Simultaneity Is the Pupil Generalised

The paper’s own sentence. Not a consequence of the transformations. Their reason.

Claim. No site can read its own now. The grain in its pupil has not held (AP51 §5). No site can read another site’s now either. Same reason, and one more. What reaches it from another site is a held record. It reaches it at the tick. Never faster. So there is no reading of “now” at any site. Only the site’s own writing and reading, which it cannot read as a record. Every other now arrives as record, delayed by the record it took to arrive. “Simultaneous” is therefore a reading. Never a fact of the record.

Intuition. You cannot see your own pupil. You cannot see mine either. What you see of me is light that left me some clicks ago. So when you say two things happened at once, you are not reporting the record. You are reporting your reading of two arrivals, corrected by the one rule. Another pile, elsewhere, reads two other arrivals and corrects them the same way. It says otherwise. Neither is wrong. There is no now to be right about. There is nothing to read.

Givens. AP51 §5 (the pupil; a record is readable only once held; the neck’s grain has not held). §2 (each operator its own neck). §3 (records cross at the tick). A.1 (the reading of a distant time-count). The author’s ruling.

Ruling (the author). “One site is always the localised reading of the other — and the distance and information at and between those sites is constrained by the speed of light.” And, on the walk: “Ticks only make sense relative to the other grains of sand — to the record history. One grain only develops meaning relative to the other grains. Meaning develops from the observation of the record-history landscape; it is an interpretation relative to the landscape itself, and it is a process of development, not an end destination or something forced from outside — the grains making sense of the grains of the landscape relative to their localised positions. The grains share the awareness; experience will vastly differ.”

Theorem — simultaneity is a reading. A site has two things of its own without any convention. Its count. The crossing record to another place (§§3–4). What it does not have is the count at which a distant event happened. It cannot read another site’s now (AP51 §5; §2). It reconstructs one. It uses the only rule the record gives it. The count at which the event’s grain arrived, less the crossing record the grain took (A.1). That reconstruction is a reading. It is not a fact of the record. The rule uses the one ruler of §3. It is the rule every site uses. Now let two events occur at two places. Let two sites in uniform relative settling each reconstruct their counts by that rule. Appendix A shows what follows. The two sites assign the two events different separations in count. They can assign them opposite orders (A.8: Δt′ = − γ v Δx). This is not the order in which grains happened to arrive. A world with a shared now and slow signals has arrival-order differences too. It corrects them away. Here the corrected orders themselves differ. No third reading adjudicates them. A third reading would have to read a now. There is none to read. So “at the same time” names a relation between reconstructions at a site. Different sites reconstruct differently. There is no fact of the matter about whether two distant events are simultaneous. “Simultaneous” would require comparing two nows. No now can be read. What the record fixes is the interval (§7). The relation between two events every site reads the same. It is written in the record, not in the reading. The relativity of simultaneity is not, in this picture, something the transformations do to time. It is what time is when it is a reading.

Theorem — one now, one record-order, no readable now. Two things are one. They are not the same thing. The record is one sequence, totally ordered (AP50 §9). Grain after grain, kept. That order is a fact of the record history. The record history is fixed. “Record-keeping has a very definite order.” The now is one too. One grain. One tick. The moment every operator writes and reads from. It is not ordered. It is potential. “Now is potential; the record history is actualised potential.” The order belongs to what has been kept. The now is where keeping is done from. Neither is a readable now. No site reads the grain in its own neck as a record at the instant it writes and reads (AP51 §5). No site reads another site’s executing grain. What arrives is a kept record. It arrives at the tick (§3). So the record’s order is not available to any reading as a shared simultaneity slice. A pair of events the record keeps one after the other, neither reachable from the other by a grain, can still be reconstructed by one site in that order and by another in the reverse. A pair where one depends on the other cannot (§7). What every site does read the same is not a now. It is the interval (§7). The Lorentzian manifold AP10 claimed is the structure of those readings. The maps under which every site’s counts transform. The quantity they all read the same. It is not a claim that the record has no order. The order is the record’s. It is the thing no reading is. This is how AP51’s “we share the now” and this paper’s “no readable now” are one sentence at two registers. The now that is shared is the moment reading and writing are done from. One grain. Every operator at it. The now that is not shared is any now a site could read as a record. There is none. The now is not a record. Said by the author: one now, one grain, always shared. Said by this paper: and never read. One thing is not settled here. Whether the record’s order enters any reading beyond the interval — whether it is bookkeeping, or does work — is not this paper’s. This paper claims only that no reading is it.

Grade. Both theorems Derived, from AP51 §5, §§2–3 and A.1. The paper’s own.

You cannot see your own pupil, and mine reaches you late. The record has an order. The now has potential. No reading is either. There is no now to agree about, because there is nothing to read.