Chapter I

The Rule Everything Obeys

One sentence. Followed to its logical end. The entire universe.

"The laws of physics are the same
in all inertial frames."

In other words: it doesn't matter where you are, how fast you're moving, or which direction you're facing. The same rules apply. No special place. No special direction. No background. Just the rules.

What This Forbids

What Would Breaking This Rule Look Like?

Try adding structure to the universe. Watch the symmetry break.

The grid is symmetric — every point is equivalent to every other. This is what the postulate demands.

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The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction.

Albert Einstein, 1918

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It appeared impossible to prove κ > 0 from the relativity principle alone.

Wolfgang Pauli

This paper supplies the missing proof Pauli said couldn't exist. The postulate's own language — velocity is displacement per unit time — requires a distinguished time direction, which forces κ > 0.

Four Properties

The Postulate Has Four Consequences

Each is not an assumption — it is a logical necessity. Violating any one requires a preferred structure the postulate forbids.

Linearity

A displaced inertial frame must also be inertial. If it weren't, there would be a preferred origin — a special point in space. The postulate forbids special points.

Group Composition

If moving from A to B is a valid transformation, and B to C is valid, then A to C must also be valid. The set of all valid moves forms a mathematical group.

Isotropy

A rotated inertial frame is still inertial. If some orientations were non-inertial, there would be a preferred direction in space — forbidden by the postulate.

Reciprocity

If you see me moving at speed v, I see you moving at speed −v. Anything else would make one frame special over another — which the postulate cannot allow.

Questions

Frequently Asked

A viewpoint that isn't accelerating — a train at perfectly constant speed, or a spacecraft drifting through empty space. Not a car turning a corner. Not a rocket firing its engines. Just steady, undisturbed motion. The postulate says the laws of physics are the same for any such observer.

Because 'no external structure' is an enormously powerful constraint. The universe has very little room once you insist the rules are truly universal. Every time you rule out a preferred direction, a preferred location, or a preferred background, you're forced into a specific mathematical structure. And that structure turns out to be the de Sitter algebra — which contains everything.

He felt it intuitively — his 1918 quote shows he sensed that one rule should be enough. But he could not prove it formally. He added the speed of light as a second postulate in 1905, and later added the equivalence principle and general covariance for general relativity. This paper shows all three are consequences of the first.

κ is a free parameter in the algebra that scales how much two successive boosts rotate the frame. When κ > 0, there is a finite invariant speed V = 1/√κ — nothing can go faster. When κ = 0, boosts commute and there is no speed limit (Galilean physics). The paper proves κ must be positive, which gives us special relativity.

It uses Lie group theory — specifically the classification of kinematic Lie algebras by Bacry and Lévy-Leblond (1968), the Killing form from Élie Cartan's work (1894), and Lovelock's uniqueness theorem (1971). These are well-established mathematical results. The paper shows that when you apply them to the relativity postulate, the conclusions are forced.

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