Searcharxiv⌕ Search

arXiv subjects

Emilio Santos

Publications and source records attributed to Emilio Santos.

At least 19 recordsLinked to original sources
arXiv2026

Quantum field theory in the Weyl-Wigner representation

The Wigner representation for quantum mechanics of particles is generalized to Bose fields. The standard Hilbert space quantization becomes, via the Weyl transform, a quantization method that consists of adding a Gaussian zeropoint field distribution to the vacuum. I comment on the possible advantages of the method in order to study quantum fields in curved spaces. I study a unified formulation of non-relativistic quantum electrodynamics in the Weyl-Wigner formalism, in terms of (classical-like) c-numbers.

physics.gen-ph↗
arXiv2026

Are Bell's conditions for local realism general enough?

Bell conditions for local realism are critically revisited. In particular for optical experiments I criticize Bell's proposed response of detectors to signals as extremely idealized. More physical conditions are proposed, whence a realistic local model of an optical experiment is possible which violates the Clauser-Horne (Bell) inequality. The possibility rests on the existence of a coincidence-time loophole in the experiments.

quant-ph↗
arXiv2025

The quantum theory of the electromagnetic field in the Weyl-Wigner representation as a local realistic model

I revisit the Wigner (or Weyl-Wigner, WW) representation of the quantum electromagnetic field. I show that, assuming that Fock states are just mathematical concepts devoid of physical reality, WW suggests a realistic interpretation which turns out to be (classical) Maxwell theory with the assumption that there is a random radiation filling space, the vacuum field. I elucidate why, in sharp constrast, non-relativistic quantum mechanics of particles does not admit a realistic interpretation via WW. I interpret experiments involving entangled light beams within WW, in particular optical tests of Bell inequalities. I show that WW provides clues in order to construct local model for those experiments. I give arguments why Bell defintion of local realism is not general enough.

physics.gen-ph↗
arXiv2025

Stochastic interpretation of quantum mechanics assuming that vacuum fields are real

I review the realistic interpretation of several typically quantum phenomena using a heuristic approach that rests on the assumption that the electromagnetic quantum vacuum is a stochastic field. I include the particle behaviour of light, the photoelectric effect, the hdrogen atom, the Casimir effect, and entanglement in the optical tests of Bell inequalities. The stochastic approach might be formally connected with the standard Hilbert space formalism via the Wigner representation of the field.

physics.gen-ph↗
arXiv2024

The quantum electromagnetic field in the Weyl-Wigner representation

The quantum electromagnetic (EM) field is formulated in the Weyl-Wigner representation (WW), which is equivalent to the standard Hilbert space one (HS). In principle it is possible to interpret within WW all experiments involving the EM field interacting with macroscopic bodies, the latter treated classically. In the WW formalism the essential difference between classical electrodynamics and the quantum theory of the EM field is\ just the assumption that there is a random EM field filling space\QTR{it}{, }i.e. the existence of a zero-point field with a Gaussian distribution for the field amplitudes. I analyze a typical optical test of a Bell inequality. The model admits an interpretation compatible with local realism, modulo a number of assumptions assumed plausible.

physics.gen-ph↗
arXiv2024

Effects of the quantum vacuum at a cosmic scale and of dark energy

The Einstein equation in a semi-classical approximation is applied to a spherical region of the universe, with the stress-energy tensor consisting of the mass density and pressure of the LambdaCDM cosmological model plus an additional contribution of the quantum vacuum. Expanding the equation in powers of Newton constant G, the vacuum contributes to second order. The result is that at least a part of the acceleration in the expansion of the universe may be due to the quantum vacuum fluctuations

gr-qc↗
arXiv2022

On the analogy between stochastic electrodynamics and nonrelativistic quantum electrodynamics

I expose nonrelativistic quantum electrodynamics in the Weyl-Wigner representation. Hence I prove that an approximation to first order in Planck constant has formal analogy with stochastic electrodynamics (SED), that is classical electrodynamics of charged particles immersed in a random radiation filling space. The analogy elucidates why SED agrees with quantum theory for particle Hamiltonians quadratic in coordinates and momenta, but fails otherwise.

quant-ph↗
arXiv2020

Local model of entangled photon experiments compatible with quantum predictions based on the reality of the vacuum fields

Arguments are provided for the reality of the quantum vacuum fields. A polarization correlation experiment with two maximally entangled photons created by spontaneous parametric down-conversion is studied in the Weyl-Wigner formalism, that reproduces the quantum predictions. An interpretation is proposed in terms of stochastic processes assuming that the quantum vacuum fields are real. This proves that local realism is compatible with a violation of Bell inequalities, thus rebutting the claim that it has been refuted by experiments. Entanglement appears as a correlation between fluctuations of a signal field and vacuum fields. Key words; local realism, Bell inequalities, entangled photons, Weyl-Wigner, loopholes,vacuum fields

quant-ph↗
arXiv2020

Stochastic electrodynamics and the interpretation of quantum theory

I propose that quantum mechanics is a stochastic theory and quantum phenomena derive from the existence of real vacuum stochastic fields filling space. I revisit stochastic electrodynamics (SED), a theory that studies classical systems of electrically charged particles immersed in an electromagnetic (zeropoint) radiation field with spectral density proportional to the cube of the frequency, Planck's constant appearing as the parameter fixing the scale. Asides from briefly reviewing known results, I make a detailed comparison between SED and quantum mechanics. Both theories make the same predictions when the stochastic equations of motion are of first order in Planck constant, but not in general. I propose that SED provides a clue for a realistic interpretation of quantum theory.

quant-ph↗
arXiv2020

Local realistic interpretation of entangled photon pairs in the Weyl-Wigner formalism

A polarization correlation experiment with two maximally entangled photons created by spontaneous parametric down-conversion is studied in the Weyl-Wigner formalism, that reproduces the quantum predictions. An interpretation is proposed in terms of stochastic processes assuming that the quantum vacuum fields are real. This proves that local realism is compatible with the violation of Bell inequalities, thus rebutting the claim that local realism has been refuted by entangled photon experiments. Entanglement appears as a correlation between fluctuations of a signal field and vacuum fields.

quant-ph↗
arXiv2018

The cosmological constant problem or how the quantum vacuum drives the slow accelerating expansion of the Universe

I argue that a solution to the cosmological constant problem is to assume that the expectation value of the quantum vacuum stress-energy tensor is proportional to the metric tensor with a negative energy density and positive pressure. This assumption is confirmed by an explicit calculation of the vacuum expectation for the free electromagnetic and Dirac fields of quantum electrodynamics. As a consequence the metric of the universe might correspond to a FLRW with accelerating expansion only after averaging over large scales, but at small scales it gives rise to an extremely rapid fluctuation between expansion and contraction in every small region, with different phases in different points. The vacuum stress-energy tensor has fluctuations that lead to short periods of expansion. A calculation with plausible approximations leads to an estimate of the accelerating expansion that fits in the observed value.

physics.gen-ph↗
arXiv2018

Dark matter as an effect of the quantum vacuum

The interaction between the quantum vacuum and a weak gravitational field is calculated for the vacuum fields of quantum electrodynamics. The result shows that the vacuum state is modified by the gravitational field, giving rise to a nonzero interaction energy. This suggests a model that fits in the main properties of the hypothetical dark matter in galactic haloes.

physics.gen-ph↗
arXiv2016

The arrow of time and the Bell inequalities

It is recalled that closed (isolated) systems are essentially reversible whilst open systems like the Earth, or living beings on it, are irreversible because they are not isolated. Earth and life irreversibility derives from the evolution of the universe, which is a consequence of its special initial conditions. It is stressed that, although relativity theory forbids that information travels faster than light, it does not forbid influences of an event on its past light cone. Therefore the violation of Bell inequalities in loophole-free experiments is compatible with relativity theory. A correlation formula, alternative to Bell's, is proposed as the starting point for hidden variables models fitting in relativity.

quant-ph↗
arXiv2016

A hidden variables model for non-relativistic quantum mechanics in terms of probabilities of particle paths

It is proved that in non-relativistic quantum mechanics (without spin) the transition probability may be described in terms of particle paths, every path having a (positive) probability. This leads to a stochastic hidden variables theory providing an intuitive picture of particle motion. The change of velocity at every time has a probability that depends on the potential over a large region, at a difference with the local action of classical dynamics. Thus the hidden variables theory is non-local like Bohm's, but not deterministic.

quant-ph↗
arXiv2016

Mathematical and physical meaning of the Bell inequalities

It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values $\left\{ 0,1\right\} $. A hidden variables model may be defined as a mapping between a set of quantum projection operators and a set of random variables. The model is noncontextual if there is a joint probability distribution. The Bell inequalities are necessary conditions for its existence. The inequalities are most relevant when measurements are performed at space-like separation, thus showing a conflict between quantum mechanics and local realism (Bell's theorem). The relations of the Bell inequalities with contextuality, Kochen-Specker theorem, and quantum entanglement are briefly discussed.

quant-ph↗
arXiv2015

Gravity effects of the quantum vacuum. Dark energy and dark matter

The stress-energy tensor of the quantum vacuum is studied for the particular case of quantum electrodynamics (QED), that is a fictituous universe where only the electromagnetic and the electron-positron fields exist. The integrals involved are ultraviolet divergent but it is suggested that a natural cut-off may exist. It is shown that, in spite of the fact that the stress-energy tensor of the electromagnetic field alone is traceless (i.e the pressure P equals 1/3 the energy density u), the total QED tensor is proportional to the metric tensor to a good approximation (i. e. P = -u). It is proposed that there is a cosmological constant in Einstein equation that exactly balances the stress-energy of the vacuum. It is shown that vacuum fluctuations give rise to a modified spacetime metric able to explain dark energy. Particular excitations of the vacuum are studied that might explain dark matter.

gr-qc↗