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Special Relativity: Time Dilation and Length Contraction
Einstein's special relativity (1905) rests on two ideas: the laws of physics are the same for everyone moving at constant velocity, and the speed of light c is the same for every observer. Together they lead to surprising effects at high speed.
The Lorentz factor
Everything depends on γ = 1/√(1 − v²/c²). At everyday speeds γ is almost exactly 1. At 87% of c, γ = 2; at 99.5% of c, γ ≈ 10. As v approaches c, γ grows without limit, which is why nothing with mass can reach the speed of light.
Time dilation
A moving clock runs slow. If a clock on a spaceship ticks a time Δτ (its proper time), observers on Earth measure a longer time Δt = γΔτ. This is real and measured: fast muons created by cosmic rays live long enough to reach the ground only because of time dilation.
Length contraction
An object moving past you is measured shorter along its direction of motion: L = L₀/γ, where L₀ is its length at rest. Lengths across the motion are unchanged. The traveller notices nothing odd about their own ship; it's the measurement between frames that differs.
Worked example
A ship travels at 0.995c, so γ ≈ 10. A trip that lasts 10 years by Earth clocks takes only about 1 year on board, and the 100 m ship is measured as about 10 m long from Earth.
Frequently asked questions
What is the Lorentz factor?
γ = 1/√(1 − v²/c²). It tells you how strongly time dilation and length contraction act at speed v. It equals 1 at rest and grows without limit as v approaches c.
Can anything travel faster than light?
No object with mass can reach or exceed the speed of light, because its energy would have to become infinite as γ grows without limit.
Is time dilation real?
Yes. It has been measured with atomic clocks on aircraft and satellites, and it explains why cosmic-ray muons reach the ground.
Does the traveller feel time slow down?
No. Their own clock and body run normally for them. The difference only appears when clocks in different frames are compared.