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Karl Hess

Publications and source records attributed to Karl Hess.

At least 19 recordsLinked to original sources
arXiv2020

On the roles of Vorob'ev cyclicities and Berry's phase in the EPR paradox and Bell-tests

The well known inequalities of John S. Bell may be regarded, from a purely mathematical viewpoint, as a direct consequence of Vorob'ev-type topological-combinatorial cyclicities formed with functions on a common probability space. However, the interpretation of these cyclicities becomes more subtle when considerations related to gauge symmetries and geometric-combinatorial phases are taken into account. These physics related considerations permit violations of all Bell-type inequalities within the realm of Einstein's causal physical-mathematics.

physics.gen-ph↗
arXiv2018

Bell's theorem and Instantaneous influences at a distance

An explicit model-example is presented to simulate Einstein-Podolsky-Rosen (EPR) experiments without invoking instantaneous influences at a distance. The model-example, together with the interpretation of past experiments by Kwiat and coworkers, uncovers logical inconsistencies in the application of Bell's theorem to actual EPR experiments. The inconsistencies originate from topological-combinatorial assumptions that are both necessary and sufficient to derive all Bell-type inequalities including those of Wigner-d'Espagnat and Clauser-Horne-Shimony-Holt. The model-example circumvents these inconsistencies.

quant-ph↗
arXiv2017

Analysis of Wigner's Set Theoretical Proof for Bell-type inequalities

We present a detailed analysis of the set theoretical proof of Wigner for Bell type inequalities with the following result. Wigner introduced a crucial assumption that is not related to Einstein's local realism, but instead, without justification, to the existence of certain joint probability measures for possible and actual measurement outcomes of Einstein-Podolsky-Rosen (EPR) experiments. His conclusions about Einstein's local realism are, therefore, not applicable to EPR experiments and the contradiction of the experimental outcomes to Wigner's results has no bearing on the validity of Einstein's local realism.

quant-ph↗
arXiv2016

From Boole to Leggett-Garg: Epistemology of Bell-type Inequalities

In 1862, George Boole derived an inequality for variables, now known as Boolean variables, that in his opinion represents a demarcation line between possible and impossible experience. This inequality forms an important milestone in the epistemology of probability theory and probability measures. In 1985 Leggett and Garg derived a physics related inequality, mathematically identical to Boole's, that according to them represents a demarcation between macroscopic realism and quantum mechanics. Their formalism, constructed for the magnetic flux of SQUIDS, includes general features and applies also to many other quantum experiments. We show that a wide gulf, a wide divide, separates the "sense impressions" and corresponding data, as well as the postulates of macroscopic realism, from the mathematical abstractions that are used to derive the inequality of Leggett-Garg. If the gulf can be bridged, one may indeed derive the said inequality, which is then clearly a demarcation between possible and impossible experience: it cannot be violated and is not violated by quantum theory. We deduce from this fact that a violation of the Leggett-Garg inequality does not mean that the SQUID-flux is not there when nobody looks, as Leggett-Garg suggest, but instead that the probability measures may not be what Leggett-Garg have assumed them to be, when no data can be secured that directly relate to them. We show that similar considerations apply to other well known quantum interpretation-puzzles including that of the two-slit experiment.

quant-ph↗
arXiv2016

Irrelevance of Bell's Theorem for experiments involving correlations in space and time: a specific loophole-free computer-example

John Bell is generally credited to have accomplished the remarkable "proof" that any theory of physics, which is both Einstein-local and "realistic" (counterfactually definite), results in a strong upper bound to the correlations that are measured in space and time. He thus predicts that Einstein-Podolsky-Rosen experiments cannot violate Bell- type inequalities. We present a counterexample to this claim, based on discrete-event computer simulations. Our model-results fully agree with the predictions of quantum theory for Einstein-Podolsky-Rosen-Bohm experiments and are free of the detection- or a coincidence-loophole.

physics.gen-ph↗
arXiv2016

Counterfactual Definiteness and Bell's Inequality

Counterfactual definiteness must be used as at least one of the postulates or axioms that are necessary to derive Bell-type inequalities. It is considered by many to be a postulate that is not only commensurate with classical physics (as for example Einstein's special relativity), but also separates and distinguishes classical physics from quantum mechanics. It is the purpose of this paper to show that Bell's choice of mathematical functions and independent variables implicitly includes counterfactual definiteness and reduces the generality of the physics of Bell-type theories so significantly that no meaningful comparison of these theories with actual Einstein-Podolsky-Rosen experiments can be made.

quant-ph↗
arXiv2011

Hidden assumptions in the derivation of the Theorem of Bell

John Bell's inequalities have already been considered by Boole in 1862. Boole established a one-to-one correspondence between experimental outcomes and mathematical abstractions of his probability theory. His abstractions are two-valued functions that permit the logical operations AND, OR and NOT and are the elements of an algebra. Violation of the inequalities indicated to Boole an inconsistency of definition of the abstractions and/or the necessity to revise the algebra. It is demonstrated in this paper, that a violation of Bell's inequality by Einstein-Podolsky-Rosen type of experiments can be explained by Boole's ideas. Violations of Bell's inequality also call for a revision of the mathematical abstractions and corresponding algebra. It will be shown that this particular view of Bell's inequalities points toward an incompleteness of quantum mechanics, rather than to any superluminal propagation or influences at a distance.

quant-ph↗
arXiv2011

Multi-order interference is generally nonzero

It is demonstrated that the third-order interference, as obtained from explicit solutions of Maxwell's equations for realistic models of three-slit devices, including an idealized version of the three-slit device used in a recent three-slit experiment with light (U. Sinha et al., Science 329, 418 (2010)), is generally nonzero. The hypothesis that the third-order interference should be zero is shown to be fatally flawed because it requires dropping the one-to-one correspondence between the symbols in the mathematical theory and the different experimental configurations.

physics.optics↗
arXiv2010

Reply to the Comment by A.J. Leggett and Anupam Garg

In their comment[1] on our Letter [arXiv:0907.0767], Leggett and Garg claim that they have introduced in their original paper (LG1) a dependence on measurement times. They also claim that Eqs.(HMDR1) and (LG2a) can therefore not be linked in such a way that the arguments of [arXiv:0907.0767] can be transcribed. However, (LG1) distinguishes only three time differences, and all experimental results corresponding to the same time differences are identically labeled and therefore treated as mathematically identical. We therefore cannot agree with the argumentation of Leggett and Garg: except for a change of nomenclature Eqs.(HMDR1) and (LG2a) are the same. A more extensive discussion of this point can be found in [arXiv:0901.2546].

quant-ph↗
arXiv2010

Extended Boole-Bell inequalities applicable to quantum theory

We address the basic meaning of apparent contradictions of quantum theory and probability frameworks as expressed by Bell's inequalities. We show that these contradictions have their origin in the incomplete considerations of the premisses of the derivation of the inequalities. A careful consideration of past work, including that of Boole and Vorob'ev, has lead us to the formulation of extended Boole-Bell inequalities that are binding for both classical and quantum models. The Einstein-Podolsky-Rosen-Bohm gedanken experiment and a macroscopic quantum coherence experiment proposed by Leggett and Garg are both shown to obey the extended Boole-Bell inequalities. These examples as well as additional discussions also provide reasons for apparent violations of these inequalities.

quant-ph↗
arXiv2008

Breakdown of Bell's Theorem for incompatible measurements

Bell's theorem contains the proposition that the Einstein-Podolsky-Rosen (EPR) theory (hypothesis) of the existence of elements of reality together with Einstein locality permits a mathematical description of EPR experiments by functions that are all defined on one common probability space. This proposition leads in turn to restrictions for possible experimental outcomes that Bell expressed in terms of his well known inequalities and that Vorob'ev and others had investigated before Bell. Summarizing several previous publications and adding new material, the above proposition is refuted by Einstein-local counterexamples from classical physics and shown to involve additional assumptions that can not be justified for mutually exclusive (incompatible) measurements and experiments. Moreover, criticism of our work by Mermin who invoked "standard sampling arguments" is shown to be false.

quant-ph↗
arXiv2006

Ab initio study of semiconducting carbon nanotubes adsorbed on the Si(100) surface: diameter- and registration-dependent atomic configurations and electronic properties

We present a first-principles study of semiconducting carbon nanotubes adsorbed on the unpassivated Si(100) surface. We have found metallicity for the combined system caused by n-doping of the silicon slab representing the surface by the SWNT. We confirm this metallicity for nanotubes of different diameters and chiral angles, and find the effect to be independent of the orientation of the nanotubes on the surface. We also present adsorption energetics and configurations which show semiconducting SWNTs farther apart from the surface and transferring less charge, in comparison with metallic SWNTs of similar diameter.

cond-mat.mtrl-sci↗
arXiv2005

Local Instruction-Set Model for the Experiment of Pan et al

We present a modified local realistic model, based on instruction sets that can be used to approximately reproduce the data of the Pan et al experiment. The data of our model are closer to the results of the actual experiment by Pan et al than the predictions of their quantum mechanical model. As a consequence the experimental results can not be used to support their claim that quantum nonlocality has been proven.

quant-ph↗
arXiv2005

The Bell Theorem as a Special Case of a Theorem of Bass

The theorem of Bell states that certain results of quantum mechanics violate inequalities that are valid for objective local random variables. We show that the inequalities of Bell are special cases of theorems found ten years earlier by Bass and stated in full generality by Vorob'ev. This fact implies precise necessary and sufficient mathematical conditions for the validity of the Bell inequalities. We show that these precise conditions differ significantly from the definition of objective local variable spaces and as an application that the Bell inequalities may be violated even for objective local random variables.

quant-ph↗
arXiv2004

Local computer model emulating the results of the Pan et al. experiment

It is a widespread current belief that objective local models can not explain the quantum optics experiment of Pan et al. By presenting a model that operates on independent computers, we show that this belief is unfounded. Three remote computers (Alice, Bob and Claire), that never communicate with each other, send measurement results to a fourth computer that is in charge of collecting the data and computing correlations. The result obtained by our local simulation is in better agreement with the ideal quantum result than the Pan et al. experiment. We also show that the local model presented by Pan et al. that can not explain the quantum results contains inappropriate reasoning with profound consequences for the possible results of any local model that uses probability theory.

quant-ph↗
arXiv2004

Bell's theorem: Critique of proofs with and without inequalities

Most of the standard proofs of the Bell theorem are based on the Kolmogorov axioms of probability theory. We show that these proofs contain mathematical steps that cannot be reconciled with the Kolmogorov axioms. Specifically we demonstrate that these proofs ignore the conclusion of a theorem of Vorob'ev on the consistency of joint distributions. As a consequence Bell's theorem stated in its full generality remains unproven, in particular, for extended parameter spaces that are still objective local and that include instrument parameters that are correlated by both time and instrument settings. Although the Bell theorem correctly rules out certain small classes of hidden variables, for these extended parameter spaces the standard proofs come to a halt. The Greenberger-Horne-Zeilinger (GHZ) approach is based on similar fallacious arguments. For this case we are able to present an objective local computer experiment that simulates the experimental test of GHZ performed by Pan, Bouwmeester, Daniell, Weinfurter and Zeilinger and that directly contradicts their claim that Einstein-local elements of reality can neither explain the results of quantum mechanical theory nor their experimental results.

quant-ph↗
arXiv2004

Possibility of a Metallic Field-Effect Transistor

We develop theoretical arguments that demonstrate the possibility of metallic field-effect transistors (METFET's) in one-dimensional systems and particularly in armchair carbon nanotubes. A very inhomogeneous electric field, such as the field of a tunnelling tip, can penetrate the relatively weakly screened nanotubes and open an energy gap. As a consequence, an energy barrier forms that impedes electron flow and thus permits transistor action. This type of metallic field effect is advantageous because of the high conductance of the metallic tubes in the ON--state.

cond-mat.mtrl-sci↗