Special Relativity Lab

Explore Einstein's special relativity through interactive visualizations. Adjust velocity as a fraction of the speed of light and watch the Lorentz factor, time dilation, length contraction, and relativistic energy change in real time.

Guided Experiment: Exploring the Lorentz Factor

How does the Lorentz factor γ change as velocity increases from 0 to nearly the speed of light? Is the relationship linear or nonlinear? At what speed do relativistic effects become significant?

Write your hypothesis in the Lab Report panel, then click Next.

Lorentz Factor γ vs β

00.20.40.60.810246810β (v/c)γ (Lorentz factor)γ = 1.15

Spacetime Diagram

lightctxct′x′β = 0.500

Length Contraction

RestL₀ = 100 mMovingL = 86.60 m86.6% of rest length at β = 0.5

Controls

0.5000
Proper time (years)1.0
Proper length (m)100

Results

0.5
1.155
1.155years
86.6m

Interpretation. A clock moving at 0.5c runs 1.155 times slower than a stationary clock. A 86.6 m ruler in the moving frame appears as 86.6 m to a stationary observer.

Data Table

(0 rows)
#β (v/c)γΔt (yr)L (m)p (kg·m/s)E (J)
0 / 500
0 / 500
0 / 500

Reference Guide

The Lorentz Factor

The Lorentz factor determines how much time, length, and momentum change at relativistic speeds. It grows without bound as velocity approaches the speed of light.

γ=11−β2,β=vc\gamma = \frac{1}{\sqrt{1 - \beta^2}}, \quad \beta = \frac{v}{c}

At everyday speeds γ is almost exactly 1. At 90% the speed of light, γ ≈ 2.3.

Time Dilation & Length Contraction

Moving clocks run slow and moving objects appear shortened in the direction of motion.

Δt=γ Δt0,L=L0γ\Delta t = \gamma \, \Delta t_0, \qquad L = \frac{L_0}{\gamma}

These are real physical effects confirmed by muon decay experiments and GPS satellite corrections.

Relativistic Energy

Mass and energy are related by Einstein's famous equation. Kinetic energy and momentum also take relativistic forms.

E=γmc2,p=γmv,E2=(pc)2+(mc2)2E = \gamma m c^2, \quad p = \gamma m v, \quad E^2 = (pc)^2 + (mc^2)^2

The rest energy E₀ = mc² shows that mass itself is a form of energy.

Velocity Addition

In relativity, velocities don't simply add. The relativistic formula ensures no combination of sub-light speeds ever exceeds c.

u=v1+v21+v1v2c2u = \frac{v_1 + v_2}{1 + \dfrac{v_1 v_2}{c^2}}

For example, 0.5c + 0.5c = 0.8c, not 1.0c as classical addition would predict.