The basic problem we study here is whether the two-spin correlation experiments together with the theoretical Bell inequalities have already excluded the possibility of introducing hidden variables into quantum theory, as is often concluded. This question is answered negatively by explicitly reproducing the quantum-mechanical two-spin correlation function by a classical model, where the spin is associated with a classical dipolemoment vector. We then study the behavior of single events in classical and quantum models and conclude that the detector efficiency may be a fundamental limitation rather than just a technical problem to be overcome by better techniques. We further show that the assumptions underlying the derivation of Bell inequalities involve statements about single events which are consistent with neither the classical nor quantum models. It is important therefore to work with explicit physical situations rather than with abstract assumptions.The basic problem we study here is whether the two-spin correlation experiments together with the theoretical Bell inequalities have already excluded the possibility of introducing hidden variables into quantum theory, as is often concluded. This question is answered negatively by explicitly reproducing the quantum-mechanical two-spin correlation function by a classical model, where the spin is associated with a classical dipolemoment vector. We then study the behavior of single events in classical and quantum models and conclude that the detector efficiency may be a fundamental limitation rather than just a technical problem to be overcome by better techniques. We further show that the assumptions underlying the derivation of Bell inequalities involve statements about single events which are consistent with neither the classical nor quantum models. It is important therefore to work with explicit physical situations rather than with abstract assumptions.

Jan 1, 20130 citations

Correlation Inequalities for Classical and Quantum XY Models

Costanza Benassi, Benjamin Lees, Daniel Ueltschi

arXiv:1611.06019Springer INdAM seriesJan 1, 20176 citations

On the Correlation Inequalities in Some Models Involving Fermions

R. Gielerak

De Gruyter eBooksDec 31, 19860 citations

Bell Inequality Violations Under Reasonable and Under Weak Hypotheses

Edson de Faria, Charles P. Tresser

Given a sequence of pairs ( ${p}_{i}$ , ${\overline{p}}_{i}$ ) of spin- $1/2$ particles in the singlet state, assume that Alice measures the normalized projections ${a}_{i}$ of the spins of the ${p}_{i}$ 's along vector $\mathbit{a}$ while Bob measures the normalized projections ${b}_{i}$ of the spins of the ${\overline{p}}_{i}$ 's along vector $\mathbit{b}$. Then quantum mechanics (QM) lets one evaluate the correlation $⟨a,b⟩$ as $\ensuremath{-}\mathrm{cos}({\ensuremath{\theta}}_{\mathbit{a}}\ensuremath{-}{\ensuremath{\theta}}_{\mathbit{b}})$ where ${\ensuremath{\theta}}_{\mathbit{v}}$ is the angle between the vector $\mathbit{v}$ and a reference vector chosen once and for all and in a fixed plane. Assuming classical microscopic realism (CMR) there exist also normalized projection pairs (${a}_{i}^{\ensuremath{'}}$, ${b}_{i}^{\ensuremath{'}}$) of the spins of the pairs ( ${p}_{i}$ , ${\overline{p}}_{i}$ ) along (${\mathbit{a}}^{\ensuremath{'}}$, ${\mathbit{b}}^{\ensuremath{'}}$) so that $⟨{a}^{\ensuremath{'}},{b}^{\ensuremath{'}}⟩=\ensuremath{-}\mathrm{cos}({\ensuremath{\theta}}_{{\mathbit{a}}^{\ensuremath{'}}}\ensuremath{-}{\ensuremath{\theta}}_{{\mathbit{b}}^{\ensuremath{'}}})$. Since all projections are in ${\ensuremath{-}1,1}$, $|⟨c,d⟩+⟨c,e⟩|+|⟨f,d⟩\ensuremath{-}⟨f,e⟩|\ensuremath{\le}2$ for $c$ , $d$ , $e$ , and $f$ in ${a,b,{a}^{\ensuremath{'}},{b}^{\ensuremath{'}}}$. Assuming locality (the impossibility of any effect of an event on another event when said events are spatially separated) beside QM and CMR, Bell's theory lets one deduce various violations of this inequality at some choices of quadruplets $Q\ensuremath{\equiv}(\mathbit{a},\mathbit{b},{\mathbit{a}}^{\ensuremath{'}},{\mathbit{b}}^{\ensuremath{'}})$. Our main result is the existence of such $Q$ 's where at least one of the above inequalities is violated if one only assumes QM, CMR, and some very mild further hypotheses that only concern the behavior of correlations that appear in these inequalities near special $Q$ 's.Given a sequence of pairs (${p}_{i}$, ${\overline{p}}_{i}$) of spin-$1/2$ particles in the singlet state, assume that Alice measures the normalized projections ${a}_{i}$ of the spins of the ${p}_{i}$'s along vector $\mathbit{a}$ while Bob measures the normalized projections ${b}_{i}$ of the spins of the ${\overline{p}}_{i}$'s along vector $\mathbit{b}$. Then quantum mechanics (QM) lets one evaluate the correlation $⟨a,b⟩$ as $\ensuremath{-}\mathrm{cos}({\ensuremath{\theta}}_{\mathbit{a}}\ensuremath{-}{\ensuremath{\theta}}_{\mathbit{b}})$ where ${\ensuremath{\theta}}_{\mathbit{v}}$ is the angle between the vector $\mathbit{v}$ and a reference vector chosen once and for all and in a fixed plane. Assuming classical microscopic realism (CMR) there exist also normalized projection pairs (${a}_{i}^{\ensuremath{'}}$, ${b}_{i}^{\ensuremath{'}}$) of the spins of the pairs (${p}_{i}$, ${\overline{p}}_{i}$) along (${\mathbit{a}}^{\ensuremath{'}}$, ${\mathbit{b}}^{\ensuremath{'}}$) so that $⟨{a}^{\ensuremath{'}},{b}^{\ensuremath{'}}⟩=\ensuremath{-}\mathrm{cos}({\ensuremath{\theta}}_{{\mathbit{a}}^{\ensuremath{'}}}\ensuremath{-}{\ensuremath{\theta}}_{{\mathbit{b}}^{\ensuremath{'}}})$. Since all projections are in ${\ensuremath{-}1,1}$, $|⟨c,d⟩+⟨c,e⟩|+|⟨f,d⟩\ensuremath{-}⟨f,e⟩|\ensuremath{\le}2$ for $c$, $d$, $e$, and $f$ in ${a,b,{a}^{\ensuremath{'}},{b}^{\ensuremath{'}}}$. Assuming locality (the impossibility of any effect of an event on another event when said events are spatially separated) beside QM and CMR, Bell's theory lets one deduce various violations of this inequality at some choices of quadruplets $Q\ensuremath{\equiv}(\mathbit{a},\mathbit{b},{\mathbit{a}}^{\ensuremath{'}},{\mathbit{b}}^{\ensuremath{'}})$. Our main result is the existence of such $Q$'s where at least one of the above inequalities is violated if one only assumes QM, CMR, and some very mild further hypotheses that only concern the behavior of correlations that appear in these inequalities near special $Q$'s.

arXiv:1212.4344Physical Review LettersJun 28, 20132 citations

On the Correlation Inequalities in Some Models Involving Fermions

Roman Gielerak

Fortschritte der Physik/Progress of PhysicsJan 1, 19860 citations

Given a sequence of pairs (

{p}_{i}

{\overline{p}}_{i}

) of spin-

1/2

particles in the singlet state, assume that Alice measures the normalized projections

{a}_{i}

of the spins of the

{p}_{i}

's along vector $\mathbit{a}$ while Bob measures the normalized projections

{b}_{i}

of the spins of the

{\overline{p}}_{i}

's along vector $\mathbit{b}$. Then quantum mechanics (QM) lets one evaluate the correlation

⟨a,b⟩

as $\ensuremath{-}\mathrm{cos}({\ensuremath{\theta}}_{\mathbit{a}}\ensuremath{-}{\ensuremath{\theta}}_{\mathbit{b}})$ where ${\ensuremath{\theta}}_{\mathbit{v}}$ is the angle between the vector $\mathbit{v}$ and a reference vector chosen once and for all and in a fixed plane. Assuming classical microscopic realism (CMR) there exist also normalized projection pairs (${a}_{i}^{\ensuremath{'}}$, ${b}_{i}^{\ensuremath{'}}$) of the spins of the pairs (

{p}_{i}

{\overline{p}}_{i}

) along (${\mathbit{a}}^{\ensuremath{'}}$, ${\mathbit{b}}^{\ensuremath{'}}$) so that $⟨{a}^{\ensuremath{'}},{b}^{\ensuremath{'}}⟩=\ensuremath{-}\mathrm{cos}({\ensuremath{\theta}}_{{\mathbit{a}}^{\ensuremath{'}}}\ensuremath{-}{\ensuremath{\theta}}_{{\mathbit{b}}^{\ensuremath{'}}})$. Since all projections are in ${\ensuremath{-}1,1}$, $|⟨c,d⟩+⟨c,e⟩|+|⟨f,d⟩\ensuremath{-}⟨f,e⟩|\ensuremath{\le}2$ for

c

d

e

, and

f

in ${a,b,{a}^{\ensuremath{'}},{b}^{\ensuremath{'}}}$. Assuming locality (the impossibility of any effect of an event on another event when said events are spatially separated) beside QM and CMR, Bell's theory lets one deduce various violations of this inequality at some choices of quadruplets $Q\ensuremath{\equiv}(\mathbit{a},\mathbit{b},{\mathbit{a}}^{\ensuremath{'}},{\mathbit{b}}^{\ensuremath{'}})$. Our main result is the existence of such

Q

's where at least one of the above inequalities is violated if one only assumes QM, CMR, and some very mild further hypotheses that only concern the behavior of correlations that appear in these inequalities near special

Q

's.