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On local-hidden-variable no-go theorems

André Allan Méthot

Published Jul 15, 2005• 11 citations
OpenAlex

Abstract

The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimatly doomed in 1964 with the work of Bell Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities and pseudo-telepathy. A discussion of the similarities and differences will follow. 1

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On local-hidden-variable no-go theorems

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The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow. PACS Nos.: 03.65.–w, 03.65.Ud, 03.65.Ta

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Realism defined in EPR paper as “In a complete theory there is an element corresponding to each element of reality.” Bell showed that there is a forbidden triangle (Realism, Quantum Statistics, and Locality), and we are only allowed to pick two out of three. In this thesis, we investigate other inequalities and no-go theorems that we face. We also discuss possible Hidden Variable Models that are tailored to be consistent with Quantum Mechanics and the specific no-go theorems. In the special case of the Leggett Inequality the proposed hidden variable is novel in the sense that the hidden variable is in the measurement device rather than the wave-function.

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In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.

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The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimatly doomed in 1964 with the work of Bell Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities and pseudo-telepathy. A discussion of the similarities and differences will follow. 1
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow. PACS Nos.: 03.65.–w, 03.65.Ud, 03.65.Ta
Realism defined in EPR paper as “In a complete theory there is an element corresponding to each element of reality.” Bell showed that there is a forbidden triangle (Realism, Quantum Statistics, and Locality), and we are only allowed to pick two out of three. In this thesis, we investigate other inequalities and no-go theorems that we face. We also discuss possible Hidden Variable Models that are tailored to be consistent with Quantum Mechanics and the specific no-go theorems. In the special case of the Leggett Inequality the proposed hidden variable is novel in the sense that the hidden variable is in the measurement device rather than the wave-function.
In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of EPR-type entangled quantum states, Bell (1964) concluded that any hidden variable theory designed to reproduce the predictions of quantum mechanics must necessarily be nonlocal and allow superluminal interactions. This doesn't immediately imply that nonlocality is a characteristic feature of quantum mechanics let alone a fundamental property of nature; however, many physicists and philosophers of science do harbor this belief. Experts in the field often use the term `nonlocality' to designate particular non-classical aspects of quantum entanglement and do not confuse the term with superluminal interactions. However, many physicists seem to take the term more literally. I endeavor to disabuse the latter of this notion by emphasizing that the correlations of Bell-type entanglement are a result of ordinary quantum superposition with no need to introduce nonlocality. The conclusion of the EPR paper wasn't that quantum mechanics is nonlocal but rather that it is an incomplete description of reality. For different reasons, many physicists, including me, agree with Einstein that quantum mechanics is necessarily an incomplete description of reality.
Quantum mechanics makes surprising predictions that defy our classical understanding of the world.Experiments done on entangled particles-particles with linked properties-prove that actions on one particle can affect the other one no matter the distance.In response, physicists came up with local hidden variable theories in an attempt to understand this quantum phenomena through a classical lens.John Bell formulated a way to test whether nature is dictated by local hidden variable theories or quantum mechanics, and since then it has been the goal of numerous physicists to experimentally test the theorem and improve upon the results.This paper describes the history of these experiments, their pros and cons, their advancements, and the potential applications that they will enable.
In our terms, this is Bell's 1964 theorem, ‘No local hidden-variable theory can reproduce exactly the quantum mechanical predictions.' Against this, and bound by what Bell takes to be Einstein's definition of locality, we refute Bell's theorem and reveal his error. We show that Einstein was right: the physical world is local; and we advance Einstein's quest to make quantum mechanics intelligible in a classical way. With respect to understanding, and taking mathematics to be the best logic, the author is as close as an email: eprb@me.com
Bell nonlocality is an intriguing property of quantum mechanics with far reaching consequences for information processing, philosophy and our fundamental understanding of nature. However, nonlocality is a statement about static correlations only. It does not take into account dynamics, i.e. time evolution of those correlations. Consider a dynamic situation where the correlations remain local for all times. Then at each moment in time there exists a local hidden-variable (LHV) model reproducing the momentary correlations. Can the time evolution of the correlations then be captured by evolving the hidden variables? In this light, we define dynamical LHV models and motivate and discuss potential additional physical and mathematical assumptions. Based on a simple counter example we conjecture that such LHV dynamics does not always exist. This is further substantiated by a rigorous no-go theorem. Our results suggest a new type of nonlocality that can be deduced from the observed time evolution of measurement statistics and which generically occurs in interacting quantum systems.