What are gravitational waves?

Two black holes spiral together and merge far from Earth. The merger itself may produce no light, yet instruments here record a short signal. A gravitational wave arrives: a propagating change in spacetime geometry that changes measured separations between free test bodies.

This is not sound travelling through cosmic air. The wave needs no material medium; in general relativity it propagates at light speed. The “chirp” you can hear in a discovery recording appears when data are converted into sound. Let us trace what oscillates, how it is measured and why the signal was linked to black holes. LIGO: waves, source and the first observation.

Relations between measured distances oscillate

Imagine a ring of small, free bodies in space. No hoop or springs connect them. A simple gravitational wave travels perpendicular to the ring’s plane. At one phase measured horizontal separations increase while vertical ones decrease. At the opposite phase, the pattern reverses.

This is the wave’s transverse action: the changes lie in a plane perpendicular to propagation. We show one linear polarization, conventionally called “plus.” Matter is not being thrown from the merger all the way to Earth, nor is compressed air carrying the wave. Proper separations between the bodies change; changing their coordinate labels cannot remove the measurable tidal effect.

The figure enormously exaggerates the distortion. Its dashed circle is a reference, rather than a material hoop. The lower diagram shows two perpendicular optical paths that turn this kind of difference into a measurement. Primary LIGO paper: transverse wave and instrument orientation, section III, figure 3.

Transverse distance changes and two optical arms

The wave travels perpendicular to the diagram; one plus polarization is shown.

Reference circle

Compare distances along x and y.

One phase

The x distance is larger and the y distance smaller.

Opposite phase

The x distance is smaller and the y distance larger.

Dots: freely falling test bodies, not air molecules. Dashes: unchanged reference circle. The solid line only connects bodies for comparison; it is not an elastic hoop.

Comparing two directions

Light from the left → beam splitter → mirrors in arms x and y → return → downward output to the photodetector.

Static teaching sketch, not GW150914 data or a time trace. Distortion is enormously exaggerated; the ellipses do not encode numerical h. Separations are small compared with the wavelength and bodies are free; the optical sketch omits real cavities, suspensions and control. Real output is reconstructed by calibration; response depends on frequency, direction and polarization.

An imaginary instrument responding equally to changes in both arms would not read the same difference. For an interferometer the wave’s orientation relative to its arms and its polarization matter. The sketch shows a favourable geometry rather than equal sensitivity in every direction.

A laser compares two return paths

Each of LIGO’s two detectors has perpendicular arms about 4 km long. Laser light is split, sent down the arms to mirrors and returned for comparison. The optical phase difference affects light at the output photodetector. A wave changes the relative light-travel times along the two routes, leaving a measurable imprint. LIGO: the instrument principle.

This is a complete experiment involving light, mirrors and return times, rather than a ruler secretly compared with “unstretched space.” The real instrument uses optical cavities: repeated passes enhance the phase response. Suspended mirrors are isolated from ground vibrations, while control systems keep the interferometer operating. Primary paper: optics, suspensions and noise, section III.

Raw electrical output is therefore not yet a ready-made cosmic waveform. Calibration accounts for optics, electronics and mirror control to reconstruct the equivalent relative change in the arm-length difference: strain, $h(t)$ . It is dimensionless. Known mirror excitations test how accurately the instrument reconstructs signal amplitude and phase. LIGO: why detector calibration matters.

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What a strain of order 10⁻²¹ means

For a simplified long-wavelength interferometer description, write the unperturbed arm length as $L$ , the individual changes as $\delta L_x$ and $\delta L_y$ , and their difference as $\Delta L$ :

$\Delta L=\delta L_x-\delta L_y,$

$h=\frac{\Delta L}{L}.$

Here $h$ is the response projected onto this detector, not a universal change of any length at any angle. For hypothetical $h=10^{-21}$ and $L=4000\ \text{m}$ :

$\Delta L=4\times10^{-18}\ \text{m}.$

This is the change in the difference between the arms, not a claim that each arm lengthens by that amount. Metres divided by metres give dimensionless $h$ . At fixed strain, doubling the baseline doubles this ideal differential change. Real cavity response depends on frequency; the equation does not replace calibration. Primary calibration paper: definition of $h$ and feedback, pp. 4–5.

The number illustrates scale. This is neither a new measurement nor a data plot; the teaching diagram exaggerates the effect enormously more.

Why the signal becomes stronger and faster

When two compact masses orbit each other, their spatial distribution changes. This nonspherical changing configuration emits gravitational radiation. It carries energy away: the binary loses orbital energy, the bodies approach and orbit faster. Near the end the wave can grow stronger and oscillate faster, producing the characteristic chirp.

For a nearly circular binary during inspiral, the dominant gravitational-wave harmonic has approximately twice the orbital frequency, with both frequencies compared in the same reference frame. Wave frequency counts cycles per second in detector data; it is neither propagation speed nor simply one body’s orbit count. The merger produces one object whose disturbance then decays. LIGO: evolution of GW150914, section II.

This does not mean every gravitational wave is a short black-hole chirp. Wave properties and frequency bands depend on the source; here we examine the particular signal type that opened direct gravitational-wave astronomy.

Measuring a wave takes more than noticing a wiggle

On 14 September 2015, LIGO’s Livingston and Hanford detectors recorded GW150914. On 11 February 2016, the LIGO and Virgo collaborations announced the discovery. Virgo participated in the scientific work; the signal itself was recorded by the two LIGO instruments. These dates distinguish the wave’s arrival at Earth from public announcement of the verified result. LIGO: discovery page.

Researchers compared signals at the two distant sites, accounted for travel time between them, searched auxiliary sensors for terrestrial disturbances and compared data with predictions. The primary publication separately displays measured strain, reconstructed waveforms and residuals after model subtraction. An observation and a mathematical curve are different objects. LIGO: figure 1 and detector validation, section IV.

A gravitational wave thus brings information about changing spacetime geometry, which an interferometer reads through a calibrated differential optical response. “Listening” to a merger is figurative: no air is required between source and Earth. Revisit the distinction between sound and a vacuum signal in the article on sound in space.