# Two invariant surface-tensors determine CSL of massive body wave function

## TL;DR

This paper introduces two geometric surface tensors that fully determine the decoherence of massive body wave functions under CSL, offering new insights and practical tools for experimental design.

## Contribution

It derives new surface integral expressions involving invariant tensors that capture positional and angular decoherence in CSL, independent of microscopic details.

## Key findings

- Decoherence is primarily a surface effect for homogeneous probes.
- Two surface-dependent invariant tensors encode complete decoherence dependence.
- The approach enables flexible design of laboratory test masses.

## Abstract

Decoherence of massive body wave function under Continuous Spontaneous Localization is reconsidered. It is shown for homogeneous probes with wave functions narrow in position and angle that decoherence is a surface effect. Corresponding new surface integrals are derived as the main result. Probe's constant density and two completely geometric surface-dependent invariant tensors encode full dependence of positional and angular decoherence of masses, irrespective of their microscopic structure. The two surface-tensors offer a new insight into CSL and a flexible approach to design laboratory test masses.