Special relativity · The central construction
Build the map,
don't receive it.
What map between two inertial frames keeps both postulates, and what does each requirement decide?
Compare competing models: which observations can actually decide?
SR-04 · Construct the map
Construct the Lorentz map
What map between two inertial frames keeps both postulates, and what does each requirement decide?
Construction result
| right-moving-light | -1.799e+8 |
| left-moving-light | -1.799e+8 |
| reciprocity | -3.600e-1 |
| isotropy | 0.000e+0 |
| identity-branch | 0.000e+0 |
| transverse-light | 0.000e+0 |
The Galilean shelf step
Slow case (observer 30 m/s, object 10 m/s): the ordinary change of frame gives -20 m/s. Light rays at v = 0.6c: right-moving 0.400000c, left-moving -1.600000c.
The slow case needs a slow observer: this is why the observer speed above is entered separately from the frame speed v used for the light-ray test.
Not modeled: non-aligned axes and rotations; accelerated frames; gravity; a fully rigorous derivation of linearity; origins that do not coincide; non-collinear composition (SR-06).
Action contract: the same construction without dragging, color, or a canvas
Every action here is a checkbox toggle or typed text entry, and every result is a text table or sentence. Enable constraints from the checklist, type a hand-built candidate's coefficients, and read the residual or the fixed map. No control depends on dragging a handle, distinguishing color alone, or reading a canvas.
Open the derivation
The Galilean shelf step
The ordinary change of frame, x′ = x − vt, works for slow objects: two speeds slower than light compose the way ordinary mechanics expects, and the deviation from the relativistic result is unmeasurably small. It fails completely for light: a ray moving at c in one frame is measured at c − v or c + v in the other, not c. That conflict, not an assumed interval, is where the construction starts.
No answer preinstalled
The engine above solves only the constraints you enable. The Lorentz factor never appears until the branch step fixes it; the Minkowski interval never appears at all in the construction, because interval preservation is a modern verification oracle, not a 1905 premise. Requiring it up front would make the derivation circular.