Existence of Faster Than Light Signals Implies Hypercomputation Already in Special Relativity

TL;DR

This paper demonstrates that the theoretical possibility of hypercomputation within special relativity hinges on the existence of faster than light signals, establishing a fundamental link between superluminal communication and computational limits.

Contribution

It provides a formal proof that hypercomputation in special relativity is possible if and only if faster than light signals exist, clarifying the conditions for superluminal computation.

Findings

Hypercomputation is possible if faster than light signals exist.

Faster than light signals are a necessary and sufficient condition for hypercomputation in special relativity.

The work formalizes the link between superluminal communication and computational power in relativistic physics.

Abstract

Within an axiomatic framework, we investigate the possibility of hypercomputation in special relativity via faster than light signals. We formally show that hypercomputation is theoretically possible in special relativity if and only if there are faster than light signals.