Physic Labs

Theory of relativity

Gravitational waves

Study two masses orbiting their barycenter and producing propagating spacetime ripples — gravitational waves at twice the orbital frequency, fGW=2forbf_{GW}=2f_{orb}. Adjust wave amplitude and time rate to inspect the ripple rings.

Research

Equipment

  • Two virtual masses orbiting the barycenter on a 3D mesh
  • Wave-amplitude slider (source parameter)
  • Time-speed slider and Pause button
  • Source-parameter readout; draggable view canvas

Procedure

  1. Identify the wave source

    Let the animation run: two masses circling their common center make the quadrupole moment vary, and ripple rings spread in the orbital plane. Drag the canvas for an oblique view — ripples appear only because the accelerating mass distribution is nonspherical.

  2. Verify $f_{GW}=2f_{orb}$

    Pause the animation, then lower the time speed: count the ripple rings emitted during exactly one orbit — one wave maximum per half-orbit gives fGW=2forbf_{GW}=2f_{orb}; for forb=5f_{orb}=5 Hz, λ=c/fGW≈3,0×107\lambda=c/f_{GW}\approx3{,}0\times10^7 m.

  3. Vary the amplitude and conclude

    Sweep the amplitude slider and read the 'source parameter': the greater the accelerating mass, the deeper the ripples. Note that in reality h ~ 10−2110^{-21}, so a detector must measure strains smaller than a proton — the reason LIGO uses Michelson interferometers with 4 km arms.

Simulation

Experiment history

Albert Einstein derived gravitational waves by linearizing his field equations in 1916 and corrected the radiation formula in 1918. Long suspected of being coordinate artifacts, they were established as physical through the 1950s work of Felix Pirani and Hermann Bondi on spacetime 'stickiness'. Joseph Weber built the first resonant bars in the 1960s, but his results could not be reproduced. The first firm evidence was indirect: the Hulse–Taylor binary pulsar (1974) lost energy at exactly the quadrupole rate. LIGO recorded the first direct wave (GW150914) on 14 September 2015, a century after the prediction.

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