Editing Vacuum (section)

=== Electromagnetism ===
In [[classical electromagnetism]], the '''vacuum of free space''', or sometimes just ''free space'' or ''perfect vacuum'', is a standard reference medium for electromagnetic effects.<ref name=weig>{{cite book
 | title = Introduction to complex mediums for optics and electromagnetics
 | author = Werner S. Weiglhofer
 | editor= Werner S. Weiglhofer
 | editor2= Akhlesh Lakhtakia
 | publisher = SPIE Press
 | chapter=§&nbsp;4.1 The classical vacuum as reference medium
 | date = 2003
 | isbn = 978-0-8194-4947-4
 | pages = 28, 34
 | chapter-url = https://books.google.com/books?id=QtIP_Lr3gngC&pg=PA34
 }}</ref><ref>{{cite book
 | title = Progress in Optics
 | volume = 51
 | chapter = Electromagnetic Fields in Linear Bianisotropic Mediums
 | author = Tom G. MacKay
 | editor = Emil Wolf
 | publisher = Elsevier
 | date = 2008
 | isbn = 978-0-444-52038-8
 | page = 143
 | chapter-url = https://books.google.com/books?id=lCm9Q18P8cMC&pg=PA143
 }}</ref> Some authors refer to this reference medium as ''classical vacuum'',<ref name=weig /> a terminology intended to separate this concept from [[QED vacuum]] or [[QCD vacuum]], where [[vacuum fluctuation]]s can produce transient [[virtual particle]] densities and a [[relative permittivity]] and [[Permeability (electromagnetism)#Relative permeability and magnetic susceptibility|relative permeability]] that are not identically unity.<ref name=Grynberg>{{cite book |url=https://books.google.com/books?id=l-l0L8YInA0C&pg=PA341 |page=341 |publisher=Cambridge University Press |date=2010 |title=Introduction to Quantum Optics: From the Semi-Classical Approach to Quantized Light |quote=...deals with the quantum vacuum where, in contrast to the classical vacuum, radiation has properties, in particular, fluctuations, with which one can associate physical effects. |isbn=978-0-521-55112-0 |author=Gilbert Grynberg |author2=Alain Aspect |author3=Claude Fabre}}</ref><ref name=Susskind>For a qualitative description of vacuum fluctuations and virtual particles, see {{cite book
|author = Leonard Susskind
|title = The cosmic landscape: string theory and the illusion of intelligent design
|publisher = Little, Brown and Co.
|date = 2006
|isbn = 978-0-316-01333-8
|url = https://books.google.com/books?id=RIW9E1sOyxUC&pg=PP60
|pages = 60 ''ff''}}</ref><ref name=Holstein>The relative permeability and permittivity of field-theoretic vacuums is described in {{cite book |title=Concepts of particle physics |volume=2 |author=Kurt Gottfried |author2=Victor Frederick Weisskopf |url=https://books.google.com/books?id=KXvoI-m9-9MC&pg=PA389 |page=389 |isbn=978-0-19-503393-9 |date=1986 |publisher=Oxford University Press}} and more recently in {{cite book
|author = John F. Donoghue
|author2 = Eugene Golowich
|author3 = Barry R. Holstein
|title = Dynamics of the standard model
|publisher = Cambridge University Press
|date = 1994
|isbn = 978-0-521-47652-2
|url = https://books.google.com/books?id=hFasRlkBbpYC&pg=PA47
|page = 47}} and also {{cite book |title=QCD and collider physics |author=R. Keith Ellis |author2=W.J. Stirling |author3=B.R. Webber |url=https://books.google.com/books?id=TqrPVoS6s0UC&pg=PA27 |pages=27–29 |isbn=978-0-521-54589-1 |date=2003 |quote=Returning to the vacuum of a relativistic field theory, we find that both paramagnetic and diamagnetic contributions are present. |publisher=Cambridge University Press}} [[QCD vacuum]] is [[Paramagnetism|paramagnetic]], while [[QED vacuum]] is [[Diamagnetism|diamagnetic]]. See {{cite book |title=Nuclear physics in a nutshell |author=Carlos A. Bertulani |url=https://books.google.com/books?id=n51yJr4b_oQC&pg=PA26 |page=26 |isbn=978-0-691-12505-3 |date=2007 |publisher=Princeton University Press|bibcode=2007npn..book.....B }}</ref>

In the theory of classical electromagnetism, free space has the following properties:
* Electromagnetic radiation travels, when unobstructed, at the [[speed of light]], the defined value 299,792,458&nbsp;m/s in [[SI units]].<ref name=NISTc>{{cite web |title=Speed of light in vacuum, ''c, c''<sub>0</sub> |website=The NIST reference on constants, units, and uncertainty: Fundamental physical constants |url=http://physics.nist.gov/cgi-bin/cuu/Value?c |publisher=NIST |access-date=2011-11-28}}</ref>
* The [[superposition principle]] is always exactly true.<ref>{{cite book
|author = Chattopadhyay, D.
|author2 = Rakshit, P.C.
|name-list-style = amp
|title = Elements of Physics
|volume = 1
|publisher = New Age International
|date = 2004
|isbn = 978-81-224-1538-4
|url = https://books.google.com/books?id=tvkoopJMQQ8C&pg=PA577
|page = 577}}</ref> For example, the electric potential generated by two charges is the simple addition of the potentials generated by each charge in isolation. The value of the [[electric field]] at any point around these two charges is found by calculating the [[Vector (mathematics and physics)|vector]] sum of the two electric fields from each of the charges acting alone.
* The [[permittivity]] and [[Permeability (electromagnetism)|permeability]] are exactly the electric constant [[vacuum permittivity|{{math|''ε''<sub>0</sub>}}]]<ref name=NISTep0>{{cite web |title=Electric constant, ε<sub>0</sub> |website=The NIST reference on constants, units, and uncertainty: Fundamental physical constants |url=http://physics.nist.gov/cgi-bin/cuu/Value?ep0|publisher=NIST |access-date=2011-11-28}}</ref> and magnetic constant [[vacuum permeability|{{math|''μ''<sub>0</sub>}}]],<ref name=NISTmu0>{{cite web |title=Magnetic constant, μ<sub>0</sub> |website=The NIST reference on constants, units, and uncertainty: Fundamental physical constants |url=http://physics.nist.gov/cgi-bin/cuu/Value?mu0|publisher=NIST |access-date=2011-11-28}}</ref> respectively (in [[SI units]]), or exactly 1 (in [[Gaussian units]]).
* The [[characteristic impedance]] ({{mvar|η}}) equals the [[impedance of free space]] {{math|''Z''<sub>0</sub>}} ≈ 376.73&nbsp;Ω.<ref name=NISTz>{{cite web |title=Characteristic impedance of vacuum, ''Z''<sub>0</sub> |website=The NIST reference on constants, units, and uncertainty: Fundamental physical constants |url=http://physics.nist.gov/cgi-bin/cuu/Value?z0 |access-date=2011-11-28}}</ref>

The vacuum of classical electromagnetism can be viewed as an idealized electromagnetic medium with the [[Constitutive equation#Electromagnetism|constitutive relations]] in SI units:<ref name=E_Wolf>{{cite book |author=Mackay, Tom G |author2=Lakhtakia, Akhlesh |name-list-style=amp |editor=Emil Wolf |title=Progress in Optics  |volume=51 |isbn=978-0-444-53211-4 |date=2008 |publisher=Elsevier |chapter-url=https://books.google.com/books?id=lCm9Q18P8cMC&pg=PA143 |chapter=§&nbsp;3.1.1 Free space |page=143 }}</ref>
:<math>\boldsymbol D(\boldsymbol r,\ t) = \varepsilon_0 \boldsymbol E(\boldsymbol r,\ t)\, </math>
:<math>\boldsymbol H(\boldsymbol r,\ t) = \frac{1}{\mu_0} \boldsymbol B(\boldsymbol r,\ t)\, </math>
relating the [[electric displacement]] field {{math|'''''D'''''}} to the [[electric field]] {{math|'''''E'''''}} and the [[magnetic field]] or ''H''-field {{math|'''''H'''''}} to the [[magnetic field|magnetic induction]] or ''B''-field {{math|'''''B'''''}}. Here {{math|'''''r'''''}} is a spatial location and {{mvar|t}} is time.