A measure of how far away an object is, affecting the observed signal strength.Distance is a fundamental measure of spatial separation between two points, and in physics it underpins the inverse-square law, which dictates that the intensity of a signal (light, sound, gravity) decreases with the square of the distance from its source. This principle is crucial for astronomical measurements, where determining how far away an object is allows scientists to infer its intrinsic luminosity, mass, or velocity. In quantum sensing, distance affects the coupling strength between a sensor and the target signal, with closer proximity yielding stronger interactions and better sensitivity.
The concept of distance has been central to physics since antiquity, but its precise astronomical measurement began with the first stellar parallax in 1838 by Friedrich Bessel. The inverse-square law for light was formulated by Johannes Kepler in the 17th century and later refined by Isaac Newton.
In practice, distance is often measured indirectly through observable effects. For example, the apparent brightness of a known light source (a 'standard candle') reveals its distance via the inverse-square law. Alternatively, parallax — the apparent shift in position of a nearby object against distant background stars as the Earth orbits the Sun — provides a geometric distance. In quantum sensors, the distance to a target is encoded in the strength of the interaction, such as the magnetic dipole coupling, which falls off as the cube of the distance, allowing precise localization of nearby objects.
Distance measurement is used in LIDAR for autonomous vehicles, in astronomical surveys to map the universe, and in quantum sensing to localize single spins or nanoparticles with nanometer resolution.
The human eye can detect a single photon, but the distance to a star is so vast that the light arriving from it is often less than one photon per second per square centimeter of telescope aperture.
| V | variable | Potential energy — potential energy joule |
| r | variable | Radial distance from source — distance metre |
| g | variable | Coupling strength (not a universal constant) joule metre |
| λ | variable | Screening length (range of interaction) — length metre |
| r | variable | distance between two points — distance metre |
| ν | variable | smoothness parameter |
| l | variable | length scale parameter — length metre |
| σ | variable | variance amplitude — variance square metre |
| Γ | operator | Gamma function, generalizes factorial — gamma function |
| K_ν | operator | Modified Bessel function of the second kind of order ν — modified bessel function second kind |
| h_{ij}^{\text{TT}} | variable | Transverse-traceless gravitational wave strain tensor — gravitational wave strain |
| D | variable | Distance from source to observer — distance metre |
| I_{ij} | variable | Mass quadrupole moment tensor — mass quadrupole moment kilogram metre squared |
| t | variable | Time — time second |
| G | constant | Constant of gravitation in Newton's law — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| c | constant | Universal speed limit and speed of light in vacuum — speed of light = 299792458 metre per second |
| d^2/dt^2 | operator | Second derivative with respect to time — second time derivative |
| F | variable | Gravitational force magnitude — force newton |
| M | variable | Mass of the central object — mass kilogram |
| m | variable | Mass of the test particle — mass kilogram |
| r | variable | Distance between masses — distance metre |
| ρ | variable | Energy density of the cosmic fluid — energy density joule per cubic metre |
| w | variable | Equation-of-state parameter of the fluid — equation of state parameter |
| G | constant | Universal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| d | variable | Euclidean distance — distance metre |
| x₁ | variable | x-coordinate of point 1 — coordinate metre |
| x₀ | variable | x-coordinate of point 0 — coordinate metre |
| y₁ | variable | y-coordinate of point 1 — coordinate metre |
| y₀ | variable | y-coordinate of point 0 — coordinate metre |
| √ | operator | takes the square root of the sum — square root |
