What question did this study set out to answer?

The aim is to find a formula for the Cosmic Microwave Background temperature using fundamental atomic constants.

March 5, 2026Open Access

A Derivation of the CMB Temperature from Atomic Constants, the Heisenberg Uncertainty Principle, and the Landauer Limit V6: a φ⁴ Lagrangian on S⁵ with exact partition function Z = 6π⁶e³

Key Points

The aim is to find a formula for the Cosmic Microwave Background temperature using fundamental atomic constants.
Numerical observation of the CMB temperature
Utilized atomic constants such as hbar, me, a0, kB, and alpha
Equated Heisenberg minimum energy with Landauer minimum thermal energy
CMB temperature calculated as T_CMB = 2.72548 K
Formula achieved five significant figures using atomic constants
Observed error margin of 0.000194%

Abstract

We report a numerical observation: the temperature of the Cosmic Microwave Background (TCMB = 2. 72548 K) can be expressed to five significant figures using only atomic constants — hbar, mₑ, a₀, kB, alpha — and the factorial 5!. The formula emerges from setting equal the Heisenberg minimum energy and the Landauer minimum thermal energy. Error: 0. 000194%. No theoretical derivation is offered.

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Judicael Brindel

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Progamme National Contre le Tuberculose

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A Derivation of the CMB Temperature from Atomic Constants, the Heisenberg Uncertainty Principle, and the Landauer Limit V6: a φ⁴ Lagrangian on S⁵ with exact partition function Z = 6π⁶e³

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Abstract

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