Wilhelm Killing — The Killing Form
Discovers a diagnostic tool for Lie algebras that, 138 years later, will prove which universe we live in. Killing publishes "Die Zusammensetzung der stetigen endlichen Transformationsgruppen" — introducing the bilinear form that bears his name.
Lorentz — Transformation Equations
Derives the transformation equations that will eventually bear his name. Gets the mathematics exactly right — but attributes the results to a physical compression of matter moving through an invisible medium called the luminiferous ether.
Poincaré — The Group Structure
Recognises that the Lorentz transformations form a group — a deep mathematical insight. Coins the term "Lorentz group." Einstein will build on this foundation the following year, but the algebraic depth of the group structure will take a century more to fully exploit.
Einstein — Special Relativity (Two Postulates)
Publishes "On the Electrodynamics of Moving Bodies." Two postulates, one revolution. Postulate I: the laws of physics are the same in all inertial frames. Postulate II: the speed of light in vacuum is the same in all inertial frames. But why two?
Ignatowski — Relativity from One Postulate
First to show that the Lorentz transformations can be derived without explicitly assuming the constancy of c. Derives the general transformation group from symmetry alone, parameterised by a constant κ. Leaves κ undetermined — neither its sign nor its value can be fixed from the algebra alone. A crucial step forward with one piece missing.
Pauli — "Nothing Can Be Said About the Sign of κ"
In his landmark encyclopaedia article on relativity, Pauli correctly identifies that the sign of κ cannot be determined from symmetry arguments alone — or so he believes. Accepts this as a fundamental limitation of the one-postulate approach. The gap becomes the received wisdom of the field.
Lévy-Leblond — Revisiting One-Postulate Relativity
Rederives the Lorentz transformations from one postulate in a more rigorous and pedagogically clear way. Confirms the existence of the three-case family (κ < 0, κ = 0, κ > 0). Still cannot fix the sign of κ from purely algebraic arguments. The gap identified by Pauli stands.
Silagadze — "Relativity Without Tears"
A comprehensive pedagogical paper revisiting the one-postulate derivation and making the argument accessible to a wider audience. Reviews the full family of transformation groups. Still κ is left undetermined — the gap persists. The paper's title is prescient: tears are still needed, until the Killing form is applied.
Drory — "The Necessity of the Second Postulate"
Argues — incorrectly, as the 2026 paper shows — that the second postulate is genuinely necessary and cannot be derived from the first. Takes Pauli's limitation as definitive. The argument is rigorous but misses the one tool that can resolve the sign: the Killing form of the resulting Lie algebra.
Mostaque — One Postulate
The Killing form — Killing's 1888 diagnostic — settles the sign. B(boosts) = 4κ must be positive for the algebra to be non-degenerate and consistent with the Lorentz group structure. κ > 0 is the only algebraically consistent possibility. Pauli's gap is closed. The second postulate was always redundant.
One may show that the sign of κ cannot be determined from these considerations.— Wolfgang Pauli, 1921 — Theory of Relativity (encyclopaedia article)
Pauli identified precisely the gap this paper closes. The sign of κ determines whether relativity is Lorentzian (κ > 0), Galilean (κ = 0), or physically inconsistent (κ < 0). For 105 years, Pauli's assessment stood as received wisdom. The Killing form changes everything — B(boosts) = 4κ must be positive for the algebra to be non-degenerate.
From 1888 to 2026 — 138 years from Killing's discovery to its application.
The tool was always there. The question was always there. Now we have the answer.