Abstract
What is the true meaning of quantum superposition? Can a particle genuinely reside in several places simultaneously? These questions lie at the heart of this paper which presents an updated survey of some important stages in the evolution of the three-boxes paradox, as well as novel conclusions drawn from it. We begin with the original thought experiment of Aharonov and Vaidman, and proceed to its non-counterfactual version. The latter was recently realized by Okamoto and Takeuchi using a quantum router. We then outline a dynamic version of this experiment, where a particle is shown to “disappear” and “re-appear” during the time evolution of the system. This surprising prediction based on self-cancellation of weak values is directly related to our notion of Quantum Oblivion. Finally, we present the non-counterfactual version of this disappearing-reappearing experiment. Within the near future, this last version of the experiment is likely to be realized in the lab, proving the existence of exotic hitherto unknown forms of superposition. With the aid of Bell’s theorem, we prove the inherent nonlocality and nontemporality underlying such pre- and post-selected systems, rendering anomalous weak values ontologically real.
Highlights
In a famous letter Einstein has replied to a bewildered letter from Louis de Broglie's PhD advisor
Came de Broglie and proposed that electrons and all other particles were waves
In terms of Two-State Vector Formalism (TSVF) [15,16,17], this unique pair of happening and unhappening can be decomposed into a sum of selfcancelling weak values [18]. This mechanism has been shown to be ubiquitous in the quantum realm [13, 18], but here we can straightforwardly see its dynamics in action – the disappearance of a particle that should have resided in the first or second box, but eventually did not, is understood through the null weak value in these boxes which is a sum of earlier +1 and -1 weak values
Summary
In a famous letter Einstein has replied to a bewildered letter from Louis de Broglie's PhD advisor. As long as not measured, resides it several locations or states. It is (strongly) measured, i.e. post-selected, and found at the state:
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