics of quantum mechanics and measurement.

David Wallace argues that we should take quantum theory seriously as an account of what the world is like--which means accepting the idea that the universe is constantly branching into new universes. He presents an accessible but rigorous account of the 'Everett interpretation', the best way to make coherent sense of quantum physics.

The quantum theory of de Broglie and Bohm solves the measurement problem, but the hypothetical corpuscles play no role in the argument. The solution finds a more natural home in the Everett interpretation.

The paper argues that the formulation of quantum mechanics proposed by Ghirardi, Rimini and Weber (GRW) is a serious candidate for being a fundamental physical theory and explores its ontological commitments from this perspective. In particular, we propose to conceive of spatial superpositions of non-massless microsystems as dispositions or powers, more precisely propensities, to generate spontaneous localizations. We set out five reasons for this view, namely that (1) it provides for a clear sense in which quantum systems in entangled states (...) possess properties even in the absence of definite values; (2) it vindicates objective, single-case probabilities; (3) it yields a clear transition from quantum to classical properties; (4) it enables to draw a clear distinction between purely mathematical and physical structures, and (5) it grounds the arrow of time in the time-irreversible manifestation of the propensities to localize. (shrink)

The aim of this paper is to construct a version of Bohm’s model that also includes the existence of backwards-in-time influences in addition to the usual forwards causation. The motivation for this extension is to remove the need in the existing model for a preferred reference frame. As is well known, Bohm’s explanation for the nonlocality of Bell’s theorem necessarily involves instantaneous changes being produced at space-like separations, in conflict with the “spirit” of special relativity even though these changes are (...) not directly observable. While this mechanism is quite adequate from a purely empirical perspective, the overwhelming experimental success of special relativity (together with the theory’s natural attractiveness), makes one reluctant to abandon it even at a “hidden” level. There are, of course, trade-offs to be made in formulating an alternative model and it is ultimately a matter of taste as to which is preferred. However, constructing an explicit example of a causally symmetric formalism allows the pros and cons of each version to be compared and highlights the consequences of imposing such symmetry. In particular, in addition to providing a natural explanation for Bell nonlocality, the new model allows us to define and work with a mathematical description in 3-dimensional space, rather than configuration space, even in the correlated many-particle case. (shrink)

Quantum mechanics has sometimes been taken to be an empiricist (vs. realist) theory. I state the empiricist's argument, then outline a recently noticed type of measurement--protective measurement--that affords a good reply for the realist. This paper is a reply to scientific empiricism (about quantum mechanics), but is neither a refutation of that position, nor an argument in favor of scientific realism. Rather, my aim is to place realism and empiricism on an even score in regards to quantum theory.

Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is relativistically invariant and fully causal. (...) A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimenre and "paradoxes." The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its "collapse." It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law (P = ii iij*), basic elements of the Copenhagen interpretation. (shrink)

Protective measurement is a new measuring method introduced by Aharonov, Vaidman, and Anandan, with the aim of measuring the expectation value of an observable on a single quantum system, even if the system is initially not in an eigenstate of the measured observable. According to these authors, this feature of protective measurements favors a realistic interpretation of the wave function. These claims were challenged by Uffink. He argued that only observables that commute with the system's Hamiltonian can be protectively measured, (...) and that an allegedly protective measurement of an observable that does not commute with the system's Hamiltonian does not actually measure this observable, but rather another related one that commutes with the system's Hamiltonian. In this paper we identify a number of unresolved issues in Uffink's proofs and argue that his alternative interpretation of what happens in a protective measurement has not been justified. (shrink)

Gao presents a critical reconsideration of a paper I wrote on the subject of protective measurement. Here, I take the occasion to reply to his objections. In particular, I retract my previous claim to have proven that in a protective measurement, the observable being measured on a system must commute with the system's Hamiltonian. However, I do maintain the viability of the interpretation I offered for protective measurements, as well as my analysis of a thought experiment proposed by Aharonov, Anandan (...) and Vaidman against Gao's objections. (shrink)