Testing Lorentz symmetry violation with an invariant minimum speed

TL;DR

This paper proposes an experimental test for Lorentz invariance violation by detecting proper time dilation effects predicted by a theory with an invariant minimum speed, using atomic clocks in ultracold gases.

Contribution

It introduces a novel experimental approach to test Lorentz violation through proper time dilation effects in a deformed special relativity framework.

Findings

Proper time of clocks near the minimum speed V dilates compared to lab time.

Radioactive decay rates increase for ultracold samples due to proper time dilation.

Potential to observe Lorentz violation effects in ultracold atomic systems.

Abstract

This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in the spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e.g.: isotope $Na^{25}$) is a thermometer for a ultracold gas like the dipolar gas $Na^{23}K^{40}$. So, according to a Deformed Special Relativity (DSR) so-called Symmetrical Special Relativity (SSR), where there emerges an invariant minimum speed $V$ in the subatomic world, one expects that the proper time of such a clock moving close to $V$ in thermal equilibrium with the ultracold gas is dilated with respect to the improper time given in lab, i.e., the proper time at ultracold systems elapses faster than the improper one for an observer in lab, thus leading to the so-called {\it proper time dilation} so that the atomic decay rate of a ultracold radioactive sample (e.g: $Na^{25}$) becomes larger than the decay rate of the same sample at room temperature. This means a suppression of the half-life time of a radioactive sample thermalized with a ultracold cloud of dipolar gas to be investigated by NASA in the Cold Atom Lab (CAL).