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| | Nice to be here there, I am Adrianne and I totally cannot get enough of that name. I am a people manager even so soon I'll be by myself. Gardening is what I do 7 days a week. Guam has always been home. See what's new on my own, personal website here: http://circuspartypanama.com<br><br>My web blog ... how to hack clash of clans - [http://circuspartypanama.com just click the next post], |
| In [[physics]], '''length scale''' is a particular [[length]] or [[distance]] 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 [[decoupling (physics)|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.
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| The idea that one can derive descriptions of physics at different length scales from one another can be quantified with the [[renormalization group]].
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| In [[quantum mechanics]] the length scale of a given phenomenon is related to its [[de Broglie wavelength]]
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| <math>\ell = \hbar/p</math> where <math>\hbar</math> is the reduced [[Planck's constant]] and <math>p</math> is the momentum that is being probed. In [[relativistic mechanics]] time and length scales are related by the [[speed of light]]. 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]] are used where length, time, energy and momentum scales are described in the same units (usually with units of energy such as [[GeV]]).
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| Length scales are usually the operative scale (or at least one of the scales) in [[dimensional analysis]]. For instance, in [[scattering theory]], the most common quantity to calculate is a [[cross section (physics)|cross section]] which has units of length squared and is measured in [[barn (unit)|barn]]s. The cross section of a given process is usually the square of the length scale.
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| ==Examples==
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| *The atomic length scale is <math>\ell_a \sim 10^{-10}</math> meters and is given by the size of hydrogen atom (''i.e.'', the [[Bohr radius]] (approximately 53 [[1 E-12 m|pm]])) which is set by the electron's [[Compton wavelength]] times the [[fine-structure constant]]: <math>\ell_{a} \sim 1/\alpha m_e</math>.
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| *The length scale for the [[strong interaction]]s (or the one derived from [[Quantum chromodynamics|QCD]] through [[dimensional transmutation]]) is around <math>\ell_{s}\sim 10^{-15}</math> meters (or in natural units 1000 MeV or 1 GeV), and the "radii" of strongly interacting particles (such as the [[proton]]) 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: <math>10^{-23}</math> seconds. The masses of strongly interacting particles are several times the associated energy scale (500 MeV to 3000 MeV).
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| *The [[electroweak]] length scale is shorter, roughly <math>\ell_{w} \sim 10^{-18}</math> meters and is set by the rest mass of the weak vector bosons which is roughly 100 GeV. 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's interaction|Fermi constant]] measured by [[neutron]] and [[muon]] decay.
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| *The [[Planck length]] (Planck scale) is much shorter yet - about <math>\ell_{P}\sim 10^{-35}</math> meters (<math>10^{19}</math> GeV in natural units), and is derived from Newton's [[gravitational constant]] which has units of length squared.
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| *The [[Mesoscopic scale]] is the length at which quantum mechanical behaviours in liquids or solid can be described by [[macroscopic]] concepts.
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| ==See also==
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| *[[Orders of magnitude (length)]]
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| *[[Extragalactic Distance Scale]]
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| *[[Scale height]]
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| {{DEFAULTSORT:Length Scale}}
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| [[Category:Concepts in physics]]
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| [[Category:Particle physics]]
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| [[Category:Renormalization group]]
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Nice to be here there, I am Adrianne and I totally cannot get enough of that name. I am a people manager even so soon I'll be by myself. Gardening is what I do 7 days a week. Guam has always been home. See what's new on my own, personal website here: http://circuspartypanama.com
My web blog ... how to hack clash of clans - just click the next post,