Abstract
At the end of Chap. 3 we mentioned Einstein’s revolt against the probabilistic aspect of quantum mechanics and the uncertainty relations. As we said, Einstein was worried about two aspects. One is the notion of a complete description of reality. He thought that a complete description is possible in principle, and that the probabilistic description is simply easier to handle. The other aspect is the notion of determinism: same causes produce same effects.
The way of paradoxes is the way of truth.
To test Reality we must see it on the tight-rope.
When the Verities become acrobats, we can judge them.
Oscar Wilde, The portrait of Dorian Gray
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Notes
- 1.
“Die Theorie liefert viel, aber dem Geheimnis des Alten bringt sie uns kaum näder. Jedenfalls bin ich überzeugt, dass Der nicht würfelt.”
- 2.
Again, Einstein never used that word.
- 3.
A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777 (1935).
- 4.
In the present context, locality means that some action at a point in space can have a detectable effect only at some other point in space within the light cone of that action. At a distance r, one must wait for a time at least equal to r / c in order to observe such an effect, it cannot be immediate.
- 5.
Bohm, D. (1951). Quantum Theory, Prentice-Hall, Englewood Cliffs, page 29, and Chap. 5 Sect. 3, and Chap. 22 Sect. 19.
- 6.
One can check that this formulation does not allow the instantaneous transmission of information. In order to see the correlations with Alice’s result, Bob must ask Alice what her result is, and the corresponding information travels (at most) at the velocity of light.
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J.S. Bell, Physics 1, 195 (1964).
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J.F. Clauser, M.A. Horne, A. Shimony, and R.A. Holt, Phys. Rev. Lett. 23, 880 (1969).
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S.J. Freedman, J.F. Clauser (1972), “Experimental test of local hidden-variable theories”, Phys. Rev. Lett. 28 (938): 938–941.
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E.S. Fry and R.C. Thompson (1976) Phys. Rev. Lett. 37, 465.
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Albert Messiah actually used the term “undrinkable”, which is much stronger than unbearable for a Frenchman.
- 13.
D.M. Greenberger, M. Horne, and A. Zeilinger, in Bells Theorem, Quantum Theory, and Conceptions of the Universe, edited by M. Kafatos, (Kluwer, Dordrecht, 1989); D.M. Greenberger, M.A. Horne, A. Shimony, and A. Zeilinger, Bell’s theorem without inequalities, Am. J. Phys. \(\mathbf 58\), 1131 (1990); N.D. Mermin, Phys. Today \(\mathbf 43\) (6),9 (1990).
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Jian-wei Pan and Anton Zeilinger, Greenberger-Horne-Zeilinger-state analyzer, Phys. Rev. 57 (3), 1998.
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Jian-Wei Pan, D. Bouwmeester, M. Daniell, H. Weinfurter and A. Zeilinger (2000). “Experimental test of quantum nonlocality in three photon GHZ entanglement”. Nature 403 (6769): 515–519; Jian-Wei Pan and Anton Zeilinger, (2002) Multi-Photon Entanglement and Quantum Non-Locality https://vcq.quantum.at/fileadmin/Publications/2002-12.pdf.
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Frank Wilczek, Entanglement made simple, Quanta Magazine, April 28, 2016.
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Herbert J. Bernstein,Simple Version of the Greenberger-Horne-Zeilinger (GHZ) Argument Against Local Realism, Foundations of Physics 29 (4):521–525 (1999).
- 18.
I am deeply gratefull to James Rich for explaining to me the whole issue, and I reproduce his presentation.
- 19.
W.K. Wooters and W.H. Zurek, Nature 299, 802 (1982).
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Peter Shor Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM Journal on Computing 26 (1997), 1484–1509.
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Basdevant, JL. (2016). Entangled States. The Way of Paradoxes. In: Lectures on Quantum Mechanics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-43479-7_17
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