Free space (electromagnetism): Difference between revisions

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#REDIRECT [[Vacuum (classical)]]
 
'''Free space''' usually refers to a perfect vacuum, devoid of all particles. The term is most often used in classical electromagnetism where it refers to a reference state,<ref name=Weiglhofer>{{cite book|title=Introduction to complex mediums for optics and electromagnetics |author=Werner S. Weiglhofer and Akhlesh Lakhtakia |year=2003 |url=http://books.google.com/books?id=QtIP_Lr3gngC&pg=PA34&hl=en#v=onepage&q&f=false|publisher=SPIE Press |isbn=0819449474 |chapter=§4.1: The classical vacuum as reference medium }}</ref> and in quantum physics where it refers to the ground state of the electromagnetic field, which is subject to fluctuations about a dormant zero average-field condition.<ref name=Shankar>{{cite book|title=Principles of quantum mechanics |author=Ramamurti Shankar |url=http://books.google.com/books?id=2zypV5EbKuIC&pg=PA507#v=onepage&q=free%20space&f=false |pages=p. 507 |isbn=0306447908 |year=1994 |edition=2nd ed. |publisher=Springer}}</ref> The classical case of vanishing fields implies all fields are source-attributed, while in the quantum case field moments can arise without sources from virtual phonon creation and destruction.<ref name=Vogel>{{cite book |title=Quantum optics |author=Werner Vogel, Dirk-Gunnar Welsch |url=http://books.google.com/books?id=qRtnP1dPGmQC&pg=PA337&hl=en#v=onepage&q&f=false |pages=p. 337 |publisher=Wiley-VCH |year=2006 |edition=3rd ed.  |isbn=3527405070}}</ref> The description of free space varies somewhat among authors, with some authors requiring only the absence of substances with electrical properties,<ref name=Pathria>{{cite book|title=The Theory of Relativity |author= RK Pathria |url=http://books.google.com/books?id=Ma4ZFefVKIYC&pg=PA119&hl=en#v=onepage&q&f=false |pages=p. 119 | |year=2003 |isbn=0486428192 |publisher=Courier Dover Publications |edition=Reprint of Hindustan 1974 2nd ed.}}</ref> or of charged matter (ions and electrons, for example).<ref name=Morris>{{cite book |title=Academic Press dictionary of science and technology |editor=Christopher G. Morris, editor |publisher=Academic |url=http://books.google.com/books?id=nauWlPTBcjIC&pg=PA880&hl=en#v=onepage&q&f=false|pages=p. 880 |year=1992 |isbn=0122004000}}</ref>
 
===Classical case===
In classical physics, free space is a concept of electromagnetic theory, corresponding to a theoretically perfect vacuum and sometimes referred to as the ''vacuum of free space'', or as ''classical vacuum'', and is appropriately viewed as a reference medium.<ref name=Weiglhofer/> In the classical case, free space is characterized by the electrical permittivity ε<sub>0</sub> and the magnetic permeability μ<sub>0</sub>.<ref name=Messier>
 
{{cite book |title=Sculptured thin films: nanoengineered morphology and optics |author=Akhlesh Lakhtakia, R. Messier |chapter=§6.2: Constitutive relations |url=http://books.google.com/books?id=yCzDND-vIhMC&pg=PA105#v=onepage&q&f=false |pages=p. 105 |publisher=SPIE Press |year=2005 |isbn=0819456063}}
 
</ref> The exact value of ε<sub>0</sub> is provided by [[NIST]] as the [http://physics.nist.gov/cgi-bin/cuu/Value?ep0 ''electric constant'']and the defined value of μ<sub>0</sub> as the [http://physics.nist.gov/cgi-bin/cuu/Value?mu0 ''magnetic constant'']:
::ε<sub>0</sub> ≈ 8.854 187 817... × 10<sup>−12</sup> F m<sup>−1</sup>
 
::μ<sub>0</sub> = 4π × 10<sup>−7</sup> ≈ 12.566 370 614... x 10<sup>−7</sup> N A<sup>−2</sup>
 
where the approximation is not a physical uncertainty (such as a measurement error) but a result of the inability to express these [[irrational numbers]] with a finite number of digits.
 
One consequence of these electromagnetic properties coupled with [[Maxwell's equations]] is that the [[speed of light]] in free space is related to ε<sub>0</sub> and μ<sub>0</sub> via the relation:<ref name=Baschek>
 
{{cite book |title= The new cosmos: an introduction to astronomy and astrophysics |author=Albrecht Unsöld, B. Baschek |url=http://books.google.com/books?id=nNnmR8ljctoC&pg=PA101 |pages=p. 101 |chapter=§4.1: Electromagnetic radiation, Equation 4.3 |isbn=3540678778 |year=2001 |publisher=Springer |edition=5th ed.}}
 
</ref>
 
::<math>c_0 = 1/\sqrt{\mu_0 \varepsilon_0}\ . </math>
 
Using the defined valued for the [http://physics.nist.gov/cgi-bin/cuu/Value?c speed of light] provided by NIST as:
 
::c<sub>0</sub> = 299 792 458 m s <sup>−1</sup>,
 
and the already mentioned defined value for μ<sub>0</sub>, this relationship leads to the exact value given above for ε<sub>0</sub>.
 
Another consequence of these electromagnetic properties is that the ratio of electric to magnetic field strengths in an [[electromagnetic wave]] propagating in free space is an exact value provided by NIST as the [http://physics.nist.gov/cgi-bin/cuu/Value?z0 characteristic impedance of free space]:
 
:: <math>Z_0 =  \sqrt{\mu_0 /\varepsilon_0} \  </math>
:::= 376.730 313 461... ohms.
 
It also can be noted that the electrical permittivity ε<sub>0</sub> and the magnetic permeability μ<sub>0</sub> do not depend upon direction, field strength, polarization, or frequency. Consequently, free space is isotropic, linear, non-dichroic, and dispersion free. Linearity, in particular, implies that the fields and/or potentials due to an assembly of charges is simply the addition of the fields/potentials due to each charge separately (that is, the  principle of superposition applies).<ref name=Pramanik>
{{cite book |title=Electro-Magnetism: Theory and Applications |author=A. Pramanik |url=http://books.google.com/books?id=gnEEwy12S5cC&pg=PT23 |pages=pp. 37-38 |chapter=§1.3 The principle of superposition |isbn=8120319575 |year=2004 |publisher=PHI Learning Pvt. Ltd}}</ref>
 
===Quantum case===
The [[Heisenberg Uncertainty Principle|Heisenberg uncertainty principle]] for a particle in one dimension does not allow a state of rest in which the particle is simultaneously at a fixed location, say the origin of coordinates, and has also zero momentum. Instead the particle has a [[zero-point energy]] and a range of momentum and spread in location attributable to quantum fluctuations.
 
This notion applies also to the electromagnetic field. Even in the vacuum, the variances of the fields cannot be zero, although their averages are zero.<ref name=Grynberg>
 
{{cite book |title=Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light |author=Gilbert Grynberg, Alain Aspect, Claude Fabre |url=http://books.google.com/books?id=l-l0L8YInA0C&pg=PA351 |pages=pp. 351 ''ff'' |§5.2.2 Vacuum fluctuations and their physical consequences |year=2010 |isbn=0521551129 |publisher=Cambridge University Press}}
 
</ref> As a result, the vacuum can be considered as a dielectric medium, and is capable of vacuum polarization.<ref name=Weisskopf>
 
{{cite book |title=Concepts of particle physics, Volume 2 |author=Kurt Gottfried, Victor Frederick Weisskopf |url=http://books.google.com/books?id=KXvoI-m9-9MC&pg=PA259 |pages=259 ''ff''  |isbn= 0195033930 |year=1986 |publisher=Oxford University Press}}
 
</ref> Its dielectric permittivity can be calculated, and it differs slightly from the simple ε<sub>0</sub> of the classical vacuum. Likewise, its permeability can be calculated and differs slightly from μ<sub>0</sub>.
 
===Attainability===
A real vacuum is itself only realizable in principle.<ref name=Hsu>
 
{{cite book |author=PAM Dirac |title=Lorentz and Poincaré invariance: 100 years of relativity |editor=Jong-Ping Hsu, Yuanzhong Zhang, editors |year=2001 |publisher=World Scientific |isbn=9810247214 |url=http://books.google.com/books?id=jryk42J8oQIC&pg=PA440 |pages=p. 440}}
 
</ref> It is an idealization, like [[absolute zero]] for temperature, that can be approached, but never actually realized. And classical vacuum is one step further removed from attainability because its permittivity ε<sub>0</sub> and permeability μ<sub>0</sub> do not allow for quantum fluctuation effects. Nonetheless, outer space and good terrestrial vacuums are modeled adequately by classical vacuum for many purposes.
 
==References==
{{reflist}}

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