The Einstein field equations

Equipment

• Virtual spacetime mesh showing sag caused by the source
• Source-density slider (dimensionless parameter)
• Time-speed slider and Pause button
• Draggable canvas; source-parameter readout

Procedure

1. Read the mesh sag

   Leave the source parameter at its middle value and press Pause. Drag the canvas to tilt the view and inspect the depth of the sag: the closer to the source, the deeper the mesh dips — a qualitative picture of $G_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu}$.

2. Vary the source density

   Raise the source-density slider from low to high and note the 'source parameter' readout together with the relative sag. The larger $T_{\mu\nu}$, the stronger the depicted curvature — the spirit of the linear relation $G_{\mu\nu}\propto T_{\mu\nu}$.

3. Compare vacuum-like conditions and predict

   Drop the source to its lowest setting: the region far from the source is nearly flat, recalling the vacuum solution $R_{\mu\nu}=0$ outside a mass. Use the time-speed slider to change the animation pace, predict the sag for a doubled source, then check.

Simulation

Experiment history

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