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The Free Will Theorem (Russian Version)

J. Conway, Simon Kochen

Published Jul 1, 2018• 0 citations
OpenAlex

Abstract

On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications.

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•Mar 27, 2016•0 citations
On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications.
I begin with description of quantum entanglement and its relevance to the EPR-type experiments, which played a decisive role in rejecting determinism and hidden-variable theories. Thereby I prove the closely-related Kochen-Specker paradox, on which also the main object of my paper, the recently published Conway and Kochen’s Free Will Theorem, is founded. It is being shown there, on the basis of three physical axioms, following from the special theory of relativity and quantum mechanics, that if the choice for a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. Therefor the response of the particles can be seen as free. In conclusion I mention some critical remarks on the theorem, expressed in subsequent responses to the original article.
Here we present an experiment which, firstly, demonstrates single-particle contextuality on the particles in one laboratory. Then, since our particles have been previously entangled with other particles in a distant laboratory, we can also reveal the EPR correlations between both laboratories. Interestingly, even though the correlations in the first laboratory can be explained by LHV theories, and the EPR correlations between the two laboratories can be explained by LHV theories, we show that there is no LHV theory explaining both of them. Our experiment is a test of the free will theorem since it implements the conditions under which axiom (i) applies, then checks axioms (ii) and (iii), and finally reveals an extreme violation of the predictions of theories in which elementary particles have no free will.
The experimental violation of the Bell inequality establishes necessary but not sufficient conditions that any theory must obey. Namely, a theory compatible with the experimental observations can satisfy at most two of the three hypotheses at the basis of Bell's theorem: free will, no signaling, and outcome independence. Quantum mechanics satisfies the first two hypotheses but not the latter. Experiments not only violate the Bell inequality, but show an excellent agreement with quantum mechanics. This fact restricts further the class of admissible theories. In this work, the author determines the form of the hidden-variable models that reproduce the quantum mechanical predictions for a spin singlet while satisfying both the hypotheses of free will and no signaling. Two classes of hidden-variable models are given as an example, and a general recipe to build infinitely many possible models is provided.
Quantum mechanics is an immensely successful theory, occupying a unique position in the history of science. It has solved mysteries ranging from macroscopic superconductivity to the microscopic theory of elementary particles and has provided deep insights into the nature of vacuum on the one hand and the description of the nucleon on the other. Whole new fields such as quantum optics and quantum electronics owe their very existence to this body of knowledge. However, despite the stunning successes of quantum mechanics, there is no general agreement on the conceptual foundations and interpretation of the subject. The theory provides unambiguous information about the outcome of a measurement of a physical object. However, many feel that it does not provide a satisfactory answer to the nature of the “reality” we should attribute to the physical objects between the acts of measurement. The conceptual difficulty comes about because the wave function |ψ〉 is usually given by a coherent superposition of various distinguishable experimental outcomes. If we denote the collection of states that represent the possible outcomes of an experiment by |ψ j 〉, then |ψ〉 = ∑ j c j |ψ j 〉 where c j = 〈ψ j |ψ〉. The probability of the outcome |ψ j 〉 is P j =|c j | 2 . In the process of measurement, the so called collapse of the wave function takes place and a single, definite state |ψ i 〉 of the physical object is chosen. The difficulty comes about in the interpretation of the mechanism by which this definite state is chosen from amongst all the possible outcomes.
The free will theorem states that if experimenters have free will in the sense that their choices are not a function of the past, so must some elementary particles. The theorem goes beyond Bell's theorem as it connects the two fundamental resources behind quantum technologies: single-particle contextuality, which supplies the power for quantum computation, and two-particle non-locality, which allows for quantum secure communication. The theorem relies on three axioms: (i) There is a maximum speed for propagation of information, (ii) single particles can exhibit contextuality, (iii) two separated particles can exhibit Einstein-Podolsky-Rosen (EPR) correlations. Here we report the first experimental test of the free will theorem. We used pairs of hyper-entangled photons entangled in path and polarization and enforced the conditions for invoking axiom (i) by measuring each photon in a different laboratory. We certified axiom (ii) by testing the violation of the Peres-Mermin non-contextuality inequality and axiom (iii) by showing EPR correlations between the two laboratories. The three axioms imply an upper bound on the sum of the correlations among the outcomes of sequential measurements in the same laboratory and the correlations between the outcomes in both laboratories. We observed a violation of this bound by more than 66 standard deviations. This reveals that quantum non-locality can be produced when single-particle contextuality is combined with correlations which are not non-local by themselves. Our results demonstrate the resources needed for quantum computation and quantum secure communication simultaneously in the same experiment and open the door to quantum machines that efficiently achieve both tasks.