Quantum entanglement and emergence of the classical Leibnitz’s principle of the identity of indiscernibles, Marek Kuś
Treating classical mechanics as an emergent theory (with quantum mechanics as the basic one), we may enumerate several elements that could be treated as “emergent”. In quantum mechanics, thus, some “elements of reality” do not exist. In general these are properties that can be revealed only in measurements of physical quantities such as position, momentum, angular momentum, etc.. An assumption that particular values of such quantities “are carried” by physical objects during their evolution, or that they “exist in a system” prior to a measurement leads to a contradiction. On the other hand, they are well defined in classical worlds and one can safely assume that they exist in a system independently of any measurements. In a similar vein, on the quantum level completely indiscernible particles (seem to) violate the Leibniz’s Principle of the Identity of Indiscernibles, that emerges on the classical level. By introducing an operational measure of the effective indistinguishability exhibited in a measurement process, we will show how the “emergent phenomenon” of Leibniz’s Principle and its dependence on purely quantum phenomenon of entanglement can be quantified.
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