a Lorentz Invariant, Microphysical Theory of Wave - Collapse

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.

Georges Lochak, Regis Dutheil

Pei Wang

Abstract We develop a quantum field theory based on random nonHermitian actions, which upon quantization lead to stochastic nonlinear Schrödinger dynamics for the state vector. In this framework, Lorentz and spacetime translation symmetries are preserved only in a statistical sense: the probability distribution of the action remains invariant under these transformations. As a result, the theory describes ensembles of quantum-state trajectories whose probability distributions remain invariant under changes of reference frame. As a concrete example, we augment the Dirac action with a purely imaginary term coupling the fermion density operator to a universal colored noise. This noise is constructed by solving the d’Alembert equation with white noise as its source, using a generalized stochastic calculus in 1+3 dimensions. We demonstrate that the colored noise drives stochastic localization of wave packets and derive the localization length analytically. Remarkably, the localization length decreases as the size of the observable universe increases. Our model thus provides a potential framework for relativistic spontaneous wave-function collapse. While establishing consistency with Born’s law remains an open challenge, the present work constitutes a step toward embedding collapse models into a Lorentz-invariant quantum field theory.

Vladimir Evgen'evich Zakharov, Evgeniy A. Kuznetsov

Jason cole

Hossein Movahhedian

Non-local forces exist in nature for two reasons. First that the recent experiments on locality are supposed to be accurate enough. Second that there is no local theory that can reproduce all the predictions of orthodox quantum theory which, almost for about a century, have been proved to be correct experimentally again and again. This thesis concerns both of these. A brief discussion of the measurement in quantum theory is followed by two comments which show that the quantum description is frame dependent and that the collapse of the wave-function of a system may occur without the relevant measurement being performed. After this the Bohm model and a modified version of the Bohm model are described. Next we introduce a new method for obtaining the Bell-type inequalities which can be used for testing locality. We derive more inequalities by this method than obtained by other existing procedures. Using Projection Valued(PV) and Positive Operator Valued Measures(POVM) measurements we have designed experiments which violates one of the Bell inequalities by a larger factor than existing violations which in turn could increase the accuracy of experiments to test for non-locality. This is our first result. After discussing the non-locality and non-Lorentz invariant features of the Bohm model, its retarded version, namely Squires' model - which is local and Lorentz invariant - is introduced. A problem with this model, that is the ambiguity in the cases where the wave-function depends on time, is removed by using the multiple-time wave-function. Finally, we apply the model to one of the experiments of locality and prove that it is in good agreement with the orthodox quantum theory.