The Problem of Hidden Variables in Quantum Mechanics

Kochen, Simon; Specker, E.

doi:10.1512/iumj.1968.17.17004

Cited by 619 publications

(822 citation statements)

References 0 publications

Supporting

Mentioning

775

Contrasting

Unclassified

Order By: Relevance

“…Due to the Kochen-Specker theorem [30], it is often said that quantum theory is "contextual", so how can this be reconciled with my claim that the Born rule is "noncontextual"?…”

Section: Noncontextualitymentioning

confidence: 99%

“…However, "it from bit" declares such counterfactuals meaningless because it says that there is no answer to questions that have not been asked. Even if we do not accept "it from bit", the Kochen-Specker theorem [30] implies that counterfactual assertions cannot all respect noncontextuality, i.e. there would have to be pairs of events E ∈ B and F ∈ B ′ such that if E occurs in B then F would not have occurred in B ′ even though quantum theory asserts that p(E|B) = p(F |B ′ ) always holds.…”

Section: Noncontextuality In Subjective Bayesianismmentioning

confidence: 99%

See 1 more Smart Citation

“It from Bit” and the Quantum Probability Rule

Leifer

2015

The Frontiers Collection

View full text Add to dashboard Cite

I argue that, on the subjective Bayesian interpretation of probability, "it from bit" requires a generalization of probability theory. This does not get us all the way to the quantum probability rule because an extra constraint, known as noncontextuality, is required. I outline the prospects for a derivation of noncontextuality within this approach and argue that it requires a realist approach to physics, or "bit from it". I then explain why this does not conflict with "it from bit". This version of the essay includes an addendum responding to the open discussion that occurred on the FQXi website. It is otherwise identical to the version submitted to the contest.

show abstract

“…Due to the Kochen-Specker theorem [30], it is often said that quantum theory is "contextual", so how can this be reconciled with my claim that the Born rule is "noncontextual"?…”

Section: Noncontextualitymentioning

confidence: 99%

Section: Noncontextuality In Subjective Bayesianismmentioning

confidence: 99%

“It from Bit” and the Quantum Probability Rule

Leifer

2015

The Frontiers Collection

View full text Add to dashboard Cite

show abstract

“…John von Neumann was the first to prove a no-go theorem for the hidden variable theories [6]. The proof of the impossibility of reproducing quantum probabilities using a hidden variable theory was gradually perfected later [7]. Since the probability model of quantum mechanics does not satisfy these axioms, this theorem shows that the "perception of knowledge view" is not right.…”

Section: Is Schrödinger's Cat Dead or Alive Or Neither?mentioning

confidence: 99%

The Game of The Biomousa: A View of Discovery and Creation

Aerts¹

1999

World Views and the Problem of Synthesis

View full text Add to dashboard Cite

Section: A Introductionmentioning

confidence: 99%

“…It is well known that (due to its non-locality) the dBB theory is not in contradiction to the Bell inequalities [6]. Due to its contextuality, the dBB theory is also not affected by the Kochen-Specker theorem [7].One mayor drawback of the dBB theory is that the pilot wave and the corresponding "quantum potential" have to be imposed by hand without further justification. In a previous work [17] it was shown that the relativistic dBB theory for a single particle is dual to a scalar theory of curved spacetime.…”

mentioning

confidence: 99%

Geometrizing the Quantum—A Toy Model

Koch¹

2009

AIP Conference Proceedings

View full text Add to dashboard Cite

It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum mechanics as a purely classical geometrical theory. The results are further generalized to interactions with an external electromagnetic field.PACS numbers: 04.62.+v, 03.65.Ta A. IntroductionIn standard quantum mechanics observables and the corresponding uncertainty are promoted to a fundamental principle. But it was shown by David Bohm that this does not necessarily have to be the case [1]. In the de Broglie-Bohm (dBB) interpretation it is explained that the uncertainty "principle" and the description by means of operators can be understood in terms of uncontrollable initial conditions and non-local interactions between an additional field (the "pilot wave") and the measuring apparatus. This theory was further generalized to relativistic quantum mechanics and quantum field theory with bosonic and fermionic fields [2][3][4][5]. It is well known that (due to its non-locality) the dBB theory is not in contradiction to the Bell inequalities [6]. Due to its contextuality, the dBB theory is also not affected by the Kochen-Specker theorem [7].One mayor drawback of the dBB theory is that the pilot wave and the corresponding "quantum potential" have to be imposed by hand without further justification. In a previous work [17] it was shown that the relativistic dBB theory for a single particle is dual to a scalar theory of curved spacetime. In this dual theory the ominous "pilot wave" can be readily interpreted as a well known physical quantity, namely a space-time dependent conformal factor of the metric. This work on the single particle has many features in common with other publications on the subject [9][10][11][12][13][14]. However, having a duality for the single particle case is not enough, because the dBB interpretation only is a consistent quantum theory when it also has the many particle case. The many particle theory is for example crucial for understanding the quantum uncertainty and for evading the non existence theorems [6,7]. Therefore, we will generalize the previous results and present a dual for the relativistic many particle dBB theory. B. Relativistic dBB for many particlesIn this section we shortly list the ingredients for the interpretation of the many particle quantum Klein-Gordon equation in terms of Bohmian trajectories. For a detailed description of subsequent topics in the dBB theory like particle creation, the theory of quantum measurement, many particle states, and quantum field theory the reader is referred to [5]. Let |0 be the vacuum and |n be an arbitrary n-particle state. The corresponding n-particle wave function is [3] ψ(x 1 ; . . . ; x n ) = Ps √ n! 0|Φ(x 1 ) . . .Φ(x n )|n , where theΦ(x j ) are scalar Klein-Gordon field operators and the symbol P s denotes symmetrization over all positions x j . For free fields, the wave function satisfies the equat...

show abstract

The Problem of Hidden Variables in Quantum Mechanics

Cited by 619 publications

References 0 publications

“It from Bit” and the Quantum Probability Rule

“It from Bit” and the Quantum Probability Rule

The Game of The Biomousa: A View of Discovery and Creation

Geometrizing the Quantum—A Toy Model

Contact Info

Product

Resources

About