Faster-Than-Light Solitons in 1 + 1 Dimensions

TL;DR

This paper demonstrates that in 1+1 dimensional classical relativistic field theories, stable faster-than-light soliton solutions can exist, challenging traditional notions of causality and relativity.

Contribution

The paper introduces two extended Klein-Gordon models that admit stable faster-than-light soliton solutions, expanding the understanding of relativistic field theories.

Findings

Existence of stable faster-than-light solitons in 1+1 dimensions

Two models with zero-energy and nonzero-energy solutions

Challenges to conventional causality principles

Abstract

The existence of a faster-than-light particle is in direct opposition to Einstein's relativity and the principle of causality. However, we show that the theory of classical relativistic fields is not inherently inconsistent with the existence of the faster-than-light particle-like soliton solutions in $1+1$ dimensions. We introduce two extended KG models ($k$-fields) that lead to a zero-energy and a nonzero-energy stable particle-like solution with faster-than light speeds, respectively.