Understanding Vacuums: From Ideal Conditions to Real-World Applications, Apuntes de Historia

¡Descarga Understanding Vacuums: From Ideal Conditions to Real-World Applications y más Apuntes en PDF de Historia solo en Docsity! Vacuum From Wikipedia, the free encyclopedia Jump to navigationJump to search This article is about empty physical space or the absence of matter. For the appliance, see vacuum cleaner. For other uses, see Vacuum (disambiguation). "Free space" redirects here. For other uses, see Free space (disambiguation). Pump to demonstrate vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective vacuus for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. [1] Physicists often discuss ideal test results that would occur in a perfect vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is considerably lower than atmospheric pressure.[2] The Latin term in vacuo is used to describe an object that is surrounded by a Vacuum. The quality of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher- quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%.[3] But higher-quality vacuums are possible. Ultra-high vacuum chambers, common in chemistry, physics, and engineering, operate below one trillionth (10-12) of atmospheric pressure (100 nPa), and can reach around 100 particles/cm3.[4] Outer space is an even higher-quality vacuum, with the equivalent of just a few hydrogen atoms per cubic meter on average in intergalactic space.[5] Vacuum has been a frequent topic of philosophical debate since ancient Greek times, but was not studied empirically until the 17th century. Evangelista Torricelli produced the first laboratory vacuum in 1643, and other experimental techniques were developed as a result of his theories of atmospheric pressure. A Torricellian vacuum is created by filling a tall glass container closed at one end with mercury, and then inverting it ina bowl to contain the mercury (see below). [6] Vacuum became a valuable industrial tool in the 20th century with the introduction of incandescent light bulbs and vacuum tubes, and a wide array of vacuum technologies has since become available. The development of human spaceflight has raised interest in the impact of vacuum on human health, and on life forms in general. A large vacuum chamber Contents 1 Etymology 2 Historical interpretation 3 Classical field theories .1 Gravity .2 Electromagnetism Quantum mechanics Outer space Measurement Relative versus absolute measurement Measurements relative to 1 atm Measuring instruments Uses 1 Vacuum-driven machines 2 Outgassing 3 Pumping and ambient air pressure Effects on humans and animals DITA NY we Examples 10 See also 11 References 12 External links Etymology The word vacuum comes from Latin 'an empty space, void', noun use of neuter of vacuus, meaning "empty", related to vacare, meaning "to be empty". Vacuum is one of the few words in the English language that contains two consecutive letters u.[7] Historical interpretation Historically, there has been much dispute over whether such a thing as a vacuum can exist. Ancient Greek philosophers debated the existence of a vacuum, or void, in the context of atomism, which posited void and atom as the fundamental explanatory elements of physics. Following Plato, even the abstract concept of a featureless void faced considerable skepticism: it could not be apprehended by the senses, it could not, itself, provide additional explanatory power beyond the physical volume with which it was commensurate and, by definition, it was quite literally nothing at all, which cannot rightly be said to exist. Aristotle believed that no void could occur naturally, because the denser surrounding material continuum would immediately fill any incipient rarity that might give rise to a void. In his Physics, book IV, Aristotle offered numerous arguments against the void: for example, that motion through a medium which offered no impediment could continue ad infinitum, there being no reason that something would come to rest anywhere in particular. Although Lucretius argued for the existence of vacuum in the first century BC and Hero of Alexandria tried unsuccessfully to create an artificial vacuum in the first century AD. [8] In the medieval Muslim world, the physicist and Islamic scholar, Al- Farabi (Alpharabius, 872-950), conducted a small experiment concerning the existence of vacuum, in which he investigated handheld plungers in water. [9] [unreliable source?] He concluded that air's volume can expand to fill available space, and he suggested that the concept of perfect vacuum was incoherent.[10] According to Nader El-Bizri, the physicist Ibn al-Haytham (Alhazen, 965-1039) and the Mu'tazili theologians disagreed This subsection needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Vacuum" - news : newspapers :* books + scholar : JSTOR (April 2014) (Learn how and when to remove this template message In general relativity, a vanishing stress-energy tensor implies, through Einstein field equations, the vanishing of all the components of the Ricci tensor. Vacuum does not mean that the curvature of space-time is necessarily flat: the gravitational field can still produce curvature in a vacuum in the form of tidal forces and gravitational waves (technically, these phenomena are the components of the Weyl tensor). The black hole (with zero electric charge) is an elegant example of a region completely "filled" with vacuum, but still showing a strong curvature. Electromagnetism In classical electromagnetism, the vacuum of free space, or sometimes just free space or perfect vacuum, is a standard reference medium for electromagnetic effects.[23][24] Some authors refer to this reference medium as classical vacuum, [23] a terminology intended to separate this concept from QED vacuum or QCD vacuum, where vacuum fluctuations can produce transient virtual particle densities and a relative permittivity and relative permeability that are not identically unity.[25][26] [27] In the theory of classical electromagnetism, free space has the following properties: Electromagnetic radiation travels, when unobstructed, at the speed of light, the defined value 299,792,458 m/s in SI units.[28] The superposition principle is always exactly true.[29] For example, the electric potential generated by two charges is the simple addition of the potentials generated by each charge in isolation. The value of the electric field at any point around these two charges is found by calculating the vector sum of the two electric fields from each of the charges acting alone. The permittivity and permeability are exactly the electric constant z¿0[30] and magnetic constant y0, [31] respectively (in SI units), or exactly 1 (in Gaussian units). The characteristic impedance (n) equals the impedance of free space ZO = 376.73 Q. [32] The vacuum of classical electromagnetism can be viewed as an idealized electromagnetic medium with the constitutive relations in SI units:[33] (idisplaystyle ([1boldsymbol (DJ) ((1boldsymbol (r)),1 t)=1varepsilon _10)(1boldsymbol (E))([1boldsymbol (r)),1 t)1,)(1boldsymbol (DJ) ((Mboldsymbol (r1)),1 t)=1varepsilon _10)(f1boldsymbol (E)) ((boldsymbol (1)),1 t)A, (Adisplaystyle [1boldsymbol (H))((1boldsymbol (r)),4 t)=[(1frac (1)(imu (0)))f1boldsymbol (B))((1boldsymbol (r)),1 t)1,)(1bo1dsymbol TEO oldsymbol ([(r)),1 t)=(1frac (1)(1mu _(0)))(1bo1dsymbol 1B)) ((boldsymbol (r)),1 t)A, relating the electric displacement field D to the electric field E and the magnetic field or H-field H to the magnetic induction or B-field B. Here r is a spatial location and t is time. Quantum mechanics Further information: QED vacuum, QCD vacuum, and Vacuum state File:Vacuum fluctuations revealed through spontaneous parametric down- conversion.ogv A video of an experiment showing vacuum fluctuations (in the red ring) amplified by spontaneous parametric down-conversion. In quantum mechanics and quantum field theory, the vacuum is defined as the state (that is, the solution to the equations of the theory) with the lowest possible energy (the ground state of the Hilbert space). In quantum electrodynamics this vacuum is referred to as 'QED vacuum' to distinguish it from the vacuum of quantum chromodynamics, denoted as QCD vacuum. QED vacuum is a state with no matter particles (hence the name), and no photons. As described above, this state is impossible to achieve experimentally. (Even if every matter particle could somehow be removed from a volume, it would be impossible to eliminate all the blackbody photons.) Nonetheless, it provides a good model for realizable vacuum, and agrees with a number of experimental observations as described next. QED vacuum has interesting and complex properties. In QED vacuum, the electric and magnetic fields have zero average values, but their variances are not zero.[34] As a result, QED vacuum contains vacuum fluctuations (virtual particles that hop into and out of existence), and a finite energy called vacuum energy. Vacuum fluctuations are an essential and ubiquitous part of quantum field theory. Some experimentally verified effects of vacuum fluctuations include spontaneous emission and the Lamb shift.[18] Coulomb's law and the electric potential in vacuum near an electric charge are modified.[35] Theoretically, in 0CD multiple vacuum states can coexist.[36] The starting and ending of cosmological inflation is thought to have arisen from transitions between different vacuum states. For theories obtained by quantization of a classical theory, each stationary point of the energy in the configuration space gives rise to a single vacuum. String theory is believed to have a huge number of vacua - the so-called string theory landscape. Outer space Main article: Outer space Structure of the magnetosphere - is not a perfect vacuum, but a tenuous plasma awash with charged particles, free elements such as hydrogen, helium and oxygen, electromagnetic fields. Outer space has very low density and pressure, and is the closest physical approximation of a perfect vacuum. But no vacuum is truly perfect, not even in interstellar space, where there are still a few hydrogen atoms per cubic meter.[5] Stars, planets, and moons keep their atmospheres by gravitational attraction, and as such, atmospheres have no clearly delineated boundary: the density of atmospheric gas simply decreases with distance from the object. The Earth's atmospheric pressure drops to about 32 millipascals (4.6x10-6 psi) at 100 kilometres (62 mi) of altitude, [37] the Kármán line, which is a common definition of the boundary with outer space. Beyond this line, isotropic gas pressure rapidly becomes insignificant when compared to radiation pressure from the Sun and the dynamic pressure of the solar winds, so the definition of pressure becomes difficult to interpret. The thermosphere in this range has large gradients of pressure, temperature and composition, and varies greatly due to space weather. Astrophysicists prefer to use number density to describe these environments, in units of particles per cubic centimetre. But although it meets the definition of outer space, the atmospheric density within the first few hundred kilometers above the Kármán line is still sufficient to produce significant drag on satellites. Most artificial satellites operate in this region called low Earth orbit and must fire their engines every couple of weeks or a few times a year (depending on solar activity) .[38] The drag here is low enough that it could theoretically be overcome by radiation pressure on solar sails, a proposed propulsion system for interplanetary travel.[39] Planets are too massive for their trajectories to be significantly affected by these forces, although their atmospheres are eroded by the solar winds.[citation needed] All of the observable universe is filled with large numbers of photons, the so-called cosmic background radiation, and quite likely a correspondingly large number of neutrinos. The current temperature of this radiation is about 3 K (-270.15 *C; -454.27 *FE). Measurement Main article: Pressure measurement The quality of a vacuum is indicated by the amount of matter remaining in the system, so that a high quality vacuum is one with very little matter left in it. Vacuum is primarily measured by its absolute pressure, but a complete characterization requires further parameters, such as temperature and chemical composition. One of the most important parameters is the mean free path (MFP) of residual gases, which indicates the average distance that molecules will travel between collisions with each other. As the gas density decreases, the MFP increases, and when the MFP is longer than the chamber, pump, spacecraft, or other objects present, the continuum assumptions of fluid mechanics do not apply. This vacuum state is called high vacuum, and the study of fluid flows in this regime is called particle gas dynamics. The MFP of air at atmospheric pressure is very short, 70 nm, but at 100 mPa (-1x10-3 Torr) the MFP of room temperature air is roughly 100 mm, which is on the order of everyday objects such as vacuum tubes. The Crookes radiometer turns when the MFP is larger than the size of the vanes. Vacuum quality is subdivided into ranges according to the technology required to achieve it or measure it. These ranges do not have universally agreed definitions, but a typical distribution is shown in the following table.[40][41] As we travel into orbit, outer space and ultimately intergalactic space, the pressure varies by several orders of magnitude . Pressure ranges of each quality of vacuum in different units Vacuum quality Torr Pa Atmosphere Atmospheric pressure 760 1.013x105 1 Low vacuum 760 to 25 1x105 to 3x103 9.87x10-1 to 3x10-2 in the steam space of the condenser, that is, the exhaust of the last stage of the turbine.[49] Mechanical or elastic gauges depend on a Bourdon tube, diaphragm, or capsule, usually made of metal, which will change shape in response to the pressure of the region in question. A variation on this idea is the capacitance manometer, in which the diaphragm makes up a part of a capacitor. A change in pressure leads to the flexure of the diaphragm, which results in a change in capacitance. These gauges are effective from 103 torr to 10-4 torr, and beyond. Thermal conductivity gauges rely on the fact that the ability of a gas to conduct heat decreases with pressure. In this type of gauge, a wire filament is heated by running current through it. A thermocouple or Resistance Temperature Detector (RTD) can then be used to measure the temperature of the filament. This temperature is dependent on the rate at which the filament loses heat to the surrounding gas, and therefore on the thermal conductivity. A common variant is the Pirani gauge which uses a single platinum filament as both the heated element and RTD. These gauges are accurate from 10 torr to 10-3 torr, but they are sensitive to the chemical composition of the gases being measured. Tonization gauges are used in ultrahigh vacuum. They come in two types: hot cathode and cold cathode. In the hot cathode version an electrically heated filament produces an electron beam. The electrons travel through the gauge and jonize gas molecules around them. The resulting jons are collected at a negative electrode. The current depends on the number of ions, which depends on the pressure in the gauge. Hot cathode gauges are accurate from 10-3 torr to 10-10 torr. The principle behind cold cathode version is the same, except that electrons are produced in a discharge created by a high voltage electrical discharge. Cold cathode gauges are accurate from 10-2 torr to 10-9 torr. lonization gauge calibration is very sensitive to construction geometry, chemical composition of gases being measured, corrosion and surface deposits. Their calibration can be invalidated by activation at atmospheric pressure or low vacuum. The composition of gases at high vacuums will usually be unpredictable, so a mass spectrometer must be used in conjunction with the ionization gauge for accurate measurement. [50] Uses Light bulbs contain a partial vacuum, usually backfilled with argon, which protects the tungsten filament Vacuum is useful in a variety of processes and devices. Its first widespread use was in the incandescent light bulb to protect the filament from chemical degradation. The chemical inertness produced by a vacuum is also useful for electron beam welding, cold welding, vacuum packing and vacuum frying. Ultra-high vacuum is used in the study of atomically clean substrates, as only a very good vacuum preserves atomic-scale clean surfaces for a reasonably long time (on the order of minutes to days). High to ultra-high vacuum removes the obstruction of air, allowing particle beams to deposit or remove materials without contamination. This is the principle behind chemical vapor deposition, physical vapor deposition, and dry etching which are essential to the fabrication of semiconductors and optical coatings, and to surface science. The reduction of convection provides the thermal insulation of thermos bottles. Deep vacuum lowers the boiling point of liquids and promotes low temperature outgassing which is used in freeze drying, adhesive preparation, distillation, metallurgy, and process purging. The electrical properties of vacuum make electron microscopes and vacuum tubes possible, including cathode ray tubes. Vacuum interrupters are used in electrical switchgear. Vacuum arc processes are industrially important for production of certain grades of steel or high purity materials. The elimination of air friction is useful for flywheel energy storage and ultracentrifuges. This shallow water well pump reduces atmospheric air pressure inside the pump chamber. Atmospheric pressure extends down into the well, and forces water up the pipe into the pump to balance the reduced pressure. Above- ground pump chambers are only effective to a depth of approximately 9 meters due to the water column weight balancing the atmospheric pressure. Vacuum-driven machines Vacuums are commonly used to produce suction, which has an even wider variety of applications. The Newcomen steam engine used vacuum instead of pressure to drive a piston. In the 19th century, vacuum was used for traction on Isambard Kingdom Brunel's experimental atmospheric railway. Vacuum brakes were once widely used on trains in the UK but, except on heritage railways, they have been replaced by air brakes. Manifold vacuum can be used to drive accessories on automobiles. The best known application is the vacuum servo, used to provide power assistance for the brakes. Obsolete applications include vacuum-driven windscreen wipers and Autovac fuel pumps. Some aircraft instruments (Attitude Indicator (Al) and the Heading Indicator (HI)) are typically vacuum- powered, as protection against loss of all (electrically powered) instruments, since early aircraft often did not have electrical systems, and since there are two readily available sources of vacuum on a moving aircraft, the engine and an external venturi. Vacuum induction melting uses electromagnetic induction within a vacuum. Maintaining a vacuum in the condenser is an important aspect of the efficient operation of steam turbines. A steam jet ejector or liquid ring vacuum pump is used for this purpose. The typical vacuum maintained in the condenser steam space at the exhaust of the turbine (also called condenser backpressure) is in the range 5 to 15 kPa (absolute), depending on the type of condenser and the ambient conditions. Outgassing Main article: Outgassing Evaporation and sublimation into a vacuum is called outgassing. All materials, solid or liquid, have a small vapour pressure, and their outgassing becomes important when the vacuum pressure falls below this vapour pressure. Outgassing has the same effect as a leak and will limit the achievable vacuum. Outgassing products may condense on nearby colder surfaces, which can be troublesome if they obscure optical instruments or react with other materials. This is of great concern to space missions, where an obscured telescope or solar cell can ruin an expensive mission. The most prevalent outgassing product in vacuum systems is water absorbed by chamber materials. It can be reduced by desiccating or baking the chamber, and removing absorbent materials. Outgassed water can condense in the oil of rotary vane pumps and reduce their net speed drastically if gas ballasting is not used. High vacuum systems must be clean and free of organic matter to minimize outgassing. Ultra-high vacuum systems are usually baked, preferably under vacuum, to temporarily raise the vapour pressure of all outgassing materials and boil them off. Once the bulk of the outgassing materials are boiled off and evacuated, the system may be cooled to lower vapour pressures and minimize residual outgassing during actual operation. Some systems are cooled well below room temperature by liquid nitrogen to shut down residual outgassing and simultaneously cryopump the system. Pumping and ambient air pressure Deep wells have the pump chamber down in the well close to the water surface, or in the water. A "sucker rod" extends from the handle down the center of the pipe deep into the well to operate the plunger. The pump handle acts as a heavy counterweight against both the sucker rod weight and the weight of the water column standing on the upper plunger up to ground level. Main article: Vacuum pump Fluids cannot generally be pulled, so a vacuum cannot be created by suction. Suction can spread and dilute a vacuum by letting a higher pressure push fluids into it, but the vacuum has to be created first before suction can occur. The easiest way to create an artificial vacuum is to expand the volume of a container. For example, the diaphragm muscle expands the chest cavity, which causes the volume of the lungs to increase. This expansion reduces the pressure and creates a partial vacuum, which is soon filled by air pushed in by atmospheric pressure. To continue evacuating a chamber indefinitely without requiring infinite growth, a compartment of the vacuum can be repeatedly closed off, exhausted, and expanded again. This is the principle behind positive displacement pumps, like the manual water pump for example. Inside the pump, a mechanism expands a small sealed cavity to create a vacuum. Because of the pressure differential, some fluid from the chamber (or the well, in our example) is pushed into the pump's small cavity. The pump's cavity is then sealed from the chamber, opened to the atmosphere, and squeezed back to a minute size. A cutaway view of a turbomolecular pump, a momentum transfer pump used to achieve high vacuum The above explanation is merely a simple introduction to vacuum pumping, and is not representative of the entire range of pumps in use. Many variations of the positive displacement pump have been developed, and many other pump designs rely on fundamentally different principles. Momentum transfer pumps, which bear some similarities to dynamic pumps used at higher pressures, can achieve much higher quality vacuums than positive displacement pumps. Entrapment pumps can capture gases in a Cryopumped MBE chamber 1x10-7 to 1x10-9 10-9 to 10-11 100 to 10,000 km 107 to 105 Pressure on the Moon approximately 1x10-9 10-11 10,000 km 4x105[63] Interplanetary space 11[1] Interstellar space 1[64] Intergalactic space 10-6[1] See also Decay of the vacuum (Pair production) Engine vacuum False vacuum Helium mass spectrometer - technical instrumentation to detect a vacuum leak Joining materials Pneumatic tube - transport system using vacuum or pressure to move containers in tubes Rarefaction - reduction of a medium's density Suction - creation of a partial vacuum Vacuum angle Vacuum cementing - natural process of solidifying homogeneous "dust" in vacuum Vacuum column - controlling loose magnetic tape in early computer data recording tape drives Vacuum deposition - process of depositing atoms and molecules in a sub- atmospheric pressure environment Vacuum engineering Vacuum flange - joining of vacuum systems References Chambers, Austin (2004). Modern Vacuum Physics. Boca Raton: CRC Press. ISBN 978-0-8493-2438-3. OCLC 55000526. [page needed] Harris, Nigel S. (1989). Modern Vacuum Practice. McGraw-Hill. p. 3. ISBN 978-0-07-707099-1. Campbell, Jeff (2005). Speed cleaning. p. 97. ISBN 978-1-59486-274-8. Note that 1 inch of water is *0.0025 atm. Gabrielse, G.; Fei, X.; Orozco, L.; Tjoelker, R.; Haas, J.; Kalinowsky, H.; Trainor, T.; Kells, W. (1990). "Thousandfold improvement in the measured antiproton mass" (PDF). Physical Review Letters. 65 (11): 1317- 1320. Bibcode:1990PhRvL..65.13176. doi:10.1103/PhysRevLett.65.1317. PMID 10042233. Tadokoro, M. (1968). "A Study of the Local Group by Use of the Virial Theorem". Publications of the Astronomical Society of Japan. 20: 230. Bibcode:19%68PASJ...20..230T. This source estimates a density of 7x10-29 g/cm3 for the Local Group. An atomic mass unit is 1.66x10-24 g, for roughly 40 atoms per cubic meter. 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Barrow, John D. (2000). The book of nothing : vacuums, voids, and the latest ideas about the origins of the universe (l1st American ed.). New York: Pantheon Books. ISBN 978-0-09-928845-9. OCLC 46600561. "The World's Largest Barometer". Archived from the original on 2008-04- 17. Retrieved 2008-04-30. Encyclopedia Britannica: Otto von Guericke Robert Hogarth Patterson, Essays in History and Art 10, 1862 Pickering, W.H. (1912). "Solar system, the motion of the, relatively to the interstellar absorbing medium". Monthly Notices of the Royal Astronomical Society. 72 (9): 740. Bibcode:1912MNRAS..72..740P. doi:10.1093/mnras/72.9.740. Werner S. Weiglhofer (2003). "S 4.1 The classical vacuum as reference medium". In Werner S. Weiglhofer; Akhlesh Lakhtakia (eds.). Introduction to complex mediums for optics and electromagnetics. SPIE Press. pp. 28, 34. ISBN 978-0-8194-4947-4. Tom G. MacKay (2008). "Electromagnetic Fields in Linear Bianisotropic Mediums". In Emil Wolf (ed.). Progress in Optics. 51. Elsevier. p. 143. ISBN 978-0-444-52038-8. Gilbert Grynberg; Alain Aspect; Claude Fabre (2010). Introduction to Quantum Optics: From the Semi-Classical Approach to Quantized Light. Cambridge University Press. p. 341. ISBN 978-0-521-55112-0. ...deals with the quantum vacuum where, in contrast to the classical vacuum, radiation has properties, in particular, fluctuations, with which one can associate physical effects. For a qualitative description of vacuum fluctuations and virtual particles, see Leonard Susskind (2006). The cosmic landscape: string theory and the illusion of intelligent design. Little, Brown and Co. pp. 60 ff. ISBN 978-0-316-01333-8. The relative permeability and permittivity of field-theoretic vacuums is described in Kurt Gottfried; Victor Frederick Weisskopf (1986). Concepts of particle physics. 2. Oxford University Press. p. 389. ISBN 978-0-19- 503393-9. and more recently in John F. Donoghue; Eugene Golowich; Barry R. Holstein (1994). Dynamics of the standard model. Cambridge University Press. p. 47. ISBN 978-0-521-47652-2. and also R. Keith Ellis; W.J. Stirling; B.R. Webber (2003). QCD and collider physics. Cambridge University Press. pp. 27-29. ISBN 978-0-521-5458%-1. Returning to the vacuum of a relativistic field theory, we find that both paramagnetic and diamagnetic contributions are present. OCD vacuum is paramagnetic, while QED vacuum is diamagnetic. See Carlos A. Bertulani (2007). Nuclear physics in a nutshell. Princeton University Press. p. 26. Bibcode:2007npn..book..... B. ISBN 978-0-691-12505-3. "Speed of light in vacuum, Cc, c0". The NIST reference on constants, units, and uncertainty: Fundamental physical constants. NIST. Retrieved 2011-11-28. Chattopadhyay, D. 8 Rakshit, P.C. (2004). Elements of Physics. 1. New Age International. p. 577. ISBN 978-81-224-1538-4. "Electric constant, 20". The NIST reference on constants, units, and uncertainty: Fundamental physical constants. NIST. Retrieved 2011-11-28. "Magnetic constant, p0". The NIST reference on constants, units, and uncertainty: Fundamental physical constants. NIST. Retrieved 2011-11-28. "Characteristic impedance of vacuum, Z0". The NIST reference on constants, units, and uncertainty: Fundamental physical constants. Retrieved 2011-11-28. Mackay, Tom G £ Lakhtakia, Akhlesh (2008). "S 3.1.1 Free space". In Emil Wolf (ed.). Progress in Optics. 51. Elsevier. p. 143. ISBN 978-0-444- 53211-4. For example, see Craig, D.P. £ Thirunamachandran, T. (1998). Molecular Quantum Electrodynamics (Reprint of Academic Press 1984 ed.). Courier Dover Publications. p. 40. ISBN 978-0-486-40214-7. In effect, the dielectric permittivity of the vacuum of classical electromagnetism is changed. For example, see Zeidler, Eberhard (2011). "S 19.1.9 Vacuum polarization in quantum electrodynamics". Quantum Field Theory 111: Gauge Theory: A Bridge Between Mathematicians and Physicists. Springer. p. 952. ISBN 978-3-642-22420-1. Altarelli, Guido (2008). "Chapter 2: Gauge theories and the Standard Model". Elementary Particles: Volume 21/A of Landolt-Bórnstein series. Springer. pp. 2-3. ISBN 978-3-540-74202-9. The fundamental state of minimum energy, the vacuum, is not unique and there are a continuum of degenerate states that altogether respect the symmetry... Squire, Tom (September 27, 2000). "U.S. Standard Atmosphere, 1976". Thermal Protection Systems Expert and Material Properties Database. Archived from the original on October 15, 2011. Retrieved 2011-10-23. "Catalog of Earth Satellite Orbits". earthobservatory.nasa.gov. 2009-09- 04. Retrieved 2019-01-28. Andrews, Dana G.; Zubrin, Robert M. (1990). "Magnetic Sails £ Interstellar Travel" (PDF). Journal of the British Interplanetary Society. 43: 265-272. doi:10.2514/3.26230. S2CID 55324095. Archived from the original (PDF) on 2019-03-02. Retrieved 2019-07-21. American Vacuum Society. "Glossary". AVS Reference Guide. Archived from the original on 2006-03-04. Retrieved 2006-03-15. 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