Recoila

Recoila accelerates, radiates, and her own light shoves her back.

The Physics

An accelerating charge radiates, and the radiation carries away energy and momentum, so the charge feels a recoil. In the non-relativistic limit that radiation-reaction force is proportional to the rate of change of acceleration, the jerk.

F_rad = (μ₀ q² / 6πc) da/dt, P = μ₀ q² a² / (6πc)

• F_rad: radiation-reaction force (N)
• μ₀: vacuum permeability (N/A²)
• q: charge (C)
• c: speed of light, 299 792 458 m/s (exact)
• a: acceleration (m/s²)
• da/dt: jerk (m/s³)
• P: radiated (Larmor) power, v ≪ c (W)

For an electron the time scale is τ = μ₀e² / (6π m_e c) ≈ 6.3 × 10⁻²⁴ s. Abraham (1903), Lorentz (1904) and Dirac (1938) built the theory.

Honest caveat: Taken literally the equation has runaway and pre-acceleration solutions. Reduced-order (Landau–Lifshitz) forms tame it; a full classical cure is still debated.

On the shirt

Front: Recoila, the pixel-art character, with the title. Back: the radiation-reaction force, the Larmor power, the electron's 6.3 × 10⁻²⁴ s, and the runaway caveat. Printed on a unisex tee.