Nonlocality Theorem Research Articles

Weak solvability of one model of a nonlinearly retarded fluid in a thermal field

For the initial-boundary value problem of the dynamics of a thermoviscoelastic medium of Oldroyd type in the planar case, a nonlocal theorem regarding the existence of a weak solution is established.

An Elementary Proof That Everett’s Quantum Multiverse Is Nonlocal: Bell-Locality and Branch-Symmetry in the Many-Worlds Interpretation

Everett’s many-worlds or multiverse theory is an attempt to find an alternative to the standard Copenhagen interpretation of quantum mechanics. Everett’s theory is often claimed to be local in the Bell sense. Here, we show that this is not the case and debunk the contradictions by analyzing in detail the Greenberger–Horne–Zeilinger (GHZ) nonlocality theorem. We discuss and compare different notions of locality often mixed in the Everettian literature and try to explain the nature of the confusion. We conclude with a discussion of probability and statistics in the many-worlds theory and stress that the strong symmetry existing between branches in the theory prohibits the definition of probability and that the theory cannot recover statistics. The only way out from this contradiction is to modify the theory by adding hidden variables à la Bohm and, as a consequence, the new theory is explicitly Bell-nonlocal.

How and when did locality become ‘local realism’? A historical and critical analysis (1963–1978)

The history of the debates on the foundational implications of the Bell non-locality theorem displayed very soon a tendency to put the theorem in a perspective that was not entirely motivated by its very assumptions, in particular in terms of a ‘local-realistic’ narrative, according to which a major target of the theorem would be the very possibility to conceive quantum theory as a theory concerning ‘real’ stuff in the world out-there. I present here a historico-critical analysis of the stages, between 1963 and 1978, through which the locality condition of the original Bell theorem almost undiscernibly turned into a ‘local realism’ condition, a circumstance which too often has affected the analysis of how serious the consequences of the Bell theorem turn out to be. In particular, the analysis puts into focus the interpretive oscillations and inconsistencies surrounding ‘local realism’, that emerge in the very descriptions that many leading figures provided themselves of the deep work they devoted to the theorem and its consequences.

Plasmonically enhanced mid-IR light source based on tunable spectrally and directionally selective thermal emission from nanopatterned graphene

We present a proof of concept for a spectrally selective thermal mid-IR source based on nanopatterned graphene (NPG) with a typical mobility of CVD-grown graphene (up to 3000 hbox {cm}^2,hbox {V}^{-1},hbox {s}^{-1}), ensuring scalability to large areas. For that, we solve the electrostatic problem of a conducting hyperboloid with an elliptical wormhole in the presence of an in-plane electric field. The localized surface plasmons (LSPs) on the NPG sheet, partially hybridized with graphene phonons and surface phonons of the neighboring materials, allow for the control and tuning of the thermal emission spectrum in the wavelength regime from lambda =3 to 12 upmum by adjusting the size of and distance between the circular holes in a hexagonal or square lattice structure. Most importantly, the LSPs along with an optical cavity increase the emittance of graphene from about 2.3% for pristine graphene to 80% for NPG, thereby outperforming state-of-the-art pristine graphene light sources operating in the near-infrared by at least a factor of 100. According to our COMSOL calculations, a maximum emission power per area of 11times 10^3 W/hbox {m}^2 at T=2000 K for a bias voltage of V=23 V is achieved by controlling the temperature of the hot electrons through the Joule heating. By generalizing Planck’s theory to any grey body and deriving the completely general nonlocal fluctuation-dissipation theorem with nonlocal response of surface plasmons in the random phase approximation, we show that the coherence length of the graphene plasmons and the thermally emitted photons can be as large as 13 upmum and 150 upmum, respectively, providing the opportunity to create phased arrays made of nanoantennas represented by the holes in NPG. The spatial phase variation of the coherence allows for beamsteering of the thermal emission in the range between 12^circ and 80^circ by tuning the Fermi energy between E_F=1.0 eV and E_F=0.25 eV through the gate voltage. Our analysis of the nonlocal hydrodynamic response leads to the conjecture that the diffusion length and viscosity in graphene are frequency-dependent. Using finite-difference time domain calculations, coupled mode theory, and RPA, we develop the model of a mid-IR light source based on NPG, which will pave the way to graphene-based optical mid-IR communication, mid-IR color displays, mid-IR spectroscopy, and virus detection.

Bell’s Non-Locality Theorem Can Be Understood in Terms of Classical Thermodynamics

Bell’s non-locality theorem can be understood in terms of classical thermodynamics, which is already considered to be a complete field. However, inconsistencies in classical thermodynamics have been discovered in the area of solid-oxide fuel cells (SOFCs). The use of samarium-doped ceria electrolytes in SOFCs lowers the open-circuit voltage (OCV) to less than the Nernst voltage. This low OCV has been explained by Wagner’s equation, which is based on chemical equilibrium theory. However, Wagner’s equation is insufficient to explain the low OCV, which should be explained by fluctuation and dissipation theorems. Considering the separation of the Boltzmann distribution and Maxwell’s demon, only carrier species with sufficient energy to overcome the activation energy can contribute to current conduction, as determined by incorporating different constants into the definitions of the chemical and electrical potentials. Then, an energy loss equal to the activation energy will occur because of the interactions between ions and electrons. This energy loss means that an additional thermodynamic law based on an advanced model of Maxwell’s demon is needed. In this report, the zero-point energy can be explained by this additional ther-modynamic law, as can Bell’s non-locality theorem.

On a problem in the dynamics of a thermoviscoelastic medium with memory

A nonlocal existence theorem for the weak solution for an initial-boundary value problem for the dynamic model of thermoviscoelasticity with memory along trajectories of motion in the planar case is established.

Local deterministic simulation of equatorial Von Neumann measurements on tripartite GHZ state

Experimental free-will or measurement independence is one of the crucial assumptions in derivation of any nonlocal theorem. Any nonlocal correlation obtained in quantum world can have a local deterministic explanation if there is no experimental free-will in choosing the measurement settings. Recently, in [Phys. Rev. Lett. {\bf105}, 250404 (2010)] it has been shown that to obtain a local deterministic description for singlet state correlation one does not need to give up measurement independence completely, but a partial measurement dependence suffices. In three party scenario considering GHZ correlation one can exhibit absolute contradiction between quantum theory and local realism. In this paper we show that such correlation also has local deterministic description if measurement independence is given up, even if not completely. We provide a local deterministic model for equatorial Von Neumann measurements on tripartite GHZ state by sacrificing measurement independence partially.

On one problem of dynamics of thermoviscoelastic medium of Oldroyd type

We establish nonlocal existence theorem for the weak solution for an initial-boundary value problem for the dynamic model of thermoviscoelasticity of Oldroyd type in the planar case.

Non Locality Proofs in Quantum Mechanics Analyzed by Ordinary Mathematical Logic

The so-called non-locality theorems aim to show that Quantum Mechanics is not consistent with the Locality Principle. Their proofs require, besides the standard postulates of Quantum Theory, further conditions, as for instance the Criterion of Reality, which cannot be formulated in the language of Standard Quantum Theory; this difficulty makes the proofs not verifiable according to usual logico-mathematical methods, and therefore it is a source of the controversial debate about the real implications of these theorems. The present work addresses this difficulty for Bell-type and Stapp’s arguments of non-locality. We supplement the formalism of Quantum Mechanics with formal statements inferred from the further conditions in the two different cases. Then an analysis of the two arguments is performed according to ordinary mathematical logic.

On strong solutions for a Navier-Stokes-Fourier-Oldroid system

The nonlocal existence and uniqueness theorem for the strong solutions for an initial--boundary value problem for the dynamic model of thermoviscoelasticity of Navier-Stokes-Fourier-Oldroid type in the planar case is established.

Analysis of non locality proofs in Quantum Mechanics

Two kinds of non-locality theorems in Quantum Mechanics are taken into account: the theorems based on the criterion of reality and the quite different theorem proposed by Stapp. In the present work the analyses of the theorem due to Greenberger, Horne, Shimony and Zeilinger, based on the criterion of reality, and of Stapp's argument are shown. The results of these analyses show that the alleged violations of locality cannot be considered definitive.

Quantum Mechanics, Can It Be Consistent with Locality?

We single out an alternative, strict interpretation of the Einstein-Podolsky-Rosen criterion of reality, and identify the implied extensions of quantum correlations. Then we prove that the theorem of Bell, and the non-locality theorems without inequalities, fail if the new extensions are adopted. Therefore, these theorems can be interpreted as arguments against the wide interpretation of the criterion of reality rather than as a violation of locality.

Hardy's non-locality and generalized non-local theory

Hardy's non-locality theorem for multiple two-level systems is explored in the context of generalized non-local theory. We find non-local but non-signaling probabilities satisfying Hardy's argument for two two-level and three two-level systems. Maximum probability of success of Hardy's argument is obtained for three two-level systems in quantum theory as well as in a more generalized theory. Interestingly, the maximum in the generalized non-local theory for both the two two-level systems and three two-level systems turns out to be the same.

Strong solutions of certain thermoviscoelastic system

For a certain model of a dynamic thermoviscoelastic continuous medium we obtain a nonlocal theorem on the unique existence of a strong solution.

Bound on Hardy’s nonlocality from the principle of information causality

Recently,the principle of nonviolation of information causality [Nature 461,1101 (2009)], has been proposed as one of the foundational properties of nature. We explore the Hardy's nonlocality theorem for two qubit systems, in the context of generalised probability theory, restricted by the principle of nonviolation of information causality. Applying, a sufficient condition for information causality violation, we derive an upper bound on the maximum success probability of Hardy's nonlocality argument. We find that the bound achieved here is higher than that allowed by quantum mechanics,but still much less than what the nosignaling condition permits. We also study the Cabello type nonlocality argument (a generalization of Hardy's argument) in this context.

QUANTUM KALEIDOSCOPES AND BELL'S THEOREM

A quantum kaleidoscope is defined as a set of observables, or states, consisting of many different subsets that provide closely related proofs of the Bell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes prove the BKS theorem through a simple parity argument, which also doubles as a proof of Bell's nonlocality theorem if use is made of the right sort of entanglement. Three closely related kaleidoscopes are introduced and discussed in this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a 60-state kaleidoscope. The close relationship of these kaleidoscopes to a configuration of 12 points and 16 lines known as Reye's configuration is pointed out. The "rotations" needed to make each kaleidoscope yield all its apparitions are laid out. The 60-state kaleidoscope, whose underlying geometrical structure is that of ten interlinked Reyes' configurations (together with their duals), possesses a total of 1120 apparitions that provide proofs of the two Bell theorems. Some applications of these kaleidoscopes to problems in quantum tomography and quantum state estimation are discussed.

Identification of All Hardy-Type Correlations for Two Photons or Particles with Spin 1/2

By using an alternative, equivalent form of the CHSH inequality and making extensive use of the experimentally testable property of physical locality we determine the 64 different Bell-type inequalities (each one involving four joint probabilities) into which Hardy's nonlocality theorem can be cast. This allows one to identify all the two-qubit correlations which can exhibit Hardy-type nonlocality.

Erratum to: Quantum Perfect Correlations and Hardy’s Nonlocality Theorem

Erratum to: Quantum Perfect Correlations and Hardy’s Nonlocality Theorem

Quantum mechanical probabilities and general probabilistic constraints for Einstein-Podolsky-Rosen-Bohm experiments

Relativistic causality, namely, the impossibility of signaling at superluminal speeds, restricts the kinds of correlations which can occur between different parts of a composite physical system. Here we establish the basic restrictions which relativistic causality imposes on the joint probabilities involved in an experiment of the Einstein–Podolsky–Rosen–Bohm type. Quantum mechanics, on the other hand, places further restrictions beyond those required by general considerations like causality and consistency. We illustrate this fact by considering the sum of correlations involved in the CHSH inequality. Within the general framework of the CHSH inequality, we also consider the nonlocality theorem derived by Hardy, and discuss the constraints that relativistic causality, on the one hand, and quantum mechanics, on the other hand, impose on it. Finally, we derive a simple inequality which can be used to test quantum mechanics against general probabilistic theories.

Impossible colorings and Bell's theorem

An argument due to Zimba and Penrose is generalized to show how all known non-coloring proofs of the Bell–Kochen–Specker (BKS) theorem can be converted into inequality-free proofs of Bell's nonlocality theorem. A compilation of many such inequality-free proofs is given.