Trails, Not Holograms

All proceeds from the sale of this book support the work of EPV Foundation, Inc., a 501(c)(3) nonprofit organization.

Physics recognizes two distinct concepts under the name entropy: state entropy, which measures uncertainty about a system's configuration at a moment, and path entropy, which measures the irreversibility accumulated along a system's trajectory. The holographic interpretation of the Bekenstein-Hawking area-entropy formula reads black hole entropy as state entropy on a boundary. This paper proposes that the same formula is better understood as accumulated path entropy along a trajectory — irreversible history deposited as a system moves through spacetime, with the traversal dimension collapsing into data and leaving a two-dimensional record that encodes the third dimension as information.

The universe does not project from a surface. It accumulates along paths. Grounded in the recently formalized distinction between state and path entropy, the principle of maximum caliber, and the physics of quantum decoherence, this work argues that the holographic interpretation selected the wrong entropy — and that reading Bekenstein-Hawking as path entropy resolves the need for a perspective no system in the universe occupies.

Every claim is referenced to the scientific literature. Where the argument extends beyond established results, the extension is identified.