A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion, field evolution and conservation laws can all be deduced from a single Lagrangian density expression. The formalism presented is Lorentz invariant. This paper follows on from a previous one which was limited to the single-particle case. The present paper treats the more general case of many (...) particles in an entangled state. It is found that describing more than one particle while maintaining a relativistic description requires the specification of final boundary conditions as well as the usual initial ones, with the experimenter’s controllable choice of the final conditions thereby exerting a backwards-in-time influence. This retrocausality then allows an important theoretical step forward to be made, namely that it becomes possible to dispense with the usual, many-dimensional description in configuration space and instead revert to a description in space–time using separate, single-particle wavefunctions. (shrink)

A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a picture of an external reality. The new formalism, developed first for the single-particle case, has the advantage of generalizing immediately to quantum field theory and to the description of relativistic phenomena such as particle creation and annihilation.

This paper is concerned with the causally symmetric version of the familiar de Broglie–Bohm interpretation, this version allowing the spacelike nonlocality and the configuration space ontology of the original model to be avoided via the addition of retrocausality. Two different features of this alternative formulation are considered here. With regard to probabilities, it is shown that the model provides a derivation of the Born rule identical to that in Bohm’s original formulation. This derivation holds just as well for a many-particle, (...) entangled state as for a single particle. With regard to “certainties”, the description of a particle’s spin is examined within the model and it is seen that a statistical description is no longer necessary once final boundary conditions are specified in addition to the usual initial state, with the particle then possessing a definite value for every spin component at intermediate times. These values are consistent with being the components of a single, underlying spin vector. The case of a two-particle entangled spin state is also examined and it is found that, due to the retrocausal aspect, each particle possesses its own definite spin during the entanglement, independent of the other particle. In formulating this picture, it is demonstrated how such a realistic model can preserve Lorentz invariance in the face of Bell’s theorem and avoid the need for a preferred reference frame. (shrink)

A Lagrangian description is presented which can be used in conjunction with particle interpretations of quantum mechanics. A special example of such an interpretation is the well-known Bohm model. The Lagrangian density introduced here also contains a potential for guiding the particle. The advantages of this description are that the field equations and the particle equations of motion can both be deduced from a single Lagrangian density expression and that conservation of energy and momentum are assured. After being developed in (...) a general form, this Lagrangian formulation is then applied to the special case of the Bohm model as an example. It is thereby demonstrated that such a Lagrangian description is compatible with the predictions of quantum mechanics. (shrink)

A generalization of the familiar de Broglie-Bohm interpretation of quantum mechanics is formulated, based on relinquishing the momentum relationship p=∇S and allowing a spread of momentum values at each position. The development of this framework also provides a new perspective on the well-known question of joint distributions for quantum mechanics. It is shown that, for an extension of the original model to be physically acceptable and consistent with experiment, it is necessary to impose certain restrictions on the associated joint distribution (...) for particle positions and momenta. These requirements thereby define a new class of possible models. In pursuing this line of reasoning, the main contributions of this paper are (i) to identify the restrictions that must be imposed, (ii) to demonstrate that joint distribution expressions satisfying them do exist, and (iii) to construct a sample model based on one such joint distribution. (shrink)