Abstract
We have accumulated enough theoretical material to tackle some aspects of an important and intriguing issue regarding the theoretical interpretation of the quantum realm.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
These sets of observables S represent the most classical structures one may extract form the whole set of observables of a quantum system. The fact that these structures are distinct and physically incompatible is one manifestation of Bohr’s complementarity principle.
- 2.
For instance, if aσ x ⊗ I + bI ⊗ σ x + cσ x ⊗ σ x = 0, multiplying by σ a ⊗ I or I ⊗ σ a and computing the partial trace gives a = b = c = 0 easily, because tr(σ a) = 0, tr(σ a σ b) = 2δ ab.
- 3.
A more complete model would include the state’s skew-symmetry (the electrons may be swapped), but we shall disregard details such as this one. When dealing with photons the spin must be replaced by the polarization, which is still described on \({\mathbb C}^2\), and the positions x i by the momenta k i; in this case the state must be symmetric when swapping the photons.
- 4.
The original paper of Bell [Bel64] presented a slightly less general inequality.
- 5.
The author is grateful to S.Mazzucchi for many clarifications and discussions on subtleties related to the content of this section.
References
V. D’Ambrosio, I. Herbauts, E. Amselem, E. Nagali, M. Bourennane, F. Sciarrinoi, A. Cabello, Experimental implementation of a Khochen-Specker set of quantum tests. Phys. Rev. X 3, 011012 (2013)
E.G. Beltrametti, G. Cassinelli, The Logic of Quantum Mechanics. Encyclopedia of Mathematics and Its Applications, vol. 15 (Addison-Wesley, Reading, 1981)
R. Bertlmann, A. Zeilinger (eds.), Quantum [Un]Speakables II. Half a Century of Bell’s Theorem (Springer, Cham, 2017)
J.S. Bell, On the Einstein Podolski Rosen paradox. Physics 1, 195–200 (1964)
J.S. Bell, On the problem of hidden variables in quantum mechanics. Rev. Mod. Phys. 38, 447–452 (1966)
J.S. Bell, The theory of local beables (1974) in Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987)
H. Bartosik, J. Klepp, C. Schmitzer, S. Sponar, A. Cabello, H. Rauch, Y. Hasegawa, Experimental test of quantum contextuality in neutron interferometry. Phys. Rev. Lett. 103, 040403 (2009)
A. Cabello, How many questions do you need to prove that unasked questions have no answers? Int. J. Quantum Inf. 04, 55 (2006)
D. Dürr, S. Teufel, Bohmian Mechanics (Springer, Heidelberg, 2009)
A. Einstein, B. Podolsky, N. Rosen, Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)
J.C. Garrison, R.Y. Chiao, Quantum Optics (Oxford University Press, Oxford, 2008)
G. Ghirardi, Sneaking a Look at God’s Cards: Unraveling the Mysteries of Quantum Mechanics, 25 Mar 2007, rev. edn. (Princeton University Press, Princeton, 2007)
R. Hanson et al., Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015)
Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, H. Rauch, Quantum contextuality in a single-neutron optical experiment. Phys. Rev. Lett. 97, 230401 (2006)
Y.-F. Huang, C.-F. Li, Y.-S. Zhang, J.-W. Pan, G.-C. Guo, Realization of all-or-nothing-type Kochen-Specker experiment with single photons. Phys. Rev. Lett. 90, 250401 (2003)
J.P. Jarret, On the physical significance of the locality conditions in the Bell arguments. Nous 18(4), 569–589 (1984), Special Issue on the Foundations of Quantum Mechanics
G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, C.F. Roos, State-independent experimental test of quantum contextuality. Nature 460, 494 (2009)
S. Kochen, E. Specker, The problem of hidden variables in quantum mechanics. J. Math. Mech. 17, 59–87 (1967)
K. Landsman, Foundations of Quantum Theory (Springer, New York, 2017)
N.D. Mermin, Simple unified form for no-hidden-variables theorems. Phys. Rev. Lett. 65, 3373–3376 (1990)
M. Michler, H. Weinfurter, M. Zukowski, Experiments towards falsification of noncontextual hidden variable theories. Phys. Rev. Lett. 84, 5457 (2000)
A. Peres, Incompatible results of quantum measurements. Phys. Lett. A 151, 107–108 (1990)
M. Redéi, Quantum Logic in Algebraic Approach (Kluwer Academic Publishers, Dordrecht, 1998)
The Stanford Encyclopedia of Philosophy http://plato.stanford.edu/
A. Shimony, in 62 Years of Uncertainty, ed. by A.I. Miller (Plenum Press, New York, 1990), p. 33
B.S. Tsirelson, Quantum Generalizations of Bell’s Inequality. Lett. Math. Phys. 4, 93 (1980)
R. Tumulka, Bohmian Mechanics, in The Routledge Companion to the Philosophy of Physics, ed. by E. Knox, A. Wilson (Routledge, New York, 2018)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Moretti, V. (2019). Realism, Non-Contextuality, Local Causality, Entanglement. In: Fundamental Mathematical Structures of Quantum Theory. Springer, Cham. https://doi.org/10.1007/978-3-030-18346-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-18346-2_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-18345-5
Online ISBN: 978-3-030-18346-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)