relativistic momentum

In ordinary physics, momentum is mass times velocity, p = m v — the 'quantity of motion' that a moving thing carries, and the thing that is conserved in collisions. But when objects move near the speed of light, that simple formula quietly breaks: use p = m v and you find momentum is no longer conserved when you switch between inertial frames. Relativistic momentum is the repaired definition that keeps the conservation law intact at any speed.

Precisely: relativistic momentum is p = gamma m v, where m is the object's mass (its ordinary rest mass), v is its velocity, and gamma = 1 / sqrt(1 - v^2/c^2) is the Lorentz factor. The extra gamma is the only change from the Newtonian p = m v, and it makes all the difference. At everyday speeds gamma is essentially 1 and you recover the familiar p = m v. But as v climbs toward c, gamma balloons toward infinity, so the momentum of a fixed mass grows without limit even though its speed can never quite reach c. This is the deep reason nothing with mass can be pushed up to light-speed: it would need infinite momentum, and infinite force to supply it.

Relativistic momentum is not a bookkeeping trick — it is measured every day in particle accelerators, where electrons and protons carry hundreds or thousands of times the momentum the naive formula predicts. Modern physics prefers to keep mass as a fixed property of the object and put all the speed-dependence into gamma, rather than talk about a 'relativistic mass' that grows with speed; the two viewpoints agree on p = gamma m v, but the fixed-mass picture is cleaner and now standard.