scholarly journals The GHSZ Argument: A Gedankenexperiment Requiring More Denken

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 759
Author(s):  
Frank Lad
Keyword(s):  
Linear Combination ◽  
Electron Spin ◽  
Hidden Variables ◽  
Local Realism ◽  
High Dimensional ◽  
Bell’S Inequality ◽  
Spin Pair ◽  
Quantum Probabilities ◽  
Double Electron ◽  
Fundamental Error

I reassess the gedankenexperiment of Greenberger, Horne, Shimony, and Zeilinger after twenty-five years, finding their influential claim to the discovery of an inconsistency inherent in high dimensional formulations of local realism to arise from a fundamental error of logic. They manage this by presuming contradictory premises: that a specific linear combination of four angles involved in their proposed parallel experiments on two pairs of electrons equals both π and 0 at the same time. Ignoring this while presuming the contradictory implications of these two conditions, they introduce the contradiction themselves. The notation they use in their “derivation” is not sufficiently ornate to represent the entanglement in the double electron spin pair problem they design, confounding their error. The situation they propose actually motivates only an understanding of the full array of symmetries involved in their problem. In tandem with the error now recognised in the supposed defiance of Bell’s inequality by quantum probabilities, my reassessment of their work should motivate a reevaluation of the current consensus outlook regarding the principle of local realism and the proposition of hidden variables.

Mahalanobis distance informed by clustering

2018 ◽  
Vol 8 (2) ◽  
pp. 377-406
Author(s):  
Almog Lahav ◽  
Ronen Talmon ◽  
Yuval Kluger
Keyword(s):  
Mahalanobis Distance ◽  
High Dimensional Data ◽  
Hidden Variables ◽  
Real Data ◽  
Risk Groups ◽  
High Dimensional ◽  
Data Sets ◽  
Kaplan Meier ◽  
Data Points ◽  
Survival Plot

Abstract A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of meaningfulness is more prominent (e.g. the Euclidean distance between images). In this paper, we propose to exploit a property of high-dimensional data that is usually ignored, which is the structure stemming from the relationships between the coordinates. Specifically, we show that organizing similar coordinates in clusters can be exploited for the construction of the Mahalanobis distance between samples. When the observable samples are generated by a nonlinear transformation of hidden variables, the Mahalanobis distance allows the recovery of the Euclidean distances in the hidden space. We illustrate the advantage of our approach on a synthetic example where the discovery of clusters of correlated coordinates improves the estimation of the principal directions of the samples. Our method was applied to real data of gene expression for lung adenocarcinomas (lung cancer). By using the proposed metric we found a partition of subjects to risk groups with a good separation between their Kaplan–Meier survival plot.

scholarly journals The Hardy’s nonlocality argument

2016 ◽  
Vol 14 (06) ◽  
pp. 1640035
Author(s):  
Sujit K Choudhary ◽  
Pankaj Agrawal
Keyword(s):  
Quantum Theory ◽  
Bell’S Theorem ◽  
Local Realism ◽  
Bell’S Inequality ◽  
Bell's Theorem ◽  
Famous Theorem ◽  
Bell's Inequality

Certain predictions of quantum theory are not compatible with the notion of local-realism. This was the content of Bell’s famous theorem of the year 1964. Bell proved this with the help of an inequality, famously known as Bell’s inequality. The alternative proofs of Bell’s theorem without using Bell’s inequality are known as “nonlocality without inequality (NLWI)” proofs. We review one such proof namely the Hardy’s proof which due to its simplicity and generality has been considered the best version of Bell’s theorem.

PROBING BELL'S INEQUALITY WITH CLASSICAL SYSTEMS

2010 ◽  
Vol 09 (04) ◽  
pp. 395-402 ◽  
Author(s):  
D. K. FERRY
Keyword(s):  
Quantum Mechanics ◽  
Bell Inequality ◽  
Hidden Variables ◽  
Optical Polarization ◽  
Bell’S Inequality ◽  
Epr Paradox ◽  
Quantum Theories ◽  
Considerable Evidence ◽  
Classical Systems ◽  
Quantum Behavior

From the early days of quantum mechanics, there has been a discussion on the concept of reality, exemplified by the EPR paradox. To many, the idea of the paradox and the possibility of local hidden variables was dismissed by the Bell inequality. Yet, there remains considerable evidence that this inequality can be violated even by classical systems, so that experiments showing quantum behavior and the violation of the inequality must be questioned. Here, we demonstrate that classical optical polarization experiments can be shown to violate the Bell inequality. Hence, such experiments cannot be used to distinguish between classical and quantum theories.

scholarly journals Determination of System Dimensionality from Observing Near-Normal Distributions

2015 ◽  
Vol 2015 ◽  
pp. 1-17
Author(s):  
Shahid Razzaq ◽  
Shehzad Khalid
Keyword(s):  
Hidden Variables ◽  
Boltzmann Distribution ◽  
Ideal Gas ◽  
High Dimensional ◽  
Distributed Data ◽  
Normal Distributions ◽  
Ellipsoidal Model ◽  
Data Points ◽  
New Distribution

This paper identifies a previously undiscovered behavior of uniformly distributed data points or vectors in high dimensional ellipsoidal models. Such models give near normal distributions for each of its dimensions. Converse of this may also be true; that is, for a normal-like distribution of an observed variable, it is possible that the distribution is a result of uniform distribution of data points in a high dimensional ellipsoidal model, to which the observed variable belongs. Given the currently held notion of normal distributions, this new behavior raises many interesting questions. This paper also attempts to answer some of those questions. We cover both volume based (filled) and surface based (shell) ellipsoidal models. The phenomenon is demonstrated using statistical as well as mathematical approaches. We also show that the dimensionality of the latent model, that is, the number of hidden variables in a system, can be calculated from the observed distribution. We call the new distribution “Tanazur” and show through experiments that it is at least observed in one real world scenario, that of the motion of particles in an ideal gas. We show that the Maxwell-Boltzmann distribution of particle speeds can be explained on the basis of Tanazur distributions.

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