TransPlanckian Particles and the Quantization of Time

TL;DR

This paper explores the quantization of time and the structure of trans-Planckian particles through black hole horizon analysis, revealing a string-bit model and demonstrating holography with Planck-scale time units.

Contribution

It introduces a novel approach to understanding trans-Planckian particles via horizon operator algebra and shows how time becomes quantized in Planck units in this framework.

Findings

Black hole horizon operators form distinct representations.

Horizon can be modeled as string bits with SO(2,1) symmetry.

Time parameter is quantized in Planck units divided by compactification period R.

Abstract

Trans-Planckian particles are elementary particles accelerated such that their energies surpass the Planck value. There are several reasons to believe that trans-Planckian particles do not represent independent degrees of freedom in Hilbert space, but they are controlled by the cis-Planckian particles. A way to learn more about the mechanisms at work here, is to study black hole horizons, starting from the scattering matrix Ansatz. By compactifying one of the three physical spacial dimensions, the scattering matrix Ansatz can be exploited more efficiently than before. The algebra of operators on a black hole horizon allows for a few distinct representations. It is found that this horizon can be seen as being built up from string bits with unit lengths, each of which being described by a representation of the SO(2,1) Lorentz group. We then demonstrate how the holographic principle works for this case, by constructing the operators corresponding to a field in space-time. The parameter t turns out to be quantized in Planckian units, divided by the period R of the compactified dimension.