Entropy and Temperature from Entangled Space and Time

TL;DR

This paper explores the relationship between entropy, temperature, and entanglement in coupled oscillators, applying these concepts to quantum systems like entangled photons and moving hadrons, revealing phase transition insights.

Contribution

It introduces a framework connecting entanglement, temperature, and phase transitions in quantum bound states and high-speed particles.

Findings

Entanglement affects the observed temperature in quantum systems.

The quark-to-parton transition can be viewed as a phase transition.

Time-like entanglement influences the behavior of rapidly moving hadrons.

Abstract

Two coupled oscillators provide a mathematical instrument for solving many problems in modern physics, including squeezed states of light and Lorentz transformations of quantum bound states. The concept of entanglement can also be studied within this mathematical framework. For the system of two entangled photons, it is of interest to study what happens to the remaining photon if the other photon is not observed. It is pointed out that this problem is an issue of Feynman's rest of the universe. For quantum bound-state problems, it is pointed out the longitudinal and time-like coordinates become entangled when the system becomes boosted. Since time-like oscillations are not observed, the problem is exactly like the two-photon system where one of the photons is not observed. While the hadron is a quantum bound state of quarks, it appears quite differently when it moves rapidly than when it moves slowly. For slow hadrons, Gell-Mann's quark model is applicable, while Feynman's parton model is applicable to hadrons with their speeds close to that of light. While observing the temperature dependence of the speed, it is possible to explain the quark-to-parton transition as a phase transition.