PAIR & ANNIHILATION
Two 511 keV photons, exactly back-to-back — the 180° derived from p-conservation, residual 0.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Two experiments share the stage. On the left, an electron and a positron erase each other into light. On the right, a photon tries to become matter. The same equation is the till for both — E equals m c squared, read in each direction.
Annihilation
At rest the total momentum is zero, and that single fact forces everything: the photons must have equal energies and opposite directions. The cosine of the opening angle computes to exactly minus one — the back-to-back is derived, not drawn. Each photon carries the electron mass at par: 511 keV. Point a ring of detectors at a patient and you have PET imaging.
Production
The displayed 1.02200 MeV floor is explicitly the infinite-target limit. A finite nucleus must absorb recoil, raising the exact threshold to 2m_ec² + 2m_e²c²/M and consuming some excess energy; one-photon production in empty space is impossible.
The boost
The sweep accelerates the positron from rest to three MeV: the photon pair leaves the symmetric split, the forward one fattening, the backward one starving — gamma one plus-or-minus beta, dopplerrel’s own machinery — while the ledger bars stay balanced to the last pixel.
Audit
Audited: annihilation angle and boosted photon ledgers close as before. Production now distinguishes the exact M→∞ floor from finite-target kinematics and quantifies the proton recoil correction instead of calling the idealized floor universally exact.