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Can Relativity be Considered Complete? From Newtonian Nonlocality to Quantum Nonlocality and Beyond

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The Message of Quantum Science

Part of the book series: Lecture Notes in Physics ((LNP,volume 899))

Abstract

We review the long history of nonlocality in physics with special emphasis on the conceptual breakthroughs over the last few years. (This was written at the end of Einstein’s year 2005, after Jürg Fröhlich invited me to talk at the Annus Mirabilis Symposium he organized et the ETH Zürich. I merely added a few relevant recent references.) Nowadays, for the first time, it is possible to study “nonlocality without signaling” from the outside, that is without all the quantum physics Hilbert space artillery. We emphasize that physics has always given a nonlocal description of Nature, except during a short 10 years gap, about from 1915 to 1925. We note that the very concept of “nonlocality without signaling” is totally foreign to the spirit of relativity, the only strictly local theory.

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Notes

  1. 1.

    Using a small rocket, so as to displace the center of mass of the moon.

  2. 2.

    My friends know well that in my mouth “engineer” has no negative connotation, quite the opposite. For me, a physicist must be a good theorist and a good engineer! Well, I warned you, dear reader, this is a somewhat subjective article.

  3. 3.

    Another story happened to me while I was a young post-doc eager to publish some work. In a paper [8] I wrote “A quantum particle may disappear from a location A and simultaneously reappear in B, without any flow in-between”. The referee accepted the paper under the condition that this outrageous sentence is removed. This referee considered his paternalist attitude so constructive that he declared himself to me: “look how helpful I am to you” (admittedly, he was politically correct).

  4. 4.

    Somewhat surprisingly, if there are only two possible questions, then there is a strategy such that the probability that both players succeed is 50 %.

  5. 5.

    Admittedly, the danger is that both student get the bad mark! But, on average, the poor student improves.

  6. 6.

    I wish someone establishes the statistics of the occurrences of the words “Bell inequality” and “nonlocality” in Physical Review Letters. I bet that a phase transition happen in the early 1990s, after Ekert’s paper on quantum cryptography, see [16]. In 1998 I started a PRL with the sentence [11]: “Quantum theory is nonlocal.” and got considerable reactions to what was felt as a provocative statement; today the same statement can be found in many papers, not provoking any reaction.

  7. 7.

    The conclusion that follows from all these experiments is so important for the physicist’s world-view, that an experiment closing simultaneously both the locality and the detection loophole is greatly needed.

  8. 8.

    A “machine” is a physicists’s terminology for an input-output black-box that is not necessarily mechanical. I believe that this terminology appeared in the quantum physics context with the “optimal cloning machines” introduced by Bužek and Hillery [58].

  9. 9.

    Actually, there are at least three different concepts behind this word [62]. (1) There is the mathematical definition given here. (2) No faster than light communication—though light plays no special role in quantum physics. And (3), there is no-signalling as Newton thought of it: no communication without a physical carrier of the information.

  10. 10.

    More precisely, 8 is the dimension of the space of non-signaling correlations [63].

  11. 11.

    No-signaling should be understood here as in the previous sub-section on the no-cloning theorem. That is, even if two parties joint, for example Eve and Bob come together, then they should not be able to infer any information about the third party’s input, e.g. Eve and Bob should not have access no Alice’s input.

  12. 12.

    One may think that Eve should sometimes send a weakly non-local machine. But all such correlations are convex combinations of local and fully non-local NL-machines. Hence, it is equivalent for Eve to always send either a local or a NL-machine, with appropriate probabilities.

  13. 13.

    In [59] we proved that a correlation P(a, b | x, y) is nonlocal iff any possible non-signaling extensions P(a, b, e | x, y, z) has positive Alice–Bob condition mutual information, conditioned on Eve, I(A, B | E), i.e. has positive intrinsic information. This nicely complements the similar result that holds for entangled quantum states and purifications [69]. In [65] we proved that the same relation between nonlocality and positive intrinsic information does also hold when Alice announces her input and Bob adapts his output in such a way as to maximize his mutual information with Alice. Proving this in full generality would be a marvelous result.

  14. 14.

    Precisely one has: I 0(B, E) = 2 ⋅ QBER 1 and I 1(B, E) = 2 ⋅ QBER 0.

  15. 15.

    Using the reduction of an OT-box (Oblivious Transfer to a PR-box) [84] one can simulate any 2-qubit state with one OT-box.

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Acknowledgements

This article has been inspired by talks I gave in 2005 at the IOP conference on Einstein in Warwick, the QUPON conference in Vienna, the Annus Mirabilis Symposium in Zurich, le séminaire de l’Observatoire de Paris and the Ehrenfest Colloquium in Leiden. This work has been supported by the EC under projects RESQ and QAP (contract n. IST-2001-37559 and IST-015848) and by the Swiss NCCR Quantum Science and Technology.

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  1. Group of Applied Physics, University of Geneva, 1211, Geneva 4, Switzerland

    Nicolas Gisin

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  1. Fakultät für Physik, Universität Bielefeld, Bielefeld, Germany

    Philippe Blanchard

  2. Institute for Theoretical Physics, ETH Zürich, Zürich, Switzerland

    Jürg Fröhlich

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Gisin, N. (2015). Can Relativity be Considered Complete? From Newtonian Nonlocality to Quantum Nonlocality and Beyond. In: Blanchard, P., Fröhlich, J. (eds) The Message of Quantum Science. Lecture Notes in Physics, vol 899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46422-9_8

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