Timescales for dynamical relaxation to the Born rule

We illustrate through explicit numerical calculations how the Born-rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie-Bohm pilot-wave theory. The time evolution of a particle distribution initially not equal to the absolute square of the wave function is calculated for a particle in a two-dimensional infinite potential square well. Under the de Broglie-Bohm ontology, the box contains an objectively-existing 'pilot wave' which guides the electron trajectory, and this is represented mathematically by a Schroedinger wave function composed of a finite out-of-phase superposition of M energy eigenstates (with M ranging from 4 to 64). The electron density distributions are found to evolve naturally into the Born-rule ones and stay there; in analogy with the classical case this represents a decay to 'quantum equilibrium'. The proximity to equilibrium is characterized by the coarse-grained subquantum H-function which is found to decrease roughly exponentially towards zero over the course of time. The timescale tau for this relaxation is calculated for various values of M and the coarse-graining length epsilon. Its dependence on M is found to disagree with an earlier theoretical prediction. A power law - tau inversely proportional to M - is found to be fairly robust for all coarse-graining lengths and, although a weak dependence of tau on epsilon is observed, it does not appear to follow any straightforward scaling. A theoretical analysis is presented to explain these results. This improvement in our understanding of timescales for relaxation to quantum equilibrium is likely to be of use in the development of models of relaxation in the early universe, with a view to constraining possible violations of the Born rule in inflationary cosmology.Comment: 27 pages, 8 figures; Replacement with small number of changes reflecting referees' comment

Existential Contextuality and the Models of Meyer, Kent and Clifton

It is shown that the models recently proposed by Meyer, Kent and Clifton (MKC) exhibit a novel kind of contextuality, which we term existential contextuality. In this phenomenon it is not simply the pre-existing value but the actual existence of an observable which is context dependent. This result confirms the point made elsewhere, that the MKC models do not, as the authors claim, ``nullify'' the Kochen-Specker theorem. It may also be of some independent interest.Comment: Revtex, 7 pages, 1 figure. Replaced with published versio

Response to Comment on `Undamped electrostatic plasma waves' [Phys. Plasmas 19, 092103 (2012)]

Numerical and experimental evidence is given for the occurrence of the plateau states and concomitant corner modes proposed in \cite{valentini12}. It is argued that these states provide a better description of reality for small amplitude off-dispersion disturbances than the conventional Bernstein-Greene-Kruskal or cnoidal states such as those proposed in \cite{comment

Hidden variable interpretation of spontaneous localization theory

The spontaneous localization theory of Ghirardi, Rimini, and Weber (GRW) is a theory in which wavepacket reduction is treated as a genuine physical process. Here it is shown that the mathematical formalism of GRW can be given an interpretation in terms of an evolving distribution of particles on configuration space similar to Bohmian mechanics (BM). The GRW wavefunction acts as a pilot wave for the set of particles. In addition, a continuous stream of noisy information concerning the precise whereabouts of the particles must be specified. Nonlinear filtering techniques are used to determine the dynamics of the distribution of particles conditional on this noisy information and consistency with the GRW wavefunction dynamics is demonstrated. Viewing this development as a hybrid BM-GRW theory, it is argued that, besides helping to clarify the relationship between the GRW theory and BM, its merits make it worth considering in its own right.Comment: 13 page

Geometrical view of quantum entanglement

Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which apparently has no classical counterpart. We demonstrate here how quantum entanglement may be within the de Broglie-Bohm interpretation of quantum mechanics visualized in geometrical terms, giving new insight into this mysterious phenomenon and a language to describe it. On the basis of our analysis of the dynamics of a pair of qubits, quantum entanglement is linked to concurrent motion of angular momenta in the Bohmian space of hidden variables and to the average angle between these momenta

On Epstein's trajectory model of non-relativistic quantum mechanics

In 1952 Bohm presented a theory about non-relativistic point-particles moving along deterministic trajectories and showed how it reproduces the predictions of standard quantum theory. This theory was actually presented before by de Broglie in 1926, but Bohm's particular formulation of the theory inspired Epstein to come up with a different trajectory model. The aim of this paper is to examine the empirical predictions of this model. It is found that the trajectories in this model are in general very different from those in the de Broglie-Bohm theory. In certain cases they even seem bizarre and rather unphysical. Nevertheless, it is argued that the model seems to reproduce the predictions of standard quantum theory (just as the de Broglie-Bohm theory).Comment: 12 pages, no figures, LaTex; v2 minor improvement

Signal-Locality and Subquantum Information in Deterministic Hidden-Variables Theories

It is proven that any deterministic hidden-variables theory, that reproduces quantum theory for a 'quantum equilibrium' distribution of hidden variables, must predict the existence of instantaneous signals at the statistical level for hypothetical 'nonequilibrium ensembles'. This 'signal-locality theorem' generalises yet another feature of the pilot-wave theory of de Broglie and Bohm, for which it is already known that signal-locality is true only in equilibrium. Assuming certain symmetries, lower bounds are derived on the 'degree of nonlocality' of the singlet state, defined as the (equilibrium) fraction of outcomes at one wing of an EPR-experiment that change in response to a shift in the distant angular setting. It is shown by explicit calculation that these bounds are satisfied by pilot-wave theory. The degree of nonlocality is interpreted as the average number of bits of 'subquantum information' transmitted superluminally, for an equilibrium ensemble. It is proposed that this quantity might provide a novel measure of the entanglement of a quantum state, and that the field of quantum information would benefit from a more explicit hidden-variables approach. It is argued that the signal-locality theorem supports the hypothesis, made elsewhere, that in the remote past the universe relaxed to a state of statistical equilibrium at the hidden-variable level, a state in which nonlocality happens to be masked by quantum noise

Metastatic Uterine Leiomyosarcoma in the Upper Buccal Gingiva Misdiagnosed as an Epulis

Uterine leiomyosarcoma (LMS) is a rare tumor constituting 1% of all uterine malignancies. This sarcoma demonstrates an aggressive growth pattern with an high rate of recurrence with hematologic dissemination; the most common sites are lung, liver, and peritoneal cavity, head and neck district being rarely interested. Only other four cases of metastasis in the oral cavity have been previously described. The treatment of choice is surgery and the use of adjuvant chemotherapy and radiation has limited impact on clinical outcome. In case of metastases, surgical excision can be performed considering extent of disease, number and type of distant lesions, disease free interval from the initial diagnosis to the time of metastases, and expected life span. We illustrate a case of uterine LMS metastasis in the upper buccal gingiva that occurred during chemotherapy in a 63-year-old woman that underwent a total abdominal hysterectomy with bilateral salpingo-oophorectomy for a diagnosis of LMS staged as pT2bN0 and that developed lung metastases eight months after primary treatment. Surgical excision of the oral mass (previously misdiagnosed as epulis at a dental center) and contemporary reconstruction with pedicled temporalis muscle flap was performed in order to improve quality of life. Even if resection was achieved in free margins, "local" relapse was observed 5 months after surgery

On the zig-zag pilot-wave approach for fermions

We consider a pilot-wave approach for the Dirac theory that was recently proposed by Colin and Wiseman. In this approach, the particles perform a zig-zag motion, due to stochastic jumps of their velocity. We respectively discuss the one-particle theory, the many-particle theory and possible extensions to quantum field theory. We also discuss the non-relativistic limit of the one-particle theory. For a single particle, the motion is always luminal, a feature that persists in the non-relativistic limit. For more than one particle the motion is in general subluminal.Comment: 23 pages, no figures, LaTe