Physic Labs

Theory of relativity

Einstein’s postulates and the Lorentz transformation

Test Einstein's two postulates via the Lorentz transformation: observe length contraction and time dilation as β=v/c\beta = v/c varies, verify γ=(1−v2/c2)−1/2\gamma = (1-v^2/c^2)^{-1/2} and the invariant s2=c2t2−x2s^2 = c^2t^2 - x^2.

Undergraduate

Equipment

  • Model of two inertial frames and their clocks
  • Speed slider β = v/c
  • γ readout and quantitative-relation chart

Procedure

  1. Set the relative speed

    Drag the "Speed β = v/c" slider from 0 to 0.6 then 0.95. Watch the readout: γ rises from 1 to about 1.25 then 3.2. In the "Two inertial frames and clocks" figure, the moving clock ticks slower and the moving ruler contracts: L=L0/γL = L_0/\gamma, Δt=γΔt0\Delta t = \gamma\Delta t_0.

  2. Check the γ(β) chart

    In the "Quantitative relations" figure, sweep the second β slider and read the chart readout. Pick three values of β and compute γ=1/1−β2\gamma = 1/\sqrt{1-\beta^2} by hand for comparison. Note γ → ∞ as β→1\beta \to 1: no inertial frame reaches light speed.

  3. Check the interval invariant

    Pick an event (a point in the figure) and read its coordinates (ct,x)(ct, x) in both frames. Compute s2=c2t2−x2s^2 = c^2t^2 - x^2 in each frame and compare: the Lorentz transformation keeps s2s^2 fixed. Use "Reset view" if disoriented; "Pause" to read static coordinates.

Simulation

Experiment history

Hendrik Lorentz and Henri Poincaré built the coordinate transformation that preserves Maxwell's equations during 1890–1904, but still tied it to the ether. In 1905 Einstein re-derived the same formulas from two postulates: the laws of physics are identical in all inertial frames, and the speed of light in vacuum is a constant. The ether became superfluous; time and space measure differently between moving frames. In 1908 Hermann Minkowski recast relativity in four-dimensional spacetime, where a Lorentz transformation is a rotation preserving s2=c2t2−x2s^2 = c^2t^2 - x^2. Time dilation was measured directly with cosmic-ray muons (Rossi–Hall, 1941) and atomic clocks flown on aircraft (Hafele–Keating, 1971).

Related physicists

Albert Einstein

Related library topics

Einstein’s postulates and the Lorentz transformation