On the spatial coordinate measurement of two identical particles

TL;DR

This paper investigates how the measurement of two identical particles' positions depends on the shrinking dimensions of detectors, revealing that certain properties like boson bunching are not well-defined and highlighting measurement interpretation issues.

Contribution

It demonstrates that the outcome of coordinate measurements for identical particles depends on the shrinking ratio of detector dimensions, challenging existing assumptions.

Findings

Detection ratios depend on the ratio of detector width to separation.

Boson bunching parameter is not a well-defined physical property.

Highlights difficulties in quantum measurement interpretation.

Abstract

Theoretically, the coordinate measurement of two identical particles at a point by two narrowly separated narrow detectors, is interpreted in the limit of shrinking width and separation, as the detection of two particles by a single narrow detector. { Ordinarily, the ratio between probabilities of point measurements is independent of the width of the narrow detectors.} We show here that not only this is not the case, but that in some scenarios the results depend on the way the dimensions shrink to zero. The ratio between the width and the separation determines the detection result. { In particular, it is shown that the bunching parameter of bosons is not a well-defined physical property. Moreover, it may suggests that } there is a difficulty in quantum measurement theory in the interpretation of coordinate measurement of two particles.