Thomsonia

Thomsonia, an archery-target guardian of the early Universe in The SI Guard, turns photons aside with her shield and sends them off the same colour.

The Physics

When light meets a free electron at low energy, its electric field shakes the electron, which re-radiates at the same frequency. This elastic scattering has a fixed total cross section, the effective target area of one electron. It is J. J. Thomson's classical result, and it is the low-energy limit of quantum electrodynamics.

σ_T = (8π/3) r_e² = 6.652 458 7051(62) × 10⁻²⁹ m²

• σ_T: Thomson cross section
• r_e: classical electron radius, e²/(4πε₀m_ec²) = 2.817 940 3205(13) × 10⁻¹⁵ m
• e: elementary charge (exact)
• ε₀: vacuum permittivity (measured)
• m_e: electron mass (measured)
• c: speed of light (exact)

Values: CODATA 2022 (NIST); both are measured, not exact. Thomson scattering kept light and matter locked together in the hot early Universe until hydrogen formed, about 380 000 years after the Big Bang; it also sets the Eddington luminosity of stars.

Honest caveat: r_e is not the electron's size. It is a length built from its charge and mass; experiments find no electron structure at all down to far smaller scales. The formula holds only for photon energies much less than m_ec² ≈ 511 keV; at higher energies the Klein–Nishina cross section takes over and the scattered photon loses energy (Compton scattering).

On the sticker

Thomsonia raises her shield, and a burst of cyan photon orbs scatters off it unchanged in colour. Printed text: THOMSONIA with the line σ = 8πr²/3. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.