Invariant lengths using existing Special Relativity

TL;DR

The paper demonstrates that boost-invariant length scales, like the Planck length, naturally arise from the statistical properties of random space-time events within standard Special Relativity, without modifications.

Contribution

It shows that invariant lengths can be derived from the fluctuation scales of a random space-time field, providing a new interpretation of Planck's length as a boost-invariant quantum gravity scale.

Findings

Nearest neighbor distance is boost invariant.

Planck length can be seen as a fluctuation scale of space-time.

Invariant lengths emerge without altering Special Relativity.

Abstract

A field of random space-time events exhibiting complete spatial-temporal randomness appears statistically identical to all observers. Boost invariant lengths naturally emerge when we examine fluctuation scales of this field such as the nearest neighbor distance. If we interpret Planck's length as the characteristic fluctuation scale of quantum gravity, its boost invariance can then be understood without modifying Special Relativity.