) To simplify, let the magnetic field point in the z-direction and vary with location x, and let the conductor translate in the positive x-direction with velocity v. Consequently, in the magnet frame where the conductor is moving, the Lorentz force points in the negative y-direction, perpendicular to both the velocity, and the B-field. {\displaystyle x} , ) {\displaystyle E'\ll mc^{2}} Sometimes forces are modelled as action at a distance and sometimes via fields (the two are logically almost equivalent). The Schrdinger equation[30] is. [35] About 0.001% of these 40K decays produce about 4000 natural positrons per day in the human body. c However, even with out the Higgs, we can say something about the origin of mass. This dramatic result has raised issues: what happened between the singularity of the Big Bang and the Planck time, which, after all, is the smallest observable time. The equation itself usually refers to the position space form, where it can be written in terms of separated space and time components which can be viewed as a generalization of the C As a general rule, forces are less helpful as a model on the very small scale, in part because position, velocity and acceleration become poorly defined in that scale. This operator is called the wave operator. 2 Now compare the last three expressions to find, E The equations of general relativity predict a non-static universe. As an example, two particles with four-momenta (5 GeV/c, 4 GeV/c, 0, 0) and (5 GeV/c, 4 GeV/c, 0, 0) each have (rest) mass 3GeV/c2 separately, but their total mass (the system mass) is 10GeV/c2. is the density of charged particles at the scattering point, Note that because the initial Fourier transformation contained Lorentz invariant quantities like 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. For instance, if one observer notes that a particle collides with the center of a bullseye, then all observers must reach the same conclusion. = A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. We will not do so here, but simply verify that this current is conserved. S. R. Jefferts et al., "Accuracy evaluation of NIST-F1". 1 [32], See dynamical systems and chaos theory, dissipative structures. ( 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.. In general, a signal is part of communication between parties and places. t Integrating over the solid angle, we obtain the Thomson cross section, The important feature is that the cross section is independent of photon frequency. the scalar field = . sin 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 From the point of view of an observer, there are two emission coefficients, r corresponding to radially polarized light and t corresponding to tangentially polarized light. [citation needed], The ALPHA experiment combines positrons with antiprotons to study properties of antihydrogen. y {\displaystyle D_{\mu }} 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. {\displaystyle S=\int _{M}d^{4}x\,{\sqrt {-g}}\left(-{\frac {1}{2}}g^{ab}\nabla _{a}\Phi \nabla _{b}\Phi -{\frac {1}{2}}m^{2}\Phi ^{2}\right)}, S dependence), Subtracting the former from the latter, we obtain, Applying this to the derivative of the current Watson, E (1979) "The St Albans Clock of Richard of Wallingford". Here, the KleinGordon equation is given for both of the two common metric signature conventions This is commonly taken as a general solution to the KleinGordon equation. Its development began in the 1920s with the description of interactions between light and electrons, culminating in the first quantum field theoryquantum electrodynamics.A major theoretical obstacle soon followed with the appearance and = So the force on the charge is not the same in both frames, but it transforms as expected according to relativity. Electromagnetic fields are not directly observable. {\displaystyle c} 4 The relations connecting time and space are ( primes denote the moving conductor frame ):[11]. 1 2 {\displaystyle \eta ^{\mu \nu }{\frac {\partial S}{\partial x^{\mu }}}{\frac {\partial S}{\partial x^{\nu }}}=-m^{2}c^{2}. It has been asserted that time is an implicit consequence of chaos (i.e. The end result is that, in general. The quantity mv of above is ordinary non-relativistic momentum of the particle and m its rest mass.The four-momentum is useful in relativistic calculations because it is a Lorentz covariant vector. v ) A d Let the origin fixed in the train have position p, as measured from the station in the x,y frame. ( The electric force between charged bodies at rest is conventionally called electrostatic force or Coulomb force. The observable quantity in the experiment, the current, is the same in either case, in accordance with the basic principle of relativity, which states: "Only relative motion is observable; there is no absolute standard of rest". Physclips The force on a charge, here due only to the B-field, is. The Lorentz force has the same form in both frames, though the fields differ, namely: = [+]. To calculate ds, observe first that ds2 = 2dsds and that, where the second step employs the field equations du/ds = 0, (x)t1 = 0, and (x)t2 x as in the observations above. For a charged particle of charge q, moving in an electromagnetic field given by the electromagnetic four-potential: This, in turn, allows the potential energy from the charged particle in an electrostatic potential and the Lorentz force on the charged particle moving in a magnetic field to be incorporated in a compact way, in relativistic quantum mechanics. F Consequences of this include relativity of simultaneity. Although it turned out that modeling the electron's spin required the Dirac equation, the KleinGordon equation correctly describes the spinless relativistic composite particles, like the pion. m These caveats made, however, we note that, on the macroscopic scale and over the vast range of practical energies and forces, Newton's laws work spectacularly well and are the foundation of a large fraction of physics and engineering. Hermann Weyl then published a paper discussing the mathematical implications of the negative energy solution. The tabulation of the equinoxes, the sandglass, and the water clock became more and more accurate, and finally reliable. A The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. {\displaystyle (\Box +m^{2})\psi (x)=0} x So a frame of reference moving at uniform velocity with respect to an inertial frame is also an inertial frame. ( v ( Of course that doesn't tell us what energy is. The absolute flux of positrons also begins to fall before 500 GeV, but peaks at energies far higher than electron energies, which peak about 10 GeV. 28.5 Relativistic Momentum. So yes, F = ma is testable and, in principle, falsifiable. {\displaystyle {\text{SU}}(2)} [24], Carl David Anderson discovered the positron on 2 August 1932,[25] for which he won the Nobel Prize for Physics in 1936. 3 The Schrdinger equation suffers from not being relativistically invariant, meaning that it is inconsistent with special relativity. That is, under the transformations, the KleinGordon equation is invariant, as is the action (see below). The film clips below use a spring to accelerate a bowling ball. x Since an ungauged For the time-independent case, the KleinGordon equation becomes. Multiplying by the left respectively by diag m Using abstract index notation and in mostly plus signature this is, S The latest Lifestyle | Daily Life news, tips, opinion and advice from The Sydney Morning Herald covering life and relationships, beauty, fashion, health & wellbeing [1] In classical, non-relativistic physics, it is a scalar quantity (often denoted by the symbol In particular, all observers must see the same speed of light c. That requirement leads to the Lorentz transformation for space and time. k This time, the system is allowed to move through configuration space at "arbitrary speed" or with "more or less energy", the field equations still assumed to hold and variation can be carried out on the integral, but instead observe. What, then, if mass varies? = Dirac acknowledged that the proton having a much greater mass than the electron was a problem, but expressed "hope" that a future theory would resolve the issue. {\displaystyle {\text{U}}(1)} x Note that we use the dash to indicate measurements with respect to the train (eg x', y', r'). [6] The positive-energy solution explained experimental results, but Dirac was puzzled by the equally valid negative-energy solution that the mathematical model allowed. In very {\displaystyle \lambda _{c}} [nb 1] In quantum field theory, the solutions of the free (noninteracting) versions of the original equations still play a role. This observation is an important one in the theory of spontaneous symmetry breaking in the Standard model. , v g In other words, the two observers would obtain the same value for the acceleration of the ball. This tells us that the electric charge (which is the coupling parameter in the theory) increases with increasing 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. M The name of gauge symmetry is somewhat misleading: it is really a redundancy, while the global symmetry is a genuine symmetry. 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. Saying this is just a rearrangement of Einstein's famous equation E=mc2. {\displaystyle \omega =E,\quad \mathbf {k} =\mathbf {p} }, p , written in covariant notation and mostly plus signature. {\displaystyle x=(ct,\mathbf {x} )} Quantum mechanics explains the properties of the periodic table of the elements. Any solution of the free Dirac equation is, for each of its four components, a solution of the free KleinGordon equation. We could, if we wished, choose one of these objects as our standard mass, in which case we now know the masses of each object. / In this case, a is the acceleration of its centre of mass. part of the gauge group. {\displaystyle M} It is known that Maxwell's electrodynamics as usually understood at the present time when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. In the International System of Units (SI), the Special relativity revised the transformation of forces in moving reference frames to be consistent with Lorentz invariance. In the frame of the magnet, a conductor experiences a magnetic force. Newton's law of motion, however, had to be modified to provide consistent particle trajectories. ) V In this frame, there is an electric field, and its curl is given by the Maxwell-Faraday equation: A charge q in the conductor will be at rest in the conductor frame. {\displaystyle \partial _{\mu }} and total momentum for is taken to be a constant function. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise assuming equality of relative motion in the two cases discussed to electric currents of the same path and intensity as those produced by the electric forces in the former case. x Graphene (/ r f i n /) is an allotrope of carbon consisting of a single layer of atoms arranged in a two-dimensional honeycomb lattice nanostructure. In this view time is a coordinate. The concept of force is a useful way of quantifying how an object interacts mechanically with its environment and vice versa and it is introduced for that reason. One way is to first define the four-velocity u = dx/d and simply define p = mu, being content that it is a four-vector with the correct units and correct behavior. ) 2 artanh 1 Analogous observations are made concerning the other forces. Here, 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. -factor into the coefficients At the time of Einstein in 1905, the field equations as represented by Maxwell's equations were properly consistent. , with the metric signature x ) You can a For ships at sea, boys were used to turn the sandglasses and to call the hours. This tensor contains both E and B fields as components, and has the same form in all frames of reference. Charles Hose and William McDougall (1912). SU {\displaystyle {\frac {E^{2}}{c^{2}}}=\mathbf {p} \cdot \mathbf {p} +m^{2}c^{2}. x c Perhaps this scale comes from the Higgs field interaction too. 1 ( + M [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. [51], Gamma rays, emitted indirectly by a positron-emitting radionuclide (tracer), are detected in positron emission tomography (PET) scanners used in hospitals. "2018 CODATA Value: electron mass energy equivalent in MeV", "Quantised Singularities in the Quantum Field", "The Use of the Proper Time in Quantum Electrodynamics I", "The Production and Properties of Positrons", "Irne Jolit-Curie, a Nobel laureate in artificial radioactivity", "Atop the Physics Wave: Rutherford Back in Cambridge, 19191937", "Antimatter caught streaming from thunderstorms on Earth", "The Discovery of Geomagnetically Trapped Cosmic-Ray Antiprotons", "Antimatter Found Orbiting EarthA First", "Riddle of matter remains unsolved: Proton and antiproton share fundamental properties", "Radiation and Radioactive Decay. Corresponding commutator relations also hold for momentum p and position q, which are conjugate variables of each other, along with a corresponding uncertainty principle in momentum and position, similar to the energy and time relation above. [5] An alternative unification of descriptions is to think of the physical entity as the electromagnetic field tensor, as described later on. ) 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. c In the frame of a conductor moving relative to the magnet, the conductor experiences a force due to an electric field. d [26] Anderson did not coin the term positron, but allowed it at the suggestion of the Physical Review journal editor to whom he submitted his discovery paper in late 1932. X-ray crystallography is based on Thomson scattering. Nevertheless, it will be a Galilean transformation to a very good approximation, at velocities much less than the speed of light. . [23] Ilya Prigogine (19172003) stated that other thermodynamic systems which, like life, are also far from equilibrium, can also exhibit stable spatio-temporal structures that reminisce life. v The LHC will accelerate two beams of either protons or lead nuclei in opposite directions in storage rings 27 km long. where If this theory turns out to be correct, then it will explain the mass of the electron but only a small fraction of the mass of the neutron and proton (which are a couple of thousand times more massive than the electron). Atomic clocks can theoretically keep accurate time for millions of years. 2 0 That the proportionality is not a coincidence is Mach's Principle. = H + This thought experiment was devised by physicist Erwin Under a gauge transformation , We assumed that, with respect to the station, the train is not accelerating, so the time derivative of v is zero. ) Can you see what they are in this case? = This field can be seen as a matrix valued field which acts on the vector space T If you did not notice this assumption, you are in good company -- it was largely unnoticed between the times of Newton and Einstein. m ( 1 4 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]. PMID23031036. = 2 Fermi and others noted that this process would have stopped after only the light elements were created, and thus did not account for the abundance of heavier elements. This means that it is easy to keep track of how it transforms under Lorentz transformations. {\displaystyle I} g p 4 [9] Persuaded by Oppenheimer's and Weyl's argument, Dirac published a paper in 1931 that predicted the existence of an as-yet-unobserved particle that he called an "anti-electron" that would have the same mass and the opposite charge as an electron and that would mutually annihilate upon contact with an electron. This Sometimes we can feel forces: we can feel, almost directly, contact forces against our feet or against our bums on chairs. At relativistic velocities, or in the presence of an electric field in the magnet frame, this equation would not be correct. They are usually somewhat removed from direct observation. The smallest time step considered theoretically observable is called the Planck time, which is approximately 5.3911044 seconds - many orders of magnitude below the resolution of current time standards. x where setting F = 0 gives the first law. i 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. = 1 Hence four-momentum is conserved as well. Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. over space is a conserved quantity for each p Here, the KleinGordon equation in natural units, ( E S2CID10413904. v The KleinGordon equation can be generalized to describe a field in some potential 3 c The scattering is best described by an emission coefficient which is defined as where dt dV d d is the energy scattered by a volume element Physclips has a module on energy, but there we relate it to forces, so, while I think that the module does tell a lot about energy, you might justifiably accuse me of circular reasoning if I claimed that this settled the matter. V ( / . ) Including sometimes, it is hoped, the elusive (and massive) Higgs. Philosophiae Naturalis Principia Mathematica, The Mathematical Principles of Natural Philosophy, "Exploring Black Holes: Introduction to General Relativity", Slashdot (25 Oct 2021) An Ultra-Precise Clock Shows How To Link the Quantum World With Gravity, (23 Oct 2019) A Brief History of Time Crystals, International Earth Rotation and Reference Systems Service, https://en.wikipedia.org/w/index.php?title=Time_in_physics&oldid=1125672502, Articles with unsourced statements from May 2008, Creative Commons Attribution-ShareAlike License 3.0, the position on the horizon of the first appearance of the sun at dawn. Disclaimer Feedback, Do Newton's laws apply? are often seen to clutter the equations, so they are therefore often expressed in natural units where = , F Some readers may be helping here: if you pay taxes in Europe, then you are helping fund the Large Hadron Collider and thus the search for the Higgs boson. Rewriting the first two terms using the inverse of the Minkowski metric diag(c2, 1, 1, 1), and writing the Einstein summation convention explicitly we get, Thus the KleinGordon equation can be written in a covariant notation. p For full reconciliation of quantum mechanics with special relativity, quantum field theory is needed, in which the KleinGordon equation reemerges as the equation obeyed by the components of all free quantum fields. 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. 2 It is possible to extend this to a non-abelian gauge theory with a gauge group Timekeeping is a complex of technological and scientific issues, and part of the foundation of recordkeeping. Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. As the ball is cooled, the caesium population cools to its ground state and emits light at its natural frequency, stated in the definition of second above. while in the conductor frame where the magnet is moving, the force is also in the negative y-direction, and now due only to the E-field with a value: The two forces differ by the Lorentz factor . This result is a consequence of requiring that observers in all inertial frames arrive at the same form for Maxwell's equations. M It also places constraints on the manner in which fields affect the acceleration and, hence, the trajectories of charged particles. r ( {\displaystyle G} In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. A strong requirement in physics is that all observers of the motion of a particle agree on the trajectory of the particle. This phenomenon is also referred to as the principle of maximal aging, and was described by Taylor and Wheeler as:[29]. ) ) ) It is second-order in space and time and manifestly Lorentz-covariant. More generally, for any two four-momenta p and q, the quantity p q is invariant. The paper did not explicitly predict a new particle but did allow for electrons having either positive or negative energy as solutions. ) Or, in general, for bodies 1 and 2, and for any interaction between them. It is natural to try to use the identity from special relativity describing the energy: Then, just inserting the quantum-mechanical operators for momentum and energy yields the equation. 2 PET scanners create detailed three-dimensional images of metabolic activity within the human body. , {\displaystyle p=(E/c,\mathbf {p} )}. is the Laplace operator. We would need a similar factor in Euclidean space if, for example, we measured width in nautical miles and depth in feet. E This often means an abbreviation in the form of. The respective clock uncertainty declined from 10,000 nanoseconds per day to 0.5 nanoseconds per day in 5 decades. An electromagnetic field (also EM field or EMF) is a classical (i.e. By Fourier transforming the field into momentum space, the solution is usually written in terms of a superposition of plane waves whose energy and momentum obey the energy-momentum dispersion relation from special relativity. ( 2 or by combining them into a four-vector So yes, F = ma really does define F and ma, and does so independently. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. = Consistency is an issue because Newtonian mechanics predicts one transformation (so-called Galilean invariance) for the forces that drive the charges and cause the current, while electrodynamics as expressed by Maxwell's equations predicts that the fields that give rise to these forces transform differently (according to Lorentz invariance). The equation is found in his notebooks from late 1925, and he appears to have prepared a manuscript applying it to the hydrogen atom. ) {\displaystyle \psi } 0 It is a vector quantity, possessing a magnitude and a direction. b : Radioactive Human Body", "Electron-positron Jets Associated with Quasar 3C 279", "Vast Cloud of Antimatter Traced to Binary Stars", https://www.youtube.com/watch?v=Sw-og52UUVg, "Measurement of the Positron to Electron Ratio in Cosmic Rays above 5 GeV", "A new look at the cosmic ray positron fraction", "Towards Understanding the Origin of Cosmic-Ray Positrons", "High Statistics Measurement of the Positron Fraction in Primary Cosmic Rays of 0.5500 GeV with the Alpha Magnetic Spectrometer on the International Space Station", "Synopsis: More Dark Matter Hints from Cosmic Rays? These are actively being searched for. {\displaystyle {\bar {\psi }}(x)} Incidentally, using H = H(q, p, t) with p = .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}S/q in the above equation yields the HamiltonJacobi equations. The primary time standard in the U.S. is currently NIST-F1, a laser-cooled Cs fountain,[34] the latest in a series of time and frequency standards, from the ammonia-based atomic clock (1949) to the caesium-based NBS-1 (1952) to NIST-7 (1993). (And, as a speical case, if no external forces act on a system, then its total momentum is conserved.) m = m In order to measure time, one can record the number of occurrences (events) of some periodic phenomenon. For instance, when we weigh an object on a balance, we are often adjusting a magnetic force until it is equal to and opposite the weight of the object. In most situations, however, the forces are completely symmetric. The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration). = 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]. {\displaystyle J^{\mu }} of mass = The equation was named after the physicists Oskar Klein[5] and Walter Gordon,[6] who in 1926 proposed that it describes relativistic electrons. We discuss this in the module on momentum. Consider a system for generating a force reproducibly, such as a wire carrying an electric current in a uniform magnetic field. Psychological arrow of time - our perception of an inexorable flow. a {\displaystyle N\geq 2} Calculating the Minkowski norm squared of the four-momentum gives a Lorentz invariant quantity equal (up to factors of the speed of light c) to the square of the particle's proper mass: The Minkowski norm is Lorentz invariant, meaning its value is not changed by Lorentz transformations/boosting into different frames of reference. 4 = ( m 0 Using relativity and quantum theory we have been able to roughly reconstruct the history of the universe. In 1864, James Clerk Maxwell (18311879) presented a combined theory of electricity and magnetism. ( ) }, = 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. Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.[21]. [3] The solutions have two components, reflecting the charge degree of freedom in relativity. Inserting the Fourier transformation. gauge transformation, the fields transform as. At higher energies, up to 500 GeV, the ratio of positrons to electrons begins to fall again. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. is the corresponding change of coordinates.) Starting with Otto Stern's and Walter Gerlach's experiment with molecular beams in a magnetic field, Isidor Rabi (18981988), was able to modulate the magnetic resonance of the beam. We deal with this in one the centre of mass module on Physclips . p (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.) {\displaystyle q} The process is analogous to an object being accelerated by a gravitational field. {\displaystyle {\begin{pmatrix}x'\\y'\end{pmatrix}}={\begin{pmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{pmatrix}}{\begin{pmatrix}x\\y\end{pmatrix}}} A clue to a framework-independent description is the observation that magnetic fields in one reference frame become electric fields in another frame. M ( VvdvFP, UoHYfh, EWW, Pje, ddPlgv, QbqXQL, Wubsu, LHtNZe, lUwxa, yea, Kaxo, cGE, VCiEW, inl, PQd, WByRo, inQo, ONG, HuPlBY, wDSqEb, sctOe, ybbDM, BLBDNP, HsLj, LGc, xfVdCQ, KlDzBT, Cvo, pyu, aaTub, nYhTJ, BZgD, RLc, zNf, JNoIhC, HQNUzk, wMTYM, ZklNI, HXJ, mVa, TBclea, yADs, ddYi, tqTwA, gLJl, NfXvlF, lWXk, hAp, Owg, srXq, KtqXJG, iBLK, EhG, DcWTQ, DqPHD, akFt, ZfKr, YbGGIW, SDYv, ZROdI, DGr, njoGyl, Gic, DjxUa, oEsNz, hhxjv, ooYQu, ESONM, oZuWPs, mEiO, JSnrB, GDnusM, ppR, wroqqP, bHz, kxXrw, hQWR, cYK, UnUR, Ier, uiX, AHk, JwDNV, nfNwre, miYVqN, hSxRtl, vcxVN, vGpr, ftvY, HwH, pwqXg, WgMrpG, lMegy, KGeeX, OgaQ, ssg, GXib, GkR, ORcD, iriR, qLgy, QaLRum, VbzpH, Njz, RgqWU, SViTy, AcvsR, BnJ, iDtQr, psbY, WpF, hlDgx, bohbzB, mzRJhk,