mobius-units

Fundamental constants and unit conversions from the eigenvalue tower — one measurement derives them all.

from mobius_units import alpha_inv, m_e, G, l_P

alpha_inv   # 137.03599917656376 (tower-derived, not CODATA lookup)
m_e         # 9.109383714e-31 kg (from tower alpha + R_inf)
G           # 6.67436e-11 m^3 kg^-1 s^-2 (tower-derived, 0.37 sigma)
l_P         # 1.61626e-35 m (tower-derived)

The Problem

Existing unit libraries (pint, astropy.units, scipy.constants) carry 20+ empirical conversion factors from CODATA lookup tables. When CODATA updates, the tables must be refreshed. No algebraic relationship connects the constants — they are independent numbers from independent measurements.

The Fix

Three algebraic equations produce three dimensionless quantities with zero measured inputs:

Combined with five SI-exact constants (c, h, e, k_B, N_A) and one measurement (the Rydberg constant R_inf), these produce the entire CODATA table.

Install

pip install mobius-units

Requires Python >= 3.9. One dependency: mobius-constant.

Constants

Every alpha-dependent constant uses the tower value, not a CODATA lookup.

Dimensionless (tower-derived)

Atomic scale (tower alpha + R_inf)

Planck scale (tower hierarchy)

Unit Systems

Three natural unit systems, all algebraically connected:

from mobius_units import AtomicUnits, PlanckUnits, ParticleUnits

# Atomic -> SI
AtomicUnits.to_si(1.0, 'energy')   # 1 Hartree in joules
AtomicUnits.to_si(1.0, 'length')   # 1 Bohr in metres
AtomicUnits.to_si(1.0, 'time')     # 1 atomic time in seconds

# SI -> Atomic
AtomicUnits.from_si(9.11e-31, 'mass')  # electron mass in atomic units (= 1)

# Planck -> SI
PlanckUnits.to_si(1.0, 'length')   # 1 Planck length in metres
PlanckUnits.to_si(1.0, 'temperature')  # 1 Planck temperature in kelvin

# Particle physics (SI-exact, no tower needed)
ParticleUnits.to_si(125.0, 'energy')  # 125 GeV in joules

# Cross-system
from mobius_units import atomic_to_planck
atomic_to_planck(1.0, 'energy')  # 1 Hartree in Planck energy units

The Alpha Source

All alpha-dependent constants trace to mobius-constant:

from mobius_constant import Alpha_inv
float(Alpha_inv)  # 137.03599917656376

This is the tower-derived value, not the CODATA adjusted average. It sits 0.3 sigma from the best measurement in physics (Fan et al., 2023). The ~4.5 sigma offset from CODATA 2018 adjusted constants traces entirely to the documented Cs-133 recoil anomaly.

See Also

• mobius-constant — Exact irrational constants
• One Measurement Derives Them All — companion paper (Carpenter, 2026)

License

MIT — Jay Carpenter, 2026