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The binary-pulsar Einstein delay is the periodic clock-rate contribution to pulse arrival times from a pulsar moving in an eccentric binary. Near closest approach, the pulsar's orbital speed is larger and the companion's gravitational potential is deeper. Time dilation and gravitational redshift therefore make its clock run at a different rate relative to a distant time coordinate.

At leading order the variable timing term is ${\Delta }_E=\gamma \sin E$, with eccentric anomaly $E$ and time amplitude $\gamma$. Constant clock-rate offsets are absorbed into the fitted pulsar spin. This term is distinct from the geometric binary-pulsar Roemer delay and the propagation Shapiro time delay. Fitting it with other orbital observables constrains the component masses and tests general relativity.^[ref]

Decreasing orbital period, distinct from spin slowdown. Joseph Hooton Taylor Jr. inferred masses using binary-pulsar periastron advance and binary-pulsar Einstein delay, then tested the independent period derivative against the general relativity quadrupole formula. Correcting differential Galactic acceleration gave indirect gravitational radiation evidence. This was not a terrestrial strain measurement.^[ref]

In particular, the raw measured derivative schematically containsHere $a_{\parallel }^{\mathrm{relative}}$ is positive when the source's recession accelerates. Its contribution follows by differentiating the leading Doppler effect. A decreasing observed orbital period alone therefore does not identify a unique energy-loss mechanism.

For fixed masses, binary orbital energy is $-G{m}_1{m}_2/(2a)$ and Kepler's third law gives $P_b\propto a^{3/2}$. Positive outgoing gravitational radiation predicted by the quadrupole formula makes the orbital energy more negative, reducing $a$ and $P_b$. This sign argument explains shrinking orbits, but a quantitative test also needs the predicted magnitude and orbital eccentricity dependence.

Binary-pulsar periastron advance is the gradual rotation of the orbit's argument of periapsis $\omega$. A closed Kepler orbit has a fixed direction of closest approach. In general relativity, the leading conservative correction makes the relative orbit precess even before gravitational radiation causes appreciable binary-pulsar orbital decay.

For nonspinning point masses $m_1,m_2$, total mass $M=m_1+m_2$, semimajor axis $a$ of the relative orbit and orbital eccentricity $0<e<1$, the first post-Newtonian advance per orbit isDivide by the orbital period $P_b$ and use Kepler's third law $n^2{a}^3=GM$, where $n=2\pi /P_b$, to obtainHere $\dot{\omega }$ is in radians per unit time. The expansion assumes $GM/[a{c}^2(1-e^2)]\ll 1$.

A pulsar acts as an orbital clock: the timing delay changes as the eccentric orbit turns relative to the line of sight. If this measured advance is dominated by the relativistic point-mass term, then $P_b,e,\dot{\omega }$ determine the total mass $M$, independently of the unknown orbital inclination. They do not separately determine both component masses. A second effect, such as the binary-pulsar Einstein delay, supplies another mass relation; additional timing parameters can then test the theory instead of merely fitting it.^[ref]

Spin-induced quadrupoles, tidal deformation and higher relativistic orders can contribute in other regimes and must be modeled before interpreting all observed precession as this term. At $e=0$, a separate periastron direction is undefined. Advance of this direction is conceptually distinct from decreasing $P_b$: conservative precession by itself is not evidence of radiated orbital energy.

Joseph Hooton Taylor Jr. and Russell Alan Hulse discovered a pulsar in a binary star system. Changes in the timing of the pulses revealed the pulsar's orbital motion, making an otherwise unseen compact companion measurable.^[ref]

Long-term pulse timing then tested general relativity. After accounting for other timing effects, the decreasing orbital period agreed with the loss of orbital energy predicted from gravitational radiation. The system supplied an indirect test of gravitational waves through their effect on an orbiting source.^[ref]

A gravitational wave produces a time-dependent tidal distortion. For a normally incident plus-polarized wave in the long-wavelength limit, two perpendicular freely suspended arms change by $\delta L_x/L=h_{+}/2$ and $\delta L_y/L=-h_{+}/2$. Their differential length is thereforefor a simple round-trip Michelson interferometer. LIGO uses kilometre-scale orthogonal arms with optical cavities that enhance the phase response, a stabilized laser and suspended mirrors in vacuum. As an illustrative scale, $h=10^{-21}$ across a 4 km arm corresponds to differential length $4\times 10^{-18}\mathrm{m}$. The measured quantity is returning light phase, not mirror displacement against a rigid external ruler. Optical storage and control loops give a frequency-dependent calibrated response.

Seismic and terrestrial disturbances dominate low frequencies, thermal motion of suspensions and mirror coatings contributes at intermediate frequencies, and photon shot noise limits high-frequency readout. Isolation and suspension systems reduce ground coupling; low-loss materials reduce thermal noise; vacuum suppresses gas scattering and forces. Greater optical power reduces shot noise but increases radiation-pressure fluctuations and thermal demands. Stable optical alignment and feedback are essential, yet their own sensor and actuator noise must be controlled. These are engineering requirements because the desired strain is extraordinarily small.^[ref]

A candidate should appear coherently at separated observatories with consistent propagation delay and antenna response. Auxiliary environmental monitors, calibration injections and time-shifted coincidence backgrounds test instrumental explanations. Matched filtering is powerful for modelled compact-binary chirps; coherent burst searches allow less predictable signals. Binary-pulsar orbital energy loss already provided indirect evidence for gravitational radiation before 2013, but it is distinct from directly measuring passing waves.^[ref] At the examination date, direct detection remained a search objective. Reliable detection requires both sufficient strain sensitivity and a demonstrated astrophysical signal rather than correlated or accidental noise.

Russell Alan Hulse and Joseph Hooton Taylor Jr. discovered this binary pulsar at Arecibo in 1974; their January 1975 paper reports a roughly $59\mathrm{ms}$ pulse period and $7.75\mathrm{h}$ orbital period. Its unseen companion was not detected as a second radio pulsar. Discovery of the orbit preceded the later binary-pulsar orbital decay test.^[ref]

The 1993 Nobel Prize in Physics recognized the discovery.^[ref]

By 1993, the system was interpreted as a pair of neutron stars.^[ref]

The mature experiment uses channel-template comparison, pulsar dedispersion, GPS clock-offset transfer, Solar system barycenter corrections and connected pulse counts.^[ref]

For a geometric illustration, let a perfectly uniform source emit pulse $n$ at $t_n=t_0+n{P}_s$, with spin period $P_s$, and let $z_1$ increase away from the observer. At leading order in orbital velocity divided by the speed of light, an extra path length $z_1$ adds ${\Delta }_R=z_1/c$. Consecutive arrivals then obeyA receding source has $v_{\parallel }>0$ and a longer apparent period. This derivation isolates the geometric Doppler effect; a precision relativistic clock model also needs gravitational redshift and time dilation.