Lamport's Arrow of Time: The Category Mistake in Logical Clocks

A provocative new paper by computer scientist Paul Borrill, titled 'Lamport's Arrow of Time: The Category Mistake in Logical Clocks,' challenges a foundational concept in distributed systems. Published on arXiv, the 14-page work argues that Leslie Lamport's seminal 1978 formalism for logical clocks, while freeing systems from synchronized physical time, inadvertently embeds a deeper, unexamined assumption. Borrill contends that the 'happens-before' relation assumes causality creates a globally well-defined, forward-in-time-only directed acyclic graph (DAG). Following philosopher Gilbert Ryle's concept of a 'category mistake,' the paper asserts this conflates an epistemic construct (the logical ordering we infer from messages) with an ontic claim about the nature of physical causality itself.

The analysis traces this conflation through Shannon's communication model, Lamport's own TLA+ specification language, and fundamental impossibility results like the Fischer-Lynch-Paterson theorem and Brewer's CAP theorem. Borrill then pivots to physics, arguing that special and general relativity permit only local causal structure, and that recent quantum information research on 'indefinite causal order' demonstrates nature admits correlations with no well-defined temporal sequence. The paper concludes by proposing that 'mutual information conservation'—a measure of shared information between systems—should replace temporal precedence as the more fundamental primitive for reasoning about distributed consistency, potentially opening new avenues for system design that are not bound by traditional assumptions of a global causal arrow.