---
title: "Listen to Spacetime with Light Interactive Lab | Sandbox Physics"
description: "How can a length change smaller than a proton become a readable signal? Through interference."
canonical_url: "https://sandboxphysics.com/labs/ligo-interferometer/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/ligo-interferometer/"
last_modified: "2026-10-27"
---

Gravitational waves · laser interferometry

# LIGO · Listening to Spacetime

**How can a length change smaller than a proton become a readable signal?** Through interference. A passing gravitational wave stretches one four-kilometer arm while squeezing the other. When the two returning laser beams recombine, that tiny difference changes how well they cancel, and the strain becomes a light signal you can read. Two observatories have to see it together before it counts.

Fly through a virtual LIGO detector. Watch freely falling masses stretch and squeeze as a gravitational wave passes, then enter the two perpendicular four-kilometre arms. Follow the laser as it splits, travels out and back, and cancels. At the end, two observatories confirm a black-hole merger together.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Every spatial distortion and optical phase shift is enormously exaggerated so you can see it. The real event GW150914 changed the relative length of LIGO's four-kilometre arms by only about $4\times10^{-18}\,\mathrm m$, roughly 1/200 of a proton diameter.

Scientific explanation

## Read the picture as a physical process

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. 1

   **The wave passes** The transverse spacetime metric oscillates

2. 2

   **Distances change** x grows while y shrinks

3. 3

   **The ring deforms** The 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 limits** This 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.

Sources and further reading [LIGO's Interferometer](https://www.ligo.caltech.edu/LA/page/ligos-ifo) [Advanced LIGO and GW150914](https://ligo.org/science-summaries/GW150914Detector/) [Advanced LIGO DC readout](https://dcc.ligo.org/public/0094/G1200743/001/G1200743v1_part3.pdf)

## Related experiments and articles

Continue exploring

### Understand, then measure

How does a tiny arm-length change become a signal at the output?

1. [You are here **LIGO · Listening to Spacetime** Take a visual tour of spacetime, arms and optical readout.](https://sandboxphysics.com/labs/ligo-interferometer/)
2. [Lab **LIGO Interferometer** Vary the bias, arm storage and recycling in the measurement model.](https://sandboxphysics.com/labs/ligo-system-interferometer/)

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)