= Equal-time momentum of an externally driven particle pair
A sum of particle <four-momenta> at specified events is a <four-vector>, but sums recomputed at simultaneous events in different <inertial frames> need not correspond to that same <four-vector>. For opposite equal <electric charges> initially at rest a distance $d$ apart, a longitudinal <electric field> switched on simultaneously in the laboratory produces zero total laboratory <three-momentum>. In a frame moving at $v>0$, the switch-on events are separated by $\gamma_vvd/c^2$; during that interval only one force acts. The late equal-time total <three-momentum> is $-2\gamma_vmv+\gamma_veEvd/c^2$, while the <Lorentz transformation> of an equal-laboratory-time sum varies as the laboratory pair's <energy> grows. Closed-system <four-momentum conservation> requires including the field and external apparatus.
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