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Barry Barish helped turn LIGO from an interferometer proposal into an operating large-scale gravitational wave observatory. He directed its construction and early operation and established the broader LIGO Scientific Collaboration.^[ref]

The scientific architecture combines sensitive laser interferometers at widely separated sites. A candidate astronomical signal must be distinguished from local disturbances, using its relative arrival times and its consistency with the detectors' responses. This made instrumental performance, calibration and cross-site comparison inseparable from the eventual measurement.^[ref]

A binary black hole is a binary system whose two components are black holes. Gravitational waves carry away orbital energy and angular momentum, gradually reducing the separation; sufficiently close systems progress through inspiral, merger and the settling of the final black hole. The increasing orbital angular velocity produces a signal whose gravitational-wave frequency rises, called a chirp. In GW150914, two LIGO interferometers recorded a signal sweeping from about 35 to 250 hertz in September 2015. Comparing that measured gravitational wave strain with general relativity waveforms inferred the component masses and the merger's properties. This permits the study of systems that need no luminous surrounding gas to be detected.^[ref]

B. P. Abbott coauthored the collaborative analyses of GW150914. Fitting general relativity waveforms to LIGO data constrained the properties of the merging binary black hole.^[ref] A companion study converted detector control-loop signals into gravitational wave strain, with an optomechanical response model and independent checks of its measurement uncertainty.^[ref]

A gravitational wave is a propagating disturbance of spacetime curvature produced by changing mass-energy multipole moments. In general relativity, its two transverse gravitational wave polarizations alternately stretch and squeeze freely falling separations. The leading radiation from a slowly moving source is governed by its mass quadrupole moment, rather than by its total mass alone.

The experimental breakthrough was GW150914: observed on 14 September 2015 and published on 11 February 2016. The LIGO Scientific Collaboration and Virgo Collaboration reported a merging pair of black holes, using the two LIGO detectors at Hanford and Livingston; Virgo was being upgraded and did not observe this event.^[ref]

The 2017 Nobel Prize in Physics recognized Rainer Weiss, Barry C. Barish and Kip S. Thorne for contributions to LIGO and gravitational wave observation. Rainer Weiss developed interferometric detection and its noise analysis; Barry C. Barish led the project into construction and operation; Kip S. Thorne developed its theoretical and astrophysical foundations. The experiment depended on a large collaboration.^[ref]

J. Aasi coauthored the LIGO instrument paper describing its advanced detectors. Their $4$-km Michelson interferometer arms use optical cavities to increase interaction with gravitational waves; improved isolation, suspended mirrors and optical design reduce competing sources of noise.^[ref]

Kip Thorne is a physicist whose research connects general relativity, black holes, neutron stars and gravitational waves. His authored Nobel autobiography describes how theoretical questions about these systems helped shape LIGO and the interpretation of its signals. The collaboration required both predicted gravitational-wave behavior and sustained experimental development; a detector's observed strain becomes astrophysical information through that connection.^[ref]

LIGO measures gravitational wave-induced changes in the relative lengths of widely separated interferometer arms. Laser light travels along perpendicular arms, reflects from suspended mirrors and recombines; a change in relative optical phase alters the detected signal. Arm optical cavities increase the interaction time, while vibration isolation and mirror suspension reduce unwanted motion.^[ref]

The strain scale is roughly the differential length change divided by arm length. Calibration converts the optical readout into strain, and agreement between separated observatories helps distinguish an astrophysical signal from a local disturbance.

Each LIGO instrument is a Michelson interferometer with approximately $4\mathrm{km}$ arms containing Fabry–Pérot interferometers. A stabilized $1064\mathrm{nm}$ laser illuminates suspended $40\mathrm{kg}$ fused-silica mirrors in vacuum. Four-stage suspensions and active isolation suppress ground motion; low-loss materials reduce thermal noise. Power recycling increases circulating power; signal recycling shapes the response to the gravitational wave.^[ref]

Why measure two perpendicular arms? In the long-wavelength limit, take a gravitational wave with plus polarization normally incident on ideal perpendicular arms. Its transverse-traceless tensor has $h_{xx}=h_{+}$ and $h_{yy}=-h_{+}$. Expanding each proper length to first order givesHere $h_{+}$ is dimensionless, whereas $\Delta L$ is a length. A stipulated $h_{+}=10^{-21}$ and $L=4000\mathrm{m}$ imply $\Delta L=4\times 10^{-18}\mathrm{m}$, with individual arm changes of opposite sign and magnitude $2\times 10^{-18}\mathrm{m}$. These are equivalent differential arm-length changes, not a photograph of mirrors moving against a rigid external ruler. The observable compares returning light phases; coordinate systems can distribute the description between mirror coordinates and light propagation.

For unit arm directions $\mathbf{u},\mathbf{v}$, define the detector tensor $D^{ij}=(u^i{u}^j-v^i{v}^j)/2$. If $e_{ij}^{+},e_{ij}^{\times }$ are the transverse polarization tensors, thenThe dimensionless factors $F_A$ encode sky direction and the polarization basis. Thus even identical sources can have different observed amplitudes and wave phases. Motion changing both arms equally cancels in this ideal differential observable, although real asymmetries can couple common disturbances into it.

Suspension supplies an inertial reference above its resonances. For example, a single ideal harmonic oscillator with support motion $y$ obeys $\ddot{x}+{\omega }_0^2(x-y)=0$. Its response at angular frequency $\omega$ is $x/y={\omega }_0^2/({\omega }_0^2-{\omega }^2)$, which decreases in magnitude as $({\omega }_0/\omega {)}^2$ well above resonance. The mirror follows slow support drift but approximately free motion in the high-frequency limit. Real multistage suspensions also require damping and alignment control; resonant frequencies are not regions of good isolation.

Rainer Weiss's 1972 report proposed suspended masses, multiple-pass optical delay lines, and a servo holding an interference fringe. Its noise analysis separately treats photon-counting fluctuations, laser frequency instability, mechanical thermal noise, radiation pressure and ground motion. Those delay lines should be distinguished from the resonant arm cavities of Advanced LIGO.^[ref]

An ideal single-round-trip Michelson interferometer converts differential length into phase difference $\delta \varphi =4\pi \Delta L/\lambda$. If its dark-port power scale is $P_0$ and its static phase offset is ${\varphi }_0$, thenExactly at a dark fringe, ${\varphi }_0=0$, power is quadratic in small displacement and loses its sign. A deliberate offset supplies an optical reference field: interference with the small signal field produces a linear term. Equivalently, $|E_{\mathrm{ref}}+E_{\mathrm{sig}}{|}^2$ contains $2\mathrm{Re}(E_{\mathrm{ref}}^{\ast }{E}_{\mathrm{sig}})$. The photodetector measures power, not a signed displacement directly.

Advanced LIGO uses this DC homodyne principle with a small differential arm offset and an output mode cleaner. Its feedback control maintains optical resonance and alignment, using actuation distributed over the suspension stages.^[ref] The simple formula above omits resonant storage: arm and recycling cavities give a frequency-dependent optical gain and delay, so no constant pass-count multiplier describes the entire observing band.

To see why a locked detector can still measure a disturbance, use a linear feedback control model. Let $x_{\mathrm{ext}}$ be the external differential displacement, $d_{\mathrm{err}}$ the residual readout, $d_{\mathrm{ctrl}}$ the recorded control command, $C(f)$ the sensing response and $A(f)$ the actuation response. With the convention $x_{\mathrm{res}}=x_{\mathrm{ext}}-A{d}_{\mathrm{ctrl}}$, reconstruction givesHere tildes denote Fourier transforms; $C$ has readout units per metre and $A$ metres per command unit. Feedback suppresses residual motion but records the compensating command. Omitting that command would suppress the reconstructed low-frequency signal too. In the actual GW150914 experiment, a modulated auxiliary laser exerted calibrated radiation pressure on a mirror to measure the response; periodic excitations monitored calibration.^[ref]

Reports on Progress in Physics 72, 076901. Primary initial-LIGO apparatus, noise and search account; not the later Advanced LIGO discovery paper.

One half went to Rainer Weiss, and one quarter each to Barry C. Barish and Kip S. Thorne, for decisive contributions to the LIGO detector and observation of gravitational waves.^[ref]

The changing mass quadrupole moment produces an inspiral gravitational wave signal whose frequency and amplitude increase toward merger. The chirp mass controls the leading frequency evolution, while higher-order phasing and the merger carry information about binary mass ratio and spins. Neutron stars also introduce tidal effects. These signals motivate a search with an interferometer such as LIGO; the supplied ranges quantify the paper's proposed detection prospects, without assuming any particular later observing-run performance.

A gravitational wave is a propagating tidal perturbation of spacetime. In the weak-field limit its transverse polarizations alternately stretch and compress the separation of freely falling test bodies. A laser interferometer such as LIGO measures the differential optical phase of orthogonal arms. The mirrors approximate free test masses over the detection band; arm cavities enhance the phase response, while suspension, seismic isolation and optical control reduce instrumental disturbances. A strain $h$ produces relative arm-length changes of order $hL$. Coincidence and waveform consistency between detectors distinguish candidate astrophysical signals from local noise.

Potential sources include black-hole and neutron-star binary inspirals and mergers, asymmetric core-collapse supernovae, nonaxisymmetric spinning neutron stars, and a stochastic background from many unresolved sources or early-Universe processes. Their detectability depends on frequency, strain, duration and detector noise; a source producing gravitational radiation need not be observable in a terrestrial interferometer's band.

For slowly varying approximately isotropic stellar wind loss, decreasing the binding mass widens the orbit. The prescribed Jeans-mode mass loss equation givesHot massive stars have metal-line-driven winds. Higher metallicity generally strengthens the radiative coupling and mass loss, increasing orbital expansion and leaving less massive black holes. The supplied initial-contact formula also assigns larger zero-age radii and initial minimum separations at higher metallicity.

The initial total mass is $2M^0$, while the final total mass is $2M_{\mathrm{BH}}$. Neglecting supernova mass loss as requested, their ratio has no additional factor of two. The wind-limited black-hole binary merger window therefore has lower boundaryA nonempty allowed initial-separation interval requires $a_{\min }^V<a_{\max }^{\mathrm{merger}}$. Substituting the supplied final masses gives the following separation bounds, all in units of $R_{\odot }$:The arguments 30 and 100 indicate the initial mass of each star in solar units.

Under these particular approximate formulae, only the $30M_{\odot }$ initial systems at $Z_{\odot }/10$ and $Z_{\odot }/20$ have overlapping bounds. The $100M_{\odot }$, $Z_{\odot }/20$ system is a near miss, not formally allowed: $75.43>71.13$. Given approximate evolutionary scalings, that small mismatch should not be treated as a precise astrophysical exclusion.

Lower metallicity favors merging remnants here through weaker winds, smaller initial stellar radii and larger final black-hole masses. More massive binaries can also produce stronger detectable signals over a suitable frequency range, although the detection volume and band limitations must be considered. The observed rate further depends on formation efficiency, metallicity history, delay times and binary survival. Common-envelope evolution, stellar rotation, supernova mass loss and natal kicks could alter this simplified channel; the wind-only inequalities do not establish that such mergers are impossible through other channels.

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.

To construct an original example rather than imitate GW150914, set $G=6.67430\times 10^{-11}{\mathrm{m}}^3\mathrm{k}{\mathrm{g}}^{-1}{\mathrm{s}}^{-2}$, $c=299792458\mathrm{m}{\mathrm{s}}^{-1}$, and adopt the rounded solar mass $M_{\odot }=1.98847\times 10^{30}\mathrm{kg}$. Compare $10+10$ and $20+20$ solar mass binaries starting at $20\mathrm{Hz}$. Stop each at the stipulated orbital compactness thresholdThis is a conservative pedagogical stopping rule, not a claimed error bound: the relative speed already reaches $\sqrt{0.10}c$. Higher-order corrections accumulate wave phase well before merger, and precision inference requires better models. The two cutoffs are approximately $102.2$ and $51.1\mathrm{Hz}$ respectively; doubling the chirp mass multiplies $\dot{f}$ at fixed $f$ by $2^{5/3}$.

For a nearby stipulated source at distance $D$, neglect redshift and define inclination $\iota$ as the angle between the orbital angular momentum and the line of sight. The leading quadrupole formula yieldsThe numerator of $A$ has units ${\mathrm{m}}^5{\mathrm{s}}^{-4}$, matching $c^{4}D$, so both polarizations are dimensionless. Its $f^{2/3}$ growth and the rising frequency produce the tightening, strengthening oscillations. For face-on viewing the polarization components have equal magnitudes in phase quadrature; for edge-on viewing the cross component vanishes, agreeing with circular-binary quadrupole radiation.

Shifting an arrival time aligns the chirp evolution, but different polarization projections need not overlay after only a sign flip. The last panel divides the ideal projected records by their known envelope factors to expose this phase difference. A physical source model must jointly explain those differences, not erase them by arbitrary rescaling. Independent integration of the separation equation, the radiated power and $d\Phi /dt=2\pi f$ checks the analytic chirp against orbital energy balance over the entire stipulated interval.