Physic Labs

Theory of relativity

Minkowski spacetime

Use the 2+1D spacetime diagram to observe relativistic distortions as the frame speed changes. Verify the invariant interval s2=c2t2−x2s^2=c^2t^2-x^2 together with length contraction and time dilation.

Undergraduate

Equipment

  • 3D spacetime diagram (two panels: geometry and quantitative relation)
  • Speed slider β = v/c; model-parameter slider
  • Reset-view and Pause buttons

Procedure

  1. Observe the diagram at β = 0

    In panel 1, set the «Speed β = v/c» slider to 0 and note the light-cone shape and the worldlines. Use «Reset view» if the scene was rotated; events sharing the same t lie on a simultaneity surface.

  2. Raise β and follow the Lorentz deformation

    Drag β to 0.6 then 0.95 in both panels. Watch the moving frame axes tilt toward the light cone and read the γ factor in panel 2. Verify γ=1/1−β2\gamma=1/\sqrt{1-\beta^2}: γ = 1.25 at β = 0.6 and γ ≈ 3.2 at β = 0.95.

  3. Check the invariance of the interval

    Pick an event on the diagram, read its (ct, x) pair at two different β values, and compute s2=c2t2−x2s^2=c^2t^2-x^2 in each case. The two results must agree although the coordinates changed — the signature of a Lorentz-invariant interval; change «Model parameter» to pick another event and repeat.

  4. Compare simultaneity between the two frames

    Hold β = 0.8, find two events simultaneous in the rest frame, and predict their time ordering in the moving frame. Use «Pause» to read the coordinates and check the prediction — the relativity of simultaneity follows directly from the Lorentz transformation.

Simulation

Experiment history

Hermann Minkowski, who had taught Einstein mathematics in Zurich, published Raum und Zeit (Space and Time) in 1908, recasting Einstein's 1905 special relativity as the geometry of a four-dimensional manifold. He famously opened by declaring that space and time separately «were doomed to fade away into mere shadows», with only their union preserving independent reality. A metric with one sign distinguishing time from space (today written ds² = c²dt² − dx² − dy² − dz²) lets Lorentz transformations appear as rotations in spacetime. Einstein at first dismissed this as «superfluous learnedness», yet Minkowski's geometry became the foundation on which he built general relativity in 1915.

Related physicists

Albert Einstein

Related library topics

Minkowski spacetime