Table of Contents
Relativistic Velocity Addition
In classical mechanics, velocities add linearly. Einstein's special relativity shows this breaks down at speeds approaching the speed of light. The relativistic formula ensures no combination of velocities exceeds c.
Adding 0.9c and 0.9c yields about 0.994c, not 1.8c. This is a consequence of the constancy of the speed of light in all reference frames.
Einstein's Formula
Classical vs Relativistic
| v | u | Classical | Relativistic |
|---|---|---|---|
| 0.5c | 0.5c | 1.0c | 0.800c |
| 0.9c | 0.9c | 1.8c | 0.994c |
| 0.99c | 0.99c | 1.98c | 0.99995c |
Frequently Asked Questions
Why can't anything exceed c?
As velocity approaches c, relativistic mass increases without limit, requiring infinite energy. The addition formula mathematically prevents any sub-light combination from reaching c.
Does this matter at everyday speeds?
At 100 km/h, the correction is about 10^-15, far below measurement precision. It matters above about 10% of light speed.
What about light itself?
If v=c, the formula gives w=c regardless of u. The speed of light is the same in all inertial frames.