Listen to Spacetime with Light Interactive Lab

What is happening

Why does the ring of masses become an ellipse?

Treat the dots as disconnected test masses in free fall. A gravitational wave arriving perpendicular to the ring does not blow them outward; it changes their proper separations. Plus polarization stretches one transverse axis while squeezing the other. Cross polarization is the same pattern rotated by 45 degrees.

Causal chain

1
The wave passesThe transverse spacetime metric oscillates
2
Distances changex grows while y shrinks
3
The ring deformsThe long and short axes swap half a cycle later

Mathematical model

\begin{aligned} L_x(t) &\approx L\left[1 + \frac{1}{2}h_{+}(t)\right] \\ L_y(t) &\approx L\left[1 - \frac{1}{2}h_{+}(t)\right] \end{aligned}

Symbols

$L$: Reference separation with no wave
$h_{+}(t)$: Dimensionless plus-polarized strain
$L_x,\,L_y$: Proper separations along two transverse axes

Model boundaryThis is the standard long-wavelength, TT-gauge teaching picture. The animation exaggerates strain by roughly 10²⁰. Coordinate positions may remain fixed while proper distances change.

What is happening

Why use two long, perpendicular arms?

LIGO does not try to measure the absolute displacement of one mirror. It compares two arms. For a plus-polarized wave aligned with the detector, one arm gains δL while the other loses δL. Subtracting the opposite responses adds the signal while suppressing common changes such as laser-frequency drift.

Causal chain

1
End mirrors approximate free massesMulti-stage suspensions isolate ground motion
2
The arms respond oppositely+δL and −δL appear together
3
Read the differenceDifferential sensing retains strain and rejects common motion

Mathematical model

\begin{aligned} \Delta L_{\mathrm{diff}} &\equiv \delta L_x - \delta L_y = h_{+}L \\ h_{+} &= \frac{\Delta L_{\mathrm{diff}}}{L} \end{aligned}

Symbols

$L$: Reference arm length; 4 km at LIGO
$\Delta L_{\mathrm{diff}}$: Differential change between the arms
$h_{+}$: Plus strain aligned with the arms

Model boundaryThe equation shows the clearest case: normal incidence with plus polarization aligned to the arms. A general sky direction and polarization introduce detector responses F₊ and F×.

What is happening

How does light turn a length change into something measurable?

A laser has a stable wavelength and phase, so it acts as an optical ruler. The beam splitter creates two paths from the same coherent field. After reflection from the end mirrors, an extra path length appears as extra optical phase. Only the relative phase of the returning beams must be compared.

Causal chain

1
Split one sourceBoth beams begin with a common phase
2
Make two round tripsEach beam records one arm’s optical path
3
RecombineRelative phase carries ΔLdiff

Mathematical model

\begin{aligned} \phi_{\mathrm{rt}} &= \frac{4\pi L}{\lambda} \\ \Delta\phi &= \frac{4\pi(L_x - L_y)}{\lambda} \end{aligned}

Symbols

$\lambda$: Laser wavelength in vacuum
$\phi_{\mathrm{rt}}$: Optical phase accumulated in one round trip
$\Delta\phi$: Phase difference between the returning beams

Model boundaryThis scene begins with a simple Michelson interferometer. Real LIGO arm cavities make the light sample an arm repeatedly; scene five adds that gain.

What is happening

Why begin with an output that is almost dark?

The returning beams are tuned nearly out of phase, so a crest from one meets a trough from the other and the output port is almost dark. A gravitational-wave phase shift makes the cancellation incomplete, sending a small amount of light to the photodetector.

Causal chain

1
Near cancellationWith no signal, the returning fields almost cancel
2
Create ΔφDifferential arm length advances one phase and delays the other
3
Output power changesA photodetector converts light power to an electrical signal

Mathematical model

\begin{aligned} E_{\mathrm{out}} &\propto E_0\sin\left(\frac{\Delta\phi}{2}\right) \\ I_{\mathrm{out}} &\propto \sin^2\left(\frac{\Delta\phi}{2}\right) \end{aligned}

Symbols

$E_{\mathrm{out}}$: Optical field amplitude at the output port
$I_{\mathrm{out}}$: Light intensity measured by the photodetector
$\Delta\phi$: Phase difference between the returning beams

Model boundaryThe picture first shows an ideal dark fringe. Advanced LIGO introduces a tiny DARM offset so a small carrier field acts as a local oscillator and provides a linear DC readout.

What is happening

When 4 km is still too short, how does LIGO gain more signal?

The input test mass near the beam splitter and the end test mass 4 km away form a Fabry–Pérot cavity. Resonant light does not leave after one trip; it reflects between the mirrors about 300 times. Each traversal samples the arm length again, accumulating the tiny phase effect.

Causal chain

1
Enter a resonant cavityFields satisfying the resonance condition build up
2
Traverse 4 km repeatedlyThe same arm change is sampled many times
3
Enhance phase responseThe stored field returns for differential comparison

Mathematical model

\begin{aligned} L_{\mathrm{effective}} &\approx N L_{\mathrm{arm}} \\ &\approx 300 \times 4\,\mathrm{km} \approx 1200\,\mathrm{km} \end{aligned}

Symbols

$N$: Effective traversal count in this teaching approximation, about 300
$L_{\mathrm{arm}}$: Physical arm-cavity length, 4 km
$L_{\mathrm{effective}}$: Intuitive effective optical path

Model boundaryThe 1200 km figure is path-length intuition. Real cavity gain also depends on finesse, storage time, and gravitational-wave frequency; it is not a fixed N at every frequency.

What is happening

How does the chirp show that both sites saw the same merger?

As a binary loses energy, its orbit shrinks and speeds up. The dominant quadrupole gravitational-wave frequency is about twice the orbital frequency, and its amplitude rises rapidly. The same chirp shape appears at Livingston and Hanford, while local instrument noise is not expected to reproduce a correlated waveform at both sites.

Causal chain

1
The orbit shrinksGravitational waves carry away energy and angular momentum
2
Frequency and amplitude riseThe inspiral becomes a chirp
3
Two sites correlateGW150914 arrived about 7 ms apart

Mathematical model

\begin{aligned} f_{\mathrm{GW}} &\approx 2f_{\mathrm{orb}} \\ \Delta t &= \frac{\hat{\mathbf n}\cdot(\mathbf r_{\mathrm H}-\mathbf r_{\mathrm L})}{c} \approx 7\,\mathrm{ms} \end{aligned}

Symbols

$f_{\mathrm{GW}}$: Dominant quadrupole gravitational-wave frequency
$f_{\mathrm{orb}}$: Binary orbital frequency
$\Delta t$: Arrival-time difference between the sites

Model boundaryThe displayed chirp is a teaching waveform, not raw detector data. Real analysis calibrates strain, models noise, and performs statistical inference with full waveform models and the detector network.

LIGO · Listening to Spacetime

Read the picture as a physical process

Why does the ring of masses become an ellipse?

Why use two long, perpendicular arms?

How does light turn a length change into something measurable?

Why begin with an output that is almost dark?

When 4 km is still too short, how does LIGO gain more signal?

How does the chirp show that both sites saw the same merger?