Long-ranged forces and energy non-conservation in (1+1)-dimensions

TL;DR

This paper investigates the potential for local energy non-conservation in (1+1)-dimensional covariant theories with long-range fields, revealing that such phenomena can occur in these simplified models.

Contribution

It demonstrates that local and causal non-conservation of energy can occur in (1+1)-dimensional theories with long-range gravitational analogs.

Findings

Energy non-conservation is possible in (1+1) dimensions.

Long-ranged fields can lead to non-conservation phenomena.

The results are specific to (1+1)-dimensional models.

Abstract

We consider whether local and causal non-conservation of energy may occur in generally covariant theories with long-ranged fields (analogs of Newton's gravity) whose source is energy--momentum. We find that such a possibility exists in (1+1) dimensions.