Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Proceedings of the National Academy of Sciences

Bell's theorem and the problem of decidability between the views of Einstein and Bohr

K. Hess, Walter Philipp

Published Nov 27, 2001• 59 citations
Publisher

Abstract

Einstein, Podolsky, and Rosen (EPR) have designed a gedanken experiment that suggested a theory that was more complete than quantum mechanics. The EPR design was later realized in various forms, with experimental results close to the quantum mechanical prediction. The experimental results by themselves have no bearing on the EPR claim that quantum mechanics must be incomplete nor on the existence of hidden parameters. However, the well known inequalities of Bell are based on the assumption that local hidden parameters exist and, when combined with conflicting experimental results, do appear to prove that local hidden parameters cannot exist. This fact leaves only instantaneous actions at a distance (called "spooky" by Einstein) to explain the experiments. The Bell inequalities are based on a mathematical model of the EPR experiments. They have no experimental confirmation, because they contradict the results of all EPR experiments. In addition to the assumption that hidden parameters exist, Bell tacitly makes a variety of other assumptions; for instance, he assumes that the hidden parameters are governed by a single probability measure independent of the analyzer settings. We argue that the mathematical model of Bell excludes a large set of local hidden variables and a large variety of probability densities. Our set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does permit derivation of the quantum result and is consistent with all known experiments.

DOI
10.1073/pnas.251525098

Related papers

A possible loophole in the theorem of Bell

K. Hess, Walter Philipp

The celebrated inequalities of Bell are based on the assumption that local hidden parameters exist. When combined with conflicting experimental results, these inequalities appear to prove that local hidden parameters cannot exist. This contradiction suggests to many that only instantaneous action at a distance can explain the Einstein, Podolsky, and Rosen type of experiments. We show that, in addition to the assumption that hidden parameters exist, Bell tacitly makes a variety of other assumptions that contribute to his being able to obtain the desired contradiction. For instance, Bell assumes that the hidden parameters do not depend on time and are governed by a single probability measure independent of the analyzer settings. We argue that the exclusion of time has neither a physical nor a mathematical basis but is based on Bell's translation of the concept of Einstein locality into the language of probability theory. Our additional set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does not permit Bell-type proofs to go forward.

Proceedings of the National Academy of Sciences•Nov 27, 2001•81 citations

Exclusion of time in the theorem of Bell

K. Hess, Walter Philipp

The celebrated inequalities of Bell are based on the assumption that local hidden parameters exist. When combined with conflicting experimental results these inequalities appear to prove that local hidden parameters cannot exist. This suggests to many that only instantaneous action at a distance can explain Einstein, Podolsky, Rosen (EPR) type of experiments. We show that Bell-type theories and proofs leading to the well-known inequalities completely exclude a large class of time dependencies in their considerations. Owing to the fact that the electrodynamics of moving bodies cannot be described by time-independent theories or models, we conclude that the Bell theorem cannot describe the physics of EPR experiments. We also show how hidden parameter theories that include time can obtain the quantum result.

Europhysics Letters (EPL)•Mar 1, 2002•46 citations

EPR and Bell Theorem

Muhammad Suhail Zubairy

The first round of the Einstein–Bohr debates took place when Einstein challenged Bohr’s principle of complementarity at the Solvay conference in 1927 and Bohr successfully defended it. The most serious challenge, however, came in 1935 when a paper by Einstein, Podolsky, and Rosen (EPR) argued that quantum mechanics was incomplete through a gedanken experiment motivating an approach based on hidden variables. In this chapter, EPR’s arguments about the incompleteness of quantum mechanics and Bohr’s reply to them are presented. The ultimate answer came almost 30 years later, almost ten years after Einstein’s death, and was nothing that Einstein would have expected. Bell’s inequality and the subsequent Bell-CHSH inequality, that are satisfied by all theories based on the “self-evident truths” of reality and locality are discussed. The startling results that quantum mechanics violates Bell’s inequality and the experimental results are in agreement with the prediction of quantum mechanics are presented.

Oxford University Press eBooks•May 7, 2020•0 citations

The Einstein-Podolsky-Rosen Argument and the Bell Inequalities

László E. Szabó

In 1935 Einstein, Podolsky, and Rosen (EPR) published an important paper in which they claimed that the whole formalism of quantum mechanics together with what they called "Reality Criterion" imply that quantum mechanics cannot be complete. That is, there must exist some elements of reality that are not described by quantum mechanics. There must be, they concluded, a more complete description of physical reality behind quantum mechanics. There must be a state, a hidden variable, characterizing the state of affairs in the world in more details than the quantum mechanical state, something that also reflects the missing elements of reality. Under some further but quite plausible assumptions, this conclusion implies that in some spin-correlation experiments the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities). The paradox consists in the fact that quantum probabilities do not satisfy these inequalities. And this paradoxical fact has been confirmed by several laboratory experiments in the last three decades. The problem is still open and hotly debated among both physicists and philosophers. It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will.

arXiv:0712.1318•Dec 9, 2007•12 citations

Is reality really real?

Muhammad Suhail Zubairy

Abstract The first round of the Einstein–Bohr debates took place when Einstein challenged Bohr’s principle of complementarity at the Solvay conference in 1927 and Bohr successfully defended it. The most serious challenge, however, came in 1935 through a paper by Einstein, Podolsky, and Rosen (EPR) when they argued about the incompleteness of quantum mechanics through a gedanken experiment motivating an approach based on hidden variables. In this chapter, the EPR argument about the incompleteness of quantum mechanics and Bohr’s reply to it, are presented. The ultimate answer came almost 30 years later, almost ten years after Einstein’s death, and the answer was nothing what Einstein would have expected. Bell’s inequality and the subsequent Bell–CHSH inequality, that are satisfied by all theories based on the “self-evident truths” of reality and locality are discussed. The startling result that quantum mechanics violates Bell’s inequality and that the experimental results are in agreement with the prediction of quantum mechanics is presented.

•Sep 14, 2023•0 citations

EINSTEIN/PODOLSKY/ROSEN ARGUMENT

In 1935 Einstein, Podolsky, and Rosen (EPR) published an important paper [17] in which they claimed that the whole formalism of quantum mechanics together with what they called "Reality Criterion" imply that quantum mechanics cannot be complete.That is, there must exist some elements of reality that are not described by quantum mechanics.There must be, they concluded, a more complete description of physical reality behind quantum mechanics.There must be a state, a hidden variable, characterizing the state of affairs in the world in more details than the quantum mechanical state, something that also reflects the missing elements of reality.Under some further but quite plausible assumptions, this conclusion implies that in some spin-correlation experiments the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities).The paradox consists in the fact that quantum probabilities do not satisfy these inequalities.And this paradoxical fact has been confirmed by several laboratory experiments in the last three decades.The problem is still open and hotly debated among both physicists and philosophers.It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will.

WORLD SCIENTIFIC eBooks•Jun 1, 2000•0 citations
Einstein, Podolsky, and Rosen (EPR) have designed a gedanken experiment that suggested a theory that was more complete than quantum mechanics. The EPR design was later realized in various forms, with experimental results close to the quantum mechanical prediction. The experimental results by themselves have no bearing on the EPR claim that quantum mechanics must be incomplete nor on the existence of hidden parameters. However, the well known inequalities of Bell are based on the assumption that local hidden parameters exist and, when combined with conflicting experimental results, do appear to prove that local hidden parameters cannot exist. This fact leaves only instantaneous actions at a distance (called "spooky" by Einstein) to explain the experiments. The Bell inequalities are based on a mathematical model of the EPR experiments. They have no experimental confirmation, because they contradict the results of all EPR experiments. In addition to the assumption that hidden parameters exist, Bell tacitly makes a variety of other assumptions; for instance, he assumes that the hidden parameters are governed by a single probability measure independent of the analyzer settings. We argue that the mathematical model of Bell excludes a large set of local hidden variables and a large variety of probability densities. Our set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does permit derivation of the quantum result and is consistent with all known experiments.
The celebrated inequalities of Bell are based on the assumption that local hidden parameters exist. When combined with conflicting experimental results, these inequalities appear to prove that local hidden parameters cannot exist. This contradiction suggests to many that only instantaneous action at a distance can explain the Einstein, Podolsky, and Rosen type of experiments. We show that, in addition to the assumption that hidden parameters exist, Bell tacitly makes a variety of other assumptions that contribute to his being able to obtain the desired contradiction. For instance, Bell assumes that the hidden parameters do not depend on time and are governed by a single probability measure independent of the analyzer settings. We argue that the exclusion of time has neither a physical nor a mathematical basis but is based on Bell's translation of the concept of Einstein locality into the language of probability theory. Our additional set of local hidden variables includes time-like correlated parameters and a generalized probability density. We prove that our extended space of local hidden variables does not permit Bell-type proofs to go forward.
The celebrated inequalities of Bell are based on the assumption that local hidden parameters exist. When combined with conflicting experimental results these inequalities appear to prove that local hidden parameters cannot exist. This suggests to many that only instantaneous action at a distance can explain Einstein, Podolsky, Rosen (EPR) type of experiments. We show that Bell-type theories and proofs leading to the well-known inequalities completely exclude a large class of time dependencies in their considerations. Owing to the fact that the electrodynamics of moving bodies cannot be described by time-independent theories or models, we conclude that the Bell theorem cannot describe the physics of EPR experiments. We also show how hidden parameter theories that include time can obtain the quantum result.
The first round of the Einstein–Bohr debates took place when Einstein challenged Bohr’s principle of complementarity at the Solvay conference in 1927 and Bohr successfully defended it. The most serious challenge, however, came in 1935 when a paper by Einstein, Podolsky, and Rosen (EPR) argued that quantum mechanics was incomplete through a gedanken experiment motivating an approach based on hidden variables. In this chapter, EPR’s arguments about the incompleteness of quantum mechanics and Bohr’s reply to them are presented. The ultimate answer came almost 30 years later, almost ten years after Einstein’s death, and was nothing that Einstein would have expected. Bell’s inequality and the subsequent Bell-CHSH inequality, that are satisfied by all theories based on the “self-evident truths” of reality and locality are discussed. The startling results that quantum mechanics violates Bell’s inequality and the experimental results are in agreement with the prediction of quantum mechanics are presented.
In 1935 Einstein, Podolsky, and Rosen (EPR) published an important paper in which they claimed that the whole formalism of quantum mechanics together with what they called "Reality Criterion" imply that quantum mechanics cannot be complete. That is, there must exist some elements of reality that are not described by quantum mechanics. There must be, they concluded, a more complete description of physical reality behind quantum mechanics. There must be a state, a hidden variable, characterizing the state of affairs in the world in more details than the quantum mechanical state, something that also reflects the missing elements of reality. Under some further but quite plausible assumptions, this conclusion implies that in some spin-correlation experiments the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities). The paradox consists in the fact that quantum probabilities do not satisfy these inequalities. And this paradoxical fact has been confirmed by several laboratory experiments in the last three decades. The problem is still open and hotly debated among both physicists and philosophers. It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will.
Abstract The first round of the Einstein–Bohr debates took place when Einstein challenged Bohr’s principle of complementarity at the Solvay conference in 1927 and Bohr successfully defended it. The most serious challenge, however, came in 1935 through a paper by Einstein, Podolsky, and Rosen (EPR) when they argued about the incompleteness of quantum mechanics through a gedanken experiment motivating an approach based on hidden variables. In this chapter, the EPR argument about the incompleteness of quantum mechanics and Bohr’s reply to it, are presented. The ultimate answer came almost 30 years later, almost ten years after Einstein’s death, and the answer was nothing what Einstein would have expected. Bell’s inequality and the subsequent Bell–CHSH inequality, that are satisfied by all theories based on the “self-evident truths” of reality and locality are discussed. The startling result that quantum mechanics violates Bell’s inequality and that the experimental results are in agreement with the prediction of quantum mechanics is presented.
In 1935 Einstein, Podolsky, and Rosen (EPR) published an important paper [17] in which they claimed that the whole formalism of quantum mechanics together with what they called "Reality Criterion" imply that quantum mechanics cannot be complete.That is, there must exist some elements of reality that are not described by quantum mechanics.There must be, they concluded, a more complete description of physical reality behind quantum mechanics.There must be a state, a hidden variable, characterizing the state of affairs in the world in more details than the quantum mechanical state, something that also reflects the missing elements of reality.Under some further but quite plausible assumptions, this conclusion implies that in some spin-correlation experiments the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities).The paradox consists in the fact that quantum probabilities do not satisfy these inequalities.And this paradoxical fact has been confirmed by several laboratory experiments in the last three decades.The problem is still open and hotly debated among both physicists and philosophers.It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will.