physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

, length scale is a particular

length Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most systems of measurement a Base unit (measurement), base unit for length is chosen, ...

distance Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two co ...

determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot affect each other and are said to decouple. The decoupling of different length scales makes it possible to have a self-consistent theory that only describes the relevant length scales for a given problem. Scientific reductionism says that the physical laws on the shortest length scales can be used to derive the effective description at larger length scales. The idea that one can derive descriptions of physics at different length scales from one another can be quantified with the renormalization group. In

quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...

the length scale of a given phenomenon is related to its de Broglie wavelength , where ''ħ'' is the

reduced Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

and ''p'' is the momentum that is being probed. In

relativistic mechanics In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non- quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities o ...

time and length scales are related by the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

. In relativistic quantum mechanics or

relativistic quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct physical models of suba ...

, length scales are related to momentum, time and energy scales through the Planck constant and the speed of light. Often in high energy physics natural units are used where length, time, energy and momentum scales are described in the same units (usually with units of energy such as GeV). Length scales are usually the operative scale (or at least one of the scales) in dimensional analysis. For instance, in

scattering theory In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiat ...

, the most common quantity to calculate is a cross section which has units of length squared and is measured in barns. The cross section of a given process is usually the square of the length scale.

Examples

* The atomic length scale is and is given by the size of hydrogen atom (''i.e.'', the Bohr radius, approximately ). * The length scale for the

strong interaction In nuclear physics and particle physics, the strong interaction, also called the strong force or strong nuclear force, is one of the four known fundamental interaction, fundamental interactions. It confines Quark, quarks into proton, protons, n ...

s (or the one derived from QCD through dimensional transmutation) is around , and the "radii" of strongly interacting particles (such as the

proton A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an e ...

) are roughly comparable. This length scale is determined by the range of the Yukawa potential. The lifetimes of strongly interacting particles, such as the rho meson, are given by this length scale divided by the speed of light: . The masses of strongly interacting particles are several times the associated energy scale ( to ). * The electroweak length scale is shorter, roughly and is set by the rest mass of the weak vector bosons, which is roughly . This length scale would be the distance where a Yukawa force is mediated by the weak vector bosons. The magnitude of weak length scale was initially inferred by the Fermi constant measured by

neutron The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...

and muon decay. * The Planck length (Planck scale) is much shorter yet – about , and is derived from the Newtonian constant of gravitation. * The Stoney length (Stoney scale) is shorter yet – about . * The mesoscopic scale is the length at which quantum mechanical behaviours in liquids or solid can be described by

macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic. Overview When applied to physical phenome ...

concepts.

References

{{DEFAULTSORT:Length Scale Orders of magnitude (length)

Examples

See also

References