Vacuum

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https://en.wikipedia.org/wiki/Vacuum 

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. 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. 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%. 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. 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.

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 in a bowl to contain the mercury (see below).

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

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.

Historical understanding

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.

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. He concluded that air's volume can expand to fill available space, and he suggested that the concept of perfect vacuum was incoherent. According to Nader El-Bizri, the physicist Ibn al-Haytham (Alhazen, 965–1039) and the Mu'tazili theologians disagreed with Aristotle and Al-Farabi, and they supported the existence of a void. Using geometry, Ibn al-Haytham mathematically demonstrated that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body. According to Ahmad Dallal, Abū Rayhān al-Bīrūnī also states that "there is no observable evidence that rules out the possibility of vacuum". The suction pump was described by Arab engineer Al-Jazari in the 13th century, and later appeared in Europe from the 15th century.

European scholars such as Roger Bacon, Blasius of Parma and Walter Burley in the 13th and 14th century focused considerable attention on issues concerning the concept of a vacuum. Eventually following Stoic physics in this instance, scholars from the 14th century onward increasingly departed from the Aristotelian perspective in favor of a supernatural void beyond the confines of the cosmos itself, a conclusion widely acknowledged by the 17th century, which helped to segregate natural and theological concerns.

Almost two thousand years after Plato, René Descartes also proposed a geometrically based alternative theory of atomism, without the problematic nothing–everything dichotomy of void and atom. Although Descartes agreed with the contemporary position, that a vacuum does not occur in nature, the success of his namesake coordinate system and more implicitly, the spatial–corporeal component of his metaphysics would come to define the philosophically modern notion of empty space as a quantified extension of volume. By the ancient definition however, directional information and magnitude were conceptually distinct.

Torricelli's mercury barometer produced one of the first sustained vacuums in a laboratory.

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. The commonly held view that nature abhorred a vacuum was called horror vacui. There was even speculation that even God could not create a vacuum if he wanted and the 1277 Paris condemnations of Bishop Etienne Tempier, which required there to be no restrictions on the powers of God, led to the conclusion that God could create a vacuum if he so wished. Jean Buridan reported in the 14th century that teams of ten horses could not pull open bellows when the port was sealed.

The Crookes tube, used to discover and study cathode rays, was an evolution of the Geissler tube.

The 17th century saw the first attempts to quantify measurements of partial vacuum. Evangelista Torricelli's mercury barometer of 1643 and Blaise Pascal's experiments both demonstrated a partial vacuum.

In 1654, Otto von Guericke invented the first vacuum pump and conducted his famous Magdeburg hemispheres experiment, showing that, owing to atmospheric pressure outside the hemispheres, teams of horses could not separate two hemispheres from which the air had been partially evacuated. Robert Boyle improved Guericke's design and with the help of Robert Hooke further developed vacuum pump technology. Thereafter, research into the partial vacuum lapsed until 1850 when August Toepler invented the Toepler Pump and in 1855 when Heinrich Geissler invented the mercury displacement pump, achieving a partial vacuum of about 10 Pa (0.1 Torr). A number of electrical properties become observable at this vacuum level, which renewed interest in further research.

While outer space provides the most rarefied example of a naturally occurring partial vacuum, the heavens were originally thought to be seamlessly filled by a rigid indestructible material called aether. Borrowing somewhat from the pneuma of Stoic physics, aether came to be regarded as the rarefied air from which it took its name. Early theories of light posited a ubiquitous terrestrial and celestial medium through which light propagated. Additionally, the concept informed Isaac Newton's explanations of both refraction and of radiant heat. 19th century experiments into this luminiferous aether attempted to detect a minute drag on the Earth's orbit. While the Earth does, in fact, move through a relatively dense medium in comparison to that of interstellar space, the drag is so minuscule that it could not be detected. In 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".

Later, in 1930, Paul Dirac proposed a model of the 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, confirmed two years later. Werner Heisenberg's uncertainty principle, formulated in 1927, predicted a fundamental limit within which instantaneous position and momentum, or energy and time can be measured. This has far reaching consequences on the "emptiness" of space between particles. In the late 20th century, so-called virtual particles that arise spontaneously from empty space were confirmed.

Classical field theories

The strictest criterion to define a vacuum is a region of space and time where all the components of the stress–energy tensor are zero. This means that this region is devoid of energy and momentum, and by consequence, it must be empty of particles and other physical fields (such as electromagnetism) that contain energy and momentum.

Gravity

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. Some authors refer to this reference medium as classical vacuum, 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.

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.
• The superposition principle is always exactly true. 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 ε₀ and magnetic constant μ₀, respectively (in SI units), or exactly 1 (in Gaussian units).
• The characteristic impedance (η) equals the impedance of free space Z₀ ≈ 376.73 Ω.

The vacuum of classical electromagnetism can be viewed as an idealized electromagnetic medium with the constitutive relations in SI units:

${\displaystyle {\boldsymbol {D}}({\boldsymbol {r}},\ t)=\varepsilon _{0}{\boldsymbol {E}}({\boldsymbol {r}},\ t)\,}$

${\displaystyle {\boldsymbol {H}}({\boldsymbol {r}},\ t)={\frac {1}{\mu _{0}}}{\boldsymbol {B}}({\boldsymbol {r}},\ t)\,}$

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

 

Play media

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. 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. Coulomb's law and the electric potential in vacuum near an electric charge are modified.

Theoretically, in QCD multiple vacuum states can coexist. 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.

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 (4.6×10⁻⁶ psi) at 100 kilometres (62 mi) of altitude, 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). 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. Planets are too massive for their trajectories to be significantly affected by these forces, although their atmospheres are eroded by the solar winds.

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 °F).

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 (~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.

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. 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	1.013×105	1
Low vacuum	760 to 25	1×105 to 3×103	9.87×10−1 to 3×10−2
Medium vacuum	25 to 1×10−3	3×103 to 1×10−1	3×10−2 to 9.87×10−7
High vacuum	1×10−3 to 1×10−9	1×10−1 to 1×10−7	9.87×10−7 to 9.87×10−13
Ultra high vacuum	1×10−9 to 1×10−12	1×10−7 to 1×10−10	9.87×10−13 to 9.87×10−16
Extremely high vacuum	< 1×10−12	< 1×10−10	< 9.87×10−16
Outer space	1×10−6 to < 1×10−17	1×10−4 to < 3×10−15	9.87×10−10 to < 2.96×10−20
Perfect vacuum	0	0	0

• 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 the pressure 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. British and German standards define ultra high vacuum as pressures below 10⁻⁶ Pa (10⁻⁸ Torr).
• Deep space is generally much more empty than any artificial vacuum. It may or may not meet the definition of high vacuum above, depending on what region of space and astronomical bodies are being considered. For example, the MFP of interplanetary space is smaller than the size of the Solar System, but larger than small planets and moons. As a result, solar winds exhibit continuum flow on the scale of the Solar System, but must be considered a bombardment of particles with respect to the Earth and Moon.
• Perfect vacuum is an ideal state of no particles at all. It cannot be achieved in a laboratory, although there may be small volumes which, for a brief moment, happen to have no particles of matter in them. Even if all particles of matter were removed, there would still be photons and gravitons, as well as dark energy, virtual particles, and other aspects of the quantum vacuum.
• Hard vacuum and soft vacuum are terms that are defined with a dividing line defined differently by different sources, such as 1 Torr, or 0.1 Torr, the common denominator being that a hard vacuum is a higher vacuum than a soft one.

Relative versus absolute measurement

Vacuum is measured in units of pressure, typically as a subtraction relative to ambient atmospheric pressure on Earth. But the amount of relative measurable vacuum varies with local conditions. On the surface of Venus, where ground level atmospheric pressure is much higher than on Earth, much higher relative vacuum readings would be possible. On the surface of the moon with almost no atmosphere, it would be extremely difficult to create a measurable vacuum relative to the local environment.

Similarly, much higher than normal relative vacuum readings are possible deep in the Earth's ocean. A submarine maintaining an internal pressure of 1 atmosphere submerged to a depth of 10 atmospheres (98 metres; a 9.8 metre column of seawater has the equivalent weight of 1 atm) is effectively a vacuum chamber keeping out the crushing exterior water pressures, though the 1 atm inside the submarine would not normally be considered a vacuum.

Therefore, to properly understand the following discussions of vacuum measurement, it is important that the reader assumes the relative measurements are being done on Earth at sea level, at exactly 1 atmosphere of ambient atmospheric pressure.

Measurements relative to 1 atm

A glass McLeod gauge, drained of mercury

The SI unit of pressure is the pascal (symbol Pa), but vacuum is often measured in torrs, named for an Italian physicist Torricelli (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 on the barometric scale or as a percentage of atmospheric pressure in bars or atmospheres. Low vacuum is often measured in millimeters of mercury (mmHg) or pascals (Pa) below standard atmospheric pressure. "Below atmospheric" means that the absolute pressure is equal to the current atmospheric pressure.

In other words, most low vacuum gauges that read, for example 50.79 Torr. Many inexpensive low vacuum gauges have a margin of error and may report a vacuum of 0 Torr but in practice this generally requires a two-stage rotary vane or other medium type of vacuum pump to go much beyond (lower than) 1 torr.

Measuring instruments

Many devices are used to measure the pressure in a vacuum, depending on what range of vacuum is needed.

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.

The kenotometer is a particular type of hydrostatic gauge, typically used in power plants using steam turbines. The kenotometer measures the vacuum in the steam space of the condenser, that is, the exhaust of the last stage of the turbine.

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.

Ionization 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 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.

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 (AI) 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 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 permeability 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 1×10⁻¹³ torrs (13 pPa). However, pressures as low as 5×10⁻¹⁷ torrs (6.7 fPa) have been indirectly measured in a 4 K (−269.15 °C; −452.47 °F) cryogenic vacuum system. This corresponds to ≈100 particles/cm³.

Effects on humans and animals

See also: Space exposure and Uncontrolled decompression

 

This painting, An Experiment on a Bird in the Air Pump by Joseph Wright of Derby, 1768, depicts an experiment performed by Robert Boyle in 1660.

Humans and animals exposed to vacuum will lose consciousness after a few seconds and die of hypoxia within minutes, but the symptoms are not nearly as graphic as commonly depicted in media and popular culture. The reduction in pressure lowers the temperature at which blood and other body fluids boil, but the elastic pressure of blood vessels ensures that this boiling point remains above the internal body temperature of 37 °C. Although the blood will not boil, the formation of gas bubbles in bodily fluids at reduced pressures, known as ebullism, is still a concern. The gas may bloat the body to twice its normal size and slow circulation, but tissues are elastic and porous enough to prevent rupture. Swelling and ebullism can be restrained by containment in a flight suit. Shuttle astronauts wore a fitted elastic garment called the Crew Altitude Protection Suit (CAPS) which prevents ebullism at pressures as low as 2 kPa (15 Torr). Rapid boiling will cool the skin and create frost, particularly in the mouth, but this is not a significant hazard.

Animal experiments show that rapid and complete recovery is normal for exposures shorter than 90 seconds, while longer full-body exposures are fatal and resuscitation has never been successful. A study by NASA on eight chimpanzees found all of them survived two and a half minute exposures to vacuum. 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. Robert Boyle was the first to show in 1660 that vacuum is lethal to small animals.

An experiment indicates that plants are able to survive in a low pressure environment (1.5 kPa) for about 30 minutes.

Cold or oxygen-rich atmospheres can sustain life at pressures much lower than atmospheric, as long as the density of oxygen is similar to that of standard sea-level atmosphere. The colder air temperatures found at altitudes of up to 3 km generally compensate for the lower pressures there. Above this altitude, oxygen enrichment is necessary to prevent altitude sickness in humans that did not undergo prior acclimatization, and spacesuits are necessary to prevent ebullism above 19 km. Most spacesuits use only 20 kPa (150 Torr) of pure oxygen. This pressure is high enough to prevent ebullism, but decompression sickness and gas embolisms can still occur if decompression rates are not managed.

Rapid decompression can be much more dangerous than vacuum exposure itself. Even if the victim does not hold his or her breath, venting through the windpipe may be too slow to prevent the fatal rupture of the delicate alveoli of the lungs. Eardrums and sinuses may be ruptured by rapid decompression, soft tissues may bruise and seep blood, and the stress of shock will accelerate oxygen consumption leading to hypoxia. Injuries caused by rapid decompression are called barotrauma. A pressure drop of 13 kPa (100 Torr), which produces no symptoms if it is gradual, may be fatal if it occurs suddenly.

Some extremophile microorganisms, such as tardigrades, can survive vacuum conditions for periods of days or weeks.

 

Expectation value (quantum mechanics)

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https://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics) 

In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which can only yield integer values may have a non-integer mean). It is a fundamental concept in all areas of quantum physics.

Operational definition

Consider an operator ${\displaystyle A}$. The expectation value is then ${\displaystyle \langle A\rangle =\langle \psi |A|\psi \rangle }$ in Dirac notation with ${\displaystyle |\psi \rangle }$ a normalized state vector.

Formalism in quantum mechanics

In quantum theory, an experimental setup is described by the observable ${\displaystyle A}$ to be measured, and the state ${\displaystyle \sigma }$ of the system. The expectation value of ${\displaystyle A}$ in the state ${\displaystyle \sigma }$ is denoted as ${\displaystyle \langle A\rangle _{\sigma }}$.

Mathematically, ${\displaystyle A}$ is a self-adjoint operator on a Hilbert space. In the most commonly used case in quantum mechanics, ${\displaystyle \sigma }$ is a pure state, described by a normalized vector ${\displaystyle \psi }$ in the Hilbert space. The expectation value of ${\displaystyle A}$ in the state ${\displaystyle \psi }$ is defined as

${\displaystyle \langle A\rangle _{\psi }=\langle \psi |A|\psi \rangle .}$

(1)

If dynamics is considered, either the vector ${\displaystyle \psi }$ or the operator ${\displaystyle A}$ is taken to be time-dependent, depending on whether the Schrödinger picture or Heisenberg picture is used. The evolution of the expectation value does not depend on this choice, however.

If ${\displaystyle A}$ has a complete set of eigenvectors ${\displaystyle \phi _{j}}$, with eigenvalues ${\displaystyle a_{j}}$, then (1) can be expressed as

${\displaystyle \langle A\rangle _{\psi }=\sum _{j}a_{j}|\langle \psi |\phi _{j}\rangle |^{2}.}$

(2)

This expression is similar to the arithmetic mean, and illustrates the physical meaning of the mathematical formalism: The eigenvalues ${\displaystyle a_{j}}$ are the possible outcomes of the experiment, and their corresponding coefficient ${\displaystyle |\langle \psi |\phi _{j}\rangle |^{2}}$ is the probability that this outcome will occur; it is often called the transition probability.

A particularly simple case arises when ${\displaystyle A}$ is a projection, and thus has only the eigenvalues 0 and 1. This physically corresponds to a "yes-no" type of experiment. In this case, the expectation value is the probability that the experiment results in "1", and it can be computed as

${\displaystyle \langle A\rangle _{\psi }=\|A|\psi \rangle \|^{2}.}$

(3)

In quantum theory, it is also possible for an operator to have a non-discrete spectrum, such as the position operator ${\displaystyle X}$ in quantum mechanics. This operator has a completely continuous spectrum, with eigenvalues and eigenvectors depending on a continuous parameter, ${\displaystyle x}$. Specifically, the operator ${\displaystyle X}$ acts on a spatial vector ${\displaystyle |x\rangle }$ as ${\displaystyle X|x\rangle =x|x\rangle }$. In this case, the vector ${\displaystyle \psi }$ can be written as a complex-valued function ${\displaystyle \psi (x)}$ on the spectrum of ${\displaystyle X}$ (usually the real line). This is formally achieved by projecting the state vector ${\displaystyle |\psi \rangle }$ onto the eigenvalues of the operator, as in the discrete case ${\textstyle \psi (x)\equiv \langle x|\psi \rangle }$. It happens that the eigenvectors of the position operator form a complete basis for the vector space of states, and therefore obey a closure relation:

$${\displaystyle \int |x\rangle \langle x|\,dx\equiv \mathbb {I} }$$

The above may be used to derive the common, integral expression for the expected value (4), by inserting identities into the vector expression of expected value, then expanding in the position basis:

$${\displaystyle {\begin{aligned}\langle X\rangle _{\psi }&=\langle \psi |X|\psi \rangle =\langle \psi |\mathbb {I} X\mathbb {I} |\psi \rangle =\iint \langle \psi |x\rangle \langle x|X|x'\rangle \langle x'|\psi \rangle dx\ dx'\\&=\iint \langle x|\psi \rangle ^{*}x'\langle x|x'\rangle \langle x'|\psi \rangle dx\ dx'=\iint \langle x|\psi \rangle ^{*}x'\delta (x-x')\langle x'|\psi \rangle dx\ dx'\\&=\int \psi (x)^{*}x\psi (x)dx=\int x\psi (x)^{*}\psi (x)dx=\int x|\psi (x)|^{2}dx\end{aligned}}}$$

Where the orthonormality relation of the position basis vectors ${\displaystyle \langle x|x'\rangle =\delta (x-x')}$, reduces the double integral to a single integral. The last line uses the modulus of a complex valued function to replace ${\displaystyle \psi ^{*}\psi }$ with ${\displaystyle |\psi |^{2}}$, which is a common substitution in quantum-mechanical integrals.

The expectation value may then be stated, where x is unbounded, as the formula

${\displaystyle \langle X\rangle _{\psi }=\int _{-\infty }^{\infty }\,x\,|\psi (x)|^{2}\,dx.}$

(4)

A similar formula holds for the momentum operator ${\displaystyle P}$, in systems where it has continuous spectrum.

All the above formulas are valid for pure states ${\displaystyle \sigma }$ only. Prominently in thermodynamics and quantum optics, also mixed states are of importance; these are described by a positive trace-class operator ${\textstyle \rho =\sum _{i}\rho _{i}|\psi _{i}\rangle \langle \psi _{i}|}$, the statistical operator or density matrix. The expectation value then can be obtained as

${\displaystyle \langle A\rangle _{\rho }=\operatorname {Trace} (\rho A)=\sum _{i}\rho _{i}\langle \psi _{i}|A|\psi _{i}\rangle =\sum _{i}\rho _{i}\langle A\rangle _{\psi _{i}}.}$

(5)

General formulation

In general, quantum states ${\displaystyle \sigma }$ are described by positive normalized linear functionals on the set of observables, mathematically often taken to be a C* algebra. The expectation value of an observable ${\displaystyle A}$ is then given by

${\displaystyle \langle A\rangle _{\sigma }=\sigma (A).}$

(6)

If the algebra of observables acts irreducibly on a Hilbert space, and if ${\displaystyle \sigma }$ is a normal functional, that is, it is continuous in the ultraweak topology, then it can be written as

$${\displaystyle \sigma (\cdot )=\operatorname {Trace} (\rho \;\cdot )}$$

with a positive trace-class operator ${\displaystyle \rho }$ of trace 1. This gives formula (5) above. In the case of a pure state, ${\displaystyle \rho =|\psi \rangle \langle \psi |}$ is a projection onto a unit vector ${\displaystyle \psi }$. Then ${\displaystyle \sigma =\langle \psi |\cdot \;\psi \rangle }$, which gives formula (1) above.

${\displaystyle A}$ is assumed to be a self-adjoint operator. In the general case, its spectrum will neither be entirely discrete nor entirely continuous. Still, one can write ${\displaystyle A}$ in a spectral decomposition,

$${\displaystyle A=\int a\,dP(a)}$$

with a projector-valued measure ${\displaystyle P}$. For the expectation value of ${\displaystyle A}$ in a pure state ${\displaystyle \sigma =\langle \psi |\cdot \,\psi \rangle }$, this means

$${\displaystyle \langle A\rangle _{\sigma }=\int a\;d\langle \psi |P(a)\psi \rangle ,}$$

which may be seen as a common generalization of formulas (2) and (4) above.

In non-relativistic theories of finitely many particles (quantum mechanics, in the strict sense), the states considered are generally normal. However, in other areas of quantum theory, also non-normal states are in use: They appear, for example. in the form of KMS states in quantum statistical mechanics of infinitely extended media, and as charged states in quantum field theory. In these cases, the expectation value is determined only by the more general formula (6).

Example in configuration space

As an example, consider a quantum mechanical particle in one spatial dimension, in the configuration space representation. Here the Hilbert space is ${\displaystyle {\mathcal {H}}=L^{2}(\mathbb {R} )}$, the space of square-integrable functions on the real line. Vectors ${\displaystyle \psi \in {\mathcal {H}}}$ are represented by functions ${\displaystyle \psi (x)}$, called wave functions. The scalar product is given by ${\textstyle \langle \psi _{1}|\psi _{2}\rangle =\int \psi _{1}^{\ast }(x)\psi _{2}(x)\,dx}$. The wave functions have a direct interpretation as a probability distribution:

$${\displaystyle p(x)dx=\psi ^{*}(x)\psi (x)dx}$$

gives the probability of finding the particle in an infinitesimal interval of length ${\displaystyle dx}$ about some point ${\displaystyle x}$.

As an observable, consider the position operator ${\displaystyle Q}$, which acts on wavefunctions ${\displaystyle \psi }$ by

$${\displaystyle (Q\psi )(x)=x\psi (x).}$$

The expectation value, or mean value of measurements, of ${\displaystyle Q}$ performed on a very large number of identical independent systems will be given by

$${\displaystyle \langle Q\rangle _{\psi }=\langle \psi |Q|\psi \rangle =\int _{-\infty }^{\infty }\psi ^{\ast }(x)\,x\,\psi (x)\,dx=\int _{-\infty }^{\infty }x\,p(x)\,dx.}$$

The expectation value only exists if the integral converges, which is not the case for all vectors ${\displaystyle \psi }$. This is because the position operator is unbounded, and ${\displaystyle \psi }$ has to be chosen from its domain of definition.

In general, the expectation of any observable can be calculated by replacing ${\displaystyle Q}$ with the appropriate operator. For example, to calculate the average momentum, one uses the momentum operator in configuration space, ${\textstyle P=-i\hbar \,{\frac {d}{dx}}}$. Explicitly, its expectation value is

$${\displaystyle \langle P\rangle _{\psi }=-i\hbar \int _{-\infty }^{\infty }\psi ^{\ast }(x)\,{\frac {d\psi (x)}{dx}}\,dx.}$$

Not all operators in general provide a measurable value. An operator that has a pure real expectation value is called an observable and its value can be directly measured in experiment.