Time Dilation: At 50% c, γ ≈ 1.155 — 10 Earth years = 8.66 ship years
At 50% the speed of light, the Lorentz factor γ ≈ 1.1547. For every 10 years that pass on Earth, only about 8.66 years pass for the traveler. The effect becomes dramatic above 90% c: at 99% c, γ ≈ 7.09, so 10 Earth years compress to just 1.41 ship years.
What Is Time Dilation?
Time dilation is one of the most profound consequences of Einstein's 1905 special theory of relativity. It states that time passes at different rates for observers in relative motion: a clock moving at velocity v relative to a stationary observer ticks more slowly by a factor of γ = 1/√(1−v²/c²), known as the Lorentz factor.
The Lorentz Factor
The Lorentz factor γ is unity at rest and grows without bound as velocity approaches c. At 50% c, γ ≈ 1.15 — a modest 15% slowdown. At 90% c, γ ≈ 2.29 — time passes at less than half the rate. At 99.99% c, γ ≈ 70.7, meaning one year of ship time corresponds to over 70 years on Earth.
Experimental Evidence
Time dilation is not merely theoretical. Muons created by cosmic rays in the upper atmosphere reach Earth's surface despite their 2.2-μs half-life because relativistic time dilation extends their observed lifetime. The Hafele–Keating experiment (1971) confirmed time dilation with cesium atomic clocks flown around the world. Today, GPS satellites apply relativistic corrections every moment to maintain positional accuracy.
Implications
Time dilation means that high-speed space travel is effectively one-way time travel to the future. A crew traveling at 99% c to a star 10 light-years away would experience only about 1.4 years of shipboard time, while 10+ years pass on Earth. This is the basis of the famous twin paradox, explored in a separate simulation.
FAQ
What is time dilation?
Time dilation is a prediction of Einstein's special relativity (1905): a clock moving relative to an observer ticks more slowly than a stationary clock. The effect is described by the Lorentz factor γ = 1/√(1−v²/c²). At everyday speeds the effect is immeasurably tiny, but at a significant fraction of the speed of light it becomes dramatic.
Has time dilation been experimentally confirmed?
Yes, repeatedly. The 1971 Hafele–Keating experiment flew atomic clocks on commercial jets and measured nanosecond-level discrepancies matching relativity's predictions. GPS satellites must correct for both special-relativistic time dilation (clocks run slow by ~7 μs/day) and general-relativistic effects (clocks run fast by ~45 μs/day) to maintain accuracy.
What is the Lorentz factor?
The Lorentz factor γ = 1/√(1−v²/c²) quantifies relativistic effects. At v=0, γ=1 (no effect). As v→c, γ→∞. It appears in time dilation (Δt' = γΔt), length contraction (L' = L/γ), and relativistic momentum (p = γmv).
Could time dilation allow time travel to the future?
Effectively, yes. A traveler moving at 99.5% c for what they experience as 1 year would return to find ~10 years have passed on Earth. This is real, not an illusion — the traveler has genuinely aged less. However, returning to the past is not possible through time dilation alone.