An observer principle for general relativity

TL;DR

This paper proves a mathematical uniqueness theorem in general relativity, showing that symmetric tensors are uniquely determined by their light cone monomial functions, implying observer measurements uniquely identify tensors at an event.

Contribution

It introduces a new observer principle theorem demonstrating the unique determination of symmetric tensors by their light cone contractions in general relativity.

Findings

Symmetric tensors are uniquely determined by their monomial functions on the light cone.

Observers' measurements via velocity vector contractions uniquely identify tensors.

The theorem establishes a fundamental link between observer measurements and tensor equality.

Abstract

We give a mathematical uniqueness theorem which in particular shows that symmetric tensors in general relativity are uniquely determined by their monomial functions on the light cone. Thus, for an observer to observe a tensor at an event in general relativity is to contract with the velocity vector of the observer, repeatedly to the rank of the tensor. Thus two symmetric tensors observed to be equal by all observers at a specific event are necessarily equal at that event.