Why Does a Maximum Speed Exist? — The Two Relativities (Galilean and Lorentzian) and the Theorem of Ignatowski.
Why does a maximum speed exist at all? Starting only from the relativity principle, the homogeneity and isotropy of space, and group structure (plus causality), the coordinate transformations between inertial frames are restricted to exactly two families: the Galilean (kappa=0, invariant speed infinite) and the Lorentzian (kappa>0, an invariant speed c=1/sqrt(kappa) that is finite). This is the theorem of Ignatowski (1910-11), later refined by Levy-Leblond (1976). Thus the constancy of the speed of light is NOT an axiom but a consequence of our universe lying on the finite branch. Distinct roots: the invariant speed (from group/structure) and the speed of light (from the photon being massless) are distinct quantities that merely coincide in value — this is the upstream of Paper 66. The result backs the corpus’s reading of “c as scaffolding, a defined value in the 2019 SI” with a theorem, and the “exactly two” enumeration is the bloodline of Papers 01/64/69. Scope: this paper does NOT rewrite or re-derive special relativity (it is a presentation of a standard alternative derivation); it does NOT solve why our universe is on the finite branch, nor the value of c (experiment decides); “OS bandwidth” is a Layer-3 non-science lens (quarantined). No new prediction.
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). Why Does a “Maximum Speed” Exist? [Paper 83]. Zenodo.
DOI: 10.5281/zenodo.21741190
ORCID: 0009-0006-8587-3450