# Closing the Door on Quantum Nonlocality

## Abstract

**:**

## 1. Introduction

## 2. Computer Simulation Experiments Using Registration Time Delays

^{2}

- Protocol 1 is consistent with a realizable protocol in SPCE. Outcomes for any pair of settings are generated, at each time, for a different “photon pair”. Thus, four pseudo-random time series of data for four different pairs of settings are generated:$$({x}_{1}(t),{x}_{2}(t),{t}_{1}^{*}(t),{t}_{2}^{*}(t))=G({\phi}_{1}(t),{\phi}_{2}(t),{\mathrm{r}}_{1}(t),{\mathrm{r}}_{2}(t),{\mathrm{a}}_{1}(t),{\mathrm{a}}_{2}(t))\text{}$$
_{1}(t), a_{2}(t)) = (a_{1}, a_{2}) for t = 1, …, N; (a_{1}(t), a_{2}(t)) = (a_{1}, a’_{2}) for t = N + 1, …, 2N; (a_{1}(t), a_{2}(t)) = (a’_{1}, a_{2}) for t = 2N + 1, …, 3N; (a_{1}(t), a_{2}(t)) = (a’_{1,}a’_{2}) for t = 3N + 1, …, 4N. - Protocol 2 is impossible to implement in SPCE and is forbidden by QM. For each “photon pair” predetermined outcomes and time delays, for all available settings, are outputted. A generated pseudo-random time series is:$$({x}_{1}(t),{x}^{\prime}{}_{1}(t),{x}_{2}(t),{x}^{\prime}{}_{2}(t),{t}_{1}^{*}(t),{t}^{\prime}{}_{1}^{*}(t),{t}_{2}^{*}(t),{t}^{\prime}{}_{2}^{*}(t))={G}_{1}({\phi}_{1}(t),{\phi}_{2}(t),{\mathrm{r}}_{1}(t),{\mathrm{r}}_{2}(t),{\mathrm{a}}_{1},{\mathrm{a}}^{\prime}{}_{1},{\mathrm{a}}_{2},{\mathrm{a}}^{\prime}{}_{2})\text{}$$

_{obs}, <AB’>

_{obs}, <A’B>

_{obs}, and<A’B’>

_{obs}are the correlations for the different pairs of settings estimated using the counterfactual spreadsheet 4 × 4N, if N tends to infinity.

_{1}, x’

_{1}, x

_{2}, and x’

_{2}, created using Equation (1)–(4), have the same properties as the samples studied by Gill. Namely:

- Protocol 1 chooses, for each “photon pair“, only two entries from a corresponding line of the spreadsheet—one for Alice, and one for Bob. It is obvious from (3) that the first N pairs of entries are chosen from the same pair of columns since the settings are changed systematically, only for at t = N + 1, 2N + 1, 3N + 1, 4N + 1. In spite of the fact that pairs of settings are not chosen randomly, generated samples have the same properties as the samples in [84].
- Protocol 2 chooses, for each “photon pair”, a complete line of the counterfactual spreadsheet. These lines form a sample drawn from some CFD-compliant joint probability distribution of four random variables. It is easy to see from [62,84] that in this case, |S| = 2 for any finite sample—thus, CHSH inequality is never violated.

## 3. Computer Simulation Experiments Using Detection Thresholds

_{1}, λ

_{2}) describes “photon pairs”; (a

_{1}, a

_{2}) are chosen settings; and P(x

_{1}|a

_{1}, λ

_{1}) and P(x

_{2}|a

_{2}, λ

_{2}) are probabilities describing stochastically independent measurements, performed in distant laboratories by Alice and Bob. If (λ

_{1}, λ

_{2}) are continuous variables, the sum in (6) is replaced by an integral. A more detailed discussion of SHVM may be found in [7,17,22].

- For each k = 1, …, N, a uniform random generator generates two floating-point numbers $0\le {\varphi}_{1,k}\le 2\pi $ and ${\varphi}_{2,k}={\varphi}_{1,k}+\pi /2$, which are inputted to the stations with settings (a
_{1}, a_{1}’) and (a_{2}, a_{2}’), respectively. The k-th event simulates the emission of a “photon pair” with maximally correlated, orthogonal polarizations for all the essential features of the laboratory experiments. - Upon receiving the input, an observation station generates two pseudo-random numbers $\left(\mathrm{r},\widehat{\mathrm{r}}\right)$ and computes:$$c=cos\left[2\left(a-\varphi \right)\right],\text{}s=sin\left[2\left(a-\varphi \right)\right]\text{}$$$$x=sign\left(1+c-2\cdot \mathrm{r}\right),\text{}v=\hat{\mathrm{r}}|s{|}^{d}\left(Vmax-Vmin\right)-Vmax\text{}$$

- Protocol 1 (implementable) is consistent with the experimental protocol used in SPCE because the outcomes, for any pair of settings, are generated each time for a different “photon pair”. Namely, four pseudo-random time series of data for four different pairs of settings may be generated:$$({x}_{1}(t),{x}_{2}(t))={F}_{1}({\phi}_{1}(t),{\phi}_{2}(t),{\mathrm{r}}_{1}(t),{\mathrm{r}}_{2}(t),{\mathrm{a}}_{1}(t),{\mathrm{a}}_{2}(t))\text{}$$
_{1}(t), a_{2}(t)) = (a_{1}, a_{2}) for t = 1, …, N; (a_{1}(t), a_{2}(t)) = (a_{1}, a’_{2}) for t = N + 1, …, 2N; (a_{1}(t), a_{2}(t)) = (a’_{1}, a_{2}) for t = 2N + 1, …, 3N; (a_{1}(t), a_{2}(t)) = (a’_{1,}a’_{2}) for t = 3N + 1, …, 4N. The fact that the settings are not randomly chosen has no impact on the properties of generated samples. - Protocol 2 (counterfactual) is impossible to realize in SPCE and QM, because it calculates and outputs, at each step, four pseudo-random values (simulating the outcomes of a simultaneous joint measurement of incompatible observables performed on each “photon pair”). The generated pseudo-random time series of outputs for the four simultaneous measurement settings may be defined as:$$({x}_{1}(t),{x}^{\prime}{}_{1}(t),{x}_{2}(t),{x}^{\prime}{}_{2}(t))={F}_{2}({\phi}_{1}(t),{\phi}_{2}(t),{\mathrm{r}}_{1}(t),{\mathrm{r}}_{2}(t),{{\mathrm{r}}^{\prime}}_{1}(t),{{\mathrm{r}}^{\prime}}_{2}(t){\mathrm{a}}_{1},{\mathrm{a}}^{\prime}{}_{1},{\mathrm{a}}_{2},{{\mathrm{a}}^{\prime}}_{2})\text{}$$

_{1}and X

_{2}are the random variables which take the values x

_{1}= ±1 and x

_{2}= ±1, respectively.

_{i}taking the values x

_{i}= ±1, which can be measured pairwise, but not all simultaneously. As mentioned in the introduction, the similar inequalities were already derived by Georges Boole [87] and generalized by Vorob’ev [88]. This is why these inequalities are violated in successive spin polarization measurements [89], in some experiments in social sciences [90,91,92], and even in classical mechanics [59]. Claims that their violations imply mysterious quantum nonlocality or super-determinism are unfounded [63].

## 4. Setting–Dependent Post-Selection

_{1}= {x

_{1}, …, x

_{n}} and S

_{2}= {y

_{1}, … ,y

_{n}}, where x

_{i}= ±1 and y

_{i}= ±1. Using a simple pairing of outcomes, we obtain a sample S

_{3}= {(x

_{1}, y

_{1}), …, (x

_{n}, y

_{n})}, for which E(XY) = 0.

- If we post-select data items, using a criterion “kept only if x
_{i}+ y_{i}= 2”, we extract a completely correlated sub-sample of S_{3}, for which E(XY) = 1. - If we post-select data items, using a criterion “kept only if x
_{i}+ y_{i}= 0”, we extract a completely anti-correlated sub-sample of S_{3}, for which E(XY) = −1. - If we randomly post-select data items from S
_{3}, we obtain an uncorrelated sub-sample for which (E(XY) = 0).

## 5. The Meaning of the Contextuality Loophole

_{a}(t) = f

_{a}(λ

_{1}(t), λ

_{a}(t), a) and x

_{b}(t) = f

_{b}(λ

_{2}(t), λ

_{b}(t), b), where (λ

_{1}(t), λ

_{2}(t)) and (λ

_{a}(t), λ

_{b}(t)) describe an “EPR pair” and the “microstates” of measuring instruments in the setting (a, b), Gill’s counterfactual spreadsheet does not exist and the only constraint we have is |S| ≤ 4. The same constraint was derived by Andrei Khrennikov in his generalization of the Kolmogorov model for SPCE experiments [99,100]. A detailed discussion of a model which is able to reproduce any correlations in SPCE may be found in [63].

_{1}= α, β

_{1}= β) are chosen settings, and (ξ

_{1}, ξ

_{2}) are some local setting-dependent hidden variables. The probability distribution of (ξ

_{1}, ξ

_{2}) depends on (α, β, W). The setting dependence in these models is a result of locally causal data generation, and any speculations about a spooky action in the distance are unfounded Contextual probabilistic models of SPCE may also be defined in a more direct and intuitive way, such as in [62,63].

## 6. Computer Simulations and Predictable Completeness of QT

_{1}, r

_{1}, T; a

_{2}, r

_{2}, T). Before entering a PBS, the ”magnetic moments” of each pair are pointing in opposite directions. During the interaction with the PBSs, they are “aligned” along the directions a

_{1}and a

_{2}, respectively, and are subsequently “sent” to corresponding detectors. It is plausible that the time needed for this alignment increases and decreases in the function of (a − φ). The model would have been closer to this physical intuition with parameters r drawn randomly from [1 − c, 1], where c is a small positive number. We see from (2) that if r is close to 0, the outputted time delay is negligible, no matter which setting is chosen.

## 7. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Peres, A. Unperformed experiments have no results. Am. J. Phys.
**1978**, 46, 745–747. [Google Scholar] [CrossRef] - Bohr, N. Essays 1958–1962 on Atomic Physics and Human Knowledge; Wiley: New York, NY, USA, 1963. [Google Scholar]
- Furry, W.H. Note on the Quantum-Mechanical Theory of Measurement. Phys. Rev.
**1936**, 49, 393. [Google Scholar] [CrossRef] - Birkhoff, G.; von Neumann, J. The logic of quantum mechanics. Ann. Math.
**1936**, 37, 823–843. [Google Scholar] [CrossRef] - Mielnik, B. Theory of filters. Commun. Math. Phys.
**1969**, 15, 1–46. [Google Scholar] [CrossRef] - Kupczynski, M. Is Hilbert space language too rich. Int. J. Theor. Phys.
**1973**, 79, 319–343. [Google Scholar] - Kupczynski, M. Bell Inequalities, Experimental Protocols and Contextuality. Found. Phys.
**2015**, 45, 735–753. [Google Scholar] [CrossRef] - Einstein, A.; Podolsky, B.; Rosen, N. Can Quantum-Mechanical Description of Physical Reality Be Considered Complete. Phys. Rev.
**1935**, 47, 777. [Google Scholar] [CrossRef] - Bohm, D. Quantum Theory; Prentice-Hall: New York, NY, USA, 1951. [Google Scholar]
- Aspect, A.; Grangier, P.; Roger, G. Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett.
**1982**, 49, 1804–1807. [Google Scholar] [CrossRef] - Weihs, G.; Jennewein, T.; Simon, C.; Weinfurther, H.; Zeilinger, A. Violation of Bell’s inequality under strict Einstein locality conditions. Phys. Rev. Lett.
**1998**, 81, 5039–5043. [Google Scholar] [CrossRef] - Christensen, B.G.; McCusker, K.T.; Altepeter, J.B.; Calkins, B.; Lim, C.C.W.; Gisin, N.; Kwiat, P.G. Detection-loophole-free test of quantum nonlocality, and applications. Phys. Rev. Lett.
**2013**, 111, 130406. [Google Scholar] [CrossRef] [PubMed] - Hensen, B.; Bernien, H.; Dreau, A.E.; Reiserer, A.; Kalb, N.; Blok, M.S.; Ruitenberg, J.; Vermeulen, R.F.L.; Schouten, R.N.; Abellán, C.; et al. Loopholefree Bell inequality violation using electron spins separated by 1.3 kilometres. Nature
**2015**, 526, 682–686. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Giustina, M.; Versteegh, M.A.M.; Wengerowsky, S.; Handsteiner, J.; Hochrainer, A.; Phelan, K.; Steinlechner, F.; Kofler, J.; Larsson, J.-Å.; Abellán, C.; et al. Significant-loophole-free test of Bell’s theorem with entangled photons. Phys. Rev. Lett.
**2015**, 115, 250401. [Google Scholar] [CrossRef] [PubMed] - Shalm, L.K.; Meyer-Scott, E.; Christensen, B.G.; Bierhorst, P.; Wayne, M.A.; Stevens, M.J.; Gerrits, T.; Glancy, S.; Hamel, D.R.; Allman, M.S.; et al. Strong loophole-free test of local realism. Phys. Rev. Lett.
**2015**, 115, 250402. [Google Scholar] [CrossRef] [PubMed] - Bell, J.S. On the Einstein-Podolsky-Rosen paradox. Physics
**1965**, 1, 195–200. [Google Scholar] [CrossRef] - Bell, J.S. Speakable and Unspeakable in Quantum Mechanics; Cambridge UP: Cambridge, UK, 2004. [Google Scholar]
- Fine, A. Hidden variables, joint probability and the Bell inequalities. Phys. Rev. Lett.
**1982**, 48, 291–295. [Google Scholar] [CrossRef] - Fine, A. Joint distributions, quantum correlations, and commuting observables. J. Math. Phys.
**1982**, 23, 1306–1310. [Google Scholar] [CrossRef] - Kupczynski, M. New Test of Completeness of Quantum Mechanics. Available online: https://inis.iaea.org/collection/NCLCollectionStore/_Public/16/072/16072622.pdf?r=1&r=1 (accessed on 10 November 2018).
- Kupczynski, M. Bertrand’s paradox and Bell’s inequalities. Phys. Lett. A
**1987**, 121, 205–207. [Google Scholar] [CrossRef] - Clauser, J.F.; Horn, M.A. Experimental consequences of objective local theories. Phys. Rev. D
**1974**, 10, 526–535. [Google Scholar] [CrossRef] - Pearle, P.M. Hidden-variable example based upon data rejection. Phys. Rev. D
**1970**, 2, 1418–1425. [Google Scholar] [CrossRef] - Pascazio, S. Time and Bell–type inequalities. Phys. Lett. A
**1986**, 118, 47–53. [Google Scholar] [CrossRef] - Larsson, J.-A.; Gill, R.D. Bell’s inequality and the coincidence-time loophole. Europhys. Lett.
**2004**, 67, 707–713. [Google Scholar] [CrossRef] - Adenier, G.; Khrennikov, A.Y. Is the fair sampling assumption supported by EPR experiments? J. Phys. B At. Mol. Opt. Phys.
**2007**, 40, 131–141. [Google Scholar] [CrossRef] - Larsson, J.Å. Loopholes in Bell inequality tests of local realism. J. Phys. A Math. Theor.
**2014**, 47, 424003. [Google Scholar] [CrossRef] [Green Version] - Hess, K.; De Raedt, H.; Khrennikov, A. Special Issue: Ever New “Loopholes” in Bell’s Argument and Experimental Tests. Open Phys.
**2017**, 15, 572–576. [Google Scholar] [CrossRef] - De Raedt, H.; Michielsen, K.; Hess, K. The photon identification loophole in EPRB experiments: Computer models with single-wing selection. Open Phys.
**2017**, 15, 713–733. [Google Scholar] [CrossRef] - Kupczynski, M. Is Einsteinian no-signalling violated in Bell tests? Open Phys.
**2017**, 15, 739–753. [Google Scholar] [CrossRef] [Green Version] - Accardi, L. Topics in quantum probability. Phys. Rep.
**1981**, 77, 169–192. [Google Scholar] [CrossRef] [Green Version] - Accardi, L. Some loopholes to save quantum nonlocality. AIP Conf. Proc.
**2005**, 750, 1–20. [Google Scholar] [Green Version] - Accardi, L.; Uchiyama, S. Universality of the EPR-chameleon model. AIP Conf. Proc.
**2007**, 962, 15–27. [Google Scholar] [Green Version] - Aerts, D. A possible explanation for the probabilities of quantum mechanics. J. Math. Phys.
**1986**, 27, 202–209. [Google Scholar] [CrossRef] - Hess, K.; Philipp, W. A possible loophole in the theorem of Bell. Proc. Natl. Acad. Sci. USA
**2001**, 98, 14224–14227. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hess, K.; Philipp, W. A possible loophole in the Bell’s theorem and the problem of decidability between the views of Einstein and Bohr. Proc. Natl. Acad. Sci. USA
**2001**, 98, 14228–142233. [Google Scholar] [CrossRef] [PubMed] - Hess, K.; Philipp, W. Bell’s theorem: Critique of proofs with and without inequalities. AIP Conf. Proc.
**2005**, 750, 150–157. [Google Scholar] [Green Version] - Hess, K.; Michielsen, K.; De Raedt, H. Possible Experience: From Boole to Bell. Europhys. Lett.
**2009**, 87, 60007. [Google Scholar] [CrossRef] - Hess, K.; De Raedt, H.; Michielsen, K. Hidden assumptions in the derivation of the theorem of Bell. Phys. Scr.
**2012**, 2012, 014002. [Google Scholar] [CrossRef] - Hess, K. Einstein Was Right! Pan: Stanford, CA, USA, 2014. [Google Scholar]
- Hess, K. Bell’s Theorem and Instantaneous Influences at a Distance. J. Modern Phys.
**2018**, 9, 1573–1590. [Google Scholar] [CrossRef] - Khrennikov, A. Interpretation of Probability; VSP: Utrecht, The Netherlands, 1999. [Google Scholar]
- Khrennikov, A.Y.; Volovich, I.V. Quantum non-locality, EPR model and Bell’s theorem. In Proceedings of the 3rd International Sakharov Conference on Physics, Moscow, Russia, 24–29 June 2002; Semikhatov, A., Ed.; World Scientific: Singapore, 2003; pp. 260–267. [Google Scholar]
- Khrennikov, A. The principle of supplementarity: Contextual probabilistic viewpoint to complementarity, the interference of probabilities, and the incompatibility of variables in quantum mechanics. Found. Phys.
**2005**, 35, 1655–1693. [Google Scholar] [CrossRef] - Khrennikov, A.Y. Bell’s inequality: Nonlocality, “death of reality”, or incompatibility of random variables. AIP Conf. Proc.
**2007**, 962, 121–131. [Google Scholar] - Khrennikov, A.Y. Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables? Entropy
**2008**, 10, 19–32. [Google Scholar] [CrossRef] [Green Version] - Khrennikov, A.Y. Violation of Bell’s inequality and nonKolmogorovness. AIP Conf. Proc.
**2009**, 1101, 86–99. [Google Scholar] - Khrennikov, A.Y. Bell’s inequality: Physics meets probability. Inf. Sci.
**2009**, 179, 492–504. [Google Scholar] [CrossRef] - Khrennikov, A. Contextual Approach to Quantum Formalism; Springer: Dordrecht, The Netherlands, 2009. [Google Scholar]
- Khrennikov, A. Ubiquitous Quantum Structure; Springer: Berlin, Germany, 2010. [Google Scholar]
- Khrennikov, A.Y. After Bell. Fortschr. Phys.
**2017**, 65, 1600044. [Google Scholar] [CrossRef] - Khrennikov, A. Probability and Randomness: Quantum Versus Classical; Imperial College Press: London, UK, 2016. [Google Scholar]
- Kupczynski, M. On some new tests of completeness of quantum mechanics. Phys. Lett. A
**1986**, 116, 417–419. [Google Scholar] [CrossRef] - Kupczynski, M. Pitovsky model and complementarity. Phys. Lett. A
**1987**, 121, 51–53. [Google Scholar] [CrossRef] - Kupczynski, M. On the completeness of quantum mechanics. arXiv, 2002; arXiv:quant-ph/028061. [Google Scholar]
- Kupczynski, M. Entanglement and Bell inequalities. J. Russ. Laser Res.
**2005**, 26, 514–523. [Google Scholar] [CrossRef] - Kupczynski, M. Seventy years of the EPR paradox. AIP Conf. Proc.
**2006**, 861, 516–523. [Google Scholar] - Kupczynski, M. EPR paradox, locality and completeness of quantum mechanics. AIP Conf. Proc.
**2007**, 962, 274–285. [Google Scholar] - Kupczynski, M. Entanglement and quantum nonlocality demystified. AIP Conf. Proc.
**2012**, 1508, 253–264. [Google Scholar] - Kupczynski, M. On operational approach to entanglement and how to certify it. Int. J. Quantum Inf.
**2016**, 14, 1640003. [Google Scholar] [CrossRef] - Kupczynski, M. Causality and local determinism versus quantum nonlocality. J. Phys. Conf. Ser.
**2014**, 504, 012015. [Google Scholar] [CrossRef] [Green Version] - Kupczynski, M. EPR Paradox, Quantum Nonlocality and Physical Reality. J. Phys. Conf. Ser.
**2016**, 701, 012021. [Google Scholar] [CrossRef] - Kupczynski, M. Can we close the Bohr–Einstein quantum debate? Philos. Trans. R. Soc. A
**2017**, 375, 20160392. [Google Scholar] [CrossRef] [PubMed] [Green Version] - De Muynck, V.M.; De Baere, W.; Martens, H. Interpretations of quantum mechanics, joint measurement of incompatible observables and counterfactual definiteness. Found. Phys.
**1994**, 24, 1589–1664. [Google Scholar] [CrossRef] - Nieuwenhuizen, T.M. Where Bell went wrong. AIP Conf. Proc.
**2009**, 1101, 127–133. [Google Scholar] - Nieuwenhuizen, T.M. Is the contextuality loophole fatal for the derivation of Bell inequalities. Found. Phys.
**2011**, 41, 580–591. [Google Scholar] [CrossRef] - Nieuwenhuizen, T.M.; Kupczynski, M. The contextuality loophole is fatal for derivation of Bell inequalities: Reply to a Comment by I. Schmelzer. Found. Phys.
**2017**, 47, 316–319. [Google Scholar] [CrossRef] - De la Peńa, L.; Cetto, A.M.; Brody, T.A. On hidden variable theories and Bell’s inequality. Lett. Nuovo Cimento
**1972**, 5, 177–181. [Google Scholar] [CrossRef] - Pitovsky, I. Deterministic model of spin statistics. Phys. Rev. D
**1983**, 27, 2316–2326. [Google Scholar] [CrossRef] - Pitovsky, I. George Boole’s conditions of possible experience and the quantum puzzle. Br. J. Philos. Sci.
**1994**, 45, 95–125. [Google Scholar] [CrossRef] - De Raedt, H.; Hess, K.; Michielsen, K. Extended Boole-Bell inequalities applicable to Quantum Theory. J. Comput. Theor. Nanosci.
**2011**, 8, 1011–1039. [Google Scholar] [CrossRef] - Valdenebro, A. Assumptions underlying Bell’s inequalities. Eur. J. Phys.
**2002**, 23, 569–577. [Google Scholar] [CrossRef] - Żukowski, M.; Brukner, Č. Quantum non-locality—It ain’t necessarily so. J. Phys. A Math. Theor.
**2014**, 47, 424009. [Google Scholar] [CrossRef] - De Raedt, H.; De Raedt, K.; Michielsen, K.; Keimpema, K.; Miyashita, S. Event-based computer simulation model of Aspect-type experiments strictly satisfying Einstein’s locality conditions. J. Phys. Soc. Jpn.
**2007**, 76, 104005. [Google Scholar] [CrossRef] - De Raedt, H.; De Raedt, K.; Michielsen, K.; Keimpema, K.; Miyashita, S. Event-by-event simulation of quantum phenomena: Application to Einstein-Podolsky-Rosen-Bohm experiments. J. Comput. Theor. Nanosci.
**2007**, 4, 957–991. [Google Scholar] [CrossRef] - Zhao, S.; De Raedt, H.; Michielsen, K. Event-by-event simulation model of Einstein-Podolsky-Rosen-Bohm experiments. Found. Phys.
**2008**, 38, 322–347. [Google Scholar] [CrossRef] - De Raedt, H.; Michielsen, K.; Jin, F. Einstein-Podolsky-Rosen-Bohm laboratory experiments: Data analysis and simulation. AIP Conf. Proc.
**2012**, 1424, 55–66. [Google Scholar] - De Raedt, H.; Jin, F.; Michielsen, K. Data analysis of Einstein-Podolsky-Rosen-Bohm laboratory experiments. Proc. SPIE
**2013**, 8832, 88321N1. [Google Scholar] - Michielsen, K.; De Raedt, H. Event-based simulation of quantum physics experiments. Int. J. Mod. Phys. C
**2014**, 25, 1430003. [Google Scholar] [CrossRef] [Green Version] - De Raedt, H.; Michielsen, K.; Hess, K. The digital computer as a metaphor for the perfect laboratory experiment: Loophole-free Bell experiments. Comp. Phys. Comm.
**2016**, 209, 42–47. [Google Scholar] [CrossRef] - De Raedt, H.; Michielsen, K.; Hess, K. Irrelevance of Bell’s Theorem for experiments involving correlations in space and time: A specific loophole-free computer-example. Comput. Phys. Commun.
**2016**, 209, 42–47. [Google Scholar] [CrossRef] - Clauser, J.F.; Horn, M.A.; Shimony, A.; Holt, R.A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett.
**1969**, 23, 880–884. [Google Scholar] [CrossRef] - Clauser, J.F.; Shimony, A. Bell’s theorem: Experimental tests and implications. Rep. Prog. Phys.
**1978**, 41, 1881–1927. [Google Scholar] [CrossRef] - Gill, R.D. Statistics, Causality and Bell’s Theorem. Stat. Sci.
**2014**, 29, 512–528. [Google Scholar] [CrossRef] [Green Version] - Vongehr, S. Exploring inequality violations by classical hidden variables numerically. Ann. Phys.
**2014**, 339, 81–88. [Google Scholar] [CrossRef] - Eberhard, P.H. Background level and counter e_ciencies required for a loophole-free Einstein-Podolsky-Rosen experiment. Phys. Rev. A
**1993**, 47, R747–R750. [Google Scholar] [CrossRef] [PubMed] - Boole, G. On the theory of probabilities. Philos. Trans. R. Soc. Lond.
**1862**, 152, 225–252. [Google Scholar] [CrossRef] - Vorob’ev, N.N. Consistent families of measures and their extensions. Theory Probab. Appl.
**1962**, 7, 147–162. [Google Scholar] [CrossRef] - Wigner, E.P. On Hidden Variables and Quantum Mechanical Probabilities. Am. J. Phys.
**1970**, 38, 1005–1009. [Google Scholar] [CrossRef] - Dzhafarov, E.N.; Kujala, J.V. Selectivity in probabilistic causality: Where psychology runs into quantum physics. J. Math. Psychol.
**2012**, 56, 54–63. [Google Scholar] [CrossRef] [Green Version] - Dzhafarov, E.N.; Kujala, J.V. No-Forcing and No-Matching theorems for classical probability applied to quantum mechanics. Found. Phys.
**2014**, 44, 248–265. [Google Scholar] [CrossRef] - Aerts, D.; Sozzo, S.; Veloz, T. New fundamental evidence of non-classical structure in the combination of natural concepts. Philos. Trans. R. Soc. A
**2015**, 374, 20150095. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Kupczynski, M.; De Raedt, H. Breakdown of statistical inference from some random experiments. Comput. Phys. Commun.
**2016**, 200, 168–175. [Google Scholar] [CrossRef] [Green Version] - Kochen, S.; Specker, E.P. The problem of hidden variables in quantum mechanics. J. Math. Mech.
**1967**, 17, 59–87. [Google Scholar] [CrossRef] - Redhead, M. Incompleteness, Nonlocality, and Realism; Clarendon: Oxford, UK, 1987. [Google Scholar]
- Home, D. Conceptual Foundations of Quantum Physics; Plenum Press: New York, NY, USA, 1997. [Google Scholar]
- Mermin, N.D. Hidden variables and the two theorems of John Bell. Rev. Mod. Phys.
**1993**, 65, 803–815. [Google Scholar] [CrossRef] [Green Version] - Liang, Y.-C.; Spekkens, R.W.; Wiseman, H.M. Specker’s parable of the overprotective seer: A road to contextuality, nonlocality and complementarity. Phys. Rep.
**2011**, 506, 1–39. [Google Scholar] [CrossRef] - Khrennikov, A.Y. Classical probability model for Bell inequality. J. Phys. Conf. Ser.
**2014**, 504, 012019. [Google Scholar] [CrossRef] [Green Version] - Khrennikov, A.Y. CHSH inequality: Quantum probabilities as classical conditional probabilities. Found. Phys.
**2015**, 45, 711–725. [Google Scholar] [CrossRef] - Kupczynski, M. Is quantum theory predictably complete? Phys. Scr.
**2009**, 2009, 014005. [Google Scholar] [CrossRef] - Kupczynski, M. Time series, stochastic processes and completeness of quantum theory. AIP. Conf. Proc.
**2011**, 1327, 394–400. [Google Scholar] - Kupczynski, M. Quantum mechanics and modelling of physical reality. Phys. Scr.
**2018**, 93, 123001. [Google Scholar] [CrossRef] - Einstein, A. Physics and reality. J. Frankl. Inst.
**1936**, 221, 349–382. [Google Scholar] [CrossRef] - Schilpp, P.A. (Ed.) Albert Einstein: Philosopher–Scientist: The Library of Living Philosophers Volume VII; Open Court: La Salle, IL, USA, 1949. [Google Scholar]
- Agüero, M.B.; Hnilo, A.A.; Kovalsky, M.G.; Larotonda, M.A. Time stamping in EPRB experiments: Application on the test of non-ergodic theories. Eur. Phys. J. D
**2009**, 55, 705. [Google Scholar] [CrossRef] - Hnilo, A.A.; Kovalsky, M.G.; Santiago, G. Low dimension dynamics in EPRB experiment with random variable analyzers. Found. Phys.
**2007**, 37, 80–102. [Google Scholar] [CrossRef] - Kovalsky, M.; Hnilo, A.; Agüero, M.B. Kolmogorov complexity of sequences of random numbers generated in Bell’s experiments. arXiv, 2018; arXiv:1805.07161. [Google Scholar]
- Aspect, A. Viewpoint: Closing the Door on Einstein and Bohr’s Quantum Debate. Physics
**2016**, 8, 123. [Google Scholar] [CrossRef] - Jung, K. Violation of Bell’s inequality: Must the Einstein locality really be abandoned? J. Phys. Conf. Ser.
**2017**, 880, 012065. [Google Scholar] [CrossRef] [Green Version] - Lou, S.Y.; Huang, F. Alice-Bob physics: Coherent solutions of nonlocal KdV systems. Sci. Rep.
**2017**, 7, 869. [Google Scholar] [CrossRef] [PubMed] - Amelino-Camelia, G.; Matassa, M.; Mercati, F.; Rosati, G. Taming nonlocality in theories with Planck-scale deformed Lorentz symmetry. Phys. Rev. Lett.
**2011**, 106, 071301. [Google Scholar] [CrossRef] [PubMed] - Coleman, S.; Glashow, S.L. High-Energy Tests of Lorentz Invariance. Phys. Rev. D
**1999**, 59, 116008. [Google Scholar] [CrossRef] - Bi, X.-J.; Yin, P.-F.; Yu, Z.-H.; Yuan, Q. Constraints and tests of the OPERA superluminal neutrinos. Phys. Rev. Lett.
**2011**, 107, 241802. [Google Scholar] [CrossRef] [PubMed]

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Kupczynski, M.
Closing the Door on Quantum Nonlocality. *Entropy* **2018**, *20*, 877.
https://doi.org/10.3390/e20110877

**AMA Style**

Kupczynski M.
Closing the Door on Quantum Nonlocality. *Entropy*. 2018; 20(11):877.
https://doi.org/10.3390/e20110877

**Chicago/Turabian Style**

Kupczynski, Marian.
2018. "Closing the Door on Quantum Nonlocality" *Entropy* 20, no. 11: 877.
https://doi.org/10.3390/e20110877