J. Acacio de Barros

The causal interpretation of dust and radiation fluid non-singular quantum cosmologies

Abstract We apply the causal interpretation of quantum mechanics to homogeneous and isotropic quantum cosmology where the sources of the gravitational field are either dust or radiation perfect fluids. We find non-singular quantum trajectories which tend to the classical one when the scale factor becomes much larger than its minimum size. There are no particle horizons.

Quantum-like model of behavioral response computation using neural oscillators

In this paper we propose the use of neural interference as the origin of quantum-like effects in the brain. We do so by using a neural oscillator model consistent with neurophysiological data. The model used was shown elsewhere to reproduce well the predictions of behavioral stimulus-response theory. The quantum-like effects are brought about by the spreading activation of incompatible oscillators, leading to an interference-like effect mediated by inhibitory and excitatory synapses.In this paper we propose the use of neural interference as the origin of quantum-like effects in the brain. We do so by using a neural oscillator model consistent with neurophysiological data. The model used was shown to reproduce well the predictions of behavioral stimulus-response theory. The quantum-like effects are obtained by the spreading activation of incompatible oscillators, leading to an interference-like effect mediated by inhibitory and excitatory synapses.

Joint probabilities and quantum cognition

In this paper we discuss the existence of joint probability distributions for quantum-like response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.

The surface Laplacian technique in EEG: Theory and methods

This paper reviews the method of surface Laplacian differentiation to study EEG. We focus on topics that are helpful for a clear understanding of the underlying concepts and its efficient implementation, which is especially important for EEG researchers unfamiliar with the technique. The popular methods of finite difference and splines are reviewed in detail. The former has the advantage of simplicity and low computational cost, but its estimates are prone to a variety of errors due to discretization. The latter eliminates all issues related to discretization and incorporates a regularization mechanism to reduce spatial noise, but at the cost of increasing mathematical and computational complexity. These and several other issues deserving further development are highlighted, some of which we address to the extent possible. Here we develop a set of discrete approximations for Laplacian estimates at peripheral electrodes. We also provide the mathematical details of finite difference approximations that are missing in the literature, and discuss the problem of computational performance, which is particularly important in the context of EEG splines where data sets can be very large. Along this line, the matrix representation of the surface Laplacian operator is carefully discussed and some figures are given illustrating the advantages of this approach. In the final remarks, we briefly sketch a possible way to incorporate finite-size electrodes into Laplacian estimates that could guide further developments.

Negative probabilities and counter-factual reasoning in quantum cognition

In this paper we discuss quantum-like decision-making experiments using negative probabilities. We do so by showing how the two-slit experiment, in the simplified version of the Mach–Zehnder interferometer, can be described by this formalism. We show that negative probabilities impose constraints to what types of counter-factual reasoning we can make with respect to (quantum) internal representations of the decision maker.

Exploring non-signalling polytopes with negative probability

Bipartite and tripartite EPR–Bell type systems are examined via joint quasi-probability distributions where probabilities are permitted to be negative. It is shown that such distributions exist only when the no-signalling condition is satisfied. A characteristic measure, the probability mass, is introduced and, via its minimization, limits the number of quasi-distributions describing a given marginal probability distribution. The minimized probability mass is shown to be an alternative way to characterize non-local systems. Non-signalling polytopes for two to eight settings in the bipartite scenario are examined and compared to prior work. Examining perfect cloning of non-local systems within the tripartite scenario suggests defining two categories of signalling. It is seen that many properties of non-local systems can be efficiently described by quasi-probability theory.

A Random-Walk Approach to Interference

In this paper we sketch a probabilistic particle approach requiring no separate concept of wave to obtain interference. We describe in some detail how things work from a physical standpoint and show with a number of figures how the standard wave concepts are developed from purely particle random walks. For the wave concepts we have in each case a matching probability concept. The preliminary theory developed here is qualitative and stresses the physical character of the assumptions. In particular, we show that the periodic behavior of light is derived from the source and not from individual photons.

VIOLATION OF BELL'S INEQUALITIES WITH A LOCAL THEORY OF PHOTONS

We use a local theory of photons purely as particles to model the single-photon experiment proposed by Tan, Walls, and Collett. Like Tanet al. we are able to derive a violation of Bells inequalities, but our local probabilistic theory does not use any specific quantum mechanical assumptions or calculations.

A particle theory of the Casimir effect

In previous works, Suppes and de Barros used a pure particle model to derive interference effects, where individual photons have well-defined trajectories, and hence no wave properties. In the present paper we extend that description to account for the Casimir effect. We consider that the linear momentum ∑ 1/2hk of the vacuum state in quantum electrodynamics corresponds to the linear momentum of virtual photons. The Casimir effect, in the cases of two parallel plates and the solid ball, is explained in terms of the pressure caused by the photons. Contrary to quantum electrodynamics, we assume a finite number of virtual photons.

Diffraction with well-defined photon trajectories: A foundational analysis

We assume: (i) Photons are emitted by harmonically oscillating sources. (ii) They have definite trajectories. (iii) They have a probability of being scattered at a slit. (iv) Detectors, like sources, are periodic. (v) Photons have positive and negative states which locally interfere, i.e., annihilate each other, when being absorbed. In this framework we are able to derive standard diffraction and interference results. We thereby eliminate in this approach wave-particle duality for photons, and give nonparadoxical answers to standard questions about interference. For example, in the two-slit experiment each photon goes through only one slit.