Editing Conservation law (section)

==Global and local conservation laws==
The total amount of some conserved quantity in the universe could remain unchanged if an equal amount were to appear at one point ''A'' and simultaneously disappear from another separate point ''B''.  For example, an amount of energy could appear on Earth without changing the total amount in the Universe if the same amount of energy were to disappear from some other region of the Universe.  This weak form of "global" conservation is really not a conservation law because it is not [[Lorentz invariant]], so phenomena like the above do not occur in nature.<ref name="Aitchison">{{cite book
 |last1       = Aitchison
 |first1      = Ian J. R.
 |last2       = Hey
 |first2      = Anthony J.G.
 |title       = Gauge Theories in Particle Physics: A Practical Introduction: From Relativistic Quantum Mechanics to QED, Fourth Edition, Vol. 1
 |publisher   = CRC Press
 |date        = 2012
 |pages       = 43
 |url         = https://books.google.com/books?id=-v6sPfuyUt8C&q=%22global+conservation%22+%22local+conservation%22&pg=PA43
 |isbn        = 978-1466512993
 |url-status  = live
 |archive-url = https://web.archive.org/web/20180504190417/https://books.google.com/books?id=-v6sPfuyUt8C&pg=PA43&dq=%22global+conservation%22+%22local+conservation%22
 |archive-date = 2018-05-04
}}</ref><ref name="Will">{{cite book
 |last1       = Will
 |first1      = Clifford M.
 |title       = Theory and Experiment in Gravitational Physics
 |publisher   = Cambridge Univ. Press
 |date        = 1993
 |pages       = 105
 |url         = https://books.google.com/books?id=BhnUITA7sDIC&q=%22global+conservation%22+%22local+conservation%22+law&pg=PA105
 |isbn        = 978-0521439732
 |url-status  = live
 |archive-url = https://web.archive.org/web/20170220012119/https://books.google.com/books?id=BhnUITA7sDIC&pg=PA105&dq=%22global+conservation%22+%22local+conservation%22+law
 |archive-date = 2017-02-20
}}</ref>  Due to [[special relativity]], if the appearance of the energy at ''A'' and disappearance of the energy at ''B'' are simultaneous in one [[inertial reference frame]], they [[Relativity of simultaneity|will not be simultaneous]] in other inertial reference frames moving with respect to the first.  In a moving frame one will occur before the other; either the energy at ''A'' will appear ''before'' or ''after'' the energy at ''B'' disappears.  In both cases, during the interval energy will not be conserved.

A stronger form of conservation law requires that, for the amount of a conserved quantity at a point to change, there must be a flow, or ''flux'' of the quantity into or out of the point.  For example, the amount of [[electric charge]] at a point is never found to change without an [[electric current]] into or out of the point that carries the difference in charge.  Since it only involves continuous ''[[principle of locality|local]]'' changes, this stronger type of conservation law is [[Lorentz invariant]]; a quantity conserved in one reference frame is conserved in all moving reference frames.<ref name="Aitchison" /><ref name="Will"/>  This is called a ''local conservation'' law.<ref name="Aitchison" /><ref name="Will"/>  Local conservation also implies global conservation; that the total amount of the conserved quantity in the Universe remains constant.  All of the conservation laws listed above are local conservation laws. A local conservation law is expressed mathematically by a ''[[continuity equation]]'', which states that the change in the quantity in a volume is equal to the total net  "flux" of the quantity through the surface of the volume.  The following sections discuss continuity equations in general.