The Earth and our Solar System. Relativity Principle and MichelsonMorley Experiment. Group property of the Lorentz transformation.
Classical Mechanics, Point Particles and Relativity - Walter Greiner
Note on the invisibility of the LorentzFitzgerald length contraction. Calculation of Surface Integrals. Basic Concepts of Mechanics. The General Linear Motion. The Harmonic Oscillator. His enthusiasm for his sciences is contagious and shines through almost every page.
Pdf Classical Mechanics Point Particles And Relativity 1989 2004
Allan Bromley, Yale University"This softcover publication Goethe University in Frankfurt. Although the textbook, by its remarkable completeness, seems to be intended for advanced students and aims to be a reference book for graduate students and teachers, it is sufficiently understandable and extensive to be used by beginners as a first introduction to theoretical physics.
It does not only provide a survey of classical theoretical mechanics, but also a respectable amount of examples and problems The subject is presented in a manner that is both interesting to the student and easily accessible. The main text is therefore accompanied by many exercises and examples that have been worked out in great detail. This should make the book useful also for students wishing to study the subject on their own.
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This idea is a consequence of special relativity alone. It really comes into its own, however, when one considers relativistic quantum mechanics.
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This work goes into increasing the energy E of the particle. Taking the dot product of equation with v gives. However, experience has shown that its introduction serves no useful purpose and may lead to confusion, and it is not used in this article.
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The invariant quantity is the rest mass m. For that reason it has not been thought necessary to add a subscript or superscript to m to emphasize that it is the rest mass rather than a velocity-dependent quantity. When subscripts are attached to a mass, they indicate the particular particle of which it is the rest mass.
If the applied force F is perpendicular to the velocity v , it follows from equation that the energy E, or, equivalently, the velocity squared v 2 , will be constant, just as in Newtonian mechanics. This will be true, for example, for a particle moving in a purely magnetic field with no electric field present. It then follows from equation that the shape of the orbits of the particle are the same according to the classical and the relativistic equations. However, the rate at which the orbits are traversed differs according to the two theories.
The first term, mc 2 , which remains even when the particle is at rest, is called the rest mass energy. For a single particle, its inclusion in the expression for energy might seem to be a matter of convention: it appears as an arbitrary constant of integration. However, for systems of particles that undergo collisions, its inclusion is essential. The relativistic law of energy - momentum conservation thus combines and generalizes in one relativistically invariant expression the separate conservation laws of prerelativistic physics: the conservation of mass , the conservation of momentum , and the conservation of energy.
In fact, the law of conservation of mass becomes incorporated in the law of conservation of energy and is modified if the amount of energy exchanged is comparable with the rest mass energy of any of the particles. In such a decay the initial kinetic energy is zero. It is precisely this process that provides the large amount of energy available during nuclear fission , for example, in the spontaneous fission of the uranium isotope.
The opposite process occurs in nuclear fusion when two particles fuse to form a particle of smaller total rest mass. If the two initial particles are both at rest, a fourth particle is required to satisfy the conservation of energy and momentum. The rest mass of this fourth particle will not change, but it will acquire kinetic energy equal to the binding energy minus the kinetic energy of the fused particles.
Perhaps the most important examples are the conversion of hydrogen to helium in the centre of stars, such as the Sun, and during thermonuclear reactions used in atomic bombs. This article has so far dealt only with particles with non-vanishing rest mass whose velocities must always be less than that of light. One may always find an inertial reference frame with respect to which they are at rest and their energy in that frame equals mc 2. However, special relativity allows a generalization of classical ideas to include particles with vanishing rest masses that can move only with the velocity of light.
Particles in nature that correspond to this possibility and that could not, therefore, be incorporated into the classical scheme are the photon , which is associated with the transmission of electromagnetic radiation, and—more speculatively—the graviton, which plays the same role with respect to gravitational waves as does the photon with respect to electromagnetic waves.
It follows from the relativistic laws of energy and momentum conservation that, if a massless particle were to decay, it could do so only if the particles produced were all strictly massless and their momenta p 1 , p 2 ,… p n were all strictly aligned with the momentum p of the original massless particle. Since this is a situation of vanishing likelihood, it follows that strictly massless particles are absolutely stable. It also follows that one or more massive particles cannot decay into a single massless particle, conserving both energy and momentum.
They can, however, decay into two or more massless particles, and indeed this is observed in the decay of the neutral pion into photons and in the annihilation of an electron and a positron pair into photons. In the latter case, the world lines of the annihilating particles meet at the space-time event where they annihilate.
This interpretation plays an important role in the quantum theory of such processes. Relativistic mechanics. Article Media. Info Print Print. Table Of Contents. Submit Feedback. Thank you for your feedback. Introduction Development of the special theory of relativity Relativistic space-time Relativistic momentum, mass, and energy.
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