Predictive approach to some quantum paradoxes

TL;DR

This paper explores how classical prediction concepts extend to quantum mechanics, showing that using non-commutative conditional expectation can resolve some quantum paradoxes.

Contribution

It introduces a quantum analogue of classical prediction theory, demonstrating how non-commutative conditional expectation can mitigate quantum paradoxes.

Findings

Non-commutative conditional expectation aligns quantum predictions with classical intuition.

Applying this approach reduces the occurrence of quantum paradoxes.

The framework offers a new perspective on quantum measurement and prediction.

Abstract

In classical probability theory, the best predictor of a future observation of a random variable $X,$ is its expected value $E_P[X]$ when no other information is available When information consisting in the observation of another random variable $Y$ is available, then the best predictor of $X$ is another random variable $E_P[X|Y].$ It is the purpose of this note to explore the analogue of this in the case of quantum mechanics. We shall see that exactly as in classical prediction theory, when the result of an observation is taken into account by means of a non-commutative conditional expectation, some of the usual paradoxes cease to be such.