Wigner's Friend Depends on Self-Contradictory Quantum Amplification

Abstract

In a recent paper, \.Zukowski and Markiewicz showed that Wigner's Friend (and, by extension, Schr\"odinger's Cat) can be eliminated as physical possibilities on purely logical grounds. I validate this result and demonstrate the source of the contradiction in a simple experiment in which a scientist S attempts to measure the position of object $|O\rangle = |A\rangle_S + |B\rangle_S$ by using measuring device M chosen so that $|A\rangle_M \approx |A\rangle_S$ and $|B\rangle_M \approx |B\rangle_S$. I assume that the measurement occurs by quantum amplification without collapse, in which M can entangle with O in a way that remains reversible by S for some nonzero time period. This assumption implies that during this "reversible" time period, $|A\rangle_M \neq |A\rangle_S$ and $|B\rangle_M \neq |B\rangle_S$ -- i.e., the macroscopic pointer state to which M evolves is uncorrelated to the position of O relative to S. When the scientist finally observes the measuring device, its macroscopic pointer state is uncorrelated to the object in position $|A\rangle_S$ or $|B\rangle_S$, rendering the notion of "reversible measurement" a logical contradiction.