Circuit rank: Difference between revisions

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{{Unreferenced stub|auto=yes|date=December 2009}}
'''Charge invariance''' refers to the fixed electrostatic [[potential]] of a particle, regardless of speed.  For example, an [[electron]] has a specific rest charge.  Accelerate that electron, and the charge remains the same (as opposed to the [[relativistic mass]] and energy increasing).  The key word here is relativistic.  Some particle characteristics are relativistically invariant ([[electric charge|charge]], [[spin (physics)|spin]], and [[magnetic moment]]).  Others are relativistic ([[mass]], [[energy]], and [[de Broglie wavelength]]).  The key is the [[Lorentz factor]],


<math>\gamma = \frac{1}{\sqrt{1-(\frac{v}{c})^2}}</math>


where <math>v</math> is [[velocity|speed]], and <math>c</math> is the [[speed of light]]. Typically, we write:
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<math>E = \gamma E_0 \,\!</math>,
<math>m = \gamma m_0 \,\!</math>,
<math>e = e_0\,\!</math>, and
<math>\frac{\hbar}{2} = \frac{\hbar_0}{2}\,\!</math>
 
where the first equation describes relativistic energy, the second – relativistic mass, the third – charge invariance, and fourth – spin invariance. Notice that <math>\gamma</math> does not appear in the third or fourth equations. <math>\gamma</math> is a function of speed (relative to some rest frame where <math>E_0</math> and <math>m_0</math> refer to rest energy and mass). So, to say "rest charge" or "rest spin" is redundant.  Notice also that as <math>v</math> (speed) increases, <math>\gamma</math> increases, and so <math>E</math> (and <math>m</math>) increases too.  The origin of charge invariance (indeed, all relativistic invariants) is under speculation presently.  There may be some hints proposed by [[string theory|string]]/[[M-theory]]. It is possible the concept of charge invariance may provide a key to unlocking the mystery of [[theory of everything|unification]] in physics (the theoretical unification of [[gravity]], [[electromagnetism]], the [[strong nuclear force|strong]], and [[weak nuclear force]]s).
 
The property of charge invariance follows from the vanishing divergence of the charge-current [[four-vector]]
<math>j^\mu=(c\rho,{\vec j})</math>,
with <math>\partial_\mu j^\mu=0</math>.
 
{{DEFAULTSORT:Charge Invariance}}
[[Category:Particle physics]]
 
 
{{Relativity-stub}}

Latest revision as of 11:14, 9 August 2014


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