What dimensionless factor equals 1/sqrt(1−v²/c²) in special relativity?

The dimensionless factor 1/sqrt(1−v²/c²) in special relativity is the Lorentz factor.

Usually written as γ, the Lorentz factor depends on the relative speed v divided by the speed of light c. It appears throughout special relativity because measurements of time, length, momentum, and energy differ between inertial observers moving relative to one another. The same factor can also be written γ = dt/dτ, relating coordinate time to the proper time measured by a moving clock.

At low speeds, γ is very close to 1, so relativistic effects are difficult to notice. As v approaches c, the denominator approaches zero and γ grows without bound. This behavior helps explain why a massive object cannot be accelerated to or beyond the speed of light. For example, at 0.8c, γ is about 1.67.

The Lorentz factor is not the Doppler factor, although both can appear in relativistic observations. The Doppler factor concerns how motion changes observed frequencies and intensities, while γ is the kinematic factor built directly into Lorentz transformations. The symbol γ is also distinct from the unrelated gamma rays and Euler’s constant.