Detecting Causality with Symplectic Quandles

TL;DR

This paper demonstrates that symplectic quandles, when combined with the Alexander-Conway polynomial, can detect causality in certain (2+1)-dimensional spacetimes, surpassing previous invariants like Alexander-Conway alone.

Contribution

It introduces the use of symplectic quandles as a new tool for causality detection in spacetime links, showing they can distinguish links that previous invariants could not.

Findings

Symplectic quandles distinguish certain links related to causality.

Combined with Alexander-Conway polynomial, they detect causality in specific spacetime models.

They provide an alternative approach aligned with contact geometry methods.

Abstract

We investigate the capability of Symplectic quandles to detect causality for (2+1)-dimensional globally hyperbolic spacetimes (X). Allen and Swenberg showed that Alexander-Conway polynomial is insufficient to distinguish connected sum of two Hopf links from the links in the family of Allen-Swenberg 2-sky like links, suggesting that it can not always detect causality in X. We find that symplectic quandles, combined with Alexander-Conway polynomial, can distinguish these two type of links, thereby suggesting their ability to detect causality in X. The fact that symplectic quandles can capture causality in the Allen-Swenberg example is intriguing since the theorem of Chernov and Nemirovski, which states that Legendrian linking equals causality, is proved using Contact Geometry methods.