Vacuum (classical)

For a discussion of the quantum vacuum, see Vacuum (quantum electrodynamic).

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 include: independence from field strengths, direction, frequency, or polarization, and from temperature. Classical vacuum is a standard medium to which others are compared. 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. The description of classical vacuum varies somewhat among authors, with some authors requiring only the absence of substances with electrical properties, or of charged matter (ions and electrons, for example).

Electromagnetic properties

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

ε₀ ≈ 8.854 187 817... × 10⁻¹² F m⁻¹

μ₀ = 4π × 10⁻⁷ ≈ 12.566 370 614... x 10⁻⁷ N A⁻²

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 ε₀ and μ₀ via the relation:

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

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

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 free space is an exact value provided by NIST as the characteristic impedance of vacuum:

$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, 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).

Attainability

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

“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

And classical vacuum is one step further removed 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.