Difference between revisions of "Free space" - New World Encyclopedia
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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.<ref name=Dittrich>Dittrich, and Gies. 2000.</ref> An approximate meaning is as follows:<ref name=Kane>Kane. 2000. Appendix A; pp. 149 ff.</ref> | 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.<ref name=Dittrich>Dittrich, and Gies. 2000.</ref> An approximate meaning is as follows:<ref name=Kane>Kane. 2000. Appendix A; pp. 149 ff.</ref> | ||
{{Quotation|Quantum vacuum describes a region devoid of real particles in its lowest energy state.}} | {{Quotation|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,"<ref name=Lambrecht>Lambrecht. 2002. page 197.</ref> and again: "it is a mistake to think of any physical vacuum as some absolutely empty void."<ref name=Ray>Ray. 1991. page 205.</ref> 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.<ref>[http://www.aip.org/pnu/1996/split/pnu300-3.htm AIP Physics News Update.] aip.org. Retrieved January 10, 2009.</ref> One measurable result of these ephemeral occurrences is the [[Casimir effect]].<ref>[http://focus.aps.org/story/v2/st28 Physical Review Focus Dec.] focus.aps.org. Retrieved January 10, 2009.</ref><ref>Capasso, F., J.N. Munday, D. Iannuzzi, and H.B. Chen. 2007. [https://www.editorial.seas.harvard.edu/capasso/publications/Capasso_STJQE_13_400_2007.pdf Casimir forces and quantum electrodynamical torques: physics and nanomechanics.] Harvard University. Retrieved January 10, 2009.</ref> Other examples are [[spontaneous emission]]<ref name=Yokoyama,>Yokoyama, and Ujihara. 1995. page 6.</ref><ref name=Fain>Fain. 2000. pages §4.4; 113ff.</ref><ref name=Scully1>Scully, and Zubairy. 1997. pages §1.5.2; 22–23</ref> and the [[Lamb shift]].<ref name=Scully2>Scully, and Zubairy. 1997. pages 13-16.</ref> 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 <ref> | + | The quantum vacuum is "by no means a simple empty space,"<ref name=Lambrecht>Lambrecht. 2002. page 197.</ref> and again: "it is a mistake to think of any physical vacuum as some absolutely empty void."<ref name=Ray>Ray. 1991. page 205.</ref> 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.<ref>[http://www.aip.org/pnu/1996/split/pnu300-3.htm AIP Physics News Update.] aip.org. Retrieved January 10, 2009.</ref> One measurable result of these ephemeral occurrences is the [[Casimir effect]].<ref>[http://focus.aps.org/story/v2/st28 Physical Review Focus Dec.] focus.aps.org. Retrieved January 10, 2009.</ref><ref>Capasso, F., J.N. Munday, D. Iannuzzi, and H.B. Chen. 2007. [https://www.editorial.seas.harvard.edu/capasso/publications/Capasso_STJQE_13_400_2007.pdf Casimir forces and quantum electrodynamical torques: physics and nanomechanics.] Harvard University. Retrieved January 10, 2009.</ref> Other examples are [[spontaneous emission]]<ref name=Yokoyama,>Yokoyama, and Ujihara. 1995. page 6.</ref><ref name=Fain>Fain. 2000. pages §4.4; 113ff.</ref><ref name=Scully1>Scully, and Zubairy. 1997. pages §1.5.2; 22–23</ref> and the [[Lamb shift]].<ref name=Scully2>Scully, and Zubairy. 1997. pages 13-16.</ref> 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 <ref>Born, M. and L. Infeld. 1934. ''Proc. Royal Soc. London''. A144:425.</ref><ref name=Jackson>Jackson. 1999. pages 10–12.</ref> 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.<ref>Di Piazza, A., K. Z. Hatsagortsyan, and C. H. Keitel. 2006. [http://arxiv.org/abs/hep-ph/0602039v2 Light diffraction by a strong standing electromagnetic wave.] ''Phys. Rev. Lett.''; Gies, Holger, Joerg Jaeckel, and Andreas Ringwald. 2006. [http://arxiv.org/abs/hep-ph/0607118v1 Polarized light propagating in a magnetic field as a probe for millicharged fermions.] ''Phys. Rev. Letts.'' 97. Retrieved January 10, 2009.</ref> The determined reader can explore various nuances of the quantum vacuum in Saunders.<ref name=Saunders>Saunders, and Brown. 1991.</ref> A more recent treatment is Genz. <ref name=Genz>Genz. 2002.</ref> |
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| − | </ref> 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.<ref> | ||
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| − | </ref> A more recent treatment is Genz. <ref name=Genz> | ||
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| − | 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#Vacuum interpretation|Unruh effect]].<ref name=Fulling> | + | 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#Vacuum interpretation|Unruh effect]].<ref name=Fulling>Fulling. 1989. page 259.</ref><ref name=Cao>Cao. 1999. page 179.</ref> Speculation abounds on the role of quantum vacuum in the expanding universe. See [[Cosmological constant#Cosmological constant problem|vacuum in cosmology]]. In addition, the quantum vacuum may exhibit spontaneous [[symmetry breaking]]. See Woit<ref name=Woit>Woit. 2006.</ref> and the articles: [[Higgs mechanism]] and [[QCD vacuum]]. |
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| − | </ref> and the articles: [[Higgs mechanism]] and [[QCD vacuum]]. | ||
| − | 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 [[Precision tests of QED|quantum electrodynamics]].<ref name=Genz2> | + | 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 [[Precision tests of QED|quantum electrodynamics]].<ref name=Genz2>Genz. 2002. page 247.</ref> |
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| − | 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.<ref name=Correa>[http://www.aetherometry.com/publications/direct/AS4-02.pdf | + | 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.<ref name=Correa>Correa, Paulo N., and Alexandra N. Correa. [http://www.aetherometry.com/publications/direct/AS4-02.pdf 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 … ". Retrieved January 10, 2009.</ref> |
==Realization of free space in a laboratory== | ==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:<ref name=CIPM>[http://physics.nist.gov/Pubs/SP330/sp330.pdf CIPM adopted Recommendation 1 (CI-1983)] Appendix 1, | + | 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:<ref name=CIPM>[http://physics.nist.gov/Pubs/SP330/sp330.pdf CIPM adopted Recommendation 1 (CI-1983)]. physics.nist.gov. Appendix 1, page 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; … ". Retrieved January 10, 2009.</ref> |
<blockquote>“in all cases any necessary corrections be applied to take account of actual conditions such as diffraction, gravitation or imperfection in the vacuum.”</blockquote> | <blockquote>“in all cases any necessary corrections be applied to take account of actual conditions such as diffraction, gravitation or imperfection in the vacuum.”</blockquote> | ||
| − | 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<sup>−11</sup> Pa.<ref name=Rozanov> | + | 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<sup>−11</sup> Pa.<ref name=Rozanov>Rozanov, and Hablanian. 2002. Figure 3.1, page 80.</ref> (The abbreviation Pa stands for the unit [[Pascal (unit)|pascal]], 1 pascal = 1 N/m<sup>2</sup>.) |
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==Realization of free space in outer space== | ==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 [[Pascal (unit)|pPa]] (1×10<sup>−11</sup> Pa)<ref> | + | While only a partial vacuum, [[outer space]] contains such sparse matter that the pressure of interstellar space is on the order of 10 [[Pascal (unit)|pPa]] (1×10<sup>−11</sup> Pa)<ref>Zheng, MiMi. 2002. [http://hypertextbook.com/facts/2002/MimiZheng.shtml Pressure in Outer Space.] The Physics Factbook. Retrieved January 10, 2009.</ref>. For comparison, the pressure at sea level (as defined in the unit of [[Atmosphere (unit)|atmospheric pressure]]) is about 101 kPa (1×10<sup>5</sup> 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/cm<sup>3</sup>.<ref name=Wynn-Williams>Wynn-Williams. 1992. page 38.</ref> |
| − | + | In the partial vacuum of [[outer space]], there are [[density|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 /cm<sup>3</sup>.<ref>Rees, Martin J. 1978. http://www.nature.com/nature/journal/v275/n5675/abs/275035a0.html Origin of pregalactic microwave background.] ''[[Nature]]''. 275:35–37.</ref><ref>This background temperature depends upon the gravitational state of the observer. See [[Unruh effect#Calculations|Unruh effect]].</ref> | |
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| − | In the partial vacuum of [[outer space]], there are [[density|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 /cm<sup>3</sup>.<ref> | ||
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." | 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 of 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).<ref> | + | 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).<ref>[http://www.uspto.gov/web/offices/ac/ido/oeip/taf/def/342.htm Classification Definitions.] U.S. Patent Classification System. - as of June 30, 2000. Retrieved January 10, 2009.</ref> This definition does not match the technical definitions of free space outlined above, which do not refer to a medium. |
| − | 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''".<ref>[http://www.uspto.gov/web/offices/ac/ido/oeip/taf/def/370.htm#310 Subclass 310: Communication over free space]</ref> This definition bears little if any relation to 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''".<ref>[http://www.uspto.gov/web/offices/ac/ido/oeip/taf/def/370.htm#310 Subclass 310: Communication over free space.] uspto.gov. Retrieved January 10, 2009.</ref> This definition bears little if any relation to other technical definitions of free space outlined above. |
==See also== | ==See also== | ||
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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. The definitions of the ampere and meter SI units are based upon measurements corrected to refer to free space.[1]
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 magnetic constant, and the defined value of the parameter ε0 called the permittivity of free space or the electric constant. [2] 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.[3]
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.[4] An approximate meaning is as follows:[5]
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,"[6] and again: "it is a mistake to think of any physical vacuum as some absolutely empty void."[7] 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.[8] One measurable result of these ephemeral occurrences is the Casimir effect.[9][10] Other examples are spontaneous emission[11][12][13] and the Lamb shift.[14] 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 [15][16] 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.[17] The determined reader can explore various nuances of the quantum vacuum in Saunders.[18] A more recent treatment is Genz. [19]
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.[20][21] 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[22] and the articles: Higgs mechanism and QCD vacuum.
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.[23]
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.[24]
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:[1]
“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.[25] (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)[26]. 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.[27] 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.[28][29]
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 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).[30] This definition does not match the technical definitions of free space outlined above, which do not refer to a medium.
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".[31] This definition bears little if any relation to other technical definitions of free space outlined above.
See also
- Permittivity
- Permeability (electromagnetism)
- Vacuum
- Virtual particle
- Goldstone boson
- Intergalactic space
- Interplanetary space
- Interstellar medium
- Outer space
- Medium (optics)
- Electric constant
- Magnetic constant
- Speed of light
- SI units
- Maxwell's equations
- Electromagnetic wave equation
Notes
- ↑ 1.0 1.1 CIPM adopted Recommendation 1 (CI-1983). physics.nist.gov. Appendix 1, page 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; … ". Retrieved January 10, 2009.
- ↑ Maxwell viewed permeability as being a quantity related to density, and he viewed dielectric constant, the reciprocal of permittivity, as being a quantity related to transverse elasticity. He used these quantities in Newton's equation for the speed of sound to obtain a wave speed equal to the speed of light c0. This famous calculation concludes around equation (136) in Part III of his 1861 paper "On Physical Lines of Force" with the estimate that c0=195,647 miles per second. The logical status of the electric and magnetic constant in SI units has shifted, however, and the velocity of light is now a defined value, not a measured or observed value. See the related articles on metre, ampere (unit) and speed of light. Maxwell, J.C. 1861. On Physical Lines of Force. vacuum-physics.com. Retrieved January 10, 2009.; Gillespie. 2008. page 14.
- ↑ Jackson. 1999. pages 10, 13.
- ↑ Dittrich, and Gies. 2000.
- ↑ Kane. 2000. Appendix A; pp. 149 ff.
- ↑ Lambrecht. 2002. page 197.
- ↑ Ray. 1991. page 205.
- ↑ AIP Physics News Update. aip.org. Retrieved January 10, 2009.
- ↑ Physical Review Focus Dec. focus.aps.org. Retrieved January 10, 2009.
- ↑ Capasso, F., J.N. Munday, D. Iannuzzi, and H.B. Chen. 2007. Casimir forces and quantum electrodynamical torques: physics and nanomechanics. Harvard University. Retrieved January 10, 2009.
- ↑ Yokoyama, and Ujihara. 1995. page 6.
- ↑ Fain. 2000. pages §4.4; 113ff.
- ↑ Scully, and Zubairy. 1997. pages §1.5.2; 22–23
- ↑ Scully, and Zubairy. 1997. pages 13-16.
- ↑ Born, M. and L. Infeld. 1934. Proc. Royal Soc. London. A144:425.
- ↑ Jackson. 1999. pages 10–12.
- ↑ Di Piazza, A., K. Z. Hatsagortsyan, and C. H. Keitel. 2006. Light diffraction by a strong standing electromagnetic wave. Phys. Rev. Lett.; Gies, Holger, Joerg Jaeckel, and Andreas Ringwald. 2006. Polarized light propagating in a magnetic field as a probe for millicharged fermions. Phys. Rev. Letts. 97. Retrieved January 10, 2009.
- ↑ Saunders, and Brown. 1991.
- ↑ Genz. 2002.
- ↑ Fulling. 1989. page 259.
- ↑ Cao. 1999. page 179.
- ↑ Woit. 2006.
- ↑ Genz. 2002. page 247.
- ↑ Correa, Paulo N., and 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 … ". Retrieved January 10, 2009.
- ↑ Rozanov, and Hablanian. 2002. Figure 3.1, page 80.
- ↑ Zheng, MiMi. 2002. Pressure in Outer Space. The Physics Factbook. Retrieved January 10, 2009.
- ↑ Wynn-Williams. 1992. page 38.
- ↑ Rees, Martin J. 1978. http://www.nature.com/nature/journal/v275/n5675/abs/275035a0.html Origin of pregalactic microwave background.] Nature. 275:35–37.
- ↑ This background temperature depends upon the gravitational state of the observer. See Unruh effect.
- ↑ Classification Definitions. U.S. Patent Classification System. - as of June 30, 2000. Retrieved January 10, 2009.
- ↑ Subclass 310: Communication over free space. uspto.gov. Retrieved January 10, 2009.
ReferencesISBN links support NWE through referral fees
- Charles Coulston Gillespie (editor) (2008). Dictionary of Scientific Biography, eBook, Charles Scribner's Sons. ISBN 0684315599.
- John David Jackson (1999). Classical electrodynamics, Third Edition, NY: Wiley, 10, 13. ISBN 0-471-30932-X.
- Walter Dittrich & Gies H (2000). Probing the quantum vacuum: perturbative effective action approach. Berlin: Springer. ISBN 3540674284.
- Gordon Kane (2000). Supersymmetry: squarks, photinos, and the unveiling of the ultimate laws. Cambridge, MA: Perseus Publishers. ISBN 0738204897.
- 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. ISBN 3540424180.
- Christopher Ray (1991). Time, space and philosophy. London/New York: Routledge, Chapter 10, p. 205. ISBN 0415032210.
- Hiroyuki Yokoyama & Ujihara K (1995). Spontaneous emission and laser oscillation in microcavities. Boca Raton: CRC Press. ISBN 0849337860.
- Benjamin Fain (2000). Irreversibilities in quantum mechanics: Fundamental theories of physics v. 113. New York:London: Springer/Kluwer Academic, §4.4 pp. 113ff. ISBN 079236581X.
- Marian O Scully & Zubairy MS (1997). Quantum optics. Cambridge UK: Cambridge University Press, §1.5.2 pp. 22–23. ISBN 0521435951.
- John David Jackson (1999). Classical electrodynamics, Third Edtion, NY: Wiley, 10–12. ISBN 0-471-30932-X.
- S Saunders & HR Brown Eds.) (1991). The philosophy of vacuum. Oxford UK: Oxford University Press. ISBN 0198244495.
- Henning Genz (2002). Nothingness: the science of empty space. Reading MA: Oxford: Perseus. ISBN 0738206105.
- Stephen A. Fulling (1989). Aspects of Quantum Field Theory in Curved Spacetime. Cambridge UK: Cambridge University Press.
- Tian Yu Cao (1999). Conceptual foundations of quantum field theory. Cambridge UK: Cambridge University Press. ISBN 0521602726.
- 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.
- LM Rozanov & Hablanian, MH (2002). Vacuum technique. London; New York: Taylor & Francis, Figure 3.1, p. 80. ISBN 041527351X.
- Gareth Wynn-Williams (1992). The fullness of space. Cambridge UK: Cambridge University Press. ISBN 0521426383.
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