Massratio

Massratio is a stone proton giant of The SI Guard with a tiny electron sprite, balanced on a long lever.

The Physics

The proton is about 1836 times heavier than the electron. This dimensionless ratio sets why atoms have a tiny heavy nucleus with a light electron cloud, why nuclei barely move in chemistry (the Born–Oppenheimer approximation), and the ratio of vibrational to electronic energies in molecules. It is measured with Penning-trap mass comparisons and precision spectroscopy of molecular hydrogen ions such as HD⁺.

μ = m_p/m_e = 1836.152 673 426(32)

• μ: proton-to-electron mass ratio (dimensionless)
• m_p: proton rest mass, measured
• m_e: electron rest mass, measured
• (32): standard uncertainty in the last two digits, about 1.7 × 10⁻¹¹ relative

Value: CODATA 2022 (NIST). μ is measured, not fixed by the 2019 SI. Astronomers compare molecular lines in distant gas clouds with lab values to test whether μ changes over cosmic time; no change has been found within their limits.

Honest caveat: The proton's mass is not the sum of its three quarks. The Higgs-given masses of the up and down quarks supply only about 1% of it; the rest is the energy of the strong interaction (QCD) inside the proton. The electron's mass, by contrast, comes directly from its coupling to the Higgs field.

On the sticker

The stone giant holds the short arm of the lever while the electron sprite sits far out on the glowing ice-blue end. Printed text: MASSRATIO with the line mp/me = 1836.15. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.