Trans-Planckian particles and the quantization of time

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 spatial 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 length, each of which are described by a representation of the Lorentz group. We then demonstrate how the holographic principle works for this case, by constructing the operators corresponding to a field . The parameter t turns out to be quantized in units of , where R is the period of the compactified dimension.