What a Point Source Does to the Lattice: Newton's Kernel, One Edge per Tick, and the Sign of Time
- 1Recognition Physics Institute
Abstract
Recognition Science derives physical structure from what a consistent record of distinguishable events requires. In it, space is a cubic lattice of cells whose state advances in discrete steps called ticks, and the gravitational field is a deformation of the lattice’s geometry, governed by a fixed lattice action: the Regge action of a canonical triangulation, with nothing adjusted but one overall scale. This paper asks what a single source does to that field. On the transverse-traceless deformations, the ones that carry gravitational waves, the field equation for a field that does not change from tick to tick is the lattice Poisson equation. Its exact response to a unit source at one cell, the lattice Green function, falls off as 1/(4πr) in every direction: Newton’s kernel, with no constant adjusted. A posting, the pair of opposite unit sources left when one unit moves to a neighbouring cell, has no 1/r field, so only the net count is felt far away. The action treats its four lattice directions alike, three of space and one along which the ticks run. Read as a rule that steps forward tick by tick, the same operator has one response from rest, and that response spreads at most one edge per tick. But for every non-uniform spatial wave the rule also has a solution that grows without bound, while, wave by wave, the operator’s own Green function decays toward both past and future at that same rate. A field that evolves in ticks therefore needs time to enter with the opposite sign from space, the sign of the wave equation. The kernel found here is that of the gravitational-wave amplitude. In general relativity the potential of a static mass lives in a different component of the metric, the time-time component; deriving its source and strength on the lattice is the next step.
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BibTeX
@misc{washburn2026what,
title = {{What a Point Source Does to the Lattice: Newton's Kernel, One Edge per Tick, and the Sign of Time}},
author = {Jonathan Washburn},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23647773},
url = {https://zenodo.org/records/23647773},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - What a Point Source Does to the Lattice: Newton's Kernel, One Edge per Tick, and the Sign of Time
AU - Jonathan Washburn
PY - 2026
DA - 2026/10/25
PB - Zenodo
DO - 10.5281/zenodo.23647773
UR - https://zenodo.org/records/23647773
AB - Recognition Science derives physical structure from what a consistent record of distinguishable events requires. In it, space is a cubic lattice of cells whose state advances in discrete steps called ticks, and the gravitational field is a deformation of the lattice’s geometry, governed by a fixed lattice action: the Regge action of a canonical triangulation, with nothing adjusted but one overall scale. This paper asks what a single source does to that field. On the transverse-traceless deformations, the ones that carry gravitational waves, the field equation for a field that does not change from tick to tick is the lattice Poisson equation. Its exact response to a unit source at one cell, the lattice Green function, falls off as 1/(4πr) in every direction: Newton’s kernel, with no constant adjusted. A posting, the pair of opposite unit sources left when one unit moves to a neighbouring cell, has no 1/r field, so only the net count is felt far away. The action treats its four lattice directions alike, three of space and one along which the ticks run. Read as a rule that steps forward tick by tick, the same operator has one response from rest, and that response spreads at most one edge per tick. But for every non-uniform spatial wave the rule also has a solution that grows without bound, while, wave by wave, the operator’s own Green function decays toward both past and future at that same rate. A field that evolves in ticks therefore needs time to enter with the opposite sign from space, the sign of the wave equation. The kernel found here is that of the gravitational-wave amplitude. In general relativity the potential of a static mass lives in a different component of the metric, the time-time component; deriving its source and strength on the lattice is the next step.
ER -