The one-way speed of light cannot be measured – the convention of simultaneity, and its fence.
Paper 95 separated convention from fact and Paper 111 wrote that light fixes only the conformal structure. This paper treats the point where the two meet: the one-way speed of light. NO NEW PHYSICAL LAW IS CLAIMED. Reichenbach’s epsilon, the fact that only the two-way speed is measurable, the epsilon coordinates and Malament’s theorem are all standard. Nothing here contradicts relativity – the work is to draw the line between what is measured and what is stipulated.
First, the round trip is the speed of light for every epsilon. Declaring the arrival of an outward signal to sit at the epsilon position between departure and return splits the one-way speeds into the speed of light over twice epsilon and over twice one minus epsilon. Yet the round-trip time comes to twice the distance over the speed of light, in which epsilon cancels, and the two-way speed is the speed of light for every epsilon (computed symbolically here, and checked at epsilon equal to a quarter, a half, three quarters and nine tenths). Only the round trip is measurable: to measure a single leg one must first have set two distant clocks, and the way of setting them is exactly epsilon. The circle cannot be escaped.
Second, and this is the core. Changing epsilon is nothing but a change of coordinates. Adding a constant multiple of position to the time coordinate makes an off-diagonal term appear in the metric. Yet solving that metric for the directions light travels along returns exactly the one-way speeds found above (agreement checked at all four values of epsilon). The set of null directions is the same; what changed is only its coordinate description. Epsilon has not moved the geometry at all. In the language of Paper 111, epsilon is not even a freedom inside the conformal structure, since the conformal structure itself is untouched. Where Paper 150’s density was a freedom that moves the geometry, epsilon is a freedom that moves nothing.
Third, nothing observable moves. The proper time along a worldline of velocity v is the same in the standard coordinates and in the epsilon coordinates (checked here). Proper time is the length of a worldline and a relabelling of simultaneity slices cannot change it. The Doppler ratio likewise reads two events on a single clock, leaving no room for a synchronisation to enter. Any experiment claiming to measure a one-way speed has therefore assumed a synchronisation somewhere: what it measures is either the round trip, or the epsilon it assumed.
Fourth, the convention has a fence. For epsilon at or below zero, or at or above one, a one-way speed becomes negative or infinite and the order of cause and effect breaks (checked here). The freedom lives only inside the open interval, whose endpoints causality closes. A convention is not a licence but a one-parameter freedom.
Fifth, the brake. Reichenbach (1928) argued that epsilon is conventional. Malament (1977), however, showed that if simultaneity is required to be an equivalence relation definable from the causal structure together with a single inertial worldline, then it is unique and is the standard synchronisation, epsilon equal to a half. Both are correct. They differ in what is allowed in a definition: Reichenbach permits any stipulation, Malament only what the causal order and one worldline can define. So the question is simultaneity conventional has no answer until one says which definitions count. One word, two roots.
A census to close with. What the corpus has called a convention falls into three depths. The epsilon of simultaneity is a choice of coordinates, and changing it moves nothing – not even the light cone. The density inside a conformal class (Paper 150) is a geometric freedom, and changing it moves the metric, volumes and distances alike. The choice of units (Papers 95 and 35) is an assignment of numbers, and changing it moves the numbers while leaving invariants alone. All three have been called conventions, and the separator is what moves when the choice is remade: nothing, the geometry, or the numbers.
IMPORTANT (scope): a census of established standard material (Layer 2). What is not claimed: any new physical law (there is none) / anything contradicting relativity (nothing does). What is added: showing in numbers that changing epsilon does not move the light cone, writing that the fence is an open interval, separating Reichenbach from Malament by what each allows in a definition, and setting the corpus’s three conventions side by side by depth. What remains: the one-way speed of light cannot be measured, and not for want of apparatus. What would have to be settled first, in order to measure it, is that very number. And changing the settlement did not move the light cone by a hair – what moved were the markings on the paper.
On the making of this work: The ideas and content of this work stem from the author’s own considerations. Assistance from an AI (a large language model) was used for structuring, English translation, and checking the algebra. Any remaining errors or misinterpretations are solely the author’s. Feedback and corrections are sincerely appreciated.
Reference
Yamagishi, Y. (2026). The One-Way Speed of Light Cannot Be Measured [Paper 24]. Zenodo.
DOI: 10.5281/zenodo.22090261
ORCID: 0009-0006-8587-3450