quantity

time delay

The difference in arrival time of a signal between two spatially separated detectors.
18 related articles · 3 formulas

Description

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.

History

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.

How it works

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.

In practice

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.

Fun fact

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.

Concept graph →

Formulas

$$\Delta t = \frac{D_{\Delta t}}{c} \Delta\phi$$
Time delay is proportional to the time delay distance and lensing potential difference.
What is in the formula
\Delta tvariabletime delay between images — time delay second
D_{\Delta t}variabletime delay distance — distance metre
\Delta\phivariabledifference in lensing potential — lensing potential difference
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
$$\Delta t = \frac{D_{\Delta t}}{c} \Delta\tau$$
Time delay from path difference in lensing.
What is in the formula
Δtvariabletime delay between two images or signals — time delay second
D_Δtvariabletime-delay distance, a combination of angular diameter distances in the lens system — time delay distance metre
Δτvariabledifference in the Fermat potential between two light paths — fermat potential difference
cconstantspeed of light in vacuum — speed of light = 299792458 metre per second
$$\tilde{h}_L(f) = \sum_j |\mu_j|^{1/2} e^{2\pi i f \Delta t_j - i\pi n_j} \tilde{h}_{\rm src}(f)$$
Lensed gravitational wave signal sum over images.
What is in the formula
h̃_LvariableLensed gravitational wave signal in frequency domain — gravitational wave strain
fvariableGravitational wave frequency — frequency hertz
μ_jvariableMagnification factor of image j — magnification
Δt_jvariableTime delay of image j relative to source — time delay second
n_jvariableMorse index of image j — morse index
h̃_srcvariableUnlensed source gravitational wave signal — gravitational wave strain
∑operatorSum over lensed images — summation
e^{...}operatorComplex exponential encoding phase shifts — exponential

Related articles · 18

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A Ruler Made of Light: Measuring Nanometers with a Pair of Photons
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Why Cosmic Data Refuse to Converge
Two rulers show slightly different lengths for the same table. That's roughly the situation in cosmology with the Hubble constant — the number that tells how fast the universe is expanding.
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Quantum Physics2026-01-051 minarXiv:2601.02470express
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