What is Bell inequality: Definition and 30 Discussions

Bell's theorem proves that quantum physics is incompatible with local hidden-variable theories. It was introduced by physicist John Stewart Bell in a 1964 paper titled "On the Einstein Podolsky Rosen Paradox", referring to a 1935 thought experiment that Albert Einstein, Boris Podolsky and Nathan Rosen used to argue that quantum physics is an "incomplete" theory. By 1935, it was already recognized that the predictions of quantum physics are probabilistic. Einstein, Podolsky and Rosen presented a scenario that, in their view, indicated that quantum particles, like electrons and photons, must carry physical properties or attributes not included in quantum theory, and the uncertainties in quantum theory's predictions were due to ignorance of these properties, later termed "hidden variables". Their scenario involves a pair of widely separated physical objects, prepared in such a way that the quantum state of the pair is entangled.
Bell carried the analysis of quantum entanglement much further. He deduced that if measurements are performed independently on the two separated halves of a pair, then the assumption that the outcomes depend upon hidden variables within each half implies a constraint on how the outcomes on the two halves are correlated. This constraint would later be named the Bell inequality. Bell then showed that quantum physics predicts correlations that violate this inequality. Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are "nonlocal", somehow associated with both halves of the pair and able to carry influences instantly between them no matter how widely the two halves are separated. As Bell wrote later, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."Multiple variations on Bell's theorem were proved in the following years, introducing other closely related conditions generally known as Bell (or "Bell-type") inequalities. These have been tested experimentally in physics laboratories many times since 1972. Often, these experiments have had the goal of ameliorating problems of experimental design or set-up that could in principle affect the validity of the findings of earlier Bell tests. This is known as "closing loopholes in Bell test experiments". To date, Bell tests have found that the hypothesis of local hidden variables is inconsistent with the way that physical systems do, in fact, behave.The exact nature of the assumptions required to prove a Bell-type constraint on correlations has been debated by physicists and by philosophers. While the significance of Bell's theorem is not in doubt, its full implications for the interpretation of quantum mechanics remain unresolved.

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  1. G

    I How to enter measurement results into Bell inequality?

    Hi. I can calculate the expectation values in the Bell (or in this case, CHSH) inequality and show that they violate it for entangled particles. But I'm confused about how to calculate them for an actual sequence of measurements, which could look like this ("Paar" is for photon pair): How do...
  2. cianfa72

    I Understanding Bell Inequality Proof: Explained from a Probability Perspective

    Starting from this link my understanding of Bell inequality proof goes as follows: Suppose we have a model of local pre-determinate hidden variables for QM. This amounts to say QM objects are in pre-determinate given states even if we do not measure it. Locality just means that spacelike...
  3. Fra

    A Game theory, quantum physics and the Bell inequality (paper)

    The reason for highlighting this paper is to highlight (and exemplify by how different researcher think about this) a new "perspective" to understanding the different between "ignorance of the physicists" which is reallly what Bell assumptions imples. And "ignorance of they players", which is...
  4. L

    B Bell inequality test without polarisation?

    Was trying to understand the inequality test. The only article ever that I've found that explains it simply is the 1981 article, Bringing home the atomic world: Quantum Mysteries For Anybody. All other explanations require trust and understanding of polarisation, which is a huge deal. So i now...
  5. V

    B Videos from Big Event 2015 (Växjö): Loophole free Bell test

    vhttps://play.lnu.se/media/t/0_hgz7034c A.Zeilinger: The Future of Bell Experiments. https://play.lnu.se/media/t/0_6jkhpefo G. Weihs: Violation of Bell’s Inequality under Strict Einstein Locality Conditions https://play.lnu.se/media/t/0_q2r30syq R. Hanson: From the first loophole-free Bell...
  6. .Scott

    B Is there another workable interpretation of the Bell Inequality?

    I just read an article in Quantum Magazine about "unitary" results and how this is tied to looking at the reversibility of quantum events. It provided an easy-to-understand mechanism for tracking the effects of adding information to a fictional universe. The example they gave for detecting a...
  7. plmustard

    B Bell Test Configuration Question

    Qutools makes quantum physics kits for educational purposes. Its quED kit is designed to help students learn about entanglement by performing Bell tests. In the manual section 5.1 it describes "the simplest test to verify entanglement of photon pairs." My question is if the entangled photons...
  8. V

    I Contextuality without incompatibility?

    see https://link.springer.com/article/10.1007/s10773-020-04666-z I think that contextuality is just another word for incompatibility. I asked may people: Point out to the dry-residue of contextuality, filtered of incompatibility. All these bright people were not able to say anything sensible on...
  9. P Grangier Closing the Door on Einstein and Bohr's Quantum Debate

    P Grangier Closing the Door on Einstein and Bohr's Quantum Debate

    This is the first video from Växjö2018 conference, from the special session devoted to the final loophole free experiments on violation of Bell's inequality; videos of other speakers can be found at my webpage, https://lnu.se/en/staff/andrei.khrennikov/ [films from Växjö conferences]
  10. Lars278

    I Sending a cryptographic key faster than the speed of light

    Quantum entanglement does not imply that you can send information faster than the speed of light since you cannot manipulate what your sending. You don't know what you have until you have measured it. But you do know that you have the corresponding photon at the other location in space no matter...
  11. RUTA

    Insights Why the Quantum | A Response to Wheeler's 1986 Paper - Comments

    Greg Bernhardt submitted a new PF Insights post Why the Quantum | A Response to Wheeler's 1986 Paper Continue reading the Original PF Insights Post.
  12. L

    I Generalizing the Bell Inequality for Arbitrary Measurement Axes

    EDIT: I realize now that I have fundamentally misunderstood a crucial aspect of deriving the Bell inequality for this case which is the existence of the third axis. The setup of the problem did state that the axes were chosen at random. Therefore I can't just look at the possibility of choosing...
  13. N

    I Bell's inequality experimental data

    Everything I've seen about Bell's inequality has had the setup of 120 degree angles between the axis of measurements. The experiment then proves that the basic hidden variable theory can't be true. But the actual measurement has always been told to me as a 0.5 correlation. 50% of the time the...
  14. E

    I How Does Bell's Inequality Reveal Quantum Nonlocality?

    Bell inequality in page 171 of https://www.scientificamerican.com/media/pdf/197911_0158.pdf is ##n[A^+B^+] \le n[A^+C^+]+n[B^+C^+]## In page 174 we can see that this causes linear dependency according to angle. How to derive this? Let us suppose that angle between ##A^+## and ##B^+## is 30°...
  15. entropy1

    Understanding Bell's inequality

    I am not sure if I am allowed to ask this, but here's my shot: I find all the explanations of Bell's theorem summed up here, very different in interpretation and also (for me) incomprehensible. I have these simple questions: How does the Bell inequality, stated as N(A, not B) + N(B, not C) ≥...
  16. J

    Violation of Bell inequalities for classical fields?

    There is a recent article (Optics July 2015) claiming violation of Bell inequalities for classical fields: "Shifting the quantum-classical boundary: theory and experiment for statistically classical optical fields" https://www.osapublishing.org/optica/abstract.cfm?URI=optica-2-7-611...
  17. DrChinese

    A Experimental loophole-free violation of a Bell inequality

    A great new experiment is reported closing simultaneously the loopholes of detection (fair sampling assumption) and distance (locality assumption): Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km B. Hensen, H. Bernien, A.E. Dréau, A...
  18. D

    Bell inequality violated with classical light in experiment

    https://www.osapublishing.org/optica/fulltext.cfm?uri=optica-2-7-611&id=321243 "In our experimental test, we used light whose statistical behavior (field second-order statistics) is indistinguishable from classical, viz., the light from a broadband laser diode operating below threshold. Our...
  19. jerromyjon

    Understanding the Bell Inequality and its Impact on Quantum Mechanics

    I went through a paper last week about the Bell inequality and how it is incompatible with QM. Something along the lines of probability in classical regards being 1/3 but in quantum mechanics it is 1/4. It went into some basic principles of how this is determined through quantum entanglement to...
  20. morrobay

    What Interpretation/Model of QM Predicts Bell Inequality Violations ?

    Are there any modern interpretations of QM that predict the correlations in a Bell Inequality violation ? Preferably a local non realistic model based on mechanisms.
  21. morrobay

    Is Superposition the Explanation for Bell Inequality Violations ?

    This form of a Bell inequality: n[x-y+] + n[y-z-] ≥ n[x+z+] is derived from spin measurements at A and B when detector settings are aligned. If it is correct that when a particle is measured at detector A and is spin up in the y direction , then its entangled twin at B is in superposition...
  22. M

    Another question about bell inequality

    I imagine that some topics and questions keep reappearing since it is hard to track through all past posts even with the query tool. So apologies if this has been covered before (as it probably has). I just want to check my intuitive understanding of the Bell experiment, having heard an...
  23. Killtech

    Deriving Measurement Operators for Realistic Detectors

    Lately I was studying the Bell and CHSH inequalities on Wikipedia (it has proven to be a good source to get an quick idea about everything). The articles are detailed and even provide the core of the proof in a mathematical derivation that is easy to understand. But it leaves me still with a...
  24. H

    Bell inequality experiments and photon polarisation issue

    I am confused by the role of photon polarisation in Bell inequality experiments. The original logic of EPR as I understand it is based on the HUP such that QM predicts that measurement of momentum on one particle should affect the measurement of position of the other particle. Yet across...
  25. D

    Examining the details of the Bell Inequality.

    Hi, I was reading Heinz Pagels' description of the nail gun experiment in the chapter about "Bell's Inequality" from his book, The Cosmic Code: Quantum Physics as the Langauge of Nature, 1982, pp. 160-176. He describes the record of hits and misses after "turning polarizer A clockwise by...
  26. E

    Bell Inequality & Quantum Mechanics: Exploring Violation & Its Significance

    Does the Bell inequality confirms the quantum mechanics? If answer is yes, why the violation of Bell inequality is more famous?
  27. W

    Bell inequality tests questions

    1. Are there any tests done actually show Bell inequality is NOT violated? 2. What are the different kinds of things the Bell inequality experiment test? I know most tests are testing spins of electrons, what are the other Bell tests, what they test?
  28. michael879

    Detecting Macroscopic Entanglement With the Bell Inequality

    So first off, Ill admit I've forgotten most of the finer details of the bell inequality so I apologize if I've gotten something wrong. From how I remember it, the bell inequality is a test of any local hidden variable theory vs. QM. It uses the fact that the inequality measured if a classical...
  29. K

    Could Bell experiments reveal a link between photon spin and gravity waves?

    When a photon's spin is measured, the photon must exert a force on the device that measures its spin.Since a force is associated with an acceleration and an acceleration with gravity,could the photon have created a gravity wave that travels through space and determines the spin of a second...
  30. Loren Booda

    Local inflation realizes Bell inequality violation

    Just as the thermal equilibrium between two relatively receding (c<v<2c) cosmological horizons is justified by inflation, such a Higgs phase transition could account locally for correlations violating the Bell inequality through superluminal (c<v<2c) "signaling."