The difference in arrival time of a signal between two spatially separated detectors.Time delay in physics refers to the difference in arrival time of a signal between two spatially separated detectors. This concept is fundamental in astronomy and particle physics, where it allows scientists to locate sources and study the properties of the medium the signal travels through. For example, in gravitational wave astronomy, the time delay between detectors like LIGO's multiple sites helps triangulate the position of a merger on the sky. Similarly, in neutrino detection, time delays can reveal information about the source and the Earth's interior.
The use of time delay in astronomy dates back to the 1960s with the first very long baseline interferometry experiments, but the concept became widely known in the 1970s with the detection of gravitational lensing time delays. In gravitational wave astronomy, the first detection in 2015 used time delays between the two LIGO detectors to estimate the source's location.
When a signal (light, gravitational waves, neutrinos) travels from a distant source, it reaches different detectors at slightly different times because the detectors are at different distances from the source. By measuring these time differences and knowing the speed of the signal, scientists can calculate the direction and distance to the source. In some cases, time delays also arise from the signal passing through different media, such as the gravitational lensing of light, where one path is longer or slowed by curved spacetime.
Time delay measurements are used in GPS satellite navigation to correct for relativistic effects, and in astronomy to measure cosmic distances and test theories of gravity.
In the first gravitational wave detection, the time delay between the two LIGO detectors was about 7 milliseconds, which allowed scientists to roughly locate the merger in the southern sky.
| \Delta t | variable | time delay between images — time delay second |
| D_{\Delta t} | variable | time delay distance — distance metre |
| \Delta\phi | variable | difference in lensing potential — lensing potential difference |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| Δt | variable | time delay between two images or signals — time delay second |
| D_Δt | variable | time-delay distance, a combination of angular diameter distances in the lens system — time delay distance metre |
| Δτ | variable | difference in the Fermat potential between two light paths — fermat potential difference |
| c | constant | speed of light in vacuum — speed of light = 299792458 metre per second |
| h̃_L | variable | Lensed gravitational wave signal in frequency domain — gravitational wave strain |
| f | variable | Gravitational wave frequency — frequency hertz |
| μ_j | variable | Magnification factor of image j — magnification |
| Δt_j | variable | Time delay of image j relative to source — time delay second |
| n_j | variable | Morse index of image j — morse index |
| h̃_src | variable | Unlensed source gravitational wave signal — gravitational wave strain |
| ∑ | operator | Sum over lensed images — summation |
| e^{...} | operator | Complex exponential encoding phase shifts — exponential |





