On the Simultaneity of Folds

Circulated for comment. This paper concerns when a fold happens, not how. It takes the fold as given and the aperture as Thale models it, and asks one question the record has not yet asked aloud: at a fold, which "now" is joined to which? Numbered for citation, following FS-212's practice, with derived results and this desk's proposals marked apart in section 7.

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1. The question

The record says plainly that there is no galactic present. With no signal ahead of a hull, there is no moment that is now everywhere, only each clock's own count and the courier work that reconciles them (Timekeeping and the Common Record). This desk keeps the pulsar ephemeris because of that sentence. The ephemeris gives any two observers a shared coordinate. It gives them no shared elapsed time and no calendar.

A fold appears to do what the sentence says nothing does. FTL Mechanics records "simultaneous visual traces at origin and destination during fold peak". For as long as the adjacency holds, two places light-years apart share a moment that can be seen. The record does not say in which state of motion that moment is shared, and this paper does not claim to know. It asks what follows from each possible answer, and what the Corps could do while the answer is unknown.

2. Proposition Q1: one fold cannot carry a hull into its past

Observers in relative motion at speed v disagree about which distant events are simultaneous, by at most v·d/c² across a distance d. Since v is always less than c, that disagreement is always less than d/c, the time light takes to cross the same distance.

So suppose a fold joins two places at a moment that is simultaneous in some state of motion, whichever it is. A hull that goes out through the fold and comes back through ordinary space, at any speed short of light's, arrives home after it left by every clock in the record. A single fold, used once and closed, cannot carry a hull into its own past. This follows from the relativity of simultaneity alone, and it holds whatever the answer to section 1 turns out to be.

3. Proposition Q2: two folds might

Now suppose the return is also by fold, through a second fold whose shared moment belongs to a different state of motion. Both legs are faster than light, so the protection in Q1, a return leg slower than light, is gone. The two offsets can add, and the round trip can close with the hull arriving home before it left, by up to roughly 2v·d/c².

The argument is old. Richard Tolman set it out for signals faster than light in 1917 CE (2117 UCSD), and Matt Visser gave the form for a ring of shortcuts, each harmless alone, in 1997 CE (2197 UCSD). The record refuses every retrocausal influence and every visit to the past (What the Record Refuses), so the case must not arise. The question is only how it is kept from arising.

The scale of the danger, at a relative speed of one hundred kilometres a second between the two shared moments:

Route length	Largest possible mismatch, v·d/c²
10 light-years	about 1.2 days
100 light-years	about 12 days
1,000 light-years	about 4 months

4. Proposition Q3: the interval rule

A loop of two folds can close only if the return fold opens within the mismatch of the outbound one. If the return opens later than that, the hull has already lived through more time than the folds could take back, and it comes home after it left, as in Q1.

This desk proposes a rule that needs no answer to section 1. Log every fold's opening against the pulsar ephemeris, and allow no return fold on the same route to open within the route's largest possible mismatch of the outbound fold. The ephemeris is the right instrument for the log precisely because it is not a calendar. It does not claim a shared now. It lets two ends that have never met agree on a phase, which is all the rule needs.

On most routes the rule costs nothing. Staging, scaffold generation and certification already take longer than a fold's crossing, often by weeks. On a route of ten or a hundred light-years, that alone exceeds the mismatch. On the longest routes it may not, and there the rule is a real constraint.

5. Proposition Q4: persistence and depth

A fold held open with its ends moving apart, or sitting at different depths in a gravity well, lets its two clocks drift, and a drifted fold behaves like a pair. Thale's FS-212, Proposition 5, reads the Corps' rule that a fold is collapsed after transfer as chronology protection done by procedure. This desk adds only the numbers.

At thirty kilometres a second of relative motion the drift is about five parts in a thousand million, and a fold of ten light-years would need some two thousand million years open to drift ten years. Depth matters far more than speed. Near the surface of a neutron star the drift reaches a tenth or more, and the same ten years would accumulate in about a century. Keeping fold ends out of the deepest wells, which the gradient rule in FTL Mechanics already requires for the aperture's sake, protects the fold's clock as well.

6. Proposition Q5: the measurement that would settle it

If every fold shares its moment in the same state of motion, no combination of folds can close a loop, and Q3 is a precaution against nothing. Whether they do is a question about the Common Manifold, where fold geometry lives, and no instrument this desk has can reach it there.

It can be reached from here. Each fold peak shows its traces at both ends at once. Read the two traces' arrival against the ephemeris at each end, across many folds on routes pointing in different directions, and ask whether every fold's shared moment fits one state of motion. If they all fit one, the Manifold keeps a single order and Q3 can be relaxed. If they fit several, Q3 is necessary. This measurement has not been made. The traces are an observed effect of fold peaks, but this desk knows of no case in which they have been timed against the ephemeris at both ends of the same fold.

Physics offers a precedent for the first outcome. Stefano Liberati, Sebastiano Sonego and Matt Visser showed in 2002 CE (2202 UCSD) that signals faster than light need produce no paradox if they all respect one preferred ordering. A single order would not make folds less strange. It would make them safe.

7. For later authors

Derived, and safe to cite as such: Q1, Q2 and the scales in its table, and the drift figures in Q4.

This desk's proposals, to be cited as proposals: the interval rule (Q3), the reading that a drifted fold behaves like a pair (Q4), and the measurement in Q5. Thale's reading of persistence drift, used in Q4, is his model, cited from FS-212 and not adopted here as a finding.

The thesis in one line: a fold joins two nows, and the record's safety depends on never letting two folds disagree about which.

8. What this paper does not claim

It does not claim to know which now a fold joins. It does not claim that any fold has ever carried anything into its own past, and the record holds no such case. Nor does it claim that the Corps' existing practice is the reason there is none. It does not touch the record's account of a correction arriving late by a Material clock while being the next thing in another register (Cosmic Cascade), which concerns two clocks and not a loop. And it excludes the harmonic channel entirely: corridors are defined at another tier, and their timing is another desk's work.

— Hester Quaile, ephemeris desk, Survey Corps Standards Office. Earth, 2827 UCSD.

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Works cited, as held in the Survey Archive: R. C. Tolman, The Theory of the Relativity of Motion (1917 CE); M. Visser, "Traversable wormholes: The Roman ring", Physical Review D 55 (1997 CE); S. Liberati, S. Sonego and M. Visser, "Faster-than-light signals, special relativity, and causality", Annals of Physics 298 (2002 CE); A. Thale, Coherence Debt as Quantum Interest, Engineering Corps working papers no. FS-212 (2826 UCSD), Proposition 5.