- Zero-point field
In

quantum field theory , the**zero-point field**is the lowest energy state of a field, i.e. itsground state , which is non zero. [*cite book | last = Gribbin | first = John | title = Q is for Quantum - An Encyclopedia of Particle Physics | publisher = Touchstone Books | year = 1998 | id = ISBN 0-684-86315-4*] This phenomenon gives the quantum vacuum a complex structure, which can be probed experimentally; see, for example, theCasimir effect . The term "zero-point field" is sometimes used as a synonym for thevacuum state of an individual quantized field. The electromagnetic zero-point field is loosely considered as a sea of background electromagnetic energy that fills the vacuum of space, and is often regarded merely as a curious outcome of the quantum mechanical requirement, namely theHeisenberg uncertainty principle , that the lowest allowableenergy level in aharmonic oscillator mode is not zero but ħv /2, where v is the characteristicfrequency of the oscillator. [*H.E. Puthoff,, Scott Little, Michael Ibison, (2000). [*]*http://www.earthtech.org/experiments/src/srcreport.htm Ground States and the Zero-Point Field*] , Earthtech International, Inc**Overview**It is believed that an electromagnetic field exists in a vacuum even when the temperature of the surrounding material is reduced towards absolute zero.cite book | last = Dodd | first = John, H. | title = Atoms and Light: Interactions | pages = (217) | publisher = Springer | year = 1991 | id = ISBN 0306437414 ] The existence of such a zero-point field has been confirmed experimentally by the Casimir experiment, i.e. the measurement of the attractive force between two parallel plates in an evacuated, near-zero temperature enclosure. That force is found to be proportional to the inverse fourth power of the distance apart of the plates; it has been shown that such a result can only be produced by a zero-point field whose spectral energy density has a frequency dependence of ρ(ν) = kν

^{3}. It has been assumed until recently, though without any experimental evidence, that there are zero-point energies for the strong andweak force s as well as theelectromagnetic force . More recently it has been understood that because the electromagnetic force, expressed by theLorentz force equation, does not require mass that the electromagnetic zero-point field and the electromagnetic force carrier, the photon, are probably fundamental to all three forces.**History**Quantum mechanics predicts the existence of what are usually called "zero-point" energies for the strong, the weak and the electromagnetic

interactions , where "zero-point" refers to the energy of the system at temperature "T=0", or the lowest quantized energy level of a quantum mechanical system. Specifically, in 1900,Max Planck derived the formula for the energy of a single "energy radiator", i.e. a vibrating atomic unit, as::$epsilon\; =\; frac\{h\; u\}\{\; e^\{frac\{h\; u\}\{kT-1\}$

:"Here, $h$ is

Planck's constant , $u$ is thefrequency , "k" isBoltzmann's constant , and "T" is thetemperature ."In 1913, using this formula as a basis,

Albert Einstein andOtto Stern published a paper of great significance in which they suggested for the first time the existence of a residual energy that all oscillators have at absolute zero. They called this "residual energy" and then "Nullpunktsenergie" (in German), which later became translated as "zero-point energy ". They carried out an analysis of the specific heat of hydrogen gas at low temperature, and concluded that the data are best represented if the vibrational energy is taken to have the form: [*cite book | last = Laidler | first = Keith, J. | title = The World of Physical Chemistry | publisher = Oxford University Press | year = 2001 | id = ISBN 0198559194*]:$epsilon\; =\; frac\{h\; u\}\{\; e^\{frac\{h\; u\}\{kT-1\}\; +\; frac\{h\; u\}\{2\}$

Thus, according to this expression, even at

absolute zero the energy of an atomic system has the value ½"hν". [*[*] Although the term*http://www.calphysics.org/zpe.html Introduction to Zero-Point Energy*] - Calphysics Institutezero-point energy applies to all three of these interactions in nature, customarily it is used in reference only to the electromagnetic case. [*http://www.calphysics.org/zpe.html Zero-point Energy and Zero-point Field*] – Calphysics Institute] Because the zero-point field has the property of beingLorentz invariant , the zero-point field becomes detectable only when a body is accelerated through space.Some experiments in 1992 have demonstrated experimentally that the familiar

spontaneous emission process in atoms may be regarded asstimulated emission by zero-point field radiation. [*S. Haroche and J.-M. Raimond, “Cavity Quantum Electrodynamics,” Sci. Am., pp. 54-62 (April 1993). Also H. Yokoyama, “Physics and Device Applications,” Science 256, pp. 66-70 (1992).*] In recent years, it has been suggested that the electromagnetic zero-point field is not merely an artifact of quantum mechanics, but a real entity with major implications for gravity, astrophysics and technology. This view is shared by a number of researchers, including Boyer (1980), McCrea (1986), Puthoff (1987) and Rueda and Haisch (1998). [*Boyer, T.H. (1980). In Foundations of Radiation Theory and Quantum Electrodynamics (ed. Barut, A.O.), Plenum, New York, 49.*] [*McCrea, W.H. (1986). Quart. J. Roy. Astr. Soc. 27, 137.*] [*Puthoff, H.E. (1987). Phys. Rev. D. 35, 3266.*] [*Rueda, A., Haisch, B. (1998). Found. Phys. 28, 1057.*]**Zero-point energy and conservation of energy**Traditionally it has been assumed that the electromagnetic zpf energy density for each quantum space equals the sum of the quantum oscillatory energy at all possible wavelengths in each of the three spatial dimensions all the way up to the

Planck length . Using this historical measure of energy density it has been estimated that there is enough zero point energy contained in one cubic meter of space to boil all of the oceans of the world.However, the historical analysis of the zpf energy density just described appears to contradict the

first law of thermodynamics and our understanding of thecosmology of the universe. The physical evidence is extensive that the universe has expanded from an origin containing essentially no space and infinite energy density in the event called theBig Bang . If our universe is defined as all that has the potential of being known to us and interacted with, then it is defined as a "closed system ". A closed system retains causality because its total energy is finite and always conserved. This is not a contradiction with the universe at time (t) = 0 because the concept of infinite energy "density" in "zero" occupied space does not equal "infinite energy" for the universe. The historical analysis of the zpf energy density used in the example of energy in one cubic meter of space does not account for the expansion of the universe. It simply increments this expanding space over time and assigns each new additional quantum space with the maximum energy density.There is a major drive in physics to create a more realistic zpf energy density model that still allows for causality and conservation of energy in the universe. There is substantial evidence in quantum physics, via the

de Broglie relations , theCasimir effect, and theZitterbewegung action of electrons that this field of energy acts as an energy intermediary in the dynamic actions of all particles. Electrons orbiting a nucleus, as one specific example, may use this energy source to move up in an orbit, and then contribute back to this energy source when they relax back into a lower orbit around the nucleus. The de Broglie relations show that the wavelength is inversely proportional to the momentum of an electron and that the frequency is directly proportional to the electron's kinetic energy. As long as the electron does not increase its average kinetic energy over time through acceleration or heating of the atom as a whole, then this wave-like movement of electrons can be seen as a direct interaction of electrons with the zpf.A potentially promising area for research is the fact that if particles become more energetic as they are heated or accelerated their gravitational field increases. Changes in gravity can perhaps be attributed to a change in a spherical zpf energy density gradient surrounding an accelerated or decelerated massive particle. This dynamic action is just an extension of the static orbiting electron wave model to a dynamic model in which the "average" kinetic energy of a particle no longer remains constant over time and energy is drawn in from the quantum vacuum but not returned. If a massive particle's ground state is defined as it's reference frame at the instant of its creation, then when a particle or body returns to this reference frame, or ground state, from an accelerated state that energy is returned to the quantum vacuum as a decrease in gravity surrounding the particle. This would be in accord with the rules of gravity on accelerated bodies as we know them, and most importantly, maintains conservation of the combined energy of both particles and the zpf, while still allowing for dynamic interaction between the two.

**Quantum fluctuations versus quantum pathways**The essential character of the zpf was originally described by

John Archibald Wheeler [*cite book | last = Wheeler | first = John | title = Geons, Black Holes, and Quantum Foam: A Life In Physics | publisher = Norton & Company | year = 1998 | id = ISBN 0393319911*] as a foamy sea of constantly emerging virtual particles and anti-particles which would come into existence spontaneously and then annihilate themselves. This description originated because it was the only way to consolidate the disparity between the enormous projected energy density of the quantum vacuum with the much smaller energy predicted from theCosmological Constant . Because the mathematics of oscillators was the origin of our understanding of the zpf it has been described as "fluctuating" in the absence of any outside force. But this seems to be a fundamental error in logic. An individual oscillator can fluctuate just as an electron's orbital wave motion can fluctuate between two different orbits. However, in both cases there should be no "change" in fluctuation as long as the energy does not change. At zero degrees Kelvin the energy from one quantum oscillator should not propagate between quantum spaces, nor should there be any change in any single quantum oscillator's strength, absent an outside force, as this would violate conservation of energy.A static, but plastic quantum foam is a better analogy to the character of the quantum vacuum, and not the kind of foam Wheeler described. It should be remembered that each quantum space represents the sum of quantum harmonic oscillator energy in each of the three spatial degrees of freedom, and that each of these three degrees of freedom can act separately, but in coordination with the other two to provide a total energy for that quantum space which is always conserved. If a photon with a specific energy and direction enters and then exits a quantum space these three degrees of freedom allow for a change in the magnitude of the energy in each of the three spatial directions while conserving the total magnitude of harmonic energy in that space - an increase in magnitude of harmonic energy in one dimension can be compensated by a decrease in the other two dimensions. The orientation and size of these changes will correlate to the direction and energy of any particle passing through that quantum space. Similarly, any particle encountering a quantum space which has recently had a particle pass through it will be affected by that previous particle, even though they are not coincident in time.

For example, in the cold reaches of space between galaxies photons from distant galaxies arrive rarely. If by chance a rare photon passes through one of these cold dark spaces it will leave a quantum signature on the oscillatory energy of each quantum space it passes through. If a quantum space has experienced a photon passing through it and no further photons pass through, then that area of space will retain a memory of the last photon it experienced. That space will then exhibit a residual force which has a magnitude and a direction that resides in the memory of that space. This force can be observed in the Zitterbewegung, or jittery action of electrons, which in principle can be extended to all particles. In effect, a pathway has been produced by this single photon. The fact that this pathway cannot be maintained in its unaltered form after measuring it, as the

Heisenberg Uncertainty Principle predicts, does not alter the fact that this pathway is retained in space until the next photon passing through creates an interference with this pathway. Acts of measurement represent an exchange of photons between the "observer" and the "observed" and are synonymous with local changes in energy. The "observed" can be an actual particle or just the pathway in space created by the particle. The appearance of fluctuation is actually the transformation of energy and information as it travels through space, but the total energy and information of the universe are always maintained. So it is seen that this quantum foam is not the kind of foam that springs back, but is more like milk foam on top of a cup of cappuccino - a straw can be pushed through the foam and a hole in the foam will remain for a time after the straw is withdrawn. But in the case of quantum foam the impression left behind is not of a hole, but rather the impression of the photon or particle with mass that passed through it. [*Habegger, E.J., Quantum Vacuum Pathway Theory, Space Technology and Applications International Forum, (STAIF 2005), AIP Conference Proceedings 746 , 1379.*] .**Curvature of space and the physical vacuum**Zero-point field theory originated from the application of thermodynamics to the problem of

Black Body radiation. This knowledge was later used byAlbert Einstein to calculate the electromagnetic residual energy of the vacuum surrounding the electron in the hydrogen atom that was required to keep it from collapsing into the nucleus. Much later the energy density of empty space was calculated to have a spectral density of $p(v)\; =\; kv^3$. This energy density is an enormous figure and is approximately 10^120 times higher than the cosmological constant predicts if, as is traditionally done, the Planck length is used for the upper bound for the frequency. The total energy of the universe does not seem to be conserved unless laws of physics are invoked that cannot be understood at the classical level. In other words, the observed expansion of the universe leads to a discrepancy from quantum physics derived vacuum energy of the order of 10^120 times. Even now, quantum theory's contradiction with the conservation of the total energy of the universe and the first law of thermodynamics, is not universally understood among the scientific community. A man who did understand this problem wasAndrei Sakharov , the famous Russian physicist and political dissident.In the West the scientific description of gravity remains centered on Einstein's original conception as described in General Relativity, i.e. gravity is the geometry of space, or

geometrodynamics . In this description space can curve not only around a large massive object but it can also be made to curve similarly around a much, much less massive object that has been accelerated close to the speed of light. This is a perfectly accurate description, but "space" in this description is an amorphous element that is similar to theclassical elements of earth, water, fire, and air, as described by early Greek, Japanese, and Hindu civilizations - there is no granularity or definition of what that space represents.Sakharov was able to see that the geometrodynamics of gravity could just as easily be subsumed within a larger description of the geometry of the energy density of the zpf. This geometry refers to a framework in which the total energy density for each quantum space can actually change and does not refer to residual electromagnetic forces represented by past history of particle trajectories referred to earlier. Rather than being viewed as process in which a photon is both entering and exiting a quantum space it should be viewed as a photon exiting the space only and leaving the total energy of the quantum space at a reduced magnitude. In this way gravity can be described similarly to the geometry of isobaric lines of equal air pressure in the atmosphere, but in the case of gravity these lines would instead be spherical surfaces of equal zpf energy density around a massive object. In this conception the spherical surfaces of lowest zpf energy density would be those closest to the massive object or particle and the energy density in space would increase at the rate equal to $p(v)-(1/r^2)$, where $r$ is the distance from the massive object or particle. (The gravitational constant, $G$, and the specific mass, $m$, are left out as they do not effect the "rate" at which gravitational force changes with distance.) Here $p(v)$ would be the "average" density of the zpf over the entire universe at any given moment in the life of the universe. At sufficient distances in open space from the massive body $p(v)-(1/r^2)$ would approximate $p(v)$.

**The Planck length**It can be noted in $p(v)$ that the volume of the universe, $v$, is expanding. If the total energy of the universe is taken as a constant based on first principles, then $p(v)$ is not a constant thoughout the life of the universe - the density gets lower as the volume of the universe expands. However it will be a "changing" constant in the sense that it is an "average" density that applies to the entire universe at any given moment in the life of the universe. It can be safely assumed that if Sakharov was correct in his analysis, something that is only tentatively accepted as of now, that there is something incorrect in our current mathematical assumptions in physics. If Sakharov's analysis is tentatively taken as true then certain results must accrue from that and other results, long assumed, must be incorrect. The final decision on whether it is worthwhile to accept his analysis is based solely on the utility, or non-utility in finding answers to problems long plagueing physics.

The Planck length defines the shortest wavelength quantum oscillator that is possible. The summation of energy of all possible wavelengths for each of the three dimensional degrees of freedom up to this limit has historically defined the energy for each quantum space. The Planck length is::$ell\_P\; =sqrtfrac\{hbar\; G\}\{c^3\}\; approx\; 1.616\; 252\; imes\; 10^\{-35\}\; mbox\{\; meters\}$ where:

*$c$ is thespeed of light in vacuum;

*$G$ is thegravitational constant ;

*$hbar$ isDirac's constant ,Planck's constant divided by 2π.If the zpf energy density decreases as the volume of the universe expands then, by definition, the upper bound for each quantum oscillator must be reduced and consequently the "average" total energy for each quantum space in the universe must be reduced correspondingly. Perhaps the Planck length is not a constant but stretches out as the universe expands? There would be some precedence for this in the stretching out of light in the

cosmic microwave background radiation . There are three constants used to create the Planck length constant, as shown above. Is it possible that the gravitational constant, always assumed to be constant throughout the expansion of the universe, is not a constant? This seems plausible, in view of structural changes that would occur in the universe as the fabric of space becomes less dense as it expands. Of the three constants included in the Planck length the gravitational constant seems to be most directly correlated with the expansion of this primordial field.If one considers fundamentally altering the status of one the three constants then altering the gravitational constant would be preferable to altering the constancy of the speed of light or changing Planck's constant. Planck's constant and the speed of light fundamentally underlie all current calculations of physical properties. The constancy of the speed of light may also be directly tied to the interaction of matter with the local density of the zpf. As the zpf density changes within gravitational fields and as the universe expands then the length measurements, which are time dependent, change along with locally changing rates of passage of time. The direct correlation of changes in both measurement of distance and measurement of time as this density changes create the constancy of the speed of light. While the gravitational constant also underlies many fundamental properties of physics, the properties affected by the gravitational constant seem to be more directly tied to contradictions that already exist between gravitational physics and quantum physics.

Only future experience will tell if more problems are "solved" or if more problems are "created" by allowing for changes in the gravitational constant during the evolution of the universe. One thing is certain though: If the Planck length stretches out as the universe expands then the zpf energy density is not even close to what it is currently assumed to be.

**Andrei Sakharov and the elasticity of space**It is a fact that Albert Einstein's equation in General Relativity for the geometrodynamics of space is one of the most beautiful equations in physics. Unfortunately, its beauty has resulted in a fixation in the West on the mathematics of geometry, including the geometry of hyper-dimensional space. This focus has resulted in Western mainstream physics ignoring the need for a mathematical definition that connects the classical General Relativity 4-dimensional and

Kaluza-Klein 5-dimensional theories of the geometry of space with new quantum mechanical derived ideas that will better correlate with them. Until an explicit mathematical equation is robustly proven to link these two disparate interpretations of physics the first law of thermodynamics for our universe appears to be conceptually violated.Andrei Sakharov's conception of the elasticity of space, though incomplete, seems to point towards an ultimate resolution of this problem. In his cosmological model space is elastic like the surface of a balloon and thins out as the volume of the universe expands over time. If the 3-dimensional "volume" of the universe is represented as a 3-dimensional "surface" of a balloon, then in its collapsed state at the beginning of time the zpf energy density of the universe is greatest. In approximately the first pico-pico second in the life of the universe the zpf energy density would be extremely high, high enough to create the proton in the hydrogen atom. The proton represents approximately 99.9 percent of the mass of the entire hydrogen atom. The estimated energy density of the physical vacuum at the instant of the proton creation would then represent approximately the amount of energy density recently calculated for the hydrogen atom using

stochastic electrodynamics . However, in this conceptual framework this zpf energy density would only exist at precisely this one moment in the life of the universe. Sakharov conceived that at the instant of the creation of fundamental massive particles that the elastic zpf energy required for their mass was transformed into inelastic energy.Though Sakharov didn't know this when he conceptualized this idea, today our experimental knowledge indicates the proton, which itself is made up of three quarks, is the only fundamental massive particle that does not undergo transformation through radioactive decay if given a long enough time of observation or a large enough quantity of protons being observed.(In the case of neutrinos, they simply transform into other kinds of neutrinos). So his idea seems to fit in with the idea of a type of "absolute" inelasticity that the

Standard Model cannot account for.So a question similar to the question Einstein proposed concerning the non-collapse of the electron into the hydrogen nucleus can be posed for the proton: Why doesn't the proton radioactively decay if the energy density of the physical vacuum is now a tiny fraction of what it was when the proton was created? The principle of asking why is exactly the same even though they apply to different processes. If the zpf energy density decreases over time the statistical probability of both processes occurring should increase. If the proton composes 99.9 percent of the energy of the hydrogen atom, is itself a composite elementary particle, an even more pertinent question would be to ask why the proton doesn't radioactively decay?

Sakharov imagined that

spin and its associatedangular momentum provided this inelasticity. Spin, and specifically inelastic spin, is a part of 5-dimensional definition that directly correlates with gravity in Kaluza-Klein theory. If one maintains the balloon metaphor then we sew in a round piece of inelastic material into our balloon while it is still in its collapsed state. We are careful to select a piece of inelastic material that has exactly the same density as the same equivalent elastic material surrounding it at that point in its expansion. As we continue to blow up the balloon its elastic material thins out symmetrically except where the inelastic patch is located. Because the area of the inelastic patch does not stretch and thin out the elastic material surrounding it must compensate by stretching and thinning even more than it otherwise would. The greatest thinning will be right on the periphery of the patch in the elastic material because this is the part of the elastic material that has the greatest concentration of stress. If we translate this idea to physics the greatest zpf stress, or thinning out, will be right on the periphery of any massive body and this is where gravity is greatest.One now returns to the question of where the missing energy went to that is required to support the proton in today's greatly expanded universe. Using pure logic it appears that the proton still has it in the form of energy pulled in from the surrounding physical vacuum. Though the inelasticity between a proton's quarks can by no means account for all the gravity in the universe it certainly can account for nearly all the gravity of nucleons, i.e., protons and neutrons. (A neutron can be included in this because it has very slightly more energy than a proton and will decay into a proton after fifteen minutes if separated from protons.) It seems that the energy density in the universe from that first pico-pico second, at least for protons, is equal to 99.9 percent of the original energy density calculated for the hydrogen atom from stochastic electrodynamics and the Casimir effect. If one accounts only for the gravity of nucleons, which is a very large proportion of the gravity implicitly assigned within the cosmological constant, then a significant proportion of the 10^120 difference between it and the traditional vacuum energy can be resolved simply by allowing for a decrease in energy density as the finite zpf energy expands into an ever increasing volume, and by subtracting that energy in nucleons from the vacuum energy. Gravity seems to be created by that subtraction. This is not gravity as we are used to understanding it, but gravity as an energy density gradient in the vacuum spreading out smoothly around any massive object. So it can be seen that the reason the proton does not decay in today's universe is because energy is pulled in from the surrounding physical vacuum. We experience that reduction in energy as gravity.

**Related**In recent years, a number of

new age books have begun to appear propounding the view that the zero-point field of physics is the secret force of the universe being used to explain such phenomena asintention ,remote viewing ,paranormal ability, etc. [*[*] [*http://homepages.ihug.co.nz/~sai/zpf_haisch.htm Brilliant Disguise: Light, Matter and the Zero-Point Field*] –Bernard Haisch , 2001 "Science & Spirit Magazine"*[*] One of the main purveyors of this view is Stanford physicist*http://homepages.ihug.co.nz/~sai/McTag_field.htm The Field: The Quest For The Secret Force Of The Universe*] –Lynne McTaggart , Book Synopsis.Harold Puthoff who spent more than thirty years examining the zero-point field.cite book | last = McTaggart | first = Lynne | title = The Intention Experiment | pages = (13) | publisher = Free Press | year = 2007 | id = ISBN 0743276957] Books that promote this view include:*

Lynne McTaggart 's 2001 "The Field - the Quest for the Secret Force of the Universe".

*Ervin Laszlo 's 2004 "Science and the Akashic Field - an Integral Theory of Everything".

*Brenda Anderson 's 2006 "Playing the Quantum Field - How Changing Your Choices Can Change Your Life".

*Masaru Emoto 's 2005 "The Hidden Messages in Water."Such views are not without controversy. Some see such discussion as pseudoscience. [

*[*] However, physicist*http://padrak.com/ine/ZPESCIAM.html Exploiting Zero-point Energy*] –Philip Yam , "Scientific American Magazine", December 1997, pp. 82-85.David Bohm and other respected scientists, have found some utility in looking at the relationship of the zero point field to matter. Bohm posited, for example, that the field might be the force from which all life unfolds. He also stated that the "nonlocality" of quantum physics might be explained through interconnections allowable via the zero point field.**References in popular culture**Though seldom used in fiction, the most notable reference to the Zero-point field is the use of

ZPM s in theStargate universe , devices which extract huge amounts of energy from a Zero-point field. In the video game "Half-Life 2 ", there is also a weapon called the "Zero-Point Energy Field Manipulator ", more commonly known as the "Gravity Gun". In their 1996 fictional book,Encounter With Tiber ,Buzz Aldrin andJohn Barnes have Alpha Centaurians visit Earth in 7200BC using laserable Zero-Point Field-based propulsion to achieve near-light speed travel. In the 2004 animated film "The Incredibles ", Syndrome's basic weapon is a zero-point energy field.**References**

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Zero-point-field**— Die Nullpunktsenergie eines quantenmechanischen Systems ist die Energie seines Grundzustands, der niedrigste Eigenwert des Energieoperators. Sie kann als Konsequenz der heisenbergschen Unschärferelation aufgefasst werden, welche besagt, dass der… … Deutsch Wikipedia**Zero-point energy**— is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero point energy, a… … Wikipedia**Point of zero charge**— The point of zero charge (pzc), in physical chemistry, is a concept relating to the phenomenon of adsorption, and it describes the condition when the electrical charge density on a surface is zero. It is usually determined in relation to an… … Wikipedia**zero**— /zear oh/, n., pl. zeros, zeroes, v., zeroed, zeroing, adj. n. 1. the figure or symbol 0, which in the Arabic notation for numbers stands for the absence of quantity; cipher. 2. the origin of any kind of measurement; line or point from which all… … Universalium**Zero crossing**— is a commonly used term in electronics, mathematics, and image processing. In mathematical terms, zero crossing basically means the changing of sign (e.g. from positive to negative), that is represented with a crossing of the axis (zero value) in … Wikipedia**Field archery**— involves shooting at targets of varying (and often unmarked) distance, often in woodland and rough terrain. One goal of field archery is to improve the techniques and abilities required for bowhunting in a more realistic outdoor setting. As with… … Wikipedia**Zero tolerance**— policies are studied in criminology and are common in formal and informal policing systems around the world.Fact|date=December 2007 The policies also appear in informal situations where there may be sexual harassment or Internet misuse in… … Wikipedia**Field hockey at the 2008 Summer Olympics**— in Beijing was held over a fourteen day period beginning on August 10, and culminating with the medal finals on August 22 and August 23.Cite web|url=http://en.beijing2008.cn/sports/hockey/index.shtml|title=Hockey Beijing Olympics… … Wikipedia**Field electron emission**— It is requested that a diagram or diagrams be included in this article to improve its quality. For more information, refer to discussion on this page and/or the listing at Wikipedia:Requested images. Field emission (FE) (also known as field… … Wikipedia**Field of definition**— In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong. Given polynomials, with coefficients in a field K , it may not be obvious… … Wikipedia