Lorentz factor (γ)

The Lorentz factor, written with the Greek letter gamma, is the single number that measures how strongly relativity bites at a given speed. It is defined as gamma = 1/sqrt(1 - v^2/c^2), where v is the speed and c the speed of light. It is the stretch factor for time dilation and the shrink factor for length contraction, and the same gamma threads through nearly every formula in special relativity.

Its behaviour is easy to feel. At rest, v is zero and gamma equals exactly 1, so nothing strange happens. At everyday speeds, even a fast jet, gamma exceeds 1 by only a hair, a few parts in a trillion, which is why relativity stays invisible in daily life. But as v climbs toward c, the term under the square root shrinks toward zero, and gamma shoots upward toward infinity.

That runaway growth is exactly why nothing with mass can reach the speed of light. As v nears c, gamma blows up, and with it the energy and momentum needed to push the object any faster, so the cost of the next sliver of speed becomes ruinous and then impossible. Light, being massless, sits permanently at c, and gamma is simply not defined there.

A useful image is a stiffening spring. Below a few tenths of c the spring barely resists, and speeds add almost normally. Push past 90 percent of c and it suddenly resists ferociously: at 99.5 percent of light speed gamma is already about 10, so clocks slow tenfold and lengths shrink tenfold, and the last sliver toward c is effectively a wall.