Motion Is Settling

The describing the derivation most needed. Without motion there are no frames to relate.

Claim. Motion is settling. Grains falling, rolling and coming to rest relative to the landscape. The landscape changing under them. One site moves relative to another when its place in the other’s reading changes with the tick. The change is bounded strictly below one grain per click. A site is a held configuration. A holding has a rest frame: the site is at rest relative to its own landscape. What crosses at one click a moment is not held. It is the ruler: the unheld grain, falling free, not yet a record (AP50 §1, §8). A held thing cannot go at the rate of the unheld. The bound holds in the settled hourglass, after the ropes pulled tight (AP48 §1: slack from the first record; taut when the building is up). Settled is never still. Settling settles into settled states, which are themselves settling. Stillness is a reading: our perception of a coupling configuration being held. The process is the variable. The grain is the constant. The case this paper feeds to §7 is uniform settling: the place changing by a constant v per tick. Accelerated settling is the neck as what curves the reading. That is the next paper.

Intuition. Nothing in the hourglass moves except by landing somewhere else. Two piles are moving apart when it takes more clicks each moment for a grain to get from one to the other. Moving together when it takes fewer. Neither pile is at rest in any absolute sense. Each is at rest relative to its own landscape. The landscape is the sand that already landed.

Givens. §3 (distance is the crossing record). §4 (time is the count). AP50 §1 (a grain falls free but never faster than one click a moment; where a grain lands depends on the landscape). The author’s describing.

Ruling (the author). “Grains fall, roll and settle. The settling is always relative to the landscape. The settling changes the landscape — the settling is always relative to the landscape — and so on. The process is the variable; the constant is the grain of sand.” And, on the walk: “Settling happens at different rates — the speed of the settling is read relative to the crossing record per tick.”

Theorem — velocity and its bound. Let a site S read another site S′ by the rule of A.1. S′’s place x is the crossing record a grain from S′ took. The count assigned to its leaving is the arrival count less that crossing record. S′ moves relative to S when x changes with the assigned count. Its velocity is that change per tick. A ratio of two counts of the same tick. A pure number. It is bounded. The bound is not the rate at which a one-way crossing record can grow. For a receding site that grows faster than one tick per tick. It is the Doppler stretch of arrivals. Nothing forbids it. The bound is that S′ is held. A site is a held configuration of grains (AP51 §1). A holding has a rest frame: the site is at rest relative to its own landscape (§1). Its place is where its grains are held. What crosses at one click a moment is not held: the unheld grain, falling free, not yet a record (AP50 §1, §8). It is the ruler, not a site. A held thing cannot go at the rate of the unheld, and the picture says why. Held means the site’s grains exchange with one another, and an exchange is a grain crossing between them at the tick (AP50 §5). A configuration whose place changed one crossing record per tick could not complete an exchange across its own extent: the crossing grain would never arrive. So it would not be held. So the place of a site cannot change as fast as one tick per tick. Relative velocity lies in the open interval from minus one to one, in units of the tick. |v| < c, strictly, as A.1 requires. That a site is held is the condition. It is the picture’s, and it is ruled, not derived: the glass is a held configuration of sand. A pile can travel as fast as its fastest grain only by ceasing to be a pile. The author: “Of course it is bounded. The only time it was not bounded was while the hourglass was tipping and the grain was in free fall — the horse ran unbounded until the ropes pulled tight — then it is bound. Unboundedness does not exist any more.” And on the second walk: “Settling settles into settled states, which in turn are settling — it is never truly still; stillness is our perception of the coupling configuration being held.” The bound is a fact of the settled hourglass (AP48). This paper reads only the settled hourglass. There is no absolute rest. A site is at rest relative to its own landscape and to nothing else (§1). The only positions are record histories (AP51 §4). If v is the same at every tick of the reader’s count, the settling is uniform. The two sites are the pair §7 relates. If v changes with the count, the settling is accelerated. That is refused here (§9).

Ruling — energy (the author, 9 September; recorded here, used in the gravity paper). “The record history is fixed; the now has potential. The record history is actualised potential — potential actualised as a specific coupling configuration. Energy is measured now relative to the record history: the record history is actualised energy, and energy is the relative relationship between the potential of now and the actualised coupling-configuration record history. Its propagation is bounded and constrained by that actualised record history and the coupling configurations held now.” This paper uses only the bound. What energy is, in the picture, is the next paper’s.

Grade. Settling, that a site is held, and the bound as a fact of the settled hourglass: Ruled. Velocity as the change of a site’s place per tick, and its strict bound from what holding is: Derived. Uniform settling as the scope of §7: Ruled. Energy: Recorded.

Nothing moves except by landing somewhere else.