The Possibility of Tachyons as Soliton Solutions in 3+1 Dimensions via k-field Models

TL;DR

This paper explores the theoretical possibility of faster-than-light soliton solutions in 3+1 dimensions within k-field models, challenging previous assumptions that such solutions must have zero energy and momentum.

Contribution

It demonstrates that certain k-field models can support energetic FTL soliton solutions in 3+1 dimensions, expanding the understanding of tachyon-like entities in classical field theory.

Findings

FTL soliton solutions with zero energy and momentum are possible.

Energetic FTL solitons can exist in specific k-field models.

Challenges the notion that FTL solutions must be non-energetic.

Abstract

Tachyons or hypothetical faster-than-light (FTL) particles would fail the principle of causality. Such particles may only be imagined when they have no energy and momentum and, thus, no observable interaction. In this paper, we show that the classical relativistic field theory with non-standard Lagrangian densities (k-field models) does not rule out the existence of FTL particle-like solutions (solitons) with zero energy and momentum in 3+1 dimensions. However, contrary to our expectation, we show that it is possible to have k-field models that lead to energetic FTL soliton solutions in 3+1 dimensions.