Logical inconsistencies in quantum mechanics

TL;DR

This paper argues that the application of Vaidman's weak measurement scheme in quantum mechanics can lead to logical inconsistencies, questioning the fundamental coherence of quantum theory.

Contribution

It demonstrates that weak measurement techniques may produce contradictions within quantum mechanics, challenging the theory's internal consistency.

Findings

Weak values of projection operators can lead to logical contradictions.

Weak measurements do not collapse the wave function, yet produce inconsistent readings.

The inconsistency arises from applying weak measurement schemes to quantum systems.

Abstract

I show that the application of the quantum-mechanical (QM) which-way weak measurement scheme of Vaidman may lead to logical inconsistencies. To this end, I study weak values of projection operators. Weak values are (normalized) amplitudes, operationally defined by a weak measurement followed by postselection. Projector weak values have a direct physical significance. This allows formulating an inconsistency in classical terms, viz., the contradiction in the readings of several measuring devices. To arrive at the contradiction, I also invoke the property of weak measurements not to collapse the wave function but to leave the state of the system unchanged (to lowest order in the weak measurement strength). My arguments rely entirely on basic QM rules plus commonly accepted weak QM measurement approximations. Therefore, the inconsistency challenges QM as such.