On the measurements regarding random observables

TL;DR

This paper proposes a unified model for classical and quantum observables as random variables, showing that measurements alter probabilistic weights while preserving spectra, challenging the view that classical and quantum measurements must be fundamentally different.

Contribution

It introduces a model that treats classical and quantum measurements uniformly, providing theoretical estimates for errors in mean values and fluctuations.

Findings

Measurements preserve observable spectra but alter probabilities.

The model offers estimations for measurement errors in mean and fluctuations.

Challenges the view that classical and quantum measurement theories are entirely distinct.

Abstract

Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding probabilistic weights (probability density or respectively the wave function). Such a model ensures theoretical estimations for predicted errors specific to the mean values as well as to the fluctuations of both types of observables. The model stands out of ourdays prevalent opinion that measurement theories must be depicted in entirely different manners in the classical respectively quantum cases.