It was shown by de Broglie and Bohm that the concept of a deterministic particle trajectory is compatible with quantum mechanics. It is demonstrated by explicit construction that there exists another more general deterministic trajectory interpretation. The method exploits an internal angular degree of freedom that is implicit in the Schrödinger equation, in addition to the particle position. The de Broglie-Bohm model is recovered when the new theory is averaged over the internal freedom. The model exhibits a strong form of entanglement which implies a primary role for the wavefunction of the Universe. The conditions of autonomy are examined, and the viability of the theory is established by application to the measurement problem.

We discuss the application of the de Broglie-Bohm theory of relativistic spin-1/2 particles to the Klein paradox and zitterbewegung,

In the context of the causal interpretation of quantum mechanics one can formulate the equation of motion of a quantal particle in the presence of a gravitational field. It is pointed out that, in the WKB limit of high quantum numbers, states exist for which one component of classical equivalence (that all bodies fall at an equal rate independent of their mass) is not recovered, due to quantum effects mediated by the quantum potential.

The causal interpretation of quantum mechanics is extended to include Fermi fields. The quantized field is a collection of spherical spin-12 rotators whose orientations may be described by sets of continuously variable Euler angles. The superwave-function depends on all the rotator coordinates and defines a set of quantum torques which cause the spin vectors to process. The analogous classical system is a set of independent rotators undergoing a Larmor-type precession. Remarks are made on the particle representation.

According to the causal interpretation of quantum mechanics, one can precisely define the state of an individual particle in a many-body system by its position, momentum, and spin. It is shown in the EPR spin experiment that the quantum torque brings about an instantaneous change in the state of one of the particles when the other undergoes a local interaction, but that such a transfer of “information” cannot be extracted by any experiment subject to the laws of quantum mechanics.

It is shown in detail how the causal interpretation of a spin-12 particle described by a Pauli spinor may be extended to treat the two-body case. All the degrees of freedom in the wavefunction may be interpreted in terms of interconnected Euclidean tensors generated by a direct product of Clifford algebras. The method extends to an n-body system. Previously stated results are proved. Remarks are made on signalling in the EPR spin-experiment, and a way of resolving problems with the interpretation using the quantum theory of rigid rotators is outlined.

We discuss generally and with reference to typical examples the classical limit of quantum mechanics, including equations of motion and the uncertainty relations, from the point of view of the causal interpretation. We show how universal criteria may be formulated in terms of sufficient conditions to be satisfied by the wavefunction in order that the classical results are recovered. These overcome the problems associated with limiting procedures such as ħ←0 or high quantum numbers On discute de facon generale et exemples a l'appui la limite classique de la mecanique quantique, y compris les equations du mouvement et les relations d'incertitude, dans l'optique de l'interpretation causale. On montre comment des criteres universels peuvent etre formules en termes de conditions suffisantes que la fonction d'onde doit satisfaire avant de retrouver les resultats classiques. Ces criteres surmontent les problemes associes aux passages a la limite tels que ħ→0 ou celle des grands nombres quantiques

Spin superposition in neutron interferometry, spin measurement, and non–local Einstein-Podolsky-Rosen spin correlations can be understood in terms of well–defined individual particle trajectories with continuously variable spin vectors.

We analyze phase-space approaches to relativistic quantum mechanics from the viewpoint of the causal interpretation. In particular, we discuss the canonical phase space associated with stochastic quantization, its relation to Hilbert space, and the Wigner-Moyal formalism. We then consider the nature of Feynman paths, and the problem of nonlocality, and conclude that a perfectly consistent relativistically covariant interpretation of quantum mechanics which retains the notion of particle trajectory is possible.

Assuming that future experiments confirm Aspect's discovery of nonlocal interactions between quantum pairs of correlated particles, we analyze the constraints imposed by the EPR reasoning on the said interactions. It is then shown that the nonlocal relativistic quantum potential approach plainly satisfies the Einstein causality criteria as well as the energy-momentum conservation in individual microprocesses. Furthermore, this approach bypasses a new causal paradox for timelike separated EPR measurements deduced by Sutherland in the frame of an approach by means of space-time zigzags with advanced potentials. It is finally demonstrated that this inherent quantum causal direct interaction establishes permanent EPR correlations which are always restricted to spacelike separations and are instantaneous only in the center-of-mass rest frame of the two-particle system.

The authors give a causal interpretation of a double Stern-Gerlach experiment on the basis of spacetime solutions to the Pauli equation. For an initial singlet state, they determine the continuous particle trajectories and spin vector orientations. The graphical results exemplify how non-local actions of the quantum potential and quantum torque give rise to a correlated evolution of dynamical variables.

The geometrical structures implicit in the de Broglie waves associated with a relativistic charged scalar quantum mechanical particle in an external field are analyzed by employing the ray concept of the causal interpretation. It is shown how an osculating Finslerian metric tensor, a torsion tensor, and a tetrad field define respectively the strain, the dislocation density, and the Burgers vector in the “natural state” of the wave, which is a non-Riemannian space of distant parallelism. A quantum torque determined by the quantum potential is introduced and the example of a screw dislocated wave is discussed.

Following suggestions of Schönberg and Bohm, we study the tensorial phase space representation of the Dirac and Feynman-Gell-Mann equations in terms of the complex Dirac algebra C4, a Jordan-Wigner algebra G4, and Wigner transformations. To do this we solve the problem of the conditions under which elements in C4 generate minimal ideals, and extend this to G4. This yields the linear theory of Dirac spin spaces and tensor representations of Dirac spinors, and the spin-1/2 wave equations are represented through fermionic state vectors in a higher space as a set of interconnected tensor relations.

Based on a recent association of quantum observable algebra with stochastic processes in the frame of the causal stochastic interpretation of quantum mechanics, a relativistic Hilbert space is defined for the Klein-Gordon case. It is demonstrated that unitary transformations in Hilbert space reflect canonical transformations in the associated phase space, manifesting thus an underlying symplectic structure.

Annals of the New York Academy of SciencesVolume 480, Issue 1 p. 579-580 Locality, Causality, and the Aharonov-Bohm Effect P. R. HOLLAND, P. R. HOLLAND Laboratoire de Physique Théorique Institut Henri Poincaré 75321 Paris Cedex 05, FranceSearch for more papers by this author P. R. HOLLAND, P. R. HOLLAND Laboratoire de Physique Théorique Institut Henri Poincaré 75321 Paris Cedex 05, FranceSearch for more papers by this author First published: December 1986 https://doi.org/10.1111/j.1749-6632.1986.tb12466.xCitations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article.Citing Literature Volume480, Issue1New Techniques and Ideas in Quantum Measurement TheoryDecember 1986Pages 579-580 RelatedInformation