Quantum measurement theory for particle oscillations

TL;DR

This paper develops a quantum measurement framework for particle oscillations, emphasizing summation over amplitudes for different detection times, leading to a modified oscillation wavelength and new dependence on decay thresholds.

Contribution

It introduces a novel quantum measurement approach for particle oscillations that challenges standard probability summation, resulting in a different oscillation wavelength and detection dependence.

Findings

Oscillation wavelength differs by a factor of two from standard predictions.

Detection probability involves summation over amplitudes, not probabilities.

Oscillation wavelength depends on decay process thresholds.

Abstract

A fundamental principle of quantum theory, clearly manifested in the two-slit experiment, is that for any alternatives that cannot be distinguished by measurement physical predictions are obtained by summation of their amplitudes. In particle oscillation experiments, a particle's time of detection is not directly measured, consequently, the detection probability should involve the summation over amplitudes corresponding to different detection times. However, in contrast to the principle above, standard treatments involve summation over probabilities rather than amplitudes; this implicitly assumes the existence of a decohering mechanism. In this work, we construct the detection probabilities for particle oscillations by summation over amplitudes, corresponding to different detection times. The resulting wavelength of particle oscillations differs from the standard expression by a factor of two. Moreover, we predict a dependence of the oscillation wavelength on the threshold of the decay process used for detection.