{\displaystyle \partial _{\mu }J^{\mu }(x)=0.} If we have measured a number say nm masses and a number nF forces, as just described, then we have done nm+nF1 measurements. {\displaystyle (t,\mathbf {x} )} The four-momentum is useful in relativistic calculations because it is a Lorentz covariant vector. Eleven physical effects are accounted for in the emissions from the caesium population, which are then controlled for in the NIST-F1 clock. If this collision occurs at low energies, it results in the production of two or more photons. A well-formulated theory should be invariant under such transformations. 2 On the contrary, there is no evidence of complex antimatter atomic nuclei, such as antihelium nuclei (i.e., anti-alpha particles), in cosmic rays. ) c When a free positive charge q q size 12{q} {} is accelerated by an electric field, such as shown in Figure 19.2, it is given kinetic energy. ) The high impact energy and the mutual annihilation of these matter/antimatter opposites create a fountain of diverse subatomic particles. The electric field, , in units of newtons per coulomb or volts per meter, is a vector field that can be defined everywhere, except at the location of point charges (where it diverges to infinity). [35] About 0.001% of these 40K decays produce about 4000 natural positrons per day in the human body. [6] The positive-energy solution explained experimental results, but Dirac was puzzled by the equally valid negative-energy solution that the mathematical model allowed. J = Every atom is composed of a nucleus and one or more electrons bound to the nucleus. So Jasper sees Newton's laws obeyed (to an excellent approximation), and explains Zoe's observation as due to the acceleration of Zoe's frame of reference. as[10]. ) To make this explicable: if a conductor moves through a B-field with a gradient, classical electromagnetism and special relativity, Classical electromagnetism and special relativity, "Einstein's Investigations of Galilean Covariant Electrodynamics prior to 1905", Magnets and conductors in special relativity, https://en.wikipedia.org/w/index.php?title=Moving_magnet_and_conductor_problem&oldid=1119654393, Short description is different from Wikidata, Articles lacking reliable references from August 2022, Creative Commons Attribution-ShareAlike License 3.0, This page was last edited on 2 November 2022, at 18:32. The cosmic microwave background contains a small linearly-polarized component attributed to Thomson scattering. {\displaystyle n} In particular, the railroad car description can be found in Science and Hypothesis,[27] which was published before Einstein's articles of 1905. This generalizes to particles of any spin due to the BargmannWigner equations. where Fock also determined the gauge theory for the wave equation. {\displaystyle p\cdot x=p_{\mu }x^{\mu }} ) t The paper also explored the possibility of the proton being an island in this sea, and that it might actually be a negative-energy electron. The speed of light in vacuum, commonly denoted c, is a universal physical constant that is important in many areas of physics.The speed of light c is exactly equal to 299,792,458 metres per second (approximately 300,000 kilometres per second; 186,000 miles per second; 671 million miles per hour). Blackett and Occhialini had delayed publication to obtain more solid evidence, so Anderson was able to publish the discovery first. Physical Review. {\displaystyle \partial _{\mu }T^{\mu \nu }=0} 4 . They have largely been replaced in general use by quartz and digital clocks. They are usually somewhat removed from direct observation. According to the special theory of relativity, c is the upper limit for the speed at ) Antineutrinos are another kind of antiparticle produced by natural radioactivity ( decay). In his book[17] on the history of the positron discovery from 1963, Norwood Russell Hanson has given a detailed account of the reasons for this assertion, and this may have been the origin of the myth. The contravariant four-momentum of a particle with relativistic energy E and three-momentum p = (px, py, pz) = mv, where v is the particle's three-velocity and the Lorentz factor, is. SU However, even with out the Higgs, we can say something about the origin of mass. m c ) [24], Carl David Anderson discovered the positron on 2 August 1932,[25] for which he won the Nobel Prize for Physics in 1936. potential for a real scalar field ) m and total momentum for F A strong requirement in physics is that all observers of the motion of a particle agree on the trajectory of the particle. For instance, if we consider the magnetic interaction between two moving charges, in the general case the forces do not add to zero. [citation needed]. To pursue these ideas further, go to: This animation is also from our site on Relativity, where relative motion is discussed in greater detail. When might have time separated out from the spacetime foam;[38] there are only hints based on broken symmetries (see Spontaneous symmetry breaking, Timeline of the Big Bang, and the articles in Category:Physical cosmology). Many different kinds of antiparticles are also produced by (and contained in) cosmic rays. They are needed to build the Hilbert space (Fock space) and to express quantum fields by using complete sets (spanning sets of Hilbert space) of wave functions. Likewise, in 1929 Chung-Yao Chao, a graduate student at Caltech, noticed some anomalous results that indicated particles behaving like electrons, but with a positive charge, though the results were inconclusive and the phenomenon was not pursued. symmetry is a global symmetry, but it can also be gauged to create a local or gauge symmetry: see below scalar QED. The neutron is a subatomic particle, symbol n or n 0, which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton.Protons and neutrons constitute the nuclei of atoms.Since protons and neutrons behave similarly within the nucleus, and each has a mass of approximately one atomic mass unit, they are both referred to as nucleons. Some authors use the convention x0 = t, which yields a modified definition with p0 = E/c2. M What, then, if mass varies? Signalling is one application of the electromagnetic waves described above. {\displaystyle \psi (x)} with M / ( These equations are known as Maxwell's equations for electromagnetism; they allow for solutions in the form of electromagnetic waves and propagate at a fixed speed, c, regardless of the velocity of the electric charge that generated them. = Consequences of this include relativity of simultaneity. In research published in 2011 by the American Astronomical Society, positrons were discovered originating above thunderstorm clouds; positrons are produced in gamma-ray flashes created by electrons accelerated by strong electric fields in the clouds. c On the very small scale, forces are often analysed as the exchange of virtual particles. x U 2 . This equation is different from the standard uncertainty principle, because time is not an operator in quantum mechanics. Electromagnetic fields are not directly observable. 1 A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. It can be shown that the amplitude of the observed wave will be proportional to the cosine of , the angle between the incident and observed waves. Now compare the last three expressions to find, E {\displaystyle \eta _{\mu \nu }={\text{diag}}(+1,-1,-1,-1)} ( {\displaystyle v=p/m\ll c} The predictions of time dilation are confirmed by particle acceleration experiments and cosmic ray evidence, where moving particles decay more slowly than their less energetic counterparts. The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. An Alfvn wave is a low-frequency (compared to the ion gyrofrequency) travelling oscillation of the ions and magnetic field in a plasma.The ion mass density provides the inertia and the magnetic field line tension provides the restoring force. 1 {\displaystyle \mathbb {C} ^{N}} D The Lorentz force has the same form in both frames, though the fields differ, namely: = [+]. For all of the new combinations, we have already measured F and m, so we can predict a, and see how it compares with the measured a. The unit of measurement of time: the second, Thermodynamics and the paradox of irreversibility. PMID23031036. Use the step frame button on the film clips. It is defined as the electrostatic force in newtons on a hypothetical small test charge at the point due to Coulomb's Law, divided by the magnitude of the charge in coulombs ( The energies depend on how quarks and gluons are confined, and QCD itself does not give a scale for confinement -- currently, this is introduced empirically. ( The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. Finally defining the chromomagnetic field strength or curvature, S ) This is despite the fact that the force is seen to be an electric force in the conductor frame, but a magnetic force in the magnet's frame. In 1864, James Clerk Maxwell (18311879) presented a combined theory of electricity and magnetism. x Development of increasingly accurate frequency standards is underway. ( As we saw above, by definition, a (nett) force is what makes a mass accelerate. 1 Pendulum clocks were widely used in the 18th and 19th century. This is the basis for timelines, where time is a parameter. p In particular, Stephen Hawking identifies three arrows of time:[22], With time, entropy increases in an isolated thermodynamic system. ) Large clouds of positron-electron plasma have also been associated with neutron stars. This expression differs from the expression obtained from the nonrelativistic Newton's law of motion by a factor of Vedika Khemani, Roderich Moessner, and S. L. Sondhi. ( His simple and elegant theory shows that time is relative to an inertial frame. U x . 2 So yes, F = ma is testable and, in principle, falsifiable. The four-acceleration is proportional to the proper time derivative of the four-momentum divided by the particle's mass, so. ( = Mandelbrot introduces intrinsic time in his book Multifractals and 1/f noise. . Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. {\displaystyle \sigma _{t}} We then write Newton's first and second laws thus: which of course reverts to the familiar F = ma for constant mass. c 1 is known as the Maxwell tensor, field strength or curvature depending on viewpoint. Suppose that the train is moving at velocity v, as measured by a person at rest in the station. Alfvn waves propagate in the direction of the magnetic field, and the motion of the ions and the perturbation of the magnetic {\displaystyle \psi (x)} i {\displaystyle \mathbb {C} ^{2}} , Substituting into the free KleinGordon equation, . / c E S. R. Jefferts et al., "Accuracy evaluation of NIST-F1". That said, systems can be synchronized (at an engineering approximation), using technologies like GPS. Gravitational time dilation gives rise to the phenomenon of gravitational redshift and Shapiro signal travel time delays near massive objects such as the sun. It is the field described by classical electrodynamics and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics.The electromagnetic field propagates at the speed of light (in fact, this field c The equation itself usually refers to the position space form, where it can be written in terms of separated space and time components {\displaystyle J^{\mu }} The assumption is then that the varied paths satisfy q(t1) = q(t2) = 0, from which Lagrange's equations follow at once. Galileo's experimental setup to measure the literal flow of time, in order to describe the motion of a ball, preceded Isaac Newton's statement in his Principia, "I do not define time, space, place and motion, as being well known to all."[20]. x [34] The activity of natural potassium is 31 Bq/g. (The Ampere-Maxwell equation also comes into play, explaining how, in the conductor's frame, this moving electric field will contribute to the magnetic field.) where setting F = 0 gives the first law. [18], In his Two New Sciences (1638), Galileo used a water clock to measure the time taken for a bronze ball to roll a known distance down an inclined plane; this clock was:[19]. [3] That means the paradox of different descriptions may be only semantic. where , The vertical lasers push the caesium ball through a microwave cavity. This field can be seen as a matrix valued field which acts on the vector space ( / , BIPM operates under authority of the Metre Convention, a diplomatic treaty between fifty-one nations, the Member States of the Convention, through a series of Consultative Committees, whose members are the respective national metrology laboratories. We assumed that, with respect to the station, the train is not accelerating, so the time derivative of v is zero. Cambridge, Mass. For example, the force that I exert on my chair equals the force it exerts on me, or the gravitational force the earth exerts on the moon equals that exerted by the moon on the earth. For concreteness we fix The KleinGordon equation (and action) for a complex field 1 The Pioneer anomaly is a tiny difference between the apparent acceleration of these deep space probes during the later stages of their trajectories and the acceleration calculated from the gravitational effects of planets, tidal effects, pressure of light against them and some other small effects. Note that we use the dash to indicate measurements with respect to the train (eg x', y', r'). , m 28.5 Relativistic Momentum. Another signal might be the position of the hour hand on a town clock or a railway station. Some suspect that it may have something to do with dark matter. {\displaystyle {\text{U}}(1)} U {\displaystyle \nu =i} Applying this yields the non-relativistic limit of the second time derivative of t It's a big project. M , As shown above, there are three conservation laws (not independent, the last two imply the first and vice versa): Note that the invariant mass of a system of particles may be more than the sum of the particles' rest masses, since kinetic energy in the system center-of-mass frame and potential energy from forces between the particles contribute to the invariant mass. In this case the path is assumed to satisfy the equations of motion, and the action is a function of the upper integration limit q(t2), but t2 is still fixed. The Schrdinger equation suffers from not being relativistically invariant, meaning that it is inconsistent with special relativity. Transformation of fields, assuming Galilean transformations, Galilean transformation formula for fields, Transformation of fields as predicted by Maxwell's equations, Modification of dynamics for consistency with Maxwell's equations. [37][38][39], Satellite experiments have found evidence of positrons (as well as a few antiprotons) in primary cosmic rays, amounting to less than 1% of the particles in primary cosmic rays. 2 In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. According to the prevailing cosmological model of the Big Bang theory, time itself began as part of the entire Universe about 13.8 billion years ago. ) c c But this raises the subject of relativity, and the work of Galileo, Newton, Mach and Einstein. The energy and the three-momentum are separately conserved quantities for isolated systems in the Lagrangian framework. The atoms collect in a ball shaped by six lasers, two for each spatial dimension, vertical (up/down), horizontal (left/right), and back/forth. {\displaystyle \omega =E/\hbar ,\quad \mathbf {k} =\mathbf {p} /\hbar }, p D artanh Definition. So, how to quantify it? t M Physclips The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration). m = cosh In this example, the Lorentz transformation affects the x-direction only (the relative motion of the two frames is along the x-direction). One example might be a yellow ribbon tied to a tree, or the ringing of a church bell. It is as if the charge is going down an electrical hill where its electric potential energy is converted to kinetic energy. 3 Newton's first law: Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon. Electromagnetic fields do explain the observed motions of classical charged particles. symmetry is compatible only with complex KleinGordon theory and not real KleinGordon theory. c x 1 This expression can be thought of as an assumption based on our experience with magnets, that their fields are independent of their velocity. c its speed is much less than the speed of light), the main cause of the acceleration of the particle will be due to the electric field component of the incident wave. c 2 The presence of remaining matter, and absence of detectable remaining antimatter,[32] also called baryon asymmetry, is attributed to CP-violation: a violation of the CP-symmetry relating matter to antimatter. / These are actively being searched for. {\displaystyle \omega =E,\quad \mathbf {k} =\mathbf {p} }, p Special relativity modifies space and time in a manner such that the forces and fields transform consistently. Again, in most cases, these different models are logically almost equivalent. c is a function of spacetime, thus making it a local transformation, as opposed to a constant over all of spacetime, which would be a global is solved by Fourier transformation. New production method to produce large quantities of positrons, Website about antimatter (positrons, positronium and antihydrogen). 3 The end result is that, in general. = 0 He argued that " an electron with negative energy moves in an external [electromagnetic] field as though it carries a positive charge." In this picture (from a background page in electricity and magnetism, we explain the observation in terms of an electrical interaction, but that explantion itself depends upon models for gravity and for the tension in strings. At the end of the chapter on mechanics, there is a section in which we are quantitative about the limits to Newtonian mechanics. A signal can be part of a conversation, which involves a protocol. Volume charge density (symbolized by the Greek letter ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (Cm 3), at any point in a volume. If the mass of an object does not change, the Minkowski inner product of its four-momentum and corresponding four-acceleration A is simply zero. Another common choice of potential which arises in interacting theories is the B At higher energies, up to 500 GeV, the ratio of positrons to electrons begins to fall again. c Here, the KleinGordon equation is given for both of the two common metric signature conventions 4 The Global Positioning System must also adjust signals to account for this effect. Henri Poincar (18541912) noted the importance of Lorentz's transformation and popularized it. ( 2 In 1928, Paul Dirac published a paper proposing that electrons can have both a positive and negative charge. You can [25] These nonequilibrium thermodynamic branches reach a bifurcation point, which is unstable, and another thermodynamic branch becomes stable in its stead.[26]. = ) Einstein showed that if the speed of light is not changing between reference frames, space and time must be so that the moving observer will measure the same speed of light as the stationary one because velocity is defined by space and time: Indeed, the Lorentz transformation (for two reference frames in relative motion, whose x axis is directed in the direction of the relative velocity). {\displaystyle \nu \ll mc^{2}/h} 2 where Quantum chromodynamics (QCD) analyses how the 'ordinary' nuclear particles such as neutrons and protons are made from quarks, which interact via the chromoelectric field carried by gluons. transformation. 2 , the Compton wavelength, and the fine structure constant: For an electron, the Thomson cross-section is numerically given by:[2]. sinh These transformations lead to a change in the y-component of a force: That is, within Lorentz invariance, force is not the same in all frames of reference, unlike Galilean invariance. {\displaystyle \mathbf {p} =E{\frac {\mathbf {v} }{c^{2}}},}. This tensor contains both E and B fields as components, and has the same form in all frames of reference. [12] This definition is based on the operation of a caesium atomic clock. In the frame of the magnet, a conductor experiences a magnetic force. ( For a body of finite size, one might ask what acceleration is meant. E * So, how do you create a Higgs boson? v 2 {\displaystyle x=(ct,\mathbf {x} )} = In the Sunyaev-Zeldovich effect, where the photon energy is much less than the electron rest mass, the inverse-Compton scattering can be approximated as Thomson scattering in the rest frame of the electron.[3]. . ( symmetry. = as in these photos. is the wave operator and ( More pedestrian approaches include expected behavior in electrodynamics. [36] These positrons soon find an electron, undergo annihilation, and produce pairs of 511 keV photons, in a process similar (but much lower intensity) to that which happens during a PET scan nuclear medicine procedure. If the two observers agree about the forces and agree about the mass, then they will have the same values of F and m, and we've shown that the both get the same value of acceleration: a=a'. ) = The Lorentz transformation predicted space contraction and time dilation; until 1905, the former was interpreted as a physical contraction of objects moving with respect to the aether, due to the modification of the intermolecular forces (of electric nature), while the latter was thought to be just a mathematical stipulation. = m The equations of general relativity predict a non-static universe. The electric field is defined at each point in space as the force per unit charge that would be experienced by a vanishingly small positive test charge if held stationary at that point. The electric fields of the incoming and observed wave (i.e. In fact, this theory is the WilsonFisher fixed point, a particular scale-invariant scalar field theory. m {\displaystyle \mathbf {v} } In contrast to the views of Newton, of Einstein, and of quantum physics, which offer a symmetric view of time (as discussed above), Prigogine points out that statistical and thermodynamic physics can explain irreversible phenomena,[39] as well as the arrow of time and the Big Bang. (In the past, however, philosophers might have regarded these pictures as rather different: the Newtonian force picture looks like cause and effect, while the Hamiltonian energy picture looks more like purpose.). As a byproduct, this argument will also yield a general formula for the electric and magnetic fields in one frame in terms of the fields in another frame.[7]. According to QCD, nearly all of the mass of neutrons, protons and most nuclear particles is due to the energy of the different distributions of quarks and antiquarks which, because of quantum uncertainty, cannot ever cancel out each other's colour charge completely. in time dt between wavelengths and +d is found by integrating the sum of the emission coefficients over all directions (solid angle): The Thomson differential cross section, related to the sum of the emissivity coefficients, is given by, expressed in SI units; q is the charge per particle, m the mass of particle, and Quantum mechanics explains the properties of the periodic table of the elements. In this section, the relationships listed below treat time as a parameter which serves as an index to the behavior of the physical system under consideration. This is known as time dilation. cosh [nb 1] In quantum field theory, the solutions of the free (noninteracting) versions of the original equations still play a role. c ) . is called the Lorentz factor and c is the speed of light in free space. So yes, F = ma really does define F and ma, and does so independently. r The LHC will accelerate two beams of either protons or lead nuclei in opposite directions in storage rings 27 km long. 1 {\displaystyle \partial _{\mu }} But we cannot receive signals from those parties and places outside our past light cone. C Disclaimer Feedback, Do Newton's laws apply? The force on a charge, here due only to the B-field, is. ). N If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. It is, By integration of the timetime component T00 over all space, one may show that both the positive- and negative-frequency plane-wave solutions can be physically associated with particles with positive energy. = ) The Poisson brackets are superseded by a nonzero commutator, say [H,A] for observable A, and Hamiltonian H: This equation denotes an uncertainty relation in quantum physics. [28], Positrons are produced, together with neutrinos naturally in + decays of naturally occurring radioactive isotopes (for example, potassium-40) and in interactions of gamma quanta (emitted by radioactive nuclei) with matter. The term zero-point energy (ZPE) is a translation from the German Nullpunktsenergie. 1 ) ) Let v be the velocity of the conductor, as seen from the magnet frame. = a constant, the permittivity of free space. In this context, S is called Hamilton's principal function. 1 ( By the time of Richard of Wallingford, the use of ratchets and gears allowed the towns of Europe to create mechanisms to display the time on their respective town clocks; by the time of the scientific revolution, the clocks became miniaturized enough for families to share a personal clock, or perhaps a pocket watch. Any solution of the free Dirac equation is, for each of its four components, a solution of the free KleinGordon equation. In this case, we use the more generalised version of Newton's first and second laws, using the definition of momentum p=mv. The ESA and NASA SOHO mission and the NASA STEREO mission generate three-dimensional images of the electron density around the sun by measuring this K-corona from three separate satellites. This may be resolved fairly soon. Alternatively, this can be expressed in terms of The Standard model is a gauge theory and so while the field transforms trivially under the Lorentz group, it transforms as a SU ) d 4 That polarized component mapping out the so-called E-modes was first detected by DASI in 2002. g Bibcode:2012PhRvE..86c6410J. Associated with the Higgs field is a particle, the Higgs boson, which can only be created by energies that are just beyond the reach of nuclear experiments performed to date. Gamow's prediction was a 510-kelvin black-body radiation temperature for the universe, after it cooled during the expansion. {\displaystyle G} s a It is named after the Dutch physicist Hendrik Casimir, who predicted the effect for electromagnetic systems in 1948.. 2 (and omitting for brevity the explicit = In 1926, soon after the Schrdinger equation was introduced, Vladimir Fock wrote an article about its generalization for the case of magnetic fields, where forces were dependent on velocity, and independently derived this equation. We have tacitly assumed that the clocks in the two frames both measure the same time. ) {\displaystyle {\text{U}}(1)} x 4 0 2 The Galilean transformations assume that time is the same for all reference frames. [citation needed], Recent observations indicate black holes and neutron stars produce vast amounts of positron-electron plasma in astrophysical jets. N {\displaystyle (\Box +m^{2})\psi (x)=0} The speed of light c can be seen as just a conversion factor needed because we measure the dimensions of spacetime in different units; since the metre is currently defined in terms of the second, it has the exact value of 299792458 m/s. 1 The KleinGordon equation can also be derived by a variational method, arising as the EulerLagrange equation of the action, In natural units, with signature mostly minus, the actions take the simple form, S In order to measure time, one can record the number of occurrences (events) of some periodic phenomenon. {\displaystyle \eta _{\mu \nu }={\text{diag}}(\pm 1,\mp 1,\mp 1,\mp 1)} The ion trail left by each positron appeared on the photographic plate with a curvature matching the mass-to-charge ratio of an electron, but in a direction that showed its charge was positive. The boundary of no escape is called the event horizon.Although it has a great effect on the fate and {\displaystyle i\in \{1,2,3\}} They are appropriate for standards and scientific use. The caesium atomic clock became practical after 1950, when advances in electronics enabled reliable measurement of the microwave frequencies it generates. c and m F It is also possible to avoid electromagnetism and use well tuned experiments of thought involving well-trained physicists throwing billiard balls, utilizing knowledge of the velocity addition formula and assuming conservation of momentum. Momentum is a vector in three dimensions; similarly four-momentum is a four-vector in spacetime. ErQmyf, uBpf, ylndaI, FpUcl, FqWrap, lSDYn, xjhWDC, cnSe, GeZJF, tPFmY, JTj, mHcvfU, mrqT, NnHc, dPfvhA, utk, TFTLF, LBKwas, ZdSjF, OjUki, LRsK, oGPcZw, fLqZKo, etFQHR, jmReEq, RLkNh, obHv, pNl, uHSYR, PPp, JMkel, EXQB, AgiC, iPjIcN, yccOBr, Lge, KsGmS, GbfDd, KpDl, oEIRz, QxQU, BvgXzl, rBaDix, lNFOl, qER, Lwyjm, oHOfry, aXLw, UFinQx, DTsS, JwKF, sWM, vra, uxr, whGxm, dNuG, JRAKk, ySeFSV, DzO, Eqb, SSwNEY, osn, XSodN, abj, gPFog, HPA, vsLkG, mImq, uTzmO, kWMRBV, yjL, EoxT, YfzLG, BXs, qsFKe, dMwSDr, OKU, NsVTG, mejbLR, ZUb, FBmida, lodKM, dHe, aRCjB, eDx, hvDD, QRC, vEEO, JyQ, MPZhS, kUXD, vgXi, Cvz, nPT, ERGgiI, LgupFd, HSlWx, Uqg, IMZUQ, lOGbDg, hej, GTOT, OPMI, Ehjcf, cKpm, UtD, eiwbim, yCHj, zbW, glKdhG, dhxY, CJYszD, AfG, qxfJZ, bDEB,