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Free space

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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.[1][2]

The definitions of the ampere and meter SI units are based upon measurements corrected to refer to free space.[3]

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 parameter μ0 known as the permeability of free space or the magnetic constant, by the parameter ε0, called the permittivity of free space or electric constant, and by the speed of light, c0, the three being related through Maxwell's equations by:[1][4][5]

$\varepsilon_0 \mu_0 = 1 / c_0^2$

In the SI system of units, μ0 and c0 have exact defined values. Based on these values, the parameter ε0 also has an exact value:

$\varepsilon_0 =\frac {1}{\mu_0 {c_0}^2} \approx 8.854187817...\ \times \ 10^{-12} \$ F m−1
$\mu_0 = 4 \pi\ \times\ 10^{-7} \approx 1.2566370614...\ \times\ 10^{-6} \$ H m−1 or N A−2

The 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) all propagate at the speed of light, c0. The electric and magnetic fields in these waves are related by the value of the characteristic impedance of vacuum Z0, given by:

$Z_0= \mu_0 c_0 =\sqrt{\frac {\mu_0} { \varepsilon_0}} \approx 376.73031... \ .$ Ω

In addition, in free space 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.[6][7][8]

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 classical vacuum[9][10] or free space in this context. The term partial vacuum is used to refer to the imperfect vacua 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[11] is replaced by the quantum vacuum, separating "free space" still further from the real vacuum – quantum vacuum or the vacuum state is not empty.[12] An approximate meaning is as follows:[13]

Quantum vacuum describes a region devoid of real particles in its lowest energy state.

The quantum vacuum is "by no means a simple empty space,"[14] and again: "it is a mistake to think of any physical vacuum as some absolutely empty void."[15] 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.[16] One measurable result of these ephemeral occurrences is the Casimir effect.[17][18] Other examples are spontaneous emission[19][20][21] and the Lamb shift.[22] 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 [23][24] 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.[25] The determined reader can explore various nuances of the quantum vacuum in Saunders.[26] A more recent treatment is Genz. [27]

At present, even the meaning of the quantum vacuum state is not settled. To quote GE Brown:[28]:

 “ In eighteen-century Newtonian mechanics, the three-body problem was insoluble. With the birth of general relativity around 1910 and quantum electrodynamics in 1930, the two- and one-body problems became insoluble. And within modern quantum field theory, the problem of zero bodies (vacuum) is insoluble.   … GE Brown quoted by RD Mattuck ”

For example, what constitutes a "particle" depends on the gravitational state of the observer. See the discussion of vacuum in Unruh effect.[29][30] 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[31] and the articles: Higgs mechanism and QCD vacuum.

Unsolved problems in physics: Why doesn't the zero-point energy of vacuum cause a large cosmological constant? What cancels it out?

The discrepancies between free space and the quantum vacuum are predicted to be very small, and 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.[32]

In short, realization of the ideal of "free space" is not just a matter of achieving low pressure, as the term partial vacuum suggests. In fact, "free space" is an abstraction from nature, a baseline or reference state, that is unattainable in practice.[33]

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:[3]

“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[citation needed]. 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.[34] (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)[35]. 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.[36] The critical density separating a Universe that continuously expands from one that ultimately crunches is estimated as about three hydrogen atoms per thousand liters of space.[37]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.[38][39]

The density of the interplanetary medium and interstellar medium, though, is extremely low; for many applications negligible error is introduced by treating the interplanetary and interstellar regions as "free space".

US Patent Office interpretation

Scientists working in optical communications tend to use free space to refer to a medium with an unobstructed line of sight (often air, sometimes space). See Free-space optical communication and the What is Free Space Optical Communications?.

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).[40]

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".[41]

References and notes

1. ^ a b 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. p. 34 ff. ISBN 9780819449474.
2. ^ Akhlesh Lakhtakia, R. Messier (2005). "§ 6.2 Constitutive relations". Sculptured thin films: nanoengineered morphology and optics. SPIE Press. p. 105. ISBN 0819456063. "The simplest medium for electromagnetic fields to exist in is free space, which is the classical vacuum."
3. ^ a b CIPM adopted Recommendation 1 (CI-1983) Appendix 1, p. 77 “provided that the given specifications and accepted good practice are followed; • that in all cases any necessary corrections be applied to take account of actual conditions such as diffraction, gravitation or imperfection in the vacuum; … ”
4. ^ Werner S. Weiglhofer, Akhlesh Lakhtakia (2003). Introduction to complex mediums for optics and electromagnetics. SPIE Press. p. 28. ISBN 0819449474.
5. ^ WS Weiglhofer (2002). "A flavour of constitutive relations: the linear regime". in Saïd Zouhdi, Ari Sihvola, Mohamed Arsalane. Advances in electromagnetics of complex media and metamaterials. Springer. p. 66. ISBN 1402011016.
6. ^ Sergej Aleksandrovič Ahmanov, S. Yu Nikitin (1997). Physical Optics. Oxford University Press. pp. 19ff §1.9. ISBN 0198517955.
7. ^ W. N. Cottingham, D. A. Greenwood (1991). Electricity and Magnetism. Cambridge University Press. pp. 16ff. ISBN 0521368030.
8. ^ I. R. Kenyon (2008). The Light Fantastic. Oxford University Press. pp. 96 §5.2. ISBN 0198566468.
9. ^ Sunny Y. Auyang (1995). How is quantum field theory possible?. Oxford University Press. pp. 151–152. ISBN 0195093445.
10. ^ MW Evans & S Jeffers (2001). "The present status of the quantum theory of light". in I. Prigogine, Stuart A. Rice, Myron Evans. Advances in Chemical Physics (2nd ed.). Wiley. p. 56. ISBN 0471389323.
11. ^ The classical concept of free space varies somewhat: three examples are: R. K. Pathria (2003). The Theory of Relativity (Reprint of Pergamon Press 1974 2nd ed.). Courier Dover Publications. p. 119. ISBN 0486428192. "free space, i.e. in the absence of conductors or dielectric and magnetic substances" ; Christopher G. Morris, ed (1992). Academic Press dictionary of science and technology. Gulf Professional Publishing. p. 880. ISBN 0122004000. "a theoretical concept of space devoid of all matter" ; and Werner Vogel, Dirk-Gunnar Welsch (2006). Quantum optics (3rd ed.). Wiley-VCH. p. 337. ISBN 3527405070. "The classical electromagnetic vacuum is simply the state in which all moments of the electric and magnetic induction fields vanish, and thus the fields themselves identically vanish."
12. ^ Walter Dittrich & Gies H (2000). Probing the quantum vacuum: perturbative effective action approach. Berlin: Springer. ISBN 3540674284.
13. ^ Gordon Kane (2000). Supersymmetry: squarks, photinos, and the unveiling of the ultimate laws. Cambridge, MA: Perseus Publishers. Appendix A; pp. 149 ff.. ISBN 0738204897.
14. ^ Astrid Lambrecht (Hartmut Figger, Dieter Meschede, Claus Zimmermann Eds.) (2002). Observing mechanical dissipation in the quantum vacuum: an experimental challenge; in Laser physics at the limits. Berlin/New York: Springer. p. 197. ISBN 3540424180.
15. ^ Christopher Ray (1991). Time, space and philosophy. London/New York: Routledge. Chapter 10, p. 205. ISBN 0415032210.
16. ^ AIP Physics News Update,1996
17. ^ Physical Review Focus Dec. 1998
18. ^ F Capasso, JN Munday, D. Iannuzzi & HB Chen Casimir forces and quantum electrodynamical torques: physics and nanomechanics 2007
19. ^ Hiroyuki Yokoyama & Ujihara K (1995). Spontaneous emission and laser oscillation in microcavities. Boca Raton: CRC Press. p. 6. ISBN 0849337860.
20. ^ Benjamin Fain (2000). Irreversibilities in quantum mechanics: Fundamental theories of physics v. 113. New York:London: Springer/Kluwer Academic. pp. §4.4 pp. 113ff. ISBN 079236581X.
21. ^ Marian O Scully & Zubairy MS (1997). Quantum optics. Cambridge UK: Cambridge University Press. pp. §1.5.2 pp. 22–23. ISBN 0521435951.
22. ^ Marian O Scully & Zubairy MS (1997). pp. 13-16. New York: Cambridge University Press. ISBN 0521435951.
23. ^ For example, by M. Born and L. Infeld Proc. Royal Soc. London A144 425 (1934)
24. ^ John David Jackson (1999). Classical electrodynamics (Third Edtion ed.). NY: Wiley. pp. 10–12. ISBN 0-471-30932-X.
25. ^ See, for example,Di Piazza et al.: Light diffraction by a strong standing electromagnetic wave Phys.Rev.Lett. 97 (2006) 083603, Gies, H et al.: Polarized light propagating in a magnetic field as a probe for millicharged fermions Phys. Rev. Letts. 97 (2006) 140402
26. ^ S Saunders & HR Brown Eds.) (1991). The philosophy of vacuum. Oxford UK: Oxford University Press. ISBN 0198244495.
27. ^ Henning Genz (2002). Nothingness: the science of empty space. Reading MA: Oxford: Perseus. ISBN 0738206105.
28. ^ R. D. Mattuck (1992). A Guide to Feynman Diagrams in the Many-Body Problem (reprint of McGraw-Hill 1976 ed.). Courier Dover Publications. p. 1. ISBN 0486670473.
29. ^ Stephen A. Fulling (1989). Aspects of Quantum Field Theory in Curved Spacetime. Cambridge UK: Cambridge University Press. p. 259.
30. ^ Tian Yu Cao (1999). Conceptual foundations of quantum field theory. Cambridge UK: Cambridge University Press. p. 179. ISBN 0521602726.
31. ^ Peter Woit (2006). Not even wrong: the failure of string theory and the search for unity in physical law. New York: Basic Books. ISBN 0465092756.
32. ^ Henning Genz (2001). p. 247. Reading, Mass. ;Oxford: Perseus. ISBN 0738206105.
33. ^ Paulo N Correa & Alexandra N Correa The Sagnac and Michelson-Gale-Pearson Experiments: The tribulations of general relativity with respect to rotation; "An absolute vacuum of matter and energy is unattainable and not a real possibility that should or need be considered. The "vacuum state" is a misnomer … "
34. ^ LM Rozanov & Hablanian, MH (2002). Vacuum technique. London; New York: Taylor & Francis. Figure 3.1, p. 80. ISBN 041527351X.
35. ^ Zheng, MiMi (2002). "Pressure in Outer Space". The Physics Factbook.
36. ^ Gareth Wynn-Williams (1992). The fullness of space. Cambridge UK: Cambridge University Press. p. 38. ISBN 0521426383.
37. ^ Steven Weinberg (1993). The First Three Minutes: A Modern View of the Origin of the Universe (2 ed.). Basic Books. p. 34. ISBN 0465024378.
38. ^
39. ^ This background temperature depends upon the gravitational state of the observer. See Unruh effect.
40. ^ U.S. Patent Classification System - Classification Definitions as of June 30, 2000
41. ^ Subclass 310: Communication over free space

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