Splitra

Splitra opens her hands in a storm of electric field and tears a gleaming electron and positron out of empty space.

The Physics

A strong enough electric field should pull electron–positron pairs out of the vacuum. In Dirac's picture an electron in the negative-energy sea must tunnel across a gap of 2mc², and the field tilts that gap. The rate is exponentially suppressed unless the field approaches a critical value, where the field does work mc² over one reduced Compton wavelength.

E_c = m²c³ / (eħ) ≈ 1.32 × 10¹⁸ V/m and rate ∝ exp(−πE_c / E)

• E_c: critical field (V/m)
• m: electron mass (kg)
• c: speed of light (m/s)
• e: elementary charge (C)
• ħ: reduced Planck constant (J s)
• E: applied electric field (V/m)

Sauter found the tunnelling factor in 1931, Heisenberg and Euler built the effective theory in 1936, and Julian Schwinger gave the full QED result in Phys. Rev. 82, 664 (1951).

Honest caveat: The exponential is the leading factor only. The effect has not yet been seen directly in the vacuum with a static field, because no lab field comes close to E_c. A “Schwinger-like” production of electron–hole plasma reported in graphene superlattices (Berdyugin et al., Science 2022) is an analogue in a material, not the vacuum effect. The pair's energy comes from the field, not from nothing.

On the shirt

Front: Splitra, the pixel-art character, with “TEARING THE VACUUM”. Back: the critical field, the leading pair-rate factor, the not-yet-seen note and the 1931, 1936 and 1951 sources. Printed on a unisex tee.