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Relativistic momentum
Intermediate
Momentum grows without bound as v approaches c.
p = γmvp = γmv grows without limit as v → c, so accelerating to c needs infinite energy. At low speeds p ≈ mv.
At 0.8c: p = 1.33 mc.
Conservation of this p holds in all frames.
In more detail
Relativistic momentum is p = γmv, which increases faster than classical momentum as speed approaches c. It reduces to mv at low speeds.
Real-world uses
- Particle accelerators use relativistic momentum to design magnets and beam paths.
- Collision physics relies on relativistic momentum conservation.
- Accelerator physicists note that the momentum of a particle grows without bound as it approaches the speed of light.
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Frequently asked questions
Why does momentum grow so fast?
Because γ increases rapidly near c, so the object's momentum increases without limit.
Is momentum conserved?
Yes, the total relativistic momentum is conserved in isolated systems.
Why does momentum grow without limit?
The relativistic factor gamma grows without bound as speed approaches c, so more and more momentum is needed for each small increase in speed.
Related topics in Relativity
Spacetime interval · Light cones and causality · Proper time · Relativistic energy · Rest energy · Energy–momentum relation