Editing Electric field (section)

=== Propagation of disturbances in electric fields ===
{{See also|Paradox of radiation of charged particles in a gravitational field}}
[[Special relativity|Special theory of relativity]] imposes the [[principle of locality]], that requires cause and effect to be time-like separated events where the [[Causality|causal efficacy]] does not travel faster than the [[speed of light]].<ref>{{Cite book |author=Naber, Gregory L. |title=The Geometry of Minkowski spacetime: an introduction to the mathematics of the special theory of relativity |date=2012 |publisher=Springer |isbn=978-1-4419-7837-0 |pages=4–5 |oclc=804823303}}</ref> [[Maxwell's equations|Maxwell's laws]] are found to confirm to this view since the general solutions of fields are given in terms of retarded time which indicate that [[Electromagnetism|electromagnetic]] disturbances travel at the [[speed of light]]. Advanced time, which also provides a solution for [[Maxwell's equations|Maxwell's law]] are ignored as an unphysical solution.[[File:Bremsstrahlung.gif|thumb|An illustrative example showing bremsstrahlung radiation: Field lines and modulus of the electric field generated by a (negative) charge first moving at a constant speed and then stopping quickly to show the electromagnetic wave generated and propagation of disturbances in electromagnetic field.]]For the motion of a [[charged particle]], considering for example the case of a moving particle with the above described electric field coming to an abrupt stop, the electric fields at points far from it do not immediately revert to that classically given for a stationary charge. On stopping, the field around the stationary points begin to revert to the expected state and this effect propagates outwards at the [[speed of light]] while the electric field lines far away from this will continue to point radially towards an assumed moving charge. This [[virtual particle]] will never be outside the range of propagation of the disturbance in [[electromagnetic field]], since charged particles are restricted to have speeds slower than that of light, which makes it impossible to construct a [[Gaussian surface]] in this region that violates [[Gauss's law]]. Another technical difficulty that supports this is that charged particles travelling faster than or equal to speed of light no longer have a unique retarded time. Since electric field lines are continuous, an [[electromagnetic pulse]] of radiation is generated that connects at the boundary of this disturbance travelling outwards at the [[speed of light]].<ref>{{Cite book |last=Purcell |first=Edward M. |title=Electricity and Magnetism |date=2013 |author2=David J. Morin |isbn=978-1-139-01297-3 |edition=Third |location=Cambridge |pages=251–255 |oclc=1105718330}}</ref> In general, any accelerating point charge radiates [[Electromagnetic radiation|electromagnetic waves]] however, [[Nonradiation condition|non-radiating acceleration]] is possible in a systems of charges.