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The Latin term in vacuo is used to describe an object as being in what would otherwise be a vacuum. The root of the word vacuum is the Latin adjective vacuus which means "empty," but space can never be perfectly empty. A perfect vacuum with a gaseous pressure of absolute zero is a philosophical concept that is never observed in practice, not least because quantum theory predicts that no volume of space can be perfectly empty in this way. Physicists often use the term "vacuum" slightly differently. They discuss ideal test results that would occur in a perfect vacuum, which they simply call "vacuum" or "free space" in this context, and use the term partial vacuum to refer to the imperfect vacua realized in practice.
The quality of a vacuum is measured in relation to how closely it approaches a perfect vacuum. The residual gas pressure is the primary indicator of quality, and is most commonly measured in units called torr, even in metric contexts. Lower pressures indicate higher quality, although other variables must also be taken into account. Quantum mechanics sets limits on the best possible quality of vacuum. Outer space is a natural high quality vacuum, mostly of much higher quality than what can be created artificially with current technology. Low quality artificial vacuums have been used for suction for millennia.
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 artifical vacuum in 1643, and other experimental techniques were developed as a result of his theories of atmospheric pressure. 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 technology has since become available. The recent development of human spaceflight has raised interest in the impact of vacuum on human health, and on life forms in general.
Vacuum is useful in a variety of processes and devices. Its first common use was in incandescent light bulbs to protect the tungsten filament from chemical degradation. Its chemical inertness is also useful for electron beam welding, chemical vapor deposition and dry etching in the fabrication of semiconductors and optical coatings, cold welding, vacuum packing and vacuum frying. The reduction of convection improves the thermal insulation of thermos bottles and double-paned windows. Deep vacuum promotes 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. The elimination of air friction is useful for flywheel energy storage and ultracentrifuges.
High to ultra-high vacuum is used in thin film deposition and surface science. High vacuum allows for contamination-free material deposition. 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).
Suction is used in a wide 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.
[édit] Outer space
- Artikel utama: Outer space
Much of outer space has the density and pressure of an almost perfect vacuum. It has effectively no friction, which allows stars, planets and moons to move freely along ideal gravitational trajectories. But no vacuum is perfect, not even in interstellar space, where there are only a few hydrogen atoms per cubic centimeter at 10 fPa (10−16 Torr). The deep vacuum of space could make it an attractive environment for certain processes, for instance those that require ultraclean surfaces; for small-scale applications, however, it is much more cost-effective to create an equivalent vacuum on Earth than to leave the Earth's gravity well.
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. In low earth orbit (about 300 km or 185 miles altitude) the atmospheric density is about 100 nPa (10-9 Torr), still sufficient to produce significant drag on satellites. Most artificial satellites operate in this region, and must fire their engines every few days to maintain orbit.
Beyond planetary atmospheres, the pressure of photons and other particles from the sun becomes significant. Spacecraft can be buffeted by solar winds, but planets are too massive to be affected. The idea of using this wind with a solar sail has been proposed for interplanetary travel.
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, or -270 degrees Celsius or -454 degrees Fahrenheit.
[édit] Effects on humans and animals
- Tempo Ogé: Human adaptation to space
Vacuum is primarily an asphyxiant. Humans exposed to vacuum will lose consciousness after a few seconds and die within minutes, but the symptoms are not nearly as graphic as commonly shown in pop culture. Robert Boyle was the first to show that vacuum is lethal to small animals. Blood and other body fluids do boil (the medical term for this condition is ebullism), and the vapour pressure may bloat the body to twice its normal size and slow circulation, but tissues are elastic and porous enough to prevent rupture. Ebullism is slowed by the pressure containment of blood vessels, so some blood remains liquid.[1][2] Swelling and ebullism can be reduced by containment in a flight suit. Shuttle astronauts wear a fitted elastic garment called the Crew Altitude Protection Suit (CAPS) which prevents ebullism at pressures as low as 15 Torr (2 kPa).[3] However, even if ebullism is prevented, simple evaporation of blood can cause decompression sickness and gas embolisms. Rapid evaporative cooling of the skin will create frost, particularly in the mouth, but this is not a significant hazard.
Animal experiments show that rapid and complete recovery is the norm for exposures of fewer than 90 seconds, while longer full-body exposures are fatal and resuscitation has never been successful.[4] There is only a limited amount of data available from human accidents, but it is consistent with animal data. Limbs may be exposed for much longer if breathing is not impaired. Rapid decompression can be much more dangerous than vacuum exposure itself. If the victim holds his breath during decompression, the delicate internal structures of the lungs can be ruptured, causing death. Eardrums may be ruptured by rapid decompression, soft tissues may bruise and seep blood, and the stress of shock will accelerate oxygen consumption leading to asphyxiation.[5]
In 1942, in one of a series of experiments on human subjects for the Luftwaffe, the Nazi regime tortured Dachau concentration camp prisoners by exposing them to vacuum in order to determine the human body's capacity to survive high-altitude conditions.
Some extremophile microrganisms, such as Tardigrades, can survive vacuum for a period of years.
[édit] Historical interpretation
Historically, there has been much dispute over whether such a thing as a vacuum can exist. Ancient Greek philosophers did not like to admit the existence of a vacuum, asking themselves "how can 'nothing' be something?". Plato found the idea of a vacuum inconceivable. He believed that all physical things were instantiations of an abstract Platonic ideal, and he could not conceive of an "ideal" form of a vacuum. Similarly, Aristotle considered the creation of a vacuum impossible — nothing could not be something. Later Greek philosophers thought that a vacuum could exist outside the cosmos, but not within it.
The philosopher Al-Farabi (850 - 970 CE) appears to have carried out the first recorded experiments concerning the existence of vacuum, in which he investigated handheld plungers in water.[6] He concluded that air's volume can expand to fill available space, and he suggested that the concept of perfect vacuum was incoherent.[7]
In the Middle Ages, the catholic church held the idea of a vacuum to be immoral or even heretical. The absence of anything implied the absence of God, and harkened back to the void prior to the creation story in the book of Genesis. Medieval thought experiments into the idea of a vacuum considered whether a vacuum was present, if only for an instant, between two flat plates when they were rapidly separated. There was much discussion of whether the air moved in quickly enough as the plates were separated, or, as Walter Burley postulated, whether a 'celestial agent' prevented the vacuum arising — that is, whether nature abhorred a vacuum. This speculation was shut down by the 1277 Paris condemnations of Bishop Etienne Tempier, which required there to be no restrictions on the powers of God, which led to the conclusion that God could create a vacuum if he so wished.[8]
Opposition to the idea of a vacuum existing in nature continued into the Scientific Revolution, with scholars such as Paolo Casati taking an anti-vacuist position. Building upon work by Galileo, Evangelista Torricelli argued in 1643 that there was a vacuum at the top of a mercury barometer. Some people believe that, although Torricelli produced the first sustained vacuum in a laboratory, it was Blaise Pascal who recognized it for what it was. In 1654, Otto von Guericke invented the first vacuum pump and conducted his famous Magdeburg hemispheres experiment, showing that teams of horses could not separate two hemispheres from which the air had been evacuated. Robert Boyle improved Guericke's design and conducted experiments on the properties of vacuum. Robert Hooke also helped Boyle produce an air pump which helped to produce the vacuum. The study of vacuum then lapsed until 1855, when Heinrich Geissler invented the mercury displacement pump and achieved a record vacuum of about 10 Pa (0.1 Torr). A number of electrical properties become observable at this vacuum level, and this renewed interest in vacuum. This, in turn, led to the development of the vacuum tube.
In the 17th century, theories of the nature of light relied upon the existence of an aethereal medium which would be the medium to convey waves of light (Newton relied on this idea to explain refraction and radiated heat). This evolved into the luminiferous aether of the 19th century, but the idea was known to have significant shortcomings - specifically that if the Earth were moving through a material medium, the medium would have to be both extremely tenuous (because the Earth is not detectably slowed in its orbit), and extremely rigid (because vibrations propagate so rapidly).
While outer space has been likened to a vacuum, early physicists postulated that an invisible luminiferous aether existed as a medium to carry light waves, or an "ether which fills the interstellar space".[9] An 1891 article by William Crookes noted: "the [freeing of] occluded gases into the vacuum of space".[10] Even up until 1912, astronomer Henry Pickering commented: "While the interstellar absorbing medium may be simply the ether, [it] is characteristic of a gas, and free gaseous molecules are certainly there".[11]
In 1887, the Michelson-Morley experiment, using an interferometer to attempt to detect the change in the speed of light caused by the Earth moving with respect to the aether, was a famous null result, showing that there really was no static, pervasive medium throughout space and through which the Earth moved as though through a wind. While there is therefore no aether, and no such entity is required for the propagation of light, space between the stars is not completely empty. Besides the various particles which comprise cosmic radiation, there is a cosmic background of photonic radiation (light), including the thermal background at about 2.7 K, seen as a relic of the Big Bang. None of these findings affect the outcome of the Michelson-Morley experiment to any significant degree.
Einstein argued that physical objects are not located in space, but rather have a spatial extent. Seen this way, the concept of empty space loses its meaning.[12] Rather, space is an abstraction, based on the relationships between local objects. Nevertheless, the general theory of relativity admits a pervasive gravitational field, which, in Einstein's words[13], may be regarded as an "aether", with properties varying from one location to another. One must take care, though, to not ascribe to it material properties such as velocity and so on.
In 1930, Paul Dirac proposed a model of vacuum as an infinite sea of particles possessing negative energy, called the Dirac sea. This theory helped refine the predictions of his earlier formulated Dirac equation, and successfully predicted the existence of the positron, discovered two years later in 1932. Despite this early success, the idea was soon abandoned in favour of the more elegant quantum field theory.
The development of quantum mechanics has complicated the modern interpretation of vacuum by requiring indeterminacy. Niels Bohr and Werner Heisenberg's uncertainty principle and Copenhagen interpretation, formulated in 1927, predict a fundamental uncertainty in the instantaneous measurability of the position and momentum of any particle, and which, not unlike the gravitational field, questions the emptiness of space between particles. In the late 20th century, this principle was understood to also predict a fundamental uncertainty in the number of particles in a region of space, leading to predictions of virtual particles arising spontaneously out of the void. In other words, there is a lower bound on the vacuum, dictated by the lowest possible energy state of the quantized fields in any region of space. Ironically, Plato was right, if only by chance.
[édit] Quantum-mechanical definition
Citakan:Detail In quantum mechanics, the vacuum is defined as the state (i.e. solution to the equations of the theory) with the lowest energy. To first approximation, this is simply a state with no particles, hence the name.
Even an ideal vacuum, thought of as the complete absence of anything, will not in practice remain empty. Consider a vacuum chamber that has been completely evacuated, so that the (classical) particle concentration is zero. The walls of the chamber will emit light in the form of black body radiation. This light carries momentum, so the vacuum does have a radiation pressure. This limitation applies even to the vacuum of interstellar space. Even if a region of space contains no particles, the Cosmic Microwave Background fills the entire universe with black body radiation.
An ideal vacuum cannot exist even inside of a molecule. Each atom in the molecule exists as a probability function of space, which has a certain non-zero value everywhere in a given volume. Thus, even "between" the atoms there is a certain probability of finding a particle, so the space cannot be said to be a vacuum.
More fundamentally, quantum mechanics predicts that vacuum energy will be different from its naive, classical value. The quantum correction to the energy is called the zero-point energy and consists of energies of virtual particles that have a brief existence. This is called vacuum fluctuation. Vacuum fluctuations may also be related to the so-called cosmological constant in cosmology. The best evidence for vacuum fluctuations is the Casimir effect and the Lamb shift.[8]
In quantum field theory and string theory, the term "vacuum" is used to represent the ground state in the Hilbert space, that is, the state with the lowest possible energy. In free (non-interacting) quantum field theories, this state is analogous to the ground state of a quantum harmonic oscillator. If the theory is 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.
[édit] Pumping
- Artikel utama: Vacuum pump
Fluids cannot be pulled, so it is technically impossible to create a vacuum by suction. Suction is the movement of fluids into a vacuum under the effect of a higher external pressure, but the vacuum has to be created first. 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 deep 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.
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 solid or absorbed state, often with no moving parts, no seals and no vibration. None of these pumps are universal; each type has important performance limitations. They all share a difficulty in pumping low molecular weight gases, especially hydrogen, helium, and neon.
The lowest pressure that can be attained in a system is also dependent on many things other than the nature of the pumps. Multiple pumps may be connected in series, called stages, to achieve higher vacuums. The choice of seals, chamber geometry, materials, and pump-down procedures will all have an impact. Collectively, these are called vacuum technique. And sometimes, the final pressure is not the only relevant characteristic. Pumping systems differ in oil contamination, vibration, preferential pumping of certain gases, pump-down speeds, intermittent duty cycle, reliability, or tolerance to high leakage rates.
In ultra high vacuum systems, some very odd leakage paths and outgassing sources must be considered. The water absorption of aluminium and palladium becomes an unacceptable source of outgassing, and even the adsorptivity of hard metals such as stainless steel or titanium must be considered. Some oils and greases will boil off in extreme vacuums. The porosity of the metallic chamber walls may have to be considered, and the grain direction of the metallic flanges should be parallel to the flange face.
The lowest pressures currently achievable in laboratory are about 10-13 Torr.[14]
[édit] Outgassing
- Artikel utama: 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. In man-made systems, outgassing has the same effect as a leak and can 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 man-made 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.
[édit] Quality
The quality of a vacuum is indicated by the amount of matter remaining in the system. 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 (~1×10-3 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.
Deep space is generally much more empty than any artificial vacuum that we can create, although many laboratories can reach lower vacuum than that of low earth orbit. In interplanetary and interstellar space, isotropic gas pressure is insignificant when compared to solar pressure, solar wind, and dynamic pressure, so the definition of pressure becomes difficult to interpret. Astrophysicists prefer to use number density to describe these environments, in units of particles per cubic centimetre. The average density of interstellar gas is about 1 atom per cubic centimeter.[15]
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 (hence the gaps below), but a typical distribution is as follows:[16][17]
| Atmospheric pressure | 760 Torr | 101 kPa |
| Low vacuum | 760 to 25 Torr | 100 to 3 kPa |
| Medium vacuum | 25 to 1×10-3 Torr | 3 kPa to 100 mPa |
| High vacuum | 1×10-3 to 1×10-9 Torr | 100 mPa to 100 nPa |
| Ultra high vacuum | 1×10-9 to 1×10-12 Torr | 100 nPa to 100 pPa |
| Extremely high vacuum | <1×10-12 Torr | <100> |
| Outer Space | 1×10-6 to <3×10-17 Torr | 100 µPa to <3fpa |
| Perfect vacuum | 0 Torr | 0 Pa |
- Atmospheric pressure is variable but standardized at 101.325 kPa (760 Torr)
- Low vacuum, also called rough vacuum or coarse vacuum, is vacuum that can be achieved or measured with rudimentary equipment such as a vacuum cleaner and a liquid column manometer.
- Medium vacuum is vacuum that can be achieved with a single pump, but is too low to measure with a liquid or mechanical manometer. It can be measured with a McLeod gauge, thermal gauge or a capacitive gauge.
- High vacuum is vacuum where the MFP of residual gases is longer than the size of the chamber or of the object under test. High vacuum usually requires multi-stage pumping and ion gauge measurement. Some texts differentiate between high vacuum and very high vacuum.
- Ultra high vacuum requires baking the chamber to remove trace gases, and other special procedures.
- Deep space is generally much more empty than any artificial vacuum that we can create. However, it is not High Vacuum with respect to the above definition, since the MFP of the molecules is smaller than the (infinite) size of the chamber.
- Perfect vacuum is an ideal state that cannot be obtained in a laboratory, nor can it be found in outer space.
[édit] Examples
| pressure in Pa | pressure in Torr | mean free path | molecules per cm2 | |
|---|---|---|---|---|
| Vacuum cleaner | approximately 80 kPa | 600 Torr | 70 nm | 1019 |
| liquid ring vacuum pump | approximately 3.2 kPa | 24 Torr | ||
| freeze drying | 100 to 10 Pa | 1 to 0.1 Torr | ||
| rotary vane pump | 100 Pa to 100 mPa | 1 Torr to 10−3 Torr | ||
| Incandescent light bulb | 10 to 1 Pa | 0.1 to 0.01 Torr | ||
| Thermos bottle | 1 to 0.1 Pa | 10−2 to 10−3 Torr | ||
| Near earth outer space | approximately 100 µPa | 10−6 Torr | ||
| Vacuum tube | 10 µPa to 10 nPa | 10−7 to 10−10 Torr | ||
| Cryopumped MBE chamber | 100 nPa to 1 nPa | 10−9 to 10−11 Torr | 1..105 km | 109..104 |
| Pressure on the Moon | approximately 1 nPa | 10−11 Torr | ||
| Interstellar space | approximately 1 fPa | 10−17 Torr | 1 |
[édit] Measurement
- Artikel utama: Pressure measurement
Vacuum is measured in units of pressure. The SI unit of pressure is the pascal (symbol Pa), but vacuum is usually measured in torrs (symbol Torr), named for Torricelli, an early Italian physicist (1608 - 1647). A torr is equal to the displacement of a millimeter of mercury (mmHg) in a manometer with 1 torr equaling 133.3223684 pascals above absolute zero pressure. Vacuum is often also measured using inches of mercury on the barometric scale or as a percentage of atmospheric pressure in bars or atmospheres. Low vacuum is often measured in inches of mercury (inHg), millimeters of mercury (mmHg) or kilopascals (kPa) below atmospheric pressure. "Below atmospheric" means that the absolute pressure is equal to the current atmospheric pressure (e.g. 29.92 inHg) minus the vacuum pressure in the same units. Thus a vacuum of 26 inHg is equivalent to an absolute pressure of 4 inHg (29.92 inHg - 26 inHg).
Many devices are used to measure the pressure in a vacuum, depending on what range of vacuum is needed.[18]
Hydrostatic gauges (such as the mercury column manometer) consist of a vertical column of liquid in a tube whose ends are exposed to different pressures. The column will rise or fall until its weight is in equilibrium with the pressure differential between the two ends of the tube. The simplest design is a closed-end U-shaped tube, one side of which is connected to the region of interest. Any fluid can be used, but mercury is preferred for its high density and low vapour pressure. Simple hydrostatic gauges can measure pressures ranging from 1 Torr (100 Pa) to above atmospheric. An important variation is the McLeod gauge which isolates a known volume of vacuum and compresses it to multiply the height variation of the liquid column. The McLeod gauge can measure vacuums as high as 10−6 Torr (0.1 mPa), which is the lowest direct measurement of pressure that is possible with current technology. Other vacuum gauges can measure lower pressures, but only indirectly by measurement of other pressure-controlled properties. These indirect measurements must be calibrated via a direct measurement, most commonly a McLeod gauge.[19]
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 10−3 Torr to 10−4 Torr.
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 platimum 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.
Ion gauges are used in ultrahigh vacua. 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 ionize gas molecules around them. The resulting ions 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. Ionization 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.[20]
[édit] Properties
Many properties of space approach non-zero values in a vacuum that approaches perfection. These ideal physical constants are often called free space constants. Some of the common ones are as follows:
- The speed of light approaches 299,792,458 m/s, but is always slower
- Index of refraction approaches 1.0, but is always higher
- Electric permittivity (
) approaches 8.8541878176x10-12 farads per meter (F/m). - Magnetic permeability (μ0) approaches 4π×10−7 N/A2.
- Characteristic impedance (Z0) approaches 376.73 Ω.
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