Signed photon momenta decide whether a zero-momentum reaction closes. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Opposite photons cancel momentum
Output momenta 20 and -20 sum to 0; output energy is 200 J; accepted bit 1.
20−20=0,E=200,a=1
Same-direction photons fail momentum
Output momenta 20 and 20 sum to 40; output energy is 200 J; accepted bit 0.
20+20=40,E=200,a=0
Unequal photons fail both totals
Output momenta 20 and -10 sum to 10; output energy is 150 J; accepted bit 0.