All Topics  
Length scale

 

 
   Email Print
   Bookmark   Link
 

 

Length scale
 
 
  Topics Length scale Topic Home

In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, length scale is a particular length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 or distance
Distance

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria ....
 determined with the precision of one order (or 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.






Discussion
Ask a question about 'Length scale'
Start a new discussion about 'Length scale'
Answer questions from other users
Full Discussion Forum



Encyclopedia


In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, length scale is a particular length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 or distance
Distance

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, a period of time, or an estimation based on other criteria ....
 determined with the precision of one order (or 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
Renormalization group

In theoretical physics, renormalization group refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views it at different distance scales....
.

In quantum mechanics
Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
 the length scale of a given phenomenon is related to its de Broglie wavelength where is the reduced Planck's constant and is the momentum that is being probed. In relativistic mechanics time and length scales are related by the speed of light
Speed of light

The speed of light in an free space is an important physical constant usually written as c, with a value of 299,792,458 metres per second....
. In relativistic quantum mechanics or relativistic quantum field theory, length scales are related to momentum, time and energy scales through Planck's constant and the speed of light. Often in high energy physics natural units
Natural units

In physics, natural units are physical units of measurement defined in such a way that certain selected universal physical constants are normalized to unity; that is, their numerical value becomes exactly 1 when measured in some system of 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
GEV

GEV may stand for:*Generalized extreme value distribution*Electronvolt*Wing-In-Ground effect vehicle*G.E.V., a tabletop game by Steve Jackson games, based on Ogre_...
).

Length scales are usually the operative scale (or at least one of the scales) in dimensional analysis
Dimensional analysis

Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving certain physical quantities....
. For instance, in scattering theory
Scattering theory

In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and Elementary particle. Prosaically, wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow....
, the most common quantity to calculate is a cross section
Cross section (physics)

In nuclear physics and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles.When particles are thrown against a foil made of a certain substance, the cross section is a hypothetical area measure around the target particles that represents a surface....
 which has units of length squared and is measured in barn
Barn (unit)

A barn is a unit of area. While the barn is not an SI unit, it is accepted for use with the SI. Originally used in nuclear physics for expressing the cross section area of nuclei and nuclear reactions, today it is used in all fields of particle physics to express the cross sections of any scattering process....
s. The cross section of a given process is usually the square of the length scale.

Examples

  • The atomic length scale is meters and is given by the size of hydrogen atom (i.e., the Bohr radius
    Bohr radius

    In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central atomic nucleus. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy....
     (approximately 53 pm
    1 E-12 m

    To help compare different orders of magnitude this page lists lengths between 10−12 metre and 10−11 m .1 E-13 m...
    )) which is set by the electron's Compton wavelength
    Compton wavelength

    The Compton wavelength is a quantum mechanics property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons ....
     times the fine-structure constant
    Fine-structure constant

    In physics, the fine-structure constant, usually denoted is the characterizing the strength of the electromagnetic interaction. A fundamental physical constant and a dimensionless quantity, its numerical value is the same in all system of units....
    : .


  • The length scale for the strong interaction
    Strong interaction

    In particle physics, the strong interaction, or strong force, or color force, holds quarks and gluons together to form protons, neutrons and other particles....
    s (or the one derived from QCD
    Quantum chromodynamics

    Quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons ....
     through dimensional transmutation
    Dimensional transmutation

    In particle physics, dimensional transmutation is a physical mechanism that transforms a dimensionless parameter into a dimensionful parameter....
    ) is around meters (or in natural units 100 MeV), and the "radii" of strongly interacting particles (such as the proton
    Proton

    The proton is a subatomic particle with an electric charge of +1 elementary charge. It is found in the nucleus of each atom but is also stable by itself and has a second identity as the hydrogen ion, H+....
    ) are roughly comparable. This length scale is determined by the range of the Yukawa potential
    Yukawa potential

    A Yukawa potential is a potential of the formHideki Yukawa showed in the 1930s that such a potential arises from the exchange of a massive scalar field such as the field of the pion whose mass is ....
    . The lifetimes of strongly interacting particles, such as the rho meson
    Rho meson

    In particle physics, a rho meson is a short-lived hadronic particle that is an isospin Spin triplet whose three states are denoted as , and . After the pions and kaons, the rho mesons are the lightest strongly interacting particle with a mass of roughly 770 MeV for all three states....
    , are given by this length scale divided by the speed of light: seconds. The masses of strongly interacting particles are several times the associated energy scale (500 MeV to 3000 MeV).


  • The electroweak length scale is shorter, roughly meters and is set by the rest mass of the weak vector bosons which is roughly 100 GeV. This length scale is would be the distance where a Yukawa force mediated by the weak vector bosons. The magnitude of weak length scale was initially inferred by the Fermi constant
    Fermi's interaction

    In physics, Fermi's interaction is an old explanation of the weak force, proposed by Enrico Fermi. Four fermions directly interact with one another....
     measured by neutron
    Neutron

    The neutron is a subatomic particle with no net electric charge and a mass slightly larger than that of a proton.Neutrons are usually found in atomic nucleus....
     and muon
    Muon

    The muon is an elementary particle similar to the electron, with negative electric charge and a spin of . Together with the electron, the tau lepton, and the three neutrinos, it is classified as a lepton....
     decay.


  • The Planck length
    Planck length

    In physics, the Planck length, denoted , is unit of length, equal to about 1.6 × 10-33 centimeters. It is a base unit in the system of Planck units, the most widely used system of natural units....
     (Planck scale) is much shorter yet - about meters ( GeV in natural units), and is derived from Newton's gravitational constant
    Gravitational constant

    The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitation between objects with mass....
     which has units of length squared.


  • The Mesoscopic scale
    Mesoscopic scale

    In physics and chemistry, the mesoscopic scale refers to the length scale at which one can reasonably discuss the properties of a material or phenomenon without having to discuss the behavior of individual atoms, and concepts of averages such as density and temperature are useful....
     is the length at which quantum mechanical behaviours in liquids or solid can be described by macroscopic
    Macroscopic

    Macroscopic is a word commonly used to describe physics objects that are measurement and observation by the naked eye. When applied to phenomena and abstract objects, it describes existence in the world as we perceive it....
     concepts.


See also

  • Orders of magnitude (length)
    Orders of magnitude (length)

    To help compare different orders of magnitude, the following list describes various lengths between 1.6 m and 1.3 m.|}Detailed List...
  • Extragalactic Distance Scale