Marina Dirac

Marina Dirac rises from a sea of filled states, and the hole she leaves behind shines like a positive electron.

The Physics

Dirac's equation for a free electron allows negative as well as positive energies, separated by a gap of 2mc². Dirac proposed that every negative-energy state is already filled, so electrons cannot fall into them. An empty state, a hole, would move like a positively charged electron.

(iħ γ^μ ∂_μ − m c) ψ = 0, E = ± √(p²c² + m²c⁴)

• ħ: reduced Planck constant (J·s)
• γ^μ: Dirac matrices (dimensionless)
• ∂_μ: spacetime derivative (1/m)
• m: electron mass (kg)
• c: speed of light (m/s)
• ψ: electron wavefunction
• E: energy (J)
• p: momentum (kg·m/s)

Dirac proposed the sea in 1930 (he first suggested the holes were protons); C. D. Anderson reported the positron in cosmic rays in 1933. The gap is 2m_ec² ≈ 1.022 MeV.

Honest caveat: The sea is a historical picture. Quantum field theory keeps the positron and drops the sea.

On the shirt

Front: Marina Dirac, the pixel-art character, with the title. Back: the Dirac equation, the two energy branches, the 1.022 MeV gap, Anderson's positron and the historical-picture note. Printed on a unisex tee.