About the Paper

One Postulate

AuthorEmad Mostaque

InstitutionIntelligent Internet

Year2026

SeriesPaper IV of IV

This paper proves that Einstein's Special Relativity rests on a single foundational principle, not two. The famous second postulate, that light travels at the same speed in every inertial frame, is not an independent axiom. It is a mathematical consequence of the first. Symmetry alone demands a universal speed limit. Experiment only tells us what that speed is.

What the Paper Proves

The argument begins with a single demand: that the laws of physics look identical in all inertial frames. From this one symmetry requirement, the paper derives the full family of possible space-time transformation groups. The family is parameterised by a single real number κ.

Three cases emerge: κ negative (rotational, Euclidean geometry, no causality), κ zero (the Galilean group, no speed limit), and κ positive (the Lorentz group, lightcones, a universal speed). The paper then deploys the Killing form (a tool from 1888 Lie theory) to show that κ must be positive. The sign is not an assumption. It is demanded by the structure of the symmetry group itself.

Once κ is known to be positive, the transformation equations carry their own internal speed: V = 1/√κ. This is a universal speed limit, derived entirely from symmetry. No measurement was needed to prove it exists. Experiment measures its value. That is all.

The Killing Form of so(1,3) — the Lorentz Algebra

B = diag(−4I₃, 4κI₃)

The negative sign in the spatial block of B forces κ to be positive. A negative or zero κ would produce an indefinite or degenerate form, incompatible with the algebra's structure. This is the proof Pauli said was impossible.

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The full derivation appears in the paper. The interactive chapters on this site trace each step from postulate to proof.

The Author

Emad Mostaque

Intelligent Internet

Emad Mostaque is the founder of Intelligent Internet. This is the fourth paper in his series exploring the mathematical foundations of physics from first principles. The series begins with the derivation of spacetime from a single symmetry rule, continues through the emergence of matter and the cosmological constant, and concludes here, showing that even the speed of light was never an assumption. It was always required.

Why This Matters

It changes what we know versus what we assumed.

Physics advances not just by discovering new phenomena but by understanding which of its foundations are truly necessary. For over a century, the constancy of the speed of light has been treated as a brute fact about electromagnetism: something we know because Michelson and Morley measured it. This paper shows the constancy is a logical consequence of the symmetry of space and time. We would have been forced to posit a universal speed even if we had never measured light at all.

It closes a gap Pauli identified in 1921.

Wolfgang Pauli noted in his landmark 1921 treatise that the parameter κ appearing in the general transformation group could not be determined from the symmetry principle alone. He accepted this as a limitation. This paper lifts the limitation: the Killing form of the resulting Lie algebra is negative semi-definite only when κ is positive, ruling out both competing cases on purely algebraic grounds. The gap is closed.

It restores the unity of physics from a single principle.

The deepest aspiration of theoretical physics is to derive everything from as few principles as possible. Einstein himself wrote that the supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built by pure deduction. This paper takes that aspiration seriously and shows that, for Special Relativity, one principle is enough. The universe is more unified than its discoverer knew.

"Experiment is needed to measure that speed, not to establish its existence. Einstein needed one postulate, not two."

— Emad Mostaque, One Postulate, Intelligent Internet, 2026

Bibliography

1.
Ignatowski, W. von. "Einige allgemeine Bemerkungen über das Relativitätsprinzip." Physikalische Zeitschrift. 1910.
2.
Pauli, W. "Theory of Relativity." Pergamon Press. 1921.
3.
Lévy-Leblond, J.-M. "One more derivation of the Lorentz transformation." American Journal of Physics. 1976.
4.
Silagadze, Z. K. "Relativity without tears." Acta Physica Polonica B. 2008.
5.
Drory, A. "The necessity of the second postulate in special relativity." Studies in History and Philosophy of Modern Physics. 2015.
6.
Mostaque, E. "One Postulate." Intelligent Internet. 2026.

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