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[edit]

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[edit]

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]

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[edit]