A discrete spacetime of events in whole numbers: why clocks slow, why nothing outruns light, and why time has a direction only where something was measured
Year: 2026
Type: preprint
Abstract: In our view nature cannot be continuous: in quantum mechanics things come in whole pieces, and a measurement gives one outcome that cannot be unmade. We propose a discrete board of time events: Nodes of whole numbers, each speaking to six neighbours once per tick, one step per tick, and a gravity content setting each Node's rate; a click is a detector's reading of the board. Each tick a Node adds its neighbours' weighted numbers, subtracts its number of one tick before, divides once, remainder kept: every step runs back. From that rule we find one bound on everything on the board, no body outrunning light and, given a two-way reading by light, the known addition of speeds, clocks slowed near matter, moving clocks slowed in the known form at first order, light slowed near matter and, in form, bent and delayed, and a board time that no body reads. None of it gives time a direction; that comes only at a click: a detector takes one whole piece, records it, wipes the rest, one step per tick. With the record the board runs back through the click; without it the backward run fails where the wiping reached, no faster than one step per tick. On the board, the direction of time is the ledger of what was measured: a place, a speed, a size. One run shows it. We propose nature's arrow appears this way. Everything here is in the public repository and can be run by anyone.
Author: Gonen, Alon
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221469955
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