Review of invariant time formulations of relativistic quantum theories

Włodzimierz M. Tulczyjew

M. D. Srinivas

Relativistic quantum theory is formulated as a theory of successive local observations, consistent with all the fundamental requirements of relativistic invariance. Based on the causal structure of the space–time of special relativity, it is argued that the nonrelativistic notion of a ’’time-ordered sequence of instantaneous observations’’should be replaced in a relativistic theory by the notion of a ’’causally ordered sequence of local observations.’’ The fundamental statistical law of relativistic quantum theory is then formulated such that it provides an unambigous prescription for the statistical correlations between the outcomes of any causally ordered sequence of local observations. It is also shown that the fundamental statistical law of the theory is consistent with the so-called ’’principle of local causes’’ which essentially states that the probability connections between a set of local events do not depend on local observations carried out in space–time regions which lie outside of their causal past. Finally, an equivalent formulation of the theory in terms of a relativistically covariant generalization of the collapse postulate is presented.

Detlef Dürr, Sheldon Goldstein, Travis Norsen +2 more

In relativistic space-time, Bohmian theories can be formulated by introducing a privileged foliation of space-time. The introduction of such a foliation-as extra absolute space-time structure-would seem to imply a clear violation of Lorentz invariance, and thus a conflict with fundamental relativity. Here, we consider the possibility that, instead of positing it as extra structure, the required foliation could be covariantly determined by the wave function. We argue that this allows for the formulation of Bohmian theories that seem to qualify as fundamentally Lorentz invariant. We conclude with some discussion of whether or not they might also qualify as fundamentally relativistic.

C. A. Lopez, M. A. Pérez

Ward Struyve

Lorentz invariance is considered a fundamental property of relativistic quantum theory. However, in standard quantum theory this invariance is only partially realized: while relativistic wave equations like the Dirac equation are Lorentz invariant, the collapse postulate is not. In the non-relativistic domain, alternative theories have been formulated, like Bohmian mechanics and spontaneous collapse theories, which dispense with the problematic collapse postulate. Extending these theories to the relativistic domain appears challenging, particularly with respect to implementing Lorentz invariance, mainly due to the unavoidable non-locality implied by Bell’s theorem. However, space-time theories can also trivially be formulated in a Lorentz-invariant way. If Lorentz invariance is to impose a genuine constraint on the content of a physical theory, one should aim for what can be called substantive Lorentz invariance. However, articulating a precise definition of this notion is notoriously difficult. This paper investigates two candidate criteria: Anderson’s criterion based on the identification of absolute objects, and a relativity principle for isolated subsystems. These criteria are applied to evaluate several Lorentz-invariant Bohmian models, a spontaneous collapse model, and a version of the Many-Worlds theory. With the exception of two Bohmian approaches, these models satisfy both criteria. Nevertheless, some Bohmian models that meet these conditions still do not appear to be substantively Lorentz-invariant, suggesting that the proposed criteria may not fully capture the intended concept. Nevertheless, they help clarify what aspects of relativity theory may need to be given up in passing from classical to quantum theory.

Koshun Suto