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Lorentz factor
Intermediate
Measures how significant relativistic effects are.
γ = 1/√(1−v²/c²)γ = 1/√(1 − v²/c²) is 1 at rest, 1.005 at 0.1c, 2 at 0.866c, 7.1 at 0.99c, and diverges as v → c. It governs all relativistic corrections.
At v = 0.6c, γ = 1.25.
Use β = v/c to simplify.
In more detail
The Lorentz factor γ = 1/sqrt(1 − v²/c²) describes how strongly relativistic effects grow with speed. At everyday speeds it is almost one, and it grows rapidly near the speed of light.
Real-world uses
- Engineers use γ to compute relativistic corrections in accelerators.
- It appears in the formulas for energy and momentum.
- Engineers designing accelerators use the Lorentz factor to find how much a particle's energy and momentum differ from classical values.
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Frequently asked questions
What is γ at 0.9c?
About 2.29.
Why does γ diverge at c?
Because the energy needed to accelerate a massive object grows without limit as it approaches the speed of light.
When is gamma close to one?
At speeds much lower than the speed of light, where relativistic effects are tiny and classical physics works well.
Related topics in Relativity
Relativity of simultaneity · Time dilation · Length contraction · Lorentz transformations · Velocity addition · Muon decay evidence