Strain

In gravitational-wave physics, strain is the fractional change in the proper distance between two free test masses caused by a passing wave: h = ΔL/L. It is dimensionless — a pure ratio — and it is the quantity a detector actually measures. Because the metric perturbation enters the geodesic-deviation equation at first order, the fractional length change is exactly one-half the strain amplitude, ΔL/L = ½ h, with the stretch along one transverse axis matched by an equal squeeze along the perpendicular one.

The strains reaching Earth are staggeringly small. The first detection, GW150914, peaked at h ≈ 1.0 × 10⁻²¹. Across LIGO's 4-kilometre arms that is a length change of about 10⁻¹⁸ metres — roughly one-thousandth the diameter of a proton. Measuring it requires laser interferometry stabilized against seismic, thermal, and quantum noise, and it is why gravitational-wave detection took a century to achieve after Einstein predicted the waves in 1916.

Strain is sourced by the second time derivative of a system's mass quadrupole moment and falls off as 1/distance (not 1/distance²), because it is a wave amplitude rather than an intensity. That slow falloff is what lets detectors reach billions of light-years: doubling sensitivity in strain doubles the observable distance and so multiplies the accessible volume eightfold.

The notion of strain as the observable of a gravitational wave was sharpened by the 1957 sticky-bead argument of Feynman and Bondi, which showed that the changing distance between free masses does real, dissipative work and therefore carries energy. It became an engineering target with Joseph Weber's resonant bars in the 1960s and, decisively, with the laser-interferometer program that culminated in LIGO's 2015 detection.