Poincaré recurrence theorem From Wikipedia, the free encyclopedia In mathematics, the Poincaré recurrence theorem states that certain systems will, after a sufficiently long but finite time, return to a state very close to the initial state. The Poincaré recurrence time is the length of time elapsed until the recurrence (this time may vary greatly depending on the exact initial state and required degree of closeness). The result applies to isolated mechanical systems subject to some constraints, e.g., all particles must be bound to a finite volume. The theorem is commonly discussed in the context of ergodic theory, dynamical systems and statistical mechanics. If the space is quantized, an exact recurrence is possible after an period of time determined in part by the size of the space and the number of elements contained. If the space is continuous, no exact recurrence can be expected because there will be an arbitrarily large distance between any two locations, no matter how close together. The size of this arbitrarily large distance is related to aleph one (for the set of real numbers). (See Continuum Hypothesis.) The theorem is named after Henri Poincaré, who published it in 1890. Contents [hide] 1 Precise formulation 2 Discussion of proof 3 Formal statement of the theorem 3.1 Theorem 1 3.2 Theorem 2 4 Quantum mechanical version 5 See also 6 References 7 Further reading 8 External links Precise formulation[edit] Any dynamical system defined by an ordinary differential equation determines a flow map f t mapping phase space on itself. The system is said to be volume-preserving if the volume of a set in phase space is invariant under the flow. For instance, all Hamiltonian systems are volume-preserving because of Liouville's theorem. The theorem is then: If a flow preserves volume and has only bounded orbits, then for each open set there exist orbits that intersect the set infinitely often.[1] As an example, the deterministic baker's map exhibits Poincaré recurrence which can be demonstrated in a particularly dramatic fashion when acting on 2D images. A given image, when sliced and squashed hundreds of times, turns into a snow of apparent "random noise". However, when the process is repeated thousands of times, the image reappears, although at times marred with greater or lesser bits of noise. Discussion of proof[edit] The proof, speaking qualitatively, hinges on two premises:[2] A finite upper bound can be set on the total potentially accessible phase space volume. For a mechanical system, this bound can be provided by requiring that the system is contained in a bounded physical region of space (so that it cannot, for example, eject particles that never return) — combined with the conservation of energy, this locks the system into a finite region in phase space. The phase volume of a finite element under dynamics is conserved. (for a mechanical system, this is ensured by Liouville's theorem) Imagine any finite starting volume of phase space and follow its path under dynamics of the system. The volume "sweeps" points of phase space as it evolves, and the "front" of this sweeping has a constant size. Over time the explored phase volume (known as a "phase tube") grows linearly, at least at first. But, because the accessible phase volume is finite, the phase tube volume must eventually saturate because it cannot grow larger than the accessible volume. This means that the phase tube must intersect itself. In order to intersect itself, however, it must do so by first passing through the starting volume. Therefore, at least a finite fraction of the starting volume is recurring. Now, consider the size of the non-returning portion of the starting phase volume—that portion that never returns to the starting volume. Using the principle just discussed in the last paragraph, we know that if the non-returning portion is finite, then a finite part of the non-returning portion must return. But that would be a contradiction, since any part of the non-returning portion that returns, also returns to the original starting volume. Thus, the non-returning portion of the starting volume cannot be finite and must be infinitely smaller than the starting volume itself. Q.E.D.. The theorem does not comment on certain aspects of recurrence which this proof cannot guarantee: There may be some special phases that never return to the starting phase volume, or that only return to the starting volume a finite number of times then never return again. These however are extremely "rare", making up an infinitesimal part of any starting volume. Not all parts of the phase volume need to return at the same time. Some will "miss" the starting volume on the first pass, only to make their return at a later time. Nothing prevents the phase tube from returning completely to its starting volume before all the possible phase volume is exhausted. A trivial example of this is the harmonic oscillator. Systems that do cover all accessible phase volume are called ergodic (this of course depends on the definition of "accessible volume"). What can be said is that for "almost any" starting phase, a system will eventually return arbitrarily close to that starting phase. The recurrence time depends on the required degree of closeness (the size of the phase volume). To achieve greater accuracy of recurrence, we need to take smaller initial volume, which means longer recurrence time. For a given phase in a volume, the recurrence is not necessarily a periodic recurrence. The second recurrence time does not need to be double the first recurrence time. Formal statement of the theorem[edit] Let (X,\Sigma,\mu) be a finite measure space and let f\colon X\to X be a measure-preserving transformation. Below are two alternative statements of the theorem. Theorem 1[edit] For any E\in \Sigma, the set of those points x of E such that f^n(x)\notin E for all n>0 has zero measure. That is, almost every point of E returns to E. In fact, almost every point returns infinitely often; i.e. \mu\left(\{x\in E:\mbox{ there exists } N \mbox{ such that } f^n(x)\notin E \mbox{ for all } n>N\}\right)=0. For a proof, see proof of Poincaré recurrence theorem 1 at PlanetMath.org. . Theorem 2[edit] The following is a topological version of this theorem: If X is a second-countable Hausdorff space and \Sigma contains the Borel sigma-algebra, then the set of recurrent points of f has full measure. That is, almost every point is recurrent. For a proof, see proof of Poincaré recurrence theorem 2 at PlanetMath.org. Quantum mechanical version[edit] For quantum mechanical systems with discrete energy eigenstates, a similar theorem holds. For every \epsilon >0 and T_{0}>0 there exists a time T larger than T_{0}, such that \left |\left | \psi(T)\right\rangle - \left |\psi(0)\right\rangle\right | < \epsilon, where \left | \psi(t)\right\rangle denotes the state vector of the system at time t.[3][4][5] The essential elements of the proof are as follows. The system evolves in time according to: \left |\psi(t)\right\rangle = \sum_{n=0}^{\infty}c_{n}\exp\left(-i E_{n} t\right)\left |\phi_{n}\right\rangle where the E_{n} are the energy eigenvalues (we use natural units, so \hbar = 1 ), and the \left |\phi_{n}\right\rangle are the energy eigenstates. The squared norm of the difference of the state vector at time T and time zero, can be written as: \left |\left | \psi(T)\right\rangle - \left |\psi(0)\right\rangle\right |^{2} = 2\sum_{n=0}^{\infty}\left | c_{n}\right |^{2}\left [1-\cos\left(E_{n}T\right)\right ] We can truncate the summation at some n = N independent of T, because \sum_{n=N+1}^{\infty}\left | c_{n}\right |^{2}\left [1-\cos\left(E_{n}T\right)\right ] \leq \sum_{n=N+1}^{\infty}\left | c_{n}\right |^{2} which can be made arbitrarily small because the summation \sum_{n=0}^{\infty}\left |c_{n}\right |^{2}, being the squared norm of the initial state, converges to 1. That the finite sum \sum_{n=0}^{N}\left | c_{n}\right |^{2}\left [1-\cos\left(E_{n}T\right)\right ] can be made arbitrarily small, follows from the existence of integers k_{n} such that \left |E_{n}T -2\pi k_{n}\right |<\delta for arbitrary \delta>0. This implies that there exists intervals for T on which 1-\cos\left(E_{n}T\right)<\frac{\delta^{2}}{2}. On such intervals, we have: 2\sum_{n=0}^{N}\left | c_{n}\right |^{2}\left [1-\cos\left(E_{n}T\right)\right ] < \delta^{2}\sum_{n=0}^{N}\left | c_{n}\right |^{2}<\delta^{2} The state vector thus returns arbitrarily closely to the initial state, infinitely often.

Quantum fluctuation From Wikipedia, the free encyclopedia File:Vacuum fluctuations revealed through spontaneous parametric down-conversion.ogv The video of an experiment showing vacuum fluctuations (in the red ring) amplified by spontaneous parametric down-conversion. In quantum physics, a quantum vacuum fluctuation (or quantum fluctuation or vacuum fluctuation) is the temporary change in the amount of energy in a point in space,[1] as explained in Werner Heisenberg's uncertainty principle. According to one formulation of the principle, energy and time can be related by the relation[2] \Delta E \Delta t \approx {h \over 2 \pi} That means that conservation of energy can appear to be violated, but only for small values of t (time). This allows the creation of particle-antiparticle pairs of virtual particles. The effects of these particles are measurable, for example, in the effective charge of the electron, different from its "naked" charge. In the modern view, energy is always conserved, but the eigenstates of the Hamiltonian (energy observable) are not the same as (i.e., the Hamiltonian doesn't commute with) the particle number operators. Quantum fluctuations may have been very important in the origin of the structure of the universe: according to the model of inflation the ones that existed when inflation began were amplified and formed the seed of all current observed structure. Contents [hide] 1 Quantum fluctuations of a field 2 See also 3 References 4 External links Quantum fluctuations of a field[edit] A quantum fluctuation is the temporary appearance of energetic particles out of empty space, as allowed by the uncertainty principle. The uncertainty principle states that for a pair of conjugate variables such as position/momentum and energy/time, it is impossible to have a precisely determined value of each member of the pair at the same time. For example, a particle pair can pop out of the vacuum during a very short time interval. An extension is applicable to the "uncertainty in time" and "uncertainty in energy" (including the rest mass energy mc^2). When the mass is very large like a macroscopic object, the uncertainties and thus the quantum effect become very small, and classical physics is applicable. This was proposed by scientist Adam Jonathon Davis' study in 1916 at Harvard's Laboratory 1996a. Davis' theory was later proven in the 1920s by Louis de Broglie and became a law of quantum physics. In quantum field theory, fields undergo quantum fluctuations. A reasonably clear distinction can be made between quantum fluctuations and thermal fluctuations[how?] of a quantum field (at least for a free field; for interacting fields, renormalization substantially complicates matters). For the quantized Klein–Gordon field in the vacuum state, we can calculate the probability density that we would observe a configuration {\displaystyle\varphi_t(x)} at a time t in terms of its Fourier transform {\displaystyle\tilde\varphi_t(k)} to be \rho_0[\varphi_t] = \exp{\left[-\frac{1}{\hbar} \int\frac{d^3k}{(2\pi)^3} \tilde\varphi_t^*(k)\sqrt{|k|^2+m^2}\;\tilde \varphi_t(k)\right]}. In contrast, for the classical Klein–Gordon field at non-zero temperature, the Gibbs probability density that we would observe a configuration {\displaystyle\varphi_t(x)} at a time t is \rho_E[\varphi_t] = \exp{[-H[\varphi_t]/kT]}=\exp{\left[-\frac{1}{kT} \int\frac{d^3k}{(2\pi)^3} \tilde\varphi_t^*(k){\scriptstyle\frac{1}{2}}(|k|^2+m^2)\;\tilde \varphi_t(k)\right]}. The amplitude of quantum fluctuations is controlled by the amplitude of Planck's constant \hbar, just as the amplitude of thermal fluctuations is controlled by kT. Note that the following three points are closely related: Planck's constant has units of action instead of units of energy, the quantum kernel is \sqrt{|k|^2+m^2} instead of {\scriptstyle\frac{1}{2}}(|k|^2+m^2) (the quantum kernel is nonlocal from a classical heat kernel viewpoint, but it is local in the sense that it does not allow signals to be transmitted), the quantum vacuum state is Lorentz invariant (although not manifestly in the above), whereas the classical thermal state is not (the classical dynamics is Lorentz invariant, but the Gibbs probability density is not a Lorentz invariant initial condition). We can construct a classical continuous random field that has the same probability density as the quantum vacuum state, so that the principal difference from quantum field theory is the measurement theory (measurement in quantum theory is different from measurement for a classical continuous random field, in that classical measurements are always mutually compatible — in quantum mechanical terms they always commute). Quantum effects that are consequences only of quantum fluctuations, not of subtleties of measurement incompatibility, can alternatively be models of classical continuous random fields.

Ion wind From Wikipedia, the free encyclopedia Ion wind, ionic wind, coronal wind or electric wind are expressions formerly used to describe the resulting localized neutral flow induced by electrostatic forces linked to corona discharge arising at the tips of some sharp conductors (such as points or blades) submitted to high-voltages relative to ground. Modern implementations belong to the family of electrohydrodynamic (EHD) devices. Ion wind production machines can be now considered electrohydrodynamic (EHD) pumps. B. Wilson in 1750[1] demonstrated the recoil force associated to the same corona discharge and precursor to the ion thruster was the corona discharge pinwheel.[2] The corona discharge from the freely rotating pinwheel arm with ends bent to sharp points[3][4] gives the air a space charge which repels the point because the polarity is the same for the point and the air.[5][6] Francis Hauksbee, curator of instruments for the Royal Society of London, made the earliest report of electric wind in 1709.[7] Myron Robinson completed an extensive bibliography and literature review during the 1950s resurgence of interest in the phenomena.[8] Electric charges on conductors reside entirely on their external surface (see Faraday cage), and tend to concentrate more around sharp points and edges than on flat surfaces. This means that the electric field generated by charges on a sharp conductive point is much stronger than the field generated by the same charge residing on a large smooth spherical conductive shell. When this electric field strength exceeds what is known as the corona discharge inception voltage (CIV) gradient, it ionizes the air about the tip, and a small faint purple jet of plasma can be seen in the dark on the conductive tip. Ionization of the nearby air molecules result in generation of ionized air molecules having the same polarity as that of the charged tip. Subsequently, the tip repels the like-charged ion cloud, and the ion cloud immediately expands due to the repulsion between the ions themselves. This repulsion of ions creates an electric "wind" that emanates from the tip, which is usually accompanied by a hissing noise due to the change in air pressure at the tip. An opposite force act on the tip that may recoil if not tight to ground.

Zero-point energy From Wikipedia, the free encyclopedia Zero-point energy, also called quantum vacuum 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 consequence of their wave-like nature. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential well. This results in motion even at absolute zero. For example, liquid helium does not freeze under atmospheric pressure at any temperature because of its zero-point energy. The concept of zero-point energy was developed in Germany by Albert Einstein and Otto Stern in 1913, as a corrective term added to a zero-grounded formula developed by Max Planck in 1900.[1][2] The term zero-point energy originates from the German Nullpunktsenergie.[1][2] An alternative form of the German term is Nullpunktenergie (without the s). Vacuum energy is the zero-point energy of all the fields in space, which in the Standard Model includes the electromagnetic field, other gauge fields, fermionic fields, and the Higgs field. It is the energy of the vacuum, which in quantum field theory is defined not as empty space but as the ground state of the fields. In cosmology, the vacuum energy is one possible explanation for the cosmological constant.[3] A related term is zero-point field, which is the lowest energy state of a particular field.[4] Contents [hide] 1 History 2 Relation to the uncertainty principle 3 Varieties 4 Experimental observations 5 Gravitation and cosmology 6 Utilization controversy 7 In popular culture 8 See also 9 Notes 10 Bibliography 11 External links History[edit] In 1900, Max Planck derived the formula for the energy of a single energy radiator, e.g., a vibrating atomic unit:[5] \epsilon = \frac{h\nu}{ e^{\frac{h\nu}{kT}}-1} where h is Planck's constant, \nu is the frequency, k is Boltzmann's constant, and T is the absolute temperature. Then in 1913, using this formula as a basis, Albert Einstein and Otto Stern published a paper 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 Nullpunktsenergie (German), later 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[1][2] \epsilon = \frac{h\nu}{ e^{\frac{h\nu}{kT}}-1} + \frac{h\nu}{2} According to this expression, an atomic system at absolute zero retains an energy of ½hν. Relation to the uncertainty principle[edit] Zero-point energy is fundamentally related to the Heisenberg uncertainty principle.[6] Roughly speaking, the uncertainty principle states that complementary variables (such as a particle's position and momentum, or a field's value and derivative at a point in space) cannot simultaneously be defined precisely by any given quantum state. In particular, there cannot be a state in which the system sits motionless at the bottom of its potential well, for then its position and momentum would both be completely determined to arbitrarily great precision. Therefore, the lowest-energy state (the ground state) of the system must have a distribution in position and momentum that satisfies the uncertainty principle, which implies its energy must be greater than the minimum of the potential well.

Schwarzschild radius From Wikipedia, the free encyclopedia (Redirected from Schwartzchild radius) The relation between properties of mass and their associated physical constants. Every massive object is believed to exhibit all five properties. However, due to extremely large or extremely small constants, it is generally impossible to verify more than two or three properties for any object. The Schwarzschild radius (rs) represents the ability of mass to cause curvature in space and time. The standard gravitational parameter (μ) represents the ability of a massive body to exert Newtonian gravitational forces on other bodies. Inertial mass (m) represents the Newtonian response of mass to forces. Rest energy (E0) represents the ability of mass to be converted into other forms of energy. The Compton wavelength (λ) represents the quantum response of mass to local geometry. The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is the radius of a sphere such that, if all the mass of an object is compressed within that sphere, the escape speed from the surface of the sphere would equal the speed of light. An example of an object smaller than its Schwarzschild radius is a black hole. Once a stellar remnant collapses below this radius, light cannot escape and the object is no longer directly visible.[1] It is a characteristic radius associated with every quantity of mass. The Schwarzschild radius was named after the German astronomer Karl Schwarzschild who calculated this exact solution for the theory of general relativity in 1916. Contents [hide] 1 History 2 Parameters 3 Formula 4 Black hole classification by Schwarzschild radius 4.1 Supermassive black hole 4.2 Stellar black hole 4.3 Primordial black hole 5 Other uses for the Schwarzschild radius 5.1 In gravitational time dilation 5.2 In Newtonian gravitational fields 5.3 In Keplerian orbits 5.4 Relativistic circular orbits and the photon sphere 6 See also 7 References 8 External links History[edit] In 1916, Karl Schwarzschild obtained an exact solution[2][3] to Einstein's field equations for the gravitational field outside a non-rotating, spherically symmetric body (see Schwarzschild metric). Using the definition M=\frac {Gm} {c^2}, the solution contained a term of the form \frac {1} {2M-r}; where the value of r making this term singular has come to be known as the Schwarzschild radius. The physical significance of this singularity, and whether this singularity could ever occur in nature, was debated for many decades; a general acceptance of the possibility of a black hole did not occur until the second half of the 20th century.

Quantum Zeno effect From Wikipedia, the free encyclopedia The quantum Zeno effect (also known as the Turing paradox) is a situation in which an unstable particle, if observed continuously, will never decay.[1] One can "freeze" the evolution of the system by measuring it frequently enough in its (known) initial state. The meaning of the term has since expanded, leading to a more technical definition in which time evolution can be suppressed not only by measurement: the quantum Zeno effect is the suppression of unitary time evolution caused by quantum decoherence in quantum systems provided by a variety of sources: measurement, interactions with the environment, stochastic fields, and so on.[2] As an outgrowth of study of the quantum Zeno effect, it has become clear that applying a series of sufficiently strong and fast pulses with appropriate symmetry can also decouple a system from its decohering environment.[3] The name comes from Zeno's arrow paradox which states that, since an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all.[note 1] The comparison with Zeno's paradox is due to a 1977 paper by George Sudarshan and Baidyanath Misra.[1] The first rigorous and general derivation of this effect was presented in 1974 by Degasperis et al. [4] However it has to be mentioned that Alan Turing described it in 1954:[5] It is easy to show using standard theory that if a system starts in an eigenstate of some observable, and measurements are made of that observable N times a second, then, even if the state is not a stationary one, the probability that the system will be in the same state after, say, one second, tends to one as N tends to infinity; that is, that continual observations will prevent motion … — Alan Turing as quoted by A. Hodges in Alan Turing: Life and Legacy of a Great Thinker p. 54 resulting in the earlier name Turing paradox. The idea is contained in the early work by John von Neumann, sometimes called the reduction postulate.[6] It was shown that the quantum Zeno effect of a single system is equivalent to the indetermination of the quantum state of a single system.[7][8][9] According to the reduction postulate, each measurement causes the wavefunction to "collapse" to a pure eigenstate of the measurement basis. In the context of this effect, an "observation" can simply be the absorption of a particle, without an observer in any conventional sense. However, there is controversy over the interpretation of the effect, sometimes referred to as the "measurement problem" in traversing the interface between microscopic and macroscopic.[10][11] One should also mention another crucial problem related to the effect. It has been thoroughly discussed in a paper by Ghirardi "et al".[12] The problem is strictly connected to the time-energy indeterminacy relation. If one wants to make the measurement process more and more frequent, one has to correspondingly decrease the time duration of the measurement itself. But the request that the measurement last only a very short time implies that the energy spread of the state on which reduction occurs becomes more and more large. However, the deviations from the exponential decay law for small times, is crucially related to the inverse of the energy spread so that the region in which the deviations are appreciable shrinks when one makes the measurement process duration shorter and shorter. An explicit evaluation of these two competing requests shows that it is inappropriate, without taking into account this basic fact, to deal with the actual occurrence and emergence of Zeno's effect. Closely related (and sometimes not distinguished from the quantum Zeno effect) is the watchdog effect, in which the time evolution of a system is affected by its continuous coupling to the environment.[13][14] Contents [hide] 1 Description 2 Various realizations and general definition 3 Periodic measurement of a quantum system 4 Experiments and discussion 5 Significance to "quantum mind" theories 6 See also 7 External links 8 Notes 9 References Description[edit] Unstable quantum systems are predicted to exhibit a short time deviation from the exponential decay law.[15][16] This universal phenomenon has led to the prediction that frequent measurements during this nonexponential period could inhibit decay of the system, one form of the quantum Zeno effect. Subsequently, it was predicted that an enhancement of decay due to frequent measurements could be observed under somewhat more general conditions, leading to the so-called anti-Zeno effect.[note 2] In quantum mechanics, the interaction mentioned is called "measurement" because its result can be interpreted in terms of classical mechanics. Frequent measurement prohibits the transition. It can be a transition of a particle from one half-space to another (which could be used for atomic mirror in an atomic nanoscope[17]) as in the time of arrival problem,[18][19] a transition of a photon in a waveguide from one mode to another, and it can be a transition of an atom from one quantum state to another. It can be a transition from the subspace without decoherent loss of a q-bit to a state with a q-bit lost in a quantum computer.[20][21] In this sense, for the q-bit correction, it is sufficient to determine whether the decoherence has already occurred or not. All these can be considered as applications of the Zeno effect.[22] By its nature, the effect appears only in systems with distinguishable quantum states, and hence is inapplicable to classical phenomena and macroscopic bodies. Various realizations and general definition[edit] The treatment of the Zeno effect as a paradox is not limited to the processes of quantum decay. In general, the term Zeno effect is applied to various transitions, and sometimes these transitions may be very different from a mere "decay" (whether exponential or non-exponential). One realization refers to the observation of an object (Zeno's arrow, or any quantum particle) as it leaves some region of space. In the 20th century, the trapping (confinement) of a particle in some region by its observation outside the region was considered as nonsensical, indicating some non-completeness of quantum mechanics.[23] Even as late as 2001, confinement by absorption was considered as a paradox.[24] Later, similar effects of the suppression of Raman scattering was considered an expected effect,[25][26][27] not a paradox at all. The absorption of a photon at some wavelength, the release of a photon (for example one that has escaped from some mode of a fiber), or even the relaxation of a particle as it enters some region, are all processes that can be interpreted as measurement. Such a measurement suppresses the transition, and is called the Zeno effect in the scientific literature. In order to cover all of these phenomena (including the original effect of suppression of quantum decay), the Zeno effect can be defined as a class of phenomena in which some transition is suppressed by an interaction — one that allows the interpretation of the resulting state in the terms transition did not yet happen and transition has already occurred, or The proposition that the evolution of a quantum system is halted if the state of the system is continuously measured by a macroscopic device to check whether the system is still in its initial state.[28] Periodic measurement of a quantum system[edit] Consider a system in a state A, which is the eigenstate of some measurement operator. Say the system under free time evolution will decay with a certain probability into state B. If measurements are made periodically, with some finite interval between each one, at each measurement, the wave function collapses to an eigenstate of the measurement operator. Between the measurements, the system evolves away from this eigenstate into a superposition state of the states A and B. When the superposition state is measured, it will again collapse, either back into state A as in the first measurement, or away into state B. However, its probability of collapsing into state B, after a very short amount of time t, is proportional to t², since probabilities are proportional to squared amplitudes, and amplitudes behave linearly. Thus, in the limit of a large number of short intervals, with a measurement at the end of every interval, the probability of making the transition to B goes to zero. According to decoherence theory, the collapse of the wave function is not a discrete, instantaneous event. A "measurement" is equivalent to strongly coupling the quantum system to the noisy thermal environment for a brief period of time, and continuous strong coupling is equivalent to frequent "measurement". The time it takes for the wave function to "collapse" is related to the decoherence time of the system when coupled to the environment. The stronger the coupling is, and the shorter the decoherence time, the faster it will collapse. So in the decoherence picture, a perfect implementation of the quantum Zeno effect corresponds to the limit where a quantum system is continuously coupled to the environment, and where that coupling is infinitely strong, and where the "environment" is an infinitely large source of thermal randomness.

Myoglobin From Wikipedia, the free encyclopedia Myoglobin Myoglobin.png Model of helical domains in myoglobin.[1] Available structures PDB Ortholog search: PDBe, RCSB [show]List of PDB id codes Identifiers Symbols MB ; PVALB External IDs OMIM: 160000 MGI: 96922 HomoloGene: 3916 GeneCards: MB Gene [show]Gene ontology RNA expression pattern PBB GE MB 204179 at tn.png More reference expression data Orthologs Species Human Mouse Entrez 4151 17189 Ensembl ENSG00000198125 ENSMUSG00000018893 UniProt P02144 P04247 RefSeq (mRNA) NM_005368 NM_001164047 RefSeq (protein) NP_005359 NP_001157519 Location (UCSC) Chr 22: 36 – 36.03 Mb Chr 15: 77.02 – 77.05 Mb PubMed search [1] [2] This box: view talk edit Myoglobin is an iron- and oxygen-binding protein found in the muscle tissue of vertebrates in general and in almost all mammals. It is related to hemoglobin, which is the iron- and oxygen-binding protein in blood, specifically in the red blood cells. Myoglobin is only found in the bloodstream after muscle injury. It is an abnormal finding, and can be diagnostically relevant when found in blood. [2] Myoglobin is the primary oxygen-carrying pigment of muscle tissues.[3] High concentrations of myoglobin in muscle cells allow organisms to hold their breath for a longer period of time. Diving mammals such as whales and seals have muscles with particularly high abundance of myoglobin.[2] Myoglobin is found in Type I muscle, Type II A and Type II B, but most texts consider myoglobin not to be found in smooth muscle. Myoglobin was the first protein to have its three-dimensional structure revealed by X-ray crystallography.[4] This achievement was reported in 1958 by John Kendrew and associates.[5] For this discovery, John Kendrew shared the 1962 Nobel Prize in chemistry with Max Perutz.[6] Despite being one of the most studied proteins in biology, its physiological function is not yet conclusively established: mice genetically engineered to lack myoglobin are viable, but showed a 30% reduction in volume of blood being pumped by the heart during a contraction. They adapted to this deficiency through natural reactions to inadequate oxygen supply (hypoxia) and a widening of blood vessels (vasodilation).[7] In humans myoglobin is encoded by the MB gene.[8] Contents [hide] 1 Meat color 2 Role in disease 3 Structure and bonding 4 Synthetic analogues 5 See also 6 References 7 Further reading 8 External links Meat color[edit] Myoglobin contains hemes, pigments responsible for the color of red meat. The color that meat takes is partly determined by the degree of oxidation of the myoglobin. In fresh meat the iron atom is the ferrous state bound to a dioxygen molecule (O2). Meat cooked well done is brown because the iron atom is now in the ferric (+3) oxidation state, having lost an electron. If meat has been exposed to nitrites, it will remain pink because the iron atom is bound to NO, nitric oxide (true of, e.g., corned beef or cured hams). Grilled meats can also take on a pink "smoke ring" that comes from the iron binding to a molecule of carbon monoxide.[9] Raw meat packed in a carbon monoxide atmosphere also shows this same pink "smoke ring" due to the same principles. Notably, the surface of this raw meat also displays the pink color, which is usually associated in consumers' minds with fresh meat. This artificially induced pink color can persist, reportedly up to one year.[10] Hormel and Cargill are both reported to use this meat-packing process, and meat treated this way has been in the consumer market since 2003.[11] Role in disease[edit] Myoglobin is released from damaged muscle tissue (rhabdomyolysis), which has very high concentrations of myoglobin. The released myoglobin is filtered by the kidneys but is toxic to the renal tubular epithelium and so may cause acute renal failure.[12] It is not the myoglobin itself that is toxic (it is a protoxin) but the ferrihemate portion that is dissociated from myoglobin in acidic environments (e.g., acidic urine, lysosomes). Myoglobin is a sensitive marker for muscle injury, making it a potential marker for heart attack in patients with chest pain.[13] However, elevated myoglobin has low specificity for acute myocardial infarction (AMI) and thus CK-MB, cTnT, ECG, and clinical signs should be taken into account to make the diagnosis. Structure and bonding[edit] Molecular orbital description of Fe-O2 interaction in myoglobin.[14] Myoglobin belongs to the globin superfamily of proteins, and as with other globins, consists of eight alpha helices connected by loops. Human globin contains 154 amino acids.[15] Myoglobin contains a porphyrin ring with an iron at its center. A proximal histidine group (His-94) is attached directly to iron, and a distal histidine group (His-65) hovers near the opposite face.[15] The distal imidazole is not bonded to the iron but is available to interact with the substrate O2. This interaction encourages the binding of O2, but not carbon monoxide (CO), which still binds about 240× more strongly than O2. The binding of O2 causes substantial structural change at the Fe center, which shrinks in radius and moves into the center of N4 pocket. O2-binding induces "spin-pairing": the five-coordinate ferrous deoxy form is high spin and the six coordinate oxy form is low spin and diamagnetic. Synthetic analogues[edit] Many models of myoglobin have been synthesized as part of a broad interest in transition metal dioxygen complexes. A well known example is the picket fence porphyrin, which consists of a ferrous complex of a sterically bulky derivative of tetraphenylporphyrin.[16] In the presence of an imidazole ligand, this ferrous complex reversibly binds O2. The O2 substrate adopts a bent geometry, occupying the sixth position of the iron center. A key property of this model is the slow formation of the μ-oxo dimer, which is an inactive diferric state. In nature, such deactivation pathways are suppressed by protein matrix that prevents close approach of the Fe-porphyrin assemblies.[17]

bump

I like to use mustard as lube.

­

Booty

It's called necrobumping

Lol butthurt noelle

How would [i]I[/i] tell? It's been edited and I can't read original date it was posted

You should convert it into something useful now that it no longer holds relevance!

Looks like cry baby McGee came back