# Life in the Rindler Reference Frame: Does an Uniformly Accelerated Charge Radiates? Is there a Bell `Paradox'? Is Unruh Effect Real?

## TL;DR

This paper examines the electromagnetic radiation of an accelerated charge, critiques alternative solutions claiming no radiation, and questions the reality of the Unruh effect, highlighting unresolved issues in quantum field theory and the equivalence principle.

## Contribution

It refutes Turakulov's non-radiating solution, analyzes implications for the equivalence principle, and challenges the existence of the Unruh effect based on rigorous mathematical considerations.

## Key findings

- Lie9nard-Wiechert solution confirms radiation from accelerated charge
- Turakulov's solution claiming no radiation is proven incorrect
- Standard derivation of the Unruh effect is not mathematically rigorous

## Abstract

The determination of the electromagnetic field generated by a charge in hyperbolic motion is a classical problem for which the majority view is that the Li\'enard-Wiechert solution which implies that the charge radiates) is the correct one. However we analyze in this paper a less known solution due to Turakulov that differs from the Li\'enard-Wiechert one and which according to him does not radiate. We prove his conclusion to be wrong. We analyze the implications of both solutions concerning the validity of the Equivalence Principle. We analyze also two other issues related to hyperbolic motion, the so-called Bell's "paradox" which is as yet source of misunderstandings and the Unruh effect, which according to its standard derivation in the majority of the texts, is a correct prediction of quantum field theory. We recall that the standard derivation of the Unruh effect does not resist any tentative of any rigorous mathematical investigation, in particular the one based in the algebraic approach to field theory which we also recall. These results make us to align with some researchers that also conclude that the Unruh effect does not exist.