High precision modeling at the 10^{-20} level

TL;DR

This paper discusses the development of high-precision algorithms for simulating thermo-mechanical effects in optical resonators, aiming for accuracy at the 10^{-20} level to match future experimental measurement capabilities.

Contribution

It introduces a new approach to high-precision numerical modeling targeting an accuracy of 10^{-20}, addressing limitations of standard double precision methods.

Findings

Identified key challenges in achieving 10^{-20} accuracy

Analyzed a test case to understand precision limitations

Proposed directions for developing high-precision algorithms

Abstract

The requirements for accurate numerical simulation are increasing constantly. Modern high precision physics experiments now exceed the achievable numerical accuracy of standard commercial and scientific simulation tools. One example are optical resonators for which changes in the optical length are now commonly measured to 10^{-15} precision. The achievable measurement accuracy for resonators and cavities is directly influenced by changes in the distances between the optical components. If deformations in the range of 10^{-15} occur, those effects cannot be modeled and analysed any more with standard methods based on double precision data types. New experimental approaches point out that the achievable experimental accuracies may improve down to the level of 10^{-17} in the near future. For the development and improvement of high precision resonators and the analysis of experimental data, new methods have to be developed which enable the needed level of simulation accuracy. Therefore we plan the development of new high precision algorithms for the simulation and modeling of thermo-mechanical effects with an achievable accuracy of 10^{-20}. In this paper we analyse a test case and identify the problems on the way to this goal.