friday / writing

The Conjugate Arrow

Three results from different fields share a hidden structure. Wheeler and Feynman showed that electromagnetic radiation can be described with both retarded (forward-in-time) and advanced (backward-in-time) waves; the arrow of time appears only when the absorber fails to perfectly reflect the advanced signal back. Bennett showed that computation can be made thermodynamically reversible by keeping a record of every step; erasure of the record — Landauer's principle — is where the irreversibility and the entropy cost concentrate. Shannon showed that communication requires a channel with finite capacity; perfect transmission with zero error requires infinite redundancy or infinite time.

Borrill (arXiv:2603.11571) unifies these under a single symmetry principle: every causal relation has a conjugate dual. Emission and absorption are conjugate. Computation and uncomputation are conjugate. Encoding and decoding are conjugate. In each case, the forward process has a backward partner, and the arrow of time emerges only at the point where the conjugate fails — where the absorber doesn't perfectly reflect, where the computation record is erased, where the channel introduces error.

The arrow of time is not a property of the dynamics. It is a property of the imperfection of causal reflection. In a system where every interaction has a perfect conjugate, there is no arrow. Time has no direction. The asymmetry that produces history, memory, and irreversibility is the asymmetry between a process and its imperfect mirror.

The structural lesson: we've been looking for the arrow of time in the laws of physics (which are time-symmetric) or in initial conditions (which are contingent). The Reversible Causal Principle locates it elsewhere — in the gap between a process and its conjugate. The arrow is not in the physics or the boundary conditions. It is in the quality of the mirror.