The (1+3)-dimensional 'quantum principle of relativity' is Einstein's principle of relativity

TL;DR

The paper demonstrates that recent extensions of the quantum principle of relativity to (1+3)-dimensional spacetime are equivalent to Einstein's original principle of relativity, showing they are not fundamentally new.

Contribution

It clarifies that the proposed superboost and superflip operators are just standard Lorentz transformations and relabelings, thus not extending beyond Einstein's relativity.

Findings

Superboost operators are equivalent to Lorentz boosts.

Superflip corresponds to relabeling space and time.

Extension to Minkowski space reduces to Einstein's principle.

Abstract

We show that the $(1+3)$-dimensional `superboost' operators, proposed in Dragan and Ekert's most recent work on superluminal reference frames \cite{Dragan:2022txt}, are simply the canonical Lorentz boosts, expressed in nonstandard notation. Their $(1+3)$-dimensional `superflip', which is claimed to interchange time and space dimensions for a superluminal observer, travelling with infinite speed, is equivalent to applying the identity operator together with an arbitrary relabeling. Physically, it corresponds to staying put within the canonical rest frame, then renaming space as `time' and time as `space'. We conclude that their extension of the `quantum principle of relativity', proposed in earlier work on $(1+1)$-dimensional spacetimes \cite{Dragan:2019grn}, to ordinary Minkowski space \cite{Dragan:2022txt}, is simply Einstein's principle of relativity, proposed in 1905.