Spacetime Explorer — Warping Space and Time
As objects move faster, something extraordinary happens: time slows down and lengths shrink. These aren't optical illusions — they are real, measurable effects predicted by Einstein's Special Relativity in 1905. Use the sliders below to fly toward the speed of light and watch spacetime transform before your eyes.
The Lorentz Factor
Everything in special relativity flows from a single quantity — the Lorentz factor:
$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$
At everyday speeds $\gamma \approx 1$ and nothing unusual happens. But as $v \to c$, the factor $\gamma$ shoots toward infinity, dragging time and space with it.
Time Dilation
A clock moving at speed $v$ ticks slower than a stationary clock:
$$\Delta t' = \gamma \, \Delta t$$
If $\gamma = 2$, one second on your watch corresponds to two seconds on the traveller's clock — time literally stretches.
Muons created in the upper atmosphere travel at $v = 0.998c$. Their rest-frame half-life is $1.56\,\mu$s. How long do they live in the Earth frame?
$$\gamma = \frac{1}{\sqrt{1 - 0.998^2}} = \frac{1}{\sqrt{1 - 0.996}} = \frac{1}{\sqrt{0.004}} \approx 15.8$$
$$\Delta t' = 15.8 \times 1.56\,\mu\text{s} \approx 24.7\,\mu\text{s}$$
The muons live 16 times longer than expected — long enough to reach the ground. This is measured every day in particle physics labs.
Length Contraction
An object moving at speed $v$ is shortened along the direction of motion:
$$L = \frac{L_0}{\gamma} = L_0 \sqrt{1 - v^2/c^2}$$
A 100-meter spaceship at $v = 0.87c$ ($\gamma = 2$) measures only 50 meters to a stationary observer.
Time dilation and length contraction are two sides of the same coin — both arise from the geometry of spacetime. The Lorentz factor $\gamma$ is the single number that controls both effects.