In a recent paper, David Albert has suggested that no quantum theory can yield a description of the world unfolding in Minkowski spacetime. This conclusion is premature; a natural extension of Stein's notion of becoming in Minkowski spacetime to accommodate the demands of quantum nonseparability yields such an account, an account that is in accord with a proposal which was made by Aharonov and Albert but which is dismissed by Albert as a ‘mere trick’. The nature of such an account is clarified by an extension to a relativistic quantum context of David Lewis' picture of objective chances evolving in time. 1Introduction 2Classical relativistic becoming 3Relativistic quantum becoming, without collapse 4Relativistic quantum becoming, with collapse 5Objective chance, conditional probability, and definite properties 6The nature of the wave function 7Conclusion
The implications of the relativistic space-time structure for a physical description by quantum mechanical wave-functions are investigated. On the basis of a detailed analysis of Bell's concept of local causality, which is violated in quantum theory, we argue that this is a subtle, as well as an important effort. A central requirement appearing in relativistic quantum mechanics, namely local commutativity, is analyzed in detail and possible justifications are given and discussed. The complexity of the implications of wave function reduction in connection with Minkowski space-time are illustrated by a quantum mechanical measurement procedure which was proposed by Aharonov and Albert. This procedure and its relativistic implications are explicitly analyzed and discussed in terms of state evolution. This analysis shows that the usual notion of state evolution fails in relativistic quantum theory. Two possible solutions of this problem are given. In particular, it is shown that also a theory with a distinguished foliation of space-time into space-like leafs - accounting for nonlocality - makes the right predictions for the Aharonov-Albert experiment. We will repeatedly encounter that an analysis of the wave-function alone does not suffice to answer the question of relativistic compatibility of the theory, but that the actual events in space time, which are predicted and described by the theory, are crucial. Relativistic versions of quantum mechanical theories which precisely describe actual processes in space-time are briefly described and discussed in the appendix.
The purpose of the present chapter is to respond to a thread of recent criticism against one candidate framework for interpreting quantum theories, a framework introduced and defended by David Albert and Barry Loewer: wave function realism, a framework for interpreting the ontology of quantum theories according to which what appears to be a nonseparable metaphysics ofentangled objects acting instantaneously across spatial distances is a manifestation of a more fundamental separable and local metaphysics in higher dimensions. Thechapterconsiders strategies for extending the wave function realist interpretation of quantum mechanics to the case of relativistic quantum theories, responding to arguments that this cannot be done.
The theories of special relativity and quantum mechanics both rely on continuous rotation groups to describe physical systems, yet one is formulated on a real spacetime manifold while the other employs a complex Hilbert space. This work investigates whether this distinction may arise from the treatment of time itself. By examining the consequences of describing a relativistic system using a single global time parameter, we explore whether such a description naturally requires a mathematical structure capable of encoding observer-dependent proper times as complex phase information. Within this framework, quantum superposition is investigated as a possible coordinate-level representation of unresolved relativistic frame assignments, while wavefunction collapse is conceptualised as the physical resolution of this ambiguity through interaction. exploring whether aspects of the quantum formalism may be understood as consequences of describing the invariant structure of Minkowski spacetime from a local perspective using a rigid notion of time.
Relativistic quantum theories are equipped with a background Minkowski spacetime and non‐relativistic quantum theories with a Galilean space‐time. Traditional investigations have distinguished their distinct space‐time structures and have examined ways in which relativistic theories become sufficiently like Galilean theories in a low velocity approximation or limit. A different way to look at their relationship is to see that both kinds of theories are special cases of a certain five‐dimensional generalization involving no limiting procedures or approximations. When one compares them, striking features emerge that bear on philosophical questions, including the ontological status of the wave function and time reversal invariance.
Two problems with the Einstein-Podolsky-Rosen argument originate from the difficult-to-explain continual dismissal of Minkowski’s demonstration that the concept of spacetime represents a real four-dimensional world and is not just a mathematical space. The uncritical employment of the traditional three-dimensional language to the description of this argument leads (e.g., in its Bohm's version) to those problems: (1) due to the collapse of the common wavefunction of the constituents 1 and 2 of a disintegrated system, caused by the measurement of 1's spin (event
E1), and due the conservation of the total spin, 2's spin is \textit{instantaneously} determined (event
E2), which in three-dimensional language inescapably means that
E2 is \textit{caused} by
E1 (using merely a different word -- `correlation' -- does not explain anything in three-dimensional language); (2) events
E1 and
E2 are simultaneous \textit{only} for an observer
A, who was at rest with respect to the disintegrated system, and therefore the total spin is not conserved for arbitrarily large periods of time for all observers in relative motion with respect to
A and there exists a class of observers
B for whom event
E2 occurs \textit{before}
E1, which demonstrates the inadequacy of the fundamental implicit assumption that the physical world is three-dimensional. When the reality of spacetime is explicitly recognized, (1) the paradoxes of the non-conservation of the total spin and that
E2 happens before
E1 for observers
B do not arise (because there is no `before' and `after' in spacetime) and the statement that there is a correlation between
E1 and
E2 makes a perfect sense, and (2) a spacetime model of the quantum object can then be considered (by also taking into account the non-fully-realized experimental fact that the quantum object \textit{actually} exists everywhere where its wavefunction is different from zero) in order to address the fundamental incompleteness of quantum mechanics -- that it deals not with the quantum object itself, but only with its states. The paper ends with a discussion of a prediction by the proposed spacetime model of the electron that can be tested experimentally probably by the quadratic Stark effect.
An extended and more rigorous version of a recent proposal for an objective stochastic formulation of quantum mechanics along with its extension to the relativistic case without spin is presented. The relativistic Klein-Gordon equation is shown to be a particular form of the relativistic Kolmogorov-Fokker-Planck equation which is derived from a covariant formulation of the Chapman-Kolmogorov condition. Complexification of probability amplitudes is again achieved only through a conformal rotation of Minkowski space-time M 4 .