arXiv subjects

Ramon Lapiedra

Publications and source records attributed to Ramon Lapiedra.

At least 19 recordsLinked to original sources

arXiv2025

Violation of Bell inequalities from Cosmic Microwave Background data

In a recent paper [R. Dale. R. Lapiedra, and J. A. Morales-Lladosa, Phys. Rev. D {\bf 107}, 023506 (2023)] a cosmic-like Clauser-Horne-Shimony-Holt (CHSH) inequality was proved for the temperature fluctuations $δT$ of the perturbed Cosmic Microwave Background (CMB), assuming local realism. This inequality can be tested from observational data. In fact, no violation for it has been found from the CMB data provided by the COBE satellite in different sky directions. This is a result which, being negative, is not conclusive in relation to the possible violation of the CHSH inequality in a cosmological context. So, the preceding analysis needs to be extended by using more precise current CMB data, like those provided by WMAP and Planck satellites. This is a task of considerable importance but, technically, much more involved in data treatments. In this work, assuming again local realism behind measurements and observational data, this extension is accomplished. The result is that a sound violation of the CHSH inequality is found, which would mean the failure of the assumed local realism in accordance with the quantum origin of the primordial temperature fluctuations in the framework of standard inflation and the orthodox interpretation of the Quantum Mechanics.

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arXiv2024

Cosmic primordial density fluctuations and Bell inequalities

The temperature measurements, $T$, of the perturbed cosmic microwave background, performed by the cosmic background explorer satellite (COBE), are considered. A dichotomist function, $f = \pm 1$, is defined such that $f =+1$ if $δT > 0$ and $f =-1$ if $δT < 0$, where $δT$ stands for the fluctuation of $T$. Then, it is assumed that behind the appearance of these fluctuations there is local realism. Under this assumption, some specific Clauser-Horne-Shimony-Holt (CHSH) inequalities are proved for these fluctuation temperatures measured by COBE in the different sky directions. The calculation of these inequalities from the actual temperature measurements shows that these inequalities are not violated. This result cannot be anticipated by calculating the commutators of the cosmic density quantum operators. This must be remarked here since, in the case of a system of two entangled spin ${\textstyle{1 \over 2}}$ particles, its CHSH inequalities violation can be inferred from the nonvanishing value of the corresponding spin measurement commutators. The above nonviolation of the observed cosmic CHSH inequalities is compatible with the existence of local realism behind the cosmic measurement results. Nevertheless, assuming again local realism, some new cosmic CHSH inequalities can be derived for the case of the WMAP measurements whose accuracy is better than the one of the above considered COBE measurements. More specifically, in the WMAP case, some significant cross correlations between the temperature and polarization maps are detected, and the new cosmic CHSH inequalities are the ones built with these cross correlations. Now, the occasional violation of these CHSH inequalities would mean the failure of the assumed local realism in accordance with the quantum origin of the primordial temperature and polarization fluctuations in the framework of standard inflation.

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arXiv2019

Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumping effects

We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the metric across this boundary could perhaps present a finite step too. However, we can assume that the metric is ${\cal C}^1$ class everywhere. In such a case, although the partial second derivatives of the metric exhibit finite (no Dirac $δ$ functions) discontinuities, the Dirac $δ$ functions will still appear in the conservation equation of the energy-momentum tensor. As a consequence, strictly speaking, the corresponding metric solutions of the Einstein field equations can only exist in the sense of distributions. Then, we assume that the metric considered is ${\cal C}^1$ class everywhere and is a solution of the Einstein field equations in this sense. We explore the consequences of these two assumptions, and in doing so we derive the general conditions that constrain the jumps in the second partial derivatives across the boundary. The example of the Oppenheimer-Snyder metric is considered and some new results are obtained on it. Then, the formalism developed in this exploration is applied to a different situation, i.e., to a given generalization of the Einstein field equations for the case where the partial second derivatives of the metric exist but are not symmetric.

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arXiv2018

Spherical symmetric parabolic dust collapse: ${\cal C}^{1}$ matching metric with zero intrinsic energy

The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions. Instead, starting from the corresponding general exact solution of these equations, depending on two arbitrary functions of the radial coordinate, the fulfillment of the Lichnerowicz matching conditions of the interior collapsing metric and the exterior Schwarzschild one is tentatively assumed (the continuity of the metric and its first derivatives on the time-like hypersurface describing the evolution of the spherical 2-surface boundary of the collapsing cloud), and the consequences of such a tentative assumption are explored. The whole analytical family of resulting models is obtained and some of them are picked out as physical better models on the basis of the finite and constant value of its {\em intrinsic} energy.

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arXiv2017

Cosmic censorship conjecture in some matching spherical collapsing metrics

A physically plausible Lema{\^ı}tre-Tolman-Bondi collapse in the marginally bound case is considered. By "physically plausible" we mean that the corresponding metric is ${\cal C}^1$ matched at the collapsing star surface and further that its {\em intrinsic} energy is, as due, stationary and finite. It is proved for this Lema{\^ı}tre-Tolman-Bondi collapse, for some parameter values, that its intrinsic central singularity is globally naked, thus violating the cosmic censorship conjecture with, for each direction, one photon, or perhaps a pencil of photons, leaving the singularity and reaching the null infinity. Our result is discussed in relation to some other cases in the current literature on the subject in which some of the central singularities are globally naked too.

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arXiv2015

Geodesic family of spherical instantons and cosmic quantum creation

The Einstein field equations for any spherically symmetric metric and a geodesic perfect fluid source are cast in a canonical simple form, both for Lorentzian metrics and for instantons. Both kinds of metrics are explicitly written for the Lema{\^ı}tre-Tolman-Bondi family and for a general $Λ$-Friedmann-Lema{\^ı}tre-Robertson-Walker universe. In the latter case (including of course the instanton version) we study whether the probability of quantum creation of our Universe vanishes or not. It is found, in accordance with previous results, that only the closed model can have a nonzero probability for quantum creation. To obtain this result, we resort to general assumptions, which are satisfied in the particular creation case considered by Vilenkin. On the other hand, Fomin and Tryon suggested that the energy of a quantically creatable universe should vanish. This is in accordance with the above result in which only the closed $Λ$FLRW model is quantically creatable while the open and flat models are not. That is so since it can be seen that this closed model has vanishing energy while the open model and the limiting flat case (suitably perturbed) have both infinite energy.

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arXiv2015

Obtaining a contradiction between local realism and quantum mechanics using only one correlation function

An ensemble consisting on systems of two entangled spin 1/2 particles, all of them in the same global quantum state, are considered. The two spins are measured, each of them, on a fixed direction, at two randomly selected measurement times. Realism, plus locality and freedom of choice referred to these chosen times, are assumed. Then, from the sole correlation function related to the two measurements, without considering any Bell inequalities, a contradiction between these assumptions and quantum mechanics is found.

quant-ph↗

arXiv2014

Stability of the intrinsic energy vanishing in the Schwarzschild metric under a slow rotation

The linearized Kerr metric is considered and put in some Gauss coordinates which are further {\em intrinsic} ones. The linear and angular 4-momenta of this metric are calculated in these coordinates and the resulting value is just zero. Thus, the global vanishing previously found for the Schwarzschild metric remains linearly stable under slow rotational perturbations of this metric.

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arXiv2014

Intrinsic energy of Lemaître-Tolman-Bondi models and cosmological implications

Recently, some Lema{\^ı}tre-Tolman-Bondi metrics have been considered as models alternative to the dark energy within the Friedmann-Lema{\^ı}tre-Robertson-Walker universes. The vanishing of the intrinsic energy of these metrics is examined since such a vanishing, in the present case and in general, could be interpreted as a necessary condition to consider the possibility of the quantum creation of a metric. More specifically, this vanishing is examined in the particular case where the Lema{\^ı}tre-Tolman-Bondi metrics behave asymptotically like a Friedmann-Lema{\^ı}tre-Robertson-Walker universe. Finally, we deal with a particular model ruled out after being confronted with cosmic observations. In a minimal agreement with this negative result, leaving aside an unstable case, the value of the intrinsic energy of this particular model does not vanish and becomes in fact minus infinite.

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arXiv2013

Macrodeterminism without non-invasive measurability

We propose a definition of determinism for a physical system that includes, besides the measured system, the measurement device and the surrounding environment. This enlarged system is assumed to follow a predefined trajectory starting from some (unknown) initial conditions that play the role of hidden variables for the experiment. These assumptions, which are different from realism, allow us to derive some Leggett-Garg inequalities, which are violated by Quantum Mechanics in the particular case of consecutive measurements on individual photon polarizations.

quant-ph↗

arXiv2013

On the uniqueness of the space-time energy in General Relativity. The illuminating case of the Schwarzschild metric

The case of asymptotic Minkowskian space-times is considered. A special class of asymptotic rectilinear coordinates at the spatial infinity, related to a specific system of free falling observers, is chosen. This choice is applied in particular to the Schwarzschild metric, obtaining a vanishing energy for this space-time. This result is compared with the result of some known theorems on the uniqueness of the energy of any asymptotic Minkowskian space, showing that there is no contradiction between both results, the differences becoming from the use of coordinates with different operational meanings. The suitability of Gauss coordinates when defining an {\em intrinsic} energy is considered and it is finally concluded that a Schwarzschild metric is a particular case of space-times with vanishing {\em intrinsic} 4-momenta.

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arXiv2013

Determinism and Quantum Mechanics with time Bell inequalities

We propose a definition of determinism for a physical system that includes, besides the measurement device, the surrounding environment. This enlarged system is assumed to follow a predefined trajectory starting from some (unknown) initial conditions that play the role of hidden variables for the experiment. These assumptions, which are different from realism, allow us to derive a type of time Bell inequalities, which are violated by Quantum Mechanics. In order to illustrate this violation, we discuss the particular case of measurements on a spin 1/2 particle.

quant-ph↗

arXiv2011

Intrinsic vanishing of energy and momenta in a universe

We present a new approach to the question of properly defining energy and momenta for non asymptotically Minkowskian spaces in general relativity, in the case where these energy and momenta are conserved. In order to do this, we first prove that there always exist some special Gauss coordinates for which the conserved linear and angular three-momenta vanish. This allows us to consider the case of creatable universes (the universes whose proper 4-momenta vanish) in a consistent way, which is the main interest of the paper. When applied to the Friedmann-Lema{\^ı}tre-Robertson-Walker case, perturbed or not, our formalism leads to previous results, according to most literature on the subject. Some future work that should be done is mentioned.

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arXiv2010

The experimental failure of macroscopic determinism: the case of an electrocardiogram

Even if never elucidated, the question of determinism is a standing question along the history of human thinking. A physical system evolves in a deterministic way if its future is completely determined once we have fixed some present characteristics of it, i.e., its initial conditions. The problem addressed in the present paper is to test determinism in the macroscopic domain. By imposing a very plausible ``separability'' assumption, we prove that determinism enters in contradiction with the recorded outcomes of a given electrocardiogram. The interest of this result comes from the fact such a basic idea as determinism has never been experimentally tested up to now in the macroscopic domain, and as far as we know not even in the quantum domain.

quant-ph↗

arXiv2009

The fail of determinism and the limits of Bohm hidden variable theory

We give a counter example to show that determinism as such is in contradiction to quantum mechanics. More precisely, we consider a simple quantum system and its environment, including the measurement device, and make the assumption that the time evolution of the global system, the quantum system plus this environment, is deterministic, i. e., the time evolution is given by a dynamical trajectory from some initial conditions. From this, we prove a type of Bell inequalities which are violated by quantum mechanics, reaching the conclusion that our quantum system evolves in a non deterministic way. In order to seize the interest of this conclusion, one must realize that it cannot be reached from the present experimental violation of Bell inequalities predicted by quantum mechanics, since this violation is compatible with non-local realism.

quant-ph↗

arXiv2008

Leggett inequalities and the completeness of quantum mechanics

We consider the so called Legget inequalities which are deduced from the assumption of general (local or non-local) realism plus the arrow of time preservation. Then, instead of assuming cryto-nonlocal hidden variables, we assume any (local or non-local) realism compatible with the joint and non-joint expected values dictated by quantum mwechaanics. Hence, we prove that this double assumption is not consistent, since the corresponding general Leggett inequalities are violated by quantum mechanics. Thus, realism plus arrow of time preservation and quntum mechanics are not compatible. In other words, quantum mechanics cannot be completed with any (local or non-local) hidden variables, provide we assume the common sense of the arrow of time. The result would deserve to be experimentally tested and we discuss why it is not invalidated by hidden variable theories as the one from Bohm.

quant-ph↗

arXiv2008

Probing the creatable character of perturbed Friedmann-Robertson-Walker universes

We discuss whether some perturbed Friedmann-Robertson-Walker (FRW) universes could be creatable, i. e., could have vanishing energy, linear momentum and angular momentum, as it could be expectable if the Universe arose as a quantum fluctuation. On account of previous results, the background is assumed to be either closed (with very small curvature) or flat. In the first case, fully arbitrary linear perturbations are considered; whereas in the flat case, it is assumed the existence of: (i) inflationary scalar perturbations, that is to say, Gaussian adiabatic scalar perturbations having an spectrum close to the Harrison-Zel'dovich one, and (ii) arbitrary tensor perturbations. We conclude that, any closed perturbed universe is creatable, and also that, irrespective of the spectrum and properties of the inflationary gravitational waves, perturbed flat FRW universes with standard inflation are not creatable. Some considerations on pre-inflationary scalar perturbations are also presented. The creatable character of perturbed FRW universes is studied, for the first time, in this paper.

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arXiv2007

Creatable Universes

We consider the question of properly defining energy and momenta for non asymptotic Minkowskian spaces in general relativity. Only spaces of this type, whose energy, linear 3-momentum, and intrinsic angular momentum vanish, would be candidates for creatable universes, that is, for universes which could have arisen from a vacuum quantum fluctuation. Given a universe, we completely characterize the family of coordinate systems for which one could sensibly say that this universe is a creatable universe.

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