# Vacuum (classical)

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The term classical vacuum is used in classical electromagnetism where it refers to an ideal reference medium, devoid of all particles, with ideal properties. These ideal properties are independent of field strength, direction, frequency, or polarization, and from temperature.[1][2] Classical vacuum is a standard medium to which others are compared, and is used in the definition of the SI units. Classical vacuum also is referred to in electromagnetism as free space or the vacuum of free space and sometimes as ideal vacuum. In the classical vacuum, vanishing fields imply there are no sources present (no charges, for example), while in contrast, in quantum vacuum moments of the fields can arise without sources by virtual photon creation and destruction.[3]

The description of free space sometimes differs from classical vacuum, with some authors defining free space as the absence of substances with electrical properties,[4] or absence of charged matter (ions and electrons, for example).[5] The U. S. Patent Office defines free space in a number of ways. For radio and radar applications the definition is "space where the movement of energy in any direction is substantially unimpeded, such as interplanetary space, the atmosphere, the ocean and other large bodies of water or the earth".[6] Another US Patent Office interpretation is "a medium which is not a wire or a waveguide".[7]

### Electromagnetic properties

The electromagnetic behavior of classical vacuum is characterized by its electrical permittivity ε0 and its magnetic permeability μ0.[8] The exact value of ε0 is provided by NIST as the electric constant [9] and the defined value of μ0 as the magnetic constant:[10]

ε0 = 8.854 187 817... × 10−12 F m−1
μ0 = 4π × 10−7 = 12.566 370 614... × 10−7 N A−2

where the '…' does not denote a physical uncertainty (such as a measurement error) but the inability to express 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 classical vacuum is related to ε0 and μ0 via the relation:[11]

${\displaystyle c_{0}=1/{\sqrt {\mu _{0}\varepsilon _{0}}}\ .}$

Using the defined valued for the speed of light provided by NIST as:[12]

c0 = 299 792 458 m s −1,

and the already mentioned defined value for μ0, this relationship leads to the exact value given above for ε0.

Another consequence of these electromagnetic properties is that the ratio of electric to magnetic field strengths in an electromagnetic wave propagating in classical vacuum is an exact value provided by NIST as the characteristic impedance of vacuum:[13]

${\displaystyle Z_{0}={\sqrt {\mu _{0}/\varepsilon _{0}}}\ }$
= 376.730 313 461... Ω.

It also can be noted that the electrical permittivity ε0 and the magnetic permeability μ0 do not depend upon direction of propagation, field strength, polarization, or frequency. Consequently, classical vacuum is isotropic, linear, non-dichroic, and dispersion free. Linearity, in particular, implies that the fields and/or potentials due to an assembly of charges are simply the addition of the fields/potentials due to each charge separately (that is, the principle of superposition applies).[14] Linearity also implies that even very close to point charges where fields become extremely large the properties of classical vacuum remain unaffected.

### Attainability

A perfect vacuum is itself realizable only in principle.[15][16] It is an idealization, like absolute zero for temperature, that can be approached, but never actually realized:[15]

 “One reason [a vacuum is not empty] is that the walls of a vacuum chamber emit light in the form of black-body radiation...If this soup of photons is in thermodynamic equilibrium with the walls, it can be said to have a particular temperature, as well as a pressure. Another reason that perfect vacuum is impossible is the Heisenberg uncertainty principle which states that no particles can ever have an exact position...More fundamentally, quantum mechanics predicts ... a correction to the energy called the zero-point energy [that] consists of energies of virtual particles that have a brief existence. This is called vacuum fluctuation.” Luciano Boi, "Creating the physical world ex nihilo?" p. 55

Predictions of quantum electrodynamic vacuum such as spontaneous emission, the Casimir effect and the Lamb shift have been experimentally verified, suggesting QED vacuum is a good model for realizable vacuum. That success removes classical vacuum further from attainability because its permittivity ε0 and permeability μ0 do not allow for quantum fluctuations. Nonetheless, outer space and good terrestrial vacuums are modeled adequately by classical vacuum for many purposes.

## References

1. Werner S. Weiglhofer and Akhlesh Lakhtakia (2003). “§4.1: The classical vacuum as reference medium”, Introduction to complex mediums for optics and electromagnetics. SPIE Press. ISBN 0819449474.
2. Daniela Dragoman, Mircea Dragoman (2004). Quantum-classical analogies. Springer, pp. 10, 11. ISBN 3540201475. “...the vacuum, which is considered as a reference medium and is characterized by the corresponding parameters ε0 and μ0.”
3. Werner Vogel, Dirk-Gunnar Welsch (2006). Quantum optics, 3rd ed.. Wiley-VCH, p. 337. ISBN 3527405070.
4. RK Pathria (2003). The Theory of Relativity, Reprint of Hindustan 1974 2nd ed.. Courier Dover Publications, p. 119. ISBN 0486428192.
5. (1992) Christopher G. Morris, editor: Academic Press dictionary of science and technology. Academic, p. 880. ISBN 0122004000.
6. Section IV–Glossary. Class 343; Communications: Radio wave antennas; Glossary. U.S. Patent and Trademark Office: Office of Classification Support (June 30, 2000). Retrieved on 2011-11-16.
7. Class 370: Multiplex communications; Subclass 310: Communication over free space. U.S. Patent Classification System - Classification Definitions. U.S. Patent and Trademark Office: Information Products Division (June 30, 2000). Retrieved on 2011-11-16.
8. Akhlesh Lakhtakia, R. Messier (2005). “§6.2: Constitutive relations”, Sculptured thin films: nanoengineered morphology and optics. SPIE Press, p. 105. ISBN 0819456063.
9. CODATA. Electric constant. 2006 CODATA recommended values. NIST. Retrieved on 2010-11-28.
10. CODATA. Magnetic constant. 2006 CODATA recommended values. NIST. Retrieved on 2010-11-28.
11. Albrecht Unsöld, B. Baschek (2001). “§4.1: Electromagnetic radiation, Equation 4.3”, The new cosmos: an introduction to astronomy and astrophysics, 5th ed.. Springer, p. 101. ISBN 3540678778.
12. CODATA. Speed of light in vacuum. 2006 CODATA recommended values. NIST. Retrieved on 2010-11-28. A defined value for the speed of light is a consequence of adoption of time of transit as the measure of length, so lengths are measured in seconds. See metre.
13. CODATA. Characteristic impedance of vacuum Z0. 2006 CODATA recommended values. NIST. Retrieved on 2010-11-28.
14. A. Pramanik (2004). “§1.3 The principle of superposition”, Electro-Magnetism: Theory and Applications. PHI Learning Pvt. Ltd, pp. 37-38. ISBN 8120319575.
15. Luciano Boi (2009). “Creating the physical world ex nihilo? On the quantum vacuum and its fluctuations”, Ernesto Carafoli, Gian Antonio Danieli, Giuseppe O. Longo, editors: The Two Cultures: Shared Problems. Springer, p. 55. ISBN 8847008689.
16. PAM Dirac (2001). Jong-Ping Hsu, Yuanzhong Zhang, editors: Lorentz and Poincaré invariance: 100 years of relativity. World Scientific, p. 440. ISBN 9810247214.