N
One Postulate
Emad Mostaque · 2026

Chapter IV

Measure It. Don't Prove It.

The algebra proved that a universal speed must exist. Experiment tells us what that speed is, and what carries it. These are two very different things.

Michelson-Morley interferometer apparatus

Experimental apparatus for measuring the speed of light: a Michelson-Morley style interferometer. The experiment measured the speed. The algebra had already established its existence.

What the Algebra Tells Us

From Postulate 1 alone

  • ◈A universal invariant speed V must exist
  • ◈V = 1/√κ where κ > 0
  • ◈Spacetime has a Lorentzian metric: ds² = c²dt² − dx² − dy² − dz²
  • ◈Moving clocks run slow, by factor γ = 1/√(1 − v²/V²)
  • ◈Moving rulers shrink, by the same factor γ
  • ◈Space and time mix under boosts

The Role of Measurement

What Experiment Tells Us

  • ◈V ≈ 299,792,458 m/s — the specific numerical value
  • ◈Electromagnetic radiation (light) travels at this speed in vacuum
  • ◈The speed is the same in every inertial frame (Michelson-Morley confirmed)
  • ◈Time dilation is real and measurable (Ives-Stilwell, Hafele-Keating)
  • ◈Length contraction is real (muon decay observations)
  • ◈The metre is now defined in terms of c (SI, 1983)

The Equations the Algebra Delivers

Time Dilation Factor

γ = 1/√(1 − v²/V²)

Moving clocks run slow by this factor. Confirmed by Ives-Stilwell (1938) and Hafele-Keating (1971).

Lorentzian Metric

ds² = V²dt² − dx² − dy² − dz²

The invariant spacetime interval. The Lorentzian signature follows from Postulate I alone, not from the constancy of light.

Universal Invariant Speed

V = 1/√κ

Algebra demands this speed exist. κ > 0 is proved by the Killing form. Experiment measures V ≈ 299,792,458 m/s.

The Division of Labour

Algebra Tells You What Must Be.
Experiment Tells You What Is.

The symmetry algebra proves that a universal invariant speed must exist. It does not tell us the numerical value of that speed, nor which physical phenomenon carries it. Those are empirical questions. Experiment answers: the speed is approximately 299,792,458 metres per second, and electromagnetic radiation (light) travels at precisely that speed in vacuum. This is a fact about the world, not a fact about the algebra.

What the algebra removes is the need for Einstein's second postulate as an independent assumption. The constancy of the speed of light in all inertial frames is not a brute empirical fact grafted onto the theory. It is a consequence of the symmetry structure that Postulate I already entails. This is the difference between redundancy and falsity. Einstein's second postulate was never wrong. It was never needed.

Postulate ISymmetry algebra+ Killing formprovesV = 1/√κ existsV must existsign κ > 0proved algebraicallymeasuredV ≈ cExperimentV = 299,792,458 m/slight carries it

A Brief History of Measurement

1

1887

Michelson-Morley

No ether drift detected; speed of light is the same in all directions.

2

1905

Einstein's Two Postulates

Einstein uses the measured constancy as a postulate, but this paper shows it wasn't needed.

3

1938

Ives-Stilwell

First direct confirmation of relativistic Doppler shift: time dilation confirmed.

4

1971

Hafele-Keating

Atomic clocks on planes confirm gravitational and velocity time dilation.

5

1983

SI Definition

The metre is defined as the distance light travels in 1/299,792,458 seconds. c is now exact by definition.

“
The second postulate was not wrong. It was redundant. There is a difference.

Einstein's observation that light travels at the same speed in every frame is experimentally true. This paper does not dispute that. What it shows is that this fact follows necessarily from the first postulate, from the symmetry of motion alone. Postulate II is a consequence, not an assumption. Describing it as a postulate was therefore redundant.

"
The hypothesis that the ether is at absolute rest... seems to me the most satisfactory.
— Hendrik Lorentz, 1904

Lorentz derived the transformation equations that bear his name, but thought they described a physical compression of matter moving through an invisible medium called the ether. Einstein showed they were a symmetry of spacetime itself. This paper shows even Einstein's second postulate wasn't needed to get there.

← the-killing-formNext → the-lab