Tachyons as a Consequence of Light-Cone Reflection Symmetry

TL;DR

This paper proposes a new symmetry called Light-Cone Reflection (LCR) that interchanges timelike and spacelike intervals, providing a symmetry-based explanation for the possible existence of tachyons, especially neutrinos.

Contribution

It introduces LCR symmetry, constructs an LCR-invariant Lagrangian, and demonstrates a symmetric spectrum between tachyons and ordinary particles, with implications for gauge invariance.

Findings

LCR symmetry interchanges timelike and spacelike intervals.

LCR combined with translations leads to larger symmetry.

Spectrum symmetry between tachyons and ordinary particles.

Abstract

We introduce a new symmetry, Light-Cone Reflection (LCR), which interchanges timelike and spacelike intervals. Our motivation is to provide a reason, based on symmetry, why tachyons might exist, with emphasis on application to neutrinos. We show that LCR, combined with translations, leads to a much larger symmetry. We construct an LCR-invariant Lagrangian, and discuss some of its properties. In a simple example, we find complete symmetry in the spectrum between tachyons and ordinary particles. We also show that the theory allows for the introduction of a further gauge invariance related to chiral symmetry.