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Velocity addition
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Speeds never add to exceed c.
Key relation
u' = (u+v)/(1+uv/c²)u' = (u + v)/(1 + uv/c²): speeds never exceed c. 0.9c + 0.9c = 0.994c.
Worked example
Light seen from a moving frame still has speed c.
Common mistake
At low speeds reduces to u + v.
In more detail
Relativistic velocity addition gives the combined speed of two velocities as u = (u1 + u2)/(1 + u1u2/c²). The result never exceeds the speed of light.
Real-world uses
- Particle collisions at high energy use relativistic velocity addition.
- It ensures that no object can exceed light speed.
- Particle physicists add velocities in relativity to find the speed of a particle emitted from a fast-moving source.
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Frequently asked questions
What is the sum of 0.5c and 0.5c?
0.8c, not c, because of the relativistic formula.
Why is this important?
It guarantees that the speed of light is a universal limit.
Can two speeds add up to more than c?
No. The relativistic velocity addition rule always gives a result below the speed of light.
Related topics in Relativity
Length contraction · Lorentz factor · Lorentz transformations · Muon decay evidence · Twin paradox · Spacetime diagrams