Length scale - Citizendia

In physics, length scale is a particular length or distance determined with the precision of one order (or a few orders) of magnitude. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. 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 Distance is a numerical description of how far apart objects are 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 Theoretical physics, renormalization group (RG refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views

In quantum mechanics the length scale of a given phenomenon is related to its de Broglie wavelength $\ell = \hbar/p$ where $\hbar$ is the reduced Planck's constant and $p$ is the momentum that is being probed. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In Physics, the de Broglie hypothesis (pronounced /brœj/ as French breuil close to "broy" is the statement that all Matter (any object has a Wave The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. In relativistic mechanics time and length scales are related by the speed of light. This page is about the scientific concept of relativity for philosophical or sociological theories about relativity see Relativism. 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. In quantum field theory (QFT the forces between particles are mediated by other particles 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). Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them In Physics, natural units are Physical units of Measurement defined in terms of universal Physical constants, such that some chosen physical

Length scales are usually the operative scale (or at least one of the scales) in dimensional analysis. Dimensional analysis is a conceptual tool often applied in Physics, Chemistry, Engineering, Mathematics and Statistics to understand For instance, in scattering theory, the most common quantity to calculate is a cross section which has units of length squared and is measured in barns. In Mathematics and Physics, scattering theory is a framework for studying and understanding the Scattering of Waves and particles. In nuclear and Particle physics, the concept of a cross section is used to express the likelihood of interaction between particles A barn (symbol b) is a unit of Area. While the barn is not an SI unit it is accepted (although discouraged for use with the SI The cross section of a given process is usually the square of the length scale.

Examples

The atomic length scale is $\ell_a \sim 10^{-10}$ meters and is given by the size of hydrogen atom (i. e. , the Bohr radius (approximately 53 pm)) which is set by the electron's Compton wavelength times the fine-structure constant: $\ell_{a} \sim 1/\alpha m_e$ . In the Bohr model of the structure of an Atom, put forward by Niels Bohr in 1913 Electrons orbit a central nucleus. To help compare different Orders of magnitude this page lists Lengths between 10&minus12 m and 10&minus11 m (1 pm and 10 pm The Compton wavelength \lambda \ of a particle is given by \lambda = \frac{h}{m c} = 2 \pi \frac{\hbar}{m c} \, where The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing

The length scale for the strong interactions (or the one derived from QCD through dimensional transmutation) is around $\ell_{s}\sim 10^{-15}$ meters (or in natural units 100 MeV), and the "radii" of strongly interacting particles (such as the proton) are roughly comparable. In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and Quantum chromodynamics (abbreviated as QCD is a theory of the Strong interaction ( color force a Fundamental force describing the interactions of the In Particle physics, dimensional transmutation is a physical mechanism that transforms a Dimensionless parameter into a Dimensionful parameter The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive This length scale is determined by the range of the Yukawa potential. A Yukawa potential (also called a screened Coulomb potential is a Potential of the form V(r= -g^2 \\frac{e^{-mr}}{r} Hideki Yukawa The lifetimes of strongly interacting particles, such as the rho meson, are given by this length scale divided by the speed of light: $10 - 23$ seconds. In Particle physics, a rho meson is a short-lived Hadronic particle that is an Isospin triplet whose three states are denoted as, and. 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 $\ell_{w} \sim 10^{-18}$ meters and is set by the rest mass of the weak vector bosons which is roughly 100 GeV. In Particle physics, the electroweak interaction is the unified description of two of the four Fundamental interactions of nature Electromagnetism and the 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 measured by neutron and muon decay. In Physics, Fermi's interaction is an old explanation of the Weak force, proposed by Enrico Fermi. This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. The muon (from the letter mu (μ--used to represent it is an Elementary particle with negative Electric charge and a spin of 1/2

The Planck length (Planck scale) is much shorter yet - about $\ell_{P}\sim 10^{-35}$ meters ( $1019$ GeV in natural units), and is derived from Newton's gravitational constant which has units of length squared. The Planck length, denoted by \scriptstyle\ell_P \, is the unit of Length approximately 1 The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass

The Mesoscopic scale is the length at which quantum mechanical behaviours in liquids or solid can be described by macroscopic concepts. 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 Macroscopic is commonly used to describe physical objects that are measurable and observable by the Naked eye.

Examples

See also