field dependent

Free space

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. The definitions of the ampere and meter SI units are based upon measurements corrected to refer to free space.

Properties of free space

The concept of free space is an abstraction from nature, a baseline or reference state, that is unattainable in practice, like the absolute zero of temperature. It is characterized by the defined value of the parameter μ0 known as the permeability of free space or the style="font-style : italic;">magnetic constant, and the defined value of the parameter ε0 called the permittivity of free space or the style="font-style : italic;">electric constant These parameters appear in Maxwell's equations for the electromagnetic fields. Parameter ε0 also enters the expression for the fine-structure constant usually denoted by α, which characterizes the strength of the electromagnetic interaction.

In the reference state of free space, according to Maxwell's equations, electromagnetic waves, such as radio waves and visible light (among other electromagnetic spectrum frequencies) propagate at the defined speed of light, c0, and according to the theory of relativity, this speed is independent of the speed of the observer or of the source of the waves. The electric and magnetic fields in these waves are related by the defined value of the characteristic impedance of vacuum Z0 In addition, in this reference state the principle of linear superposition of potentials and fields holds: for example, the electric potential generated by two charges is the simple addition of the potentials generated by each charge in isolation.

The ideal vacuum of free space is not the same as a physically obtainable vacuum.

What is the vacuum?

Physicists use the term "vacuum" in several ways. One use is to discuss ideal test results that would occur in a perfect vacuum, which physicists simply call vacuum or free space in this context. The term partial vacuum is used to refer to the imperfect vacuo realizable in practice. The physicist's term "partial vacuum" does suggest one major source of departure of a realizable vacuum from free space, namely non-zero pressure. Today, however, the classical concept of vacuum as a simple void is replaced by the quantum vacuum, separating "free space" still further from the real vacuum – quantum vacuum or the vacuum state is not empty. An approximate meaning is as follows: The quantum vacuum is "by no means a simple empty space"., and again: "it is a mistake to think of any physical vacuum as some absolutely empty void." According to quantum mechanics, empty space (the "vacuum") is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence. One measurable result of these ephemeral occurrences is the Casimir effect. Other examples are spontaneous emission and the Lamb shift. Related to these differences, quantum vacuum differs from free space in exhibiting nonlinearity in the presence of strong electric or magnetic fields (violation of linear superposition). Even in classical physics it was realized that the vacuum must have a field-dependent permittivity in the strong fields found near point charges. These field-dependent properties of the quantum vacuum continue to be an active area of research. The determined reader can explore various nuances of the quantum vacuum in Saunders. A more recent treatment is Genz.

At present, even the meaning of the quantum vacuum state is not settled. For example, what constitutes a "particle" depends on the gravitational state of the observer. See the discussion of vacuum in Unruh effect. Speculation abounds on the role of quantum vacuum in the expanding universe. See vacuum in cosmology. In addition, the quantum vacuum may exhibit spontaneous symmetry breaking. See Woit and the articles: Higgs mechanism and QCD vacuum. To date, there is no suggestion that these uncertainties affect the use of SI units, whose implementation is predicated upon the undisputed predictions of quantum electrodynamics.

In short, realization of the ideal of "free space" is not entirely a matter of achieving low pressure, as the term partial vacuum suggests.

Realization of free space in a laboratory

By "realization" is meant the reduction to practice, or experimental embodiment, of the term "free space", for example, a partial vacuum. What is the operational definition of free space? Although in principle free space is unattainable, like the absolute zero of temperature, the SI units are referred to free space, and so an estimate of the necessary correction to a real measurement is needed. An example might be a correction for non-zero pressure of a partial vacuum. Regarding measurements taken in a real environment (for example, partial vacuum) that are to be related to "free space", the CIPM cautions that:

"in all cases any necessary corrections be applied to take account of actual conditions such as diffraction, gravitation or imperfection in the vacuum."

In practice, a partial vacuum can be produced in the laboratory that is a very good realization of free space. Some of the issues involved in obtaining a high vacuum are described in the article on ultra high vacuum. The lowest measurable pressure today is about 10−11 Pa. (The abbreviation Pa stands for the unit pascal, 1 pascal = 1 N/m2.)

Realization of free space in outer space

While only a partial vacuum, outer space contains such sparse matter that the pressure of interstellar space is on the order of 10 pPa (1×10−11 Pa). For comparison, the pressure at sea level (as defined in the unit of atmospheric pressure) is about 101 kPa (1×105 Pa). The gases in outer space are not uniformly distributed, of course. The density of hydrogen in our galaxy is estimated at 1 hydrogen atom/cm3. In the partial vacuum of outer space, there are small quantities of matter (mostly hydrogen), cosmic dust and cosmic noise. See intergalactic space. In addition, there is a cosmic microwave background with a temperature of 2.725 K, which implies a photon density of about 400 /cm3.

The density of the interplanetary medium and interstellar medium, though, is extremely low; and, for many applications, the interplanetary and interstellar regions are "free space".

US Patent Office interpretation of free space

The United States 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 the atmosphere, the ocean, or the earth" (Glossary in US Patent Class 342, Class Notes). This definition matches other technical definitions of free space outlined above.

Another US Patent Office interpretation is Subclass 310: Communication over free space, where the definition is "a medium which is not a wire or a waveguide". This definition bears little if any relation to other technical definitions of free space outlined above.

References and notes

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