Superluminal travel requires negative energies

TL;DR

This paper explores the connection between faster-than-light travel and negative energy densities, proving that superluminal travel necessitates violations of the weak energy condition under a specific definition.

Contribution

It introduces a precise definition of superluminal travel in curved spacetime and proves that such travel requires weak-energy-condition violation assuming the generic condition.

Findings

Superluminal travel requires negative energy densities.

A new definition of superluminal travel based on reaching a destination earlier.

Demonstrates that apparent superluminal paths in flat space are not genuine.

Abstract

I investigate the relationship between faster-than-light travel and weak-energy-condition violation, i.e., negative energy densities. In a general spacetime it is difficult to define faster-than-light travel, and I give an example of a metric which appears to allow superluminal travel, but in fact is just flat space. To avoid such difficulties, I propose a definition of superluminal travel which requires that the path to be traveled reach a destination surface at an earlier time than any neighboring path. With this definition (and assuming the generic condition) I prove that superluminal travel requires weak-energy-condition violation.