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Hyperbolic Motion (relativity)
Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity. It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola, as can be seen when graphed on a Minkowski diagram whose coordinates represent a suitable inertial (non-accelerated) frame. This motion has several interesting features, among them that it is possible to outrun a photon if given a sufficient head start, as may be concluded from the diagram. History Hermann Minkowski (1908) showed the relation between a point on a worldline and the magnitude of four-acceleration and a "curvature hyperbola" (german: Krümmungshyperbel). In the context of Born rigidity, Max Born (1909) subsequently coined the term "hyperbolic motion" (german: Hyperbelbewegung) for the case of constant magnitude of four-acceleration, then provided a detailed description for charged particles in hyperbolic motion, and introduced the corresponding " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfgang Pauli
Wolfgang Ernst Pauli (; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics for his "decisive contribution through his discovery of a new law of Nature, the exclusion principle or Pauli principle". The discovery involved spin theory, which is the basis of a theory of the structure of matter. Early years Pauli was born in Vienna to a chemist, Wolfgang Joseph Pauli (''né'' Wolf Pascheles, 1869–1955), and his wife, Bertha Camilla Schütz; his sister was Hertha Pauli, a writer and actress. Pauli's middle name was given in honor of his godfather, physicist Ernst Mach. Pauli's paternal grandparents were from prominent families of Prague; his great-grandfather was the publisher Wolf Pascheles. Pauli's mother, Bertha Schütz, was raised in her mother's Roman Catholic religion; Pauli was raised as a Roman Cathol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Bondi
Sir Hermann Bondi (1 November 1919 – 10 September 2005) was an Austrian- British mathematician and cosmologist. He is best known for developing the steady state model of the universe with Fred Hoyle and Thomas Gold as an alternative to the Big Bang theory. He contributed to the theory of general relativity,Obituaries: Professor Sir Hermann Bondi(12 September 2005) in ''The Independent''. Professor Sir Hermann Bondi(2005-09-13) in ''The Telegraph''. Sir Hermann Bondi(2005-09-14) in ''The Guardian''. Sir Hermann Bondi: 1919–2005(2005-09-14) in '' Physics World'', IOP. Black hole scientist Bondi dies(2005-09-17), BBC News. and was the first to analyze the inertial and gravitational interaction of negative mass and the first to explicate correctly the nature of gravitational waves. In his 1990 autobiography, Bondi regarded the 1962 work on gravitational waves as his "best scientific work". Early life Bondi was born in Vienna, the son of a Jewish medical doctor. He was b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charged Particle
In physics, a charged particle is a particle with an electric charge. It may be an ion, such as a molecule or atom with a surplus or deficit of electrons relative to protons. It can also be an electron or a proton, or another elementary particle, which are all believed to have the same charge (except antimatter). Another charged particle may be an atomic nucleus devoid of electrons, such as an alpha particle. A plasma is a collection of charged particles, atomic nuclei and separated electrons, but can also be a gas containing a significant proportion of charged particles. Charges are arbitrarily labeled as ''positive''(+) or ''negative''(-). Only the existence of two 'types' of charges is known, there isn't anything inherent about positive charges that makes them positive, and the same goes for the negative charge. Examples Positively charged particles * protons and atomic nuclei * positrons (antielectrons) * alpha particles * positive charged pions * cation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical counterpart to the quantized electromagnetic field tensor in quantum electrodynamics (a quantum field theory). The electromagnetic field propagates at the speed of light (in fact, this field can be identified ''as'' light) and interacts with charges and currents. Its quantum counterpart is one of the four fundamental forces of nature (the others are gravitation, weak interaction and strong interaction.) The field can be viewed as the combination of an electric field and a magnetic field. The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rapidity
In relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates. For one-dimensional motion, rapidities are additive whereas velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velocity are proportional but, for higher velocities, rapidity takes a larger value, with the rapidity of light being infinite. Using the inverse hyperbolic function , the rapidity corresponding to velocity is where ''c'' is the velocity of light. For low speeds, is approximately . Since in relativity any velocity is constrained to the interval the ratio satisfies . The inverse hyperbolic tangent has the unit interval for its domain and the whole real line for its image; that is, the interval maps onto . History In 1908 Hermann Minkowski ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proper Time
In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. It is thus independent of coordinates, and is a Lorentz scalar. The proper time interval between two events on a world line is the change in proper time. This interval is the quantity of interest, since proper time itself is fixed only up to an arbitrary additive constant, namely the setting of the clock at some event along the world line. The proper time interval between two events depends not only on the events, but also the world line connecting them, and hence on the motion of the clock between the events. It is expressed as an integral over the world line (analogous to arc length in Euclidean space). An accelerated clock will measure a smaller elapsed time between two events than that measured by a non-accelerated (inertial) clock between the same two events. The twin paradox is an example of this effect. By convention ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation Of Motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.''Encyclopaedia of Physics'' (second Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1 (VHC Inc.) 0-89573-752-3 More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.''Analytical Mechanics'', L.N. Hand, J.D. Finch, Cambridge University Press, 2008, The functions are defined in a Euclidean space in classical mechanics, but are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions for the differential equations descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Speed Of Light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space. All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects. Starlight viewed on Earth left the stars many years ago, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes, it can take minutes to hours for signals to travel from Earth to the spacecraft and vice versa. In computing, the speed of light fixes the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Factor
The Lorentz factor or Lorentz term is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz. It is generally denoted (the Greek lowercase letter gamma). Sometimes (especially in discussion of superluminal motion) the factor is written as (Greek uppercase-gamma) rather than . Definition The Lorentz factor is defined as :\gamma = \frac = \frac = \frac , where: *''v'' is the relative velocity between inertial reference frames, *''c'' is the ''speed of light in a vacuum'', * is the ratio of ''v'' to ''c'', *''t'' is coordinate time, * is the proper time for an observer (measuring time intervals in the observer's own frame). This is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acceleration (special Relativity)
Accelerations in special relativity (SR) follow, as in Newtonian Mechanics, by differentiation of velocity with respect to time. Because of the Lorentz transformation and time dilation, the concepts of time and distance become more complex, which also leads to more complex definitions of "acceleration". SR as the theory of flat Minkowski spacetime remains valid in the presence of accelerations, because general relativity (GR) is only required when there is curvature of spacetime caused by the energy–momentum tensor (which is mainly determined by mass). However, since the amount of spacetime curvature is not particularly high on Earth or its vicinity, SR remains valid for most practical purposes, such as experiments in particle accelerators. One can derive transformation formulas for ordinary accelerations in three spatial dimensions (three-acceleration or coordinate acceleration) as measured in an external inertial frame of reference, as well as for the special case of proper ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
