Editing Scientific law (section)

=== Conservation laws ===

==== Conservation and symmetry ====
{{Main|Symmetry (physics)}}

[[Conservation laws]] are fundamental laws that follow from the homogeneity of space, time and [[phase (waves)|phase]], in other words ''symmetry''.
* '''[[Noether's theorem]]:''' Any quantity with a continuously differentiable symmetry in the action has an associated conservation law.
* [[Conservation of mass]] was the first law to be understood since most macroscopic physical processes involving masses, for example, collisions of massive particles or fluid flow, provide the apparent belief that mass is conserved. Mass conservation was observed to be true for all chemical reactions. In general, this is only approximative because with the advent of relativity and experiments in nuclear and particle physics: mass can be transformed into energy and vice versa, so mass is not always conserved but part of the more general conservation of [[mass–energy equivalence|mass–energy]].
* '''[[Conservation of energy]]''', '''[[Conservation of momentum|momentum]]''' and '''[[Conservation of angular momentum|angular momentum]]''' for isolated systems can be found to be [[Time translation symmetry|symmetries in time]], translation, and rotation.
* '''[[Conservation of charge]]''' was also realized since charge has never been observed to be created or destroyed and only found to move from place to place.

==== Continuity and transfer ====

Conservation laws can be expressed using the general [[continuity equation]] (for a conserved quantity) can be written in differential form as:
: <math>\frac{\partial \rho}{\partial t}=-\nabla \cdot \mathbf{J} </math>
where ''ρ'' is some quantity per unit volume, '''J''' is the [[flux]] of that quantity (change in quantity per unit time per unit area). Intuitively, the [[divergence]] (denoted ∇⋅) of a [[vector field]] is a measure of flux diverging radially outwards from a point, so the negative is the amount piling up at a point; hence the rate of change of density in a region of space must be the amount of flux leaving or collecting in some region (see the main article for details). In the table below, the fluxes flows for various physical quantities in transport, and their associated continuity equations, are collected for comparison.

:{| class="wikitable" align="center"
|-
! scope="col" style="width:150px;"| Physics, conserved quantity
! scope="col" style="width:140px;"| Conserved quantity ''q'' 
! scope="col" style="width:140px;"| Volume density ''ρ'' (of ''q'') 
! scope="col" style="width:140px;"| Flux '''J''' (of ''q'')
! scope="col" style="width:10px;"| Equation
|-
| [[Hydrodynamics]], [[fluid]]s <br />
| ''m'' = [[mass]] (kg)
| ''ρ'' = volume [[mass density]] (kg m<sup>−3</sup>)
| ''ρ'' '''u''', where<br />
'''u''' = [[velocity field]] of fluid (m s<sup>−1</sup>)
| <math> \frac{\partial \rho}{\partial t} = - \nabla \cdot (\rho \mathbf{u}) </math>
|-
| [[Electromagnetism]], [[electric charge]]
| ''q'' = electric charge (C)
| ''ρ'' = volume electric [[charge density]] (C m<sup>−3</sup>)
| '''J''' = electric [[current density]] (A m<sup>−2</sup>)
| <math> \frac{\partial \rho}{\partial t} = - \nabla \cdot \mathbf{J} </math> 
|-
| [[Thermodynamics]], [[energy]]
| ''E'' = energy (J)
| ''u'' = volume [[energy density]] (J m<sup>−3</sup>)
| '''q''' = [[heat flux]] (W m<sup>−2</sup>)
| <math> \frac{\partial u}{\partial t}=- \nabla \cdot \mathbf{q} </math> 
|-
| [[Quantum mechanics]], [[probability]] 
| ''P'' = ('''r''', ''t'') = ∫|Ψ|<sup>2</sup>d<sup>3</sup>'''r''' = [[probability distribution]]
| ''ρ'' = ''ρ''('''r''', ''t'') = |Ψ|<sup>2</sup> = [[probability density function]] (m<sup>−3</sup>),<br />
Ψ = [[wavefunction]] of quantum system
| '''j''' = [[probability current]]/flux
| <math> \frac{\partial |\Psi|^2}{\partial t}=-\nabla \cdot \mathbf{j} </math> 
|}

More general equations are the [[convection–diffusion equation]] and [[Boltzmann transport equation]], which have their roots in the continuity equation.