The Leggett-Garg inequality and Page-Wootters mechanism

Abstract

Violation of the Leggett-Garg inequality (LGI) implies quantum phenomena. In this light we establish that Moreva et al.'s (Phys. Rev. A, 89 (2014) 052122) experiment demonstrating Page-Wootters' mechanism (Page D. N. and Wootters W. K., Phys. Rev. D, 27 (1983) 2885; Wootters W. K., Int. J. Theor. Phys., 23 (1984) 701). falls in the quantum domain. An observer outside a 2-photons world does not detect any change in the 2-photons state, i.e., there is no time parameter for the outside observer. But an observer attached to one of the photons sees the other photon evolving and this means that there is an “internal” time. The LGI is violated for the clock photon whose state evolves with the internal time as measured by the system photon. Conditional probabilities in this 2-photons system are computed for both sharp and unsharp measurements. The conditional probability increases for entangled states as obtained by Page and Wootters for both ideal and also unsharp measurements.