# Delayed choice experiments and causality in quantum mechanics

## TL;DR

This paper analyzes delayed choice experiments in quantum mechanics, demonstrating that they do not violate causality when interpreted through the Many-Worlds view, and explores the relationship between interference, correlations, and the nature of objective reality.

## Contribution

It provides a mathematical framework linking which-path information, interference, and correlations, and clarifies the role of observers in quantum measurement, addressing the measurement problem.

## Key findings

- Delayed choice experiments do not contradict causality under Many-Worlds interpretation.
- Interference and correlation are complementary phenomena in quantum systems.
- There is no objective reality in the Einstein-Podolsky-Rosen sense.

## Abstract

Although it may seem The Delayed Choice experiments contradict causality and one could construct an experiment which could possibly affect the past, using Many World interpretation we prove it is not possible. We also find a mathematical background to Which-path information and show why its obtainability prevents system from interfering. We find a system which exhibit both interference and correlation and show why one-particle interference and correlations are complementary. Better visible interference pattern leads to worse correlations and vice versa. Then, using knowledge gained from Quantum Eraser and Delayed Choice experiments we prove there is not an objective reality in a sense of Einstein, Podolsky and Rosen. Furthermore, we discuss the difference between ``outer'' (non-interacting) and ``inner'' (interacting) observer. We find the mathematical relationship between the ``universal'' wave function used by ``outer'' observer and processes the ``inner'' observer sees, which is our small contribution to the measurement problem.