Hardy's Setup and Elements of Reality

TL;DR

This paper revisits Hardy's argument on Lorentz-invariant elements of reality, analyzing their compatibility with quantum mechanics and exploring the use of light cones to define such elements, revealing nuanced inconsistencies.

Contribution

It provides a detailed analysis of Hardy's argument and investigates the conditions under which Lorentz-invariant elements of reality can be defined in quantum mechanics.

Findings

Hardy's argument suggests incompatibility of Lorentz-invariant elements of reality with quantum mechanics.

Using light cones, some Lorentz-invariant elements of reality can be defined, but they may not always multiply.

The paradoxes in Hardy's experiment can be better understood through these considerations.

Abstract

Several arguments have been proposed some years ago, attempting to prove the impossibility of defining Lorentz-invariant elements of reality. Here I revisit that question, and bring a number of additional considerations to it. I will first analyze Hardy's argument, which was meant to show that Lorentz-invariant elements of reality are indeed inconsistent with quantum mechanics. I will then investigate to what extent the light cone associated with an event can be used to define Lorentz-invariant elements of reality. It turns out to be possible, but elements of reality associated with a product of two commuting operators will not always be equal to the product of elements of reality associated with each operator. I will finally examine a number of ways in which the paradoxical features of Hardy's experiment can be better understood.