Physics
Relativistic Mechanics
Relativistic mechanics is a branch of physics that describes the motion of objects at speeds approaching the speed of light. It is based on Albert Einstein's theory of special relativity, which revolutionized classical mechanics by introducing concepts such as time dilation, length contraction, and the equivalence of mass and energy (E=mc^2). Relativistic mechanics provides a more accurate description of motion at high speeds than classical mechanics.
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11 Key excerpts on "Relativistic Mechanics"
eBook - PDFGravity from the Ground Up
An Introductory Guide to Gravity and General Relativity
- Bernard Schutz(Author)
- 2003(Publication Date)
- Cambridge University Press(Publisher)
Fast motion means relativity Unfortunately, special and general relativity are probably the worst-named theories In this section: relativity theory is required when motions can be a significant fraction of the speed of light. Gravitational fields that are strong enough to accelerate bodies to such speeds must be described by a theory of gravity that is compatible with the principles of relativity. of modern physics. Their names convey little meaning, and this sometimes causes confusion right from the start. Here are thumbnail definitions of what the theories are really about. Special relativity is Einstein’s description of how some of the basic mea- surable quantities of physics – time, distance, mass, energy – depend on the speed of the measuring apparatus relative to the object being stud- ied. It shows how they must change in order to guarantee that Galileo’s principle of relativity (that the laws of physics should be the same for 180 Chapter 15. Physics at speed every experimenter, regardless of speed – recall the discussion in Chap- ter 1) should hold even at speeds near that of light. Because it deals with the general properties of measurements, special relativity is not really a theory about any particular physical system. Rather, it is a set of general principles that all the other theories of physics have to obey to deal correctly with fast-moving bodies. All the theories of physical phenomena – for example, mechan- ics (the theory of forces and motion), electromagnetism (the theory of electricity and magnetism), and quantum theory (the theory of the sub-microscopic physics of electrons, protons, and other particles) – have relativistic versions that physicists use when they need to understand a situation where speeds get close to that of light. Gravity is no exception: it must also follow the principles of special relativity. General relativity is Einstein’s relativistic theory of gravity.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
In addition, particle accelerators routinely accelerate and measure the properties of particles moving at near the speed of light, where their behavior is completely consistent with relativity theory and inconsistent with the earlier Newtonian mechanics. These machines would simply not work if they were not engineered according to relativistic principles. General relativity A simulated black hole of ten solar masses as seen from a distance of 600 kilometers with the Milky Way in the background. ________________________ WORLD TECHNOLOGIES ________________________ General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. It generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations. Many predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, the gravitational redshift of light, and the gravitational time delay. General relativity's predictions have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data.
eBook - PDF- David Agmon, Paul Gluck;;;(Authors)
- 2009(Publication Date)
- WSPC(Publisher)
Chapter 12 The Special Theory of Relativity — Kinematics We must do science because it reveals the beauty of nature. 12.1 Introduction Einstein Newtonian mechanics is concerned with the motion of bodies acted upon by forces. Each chapter in its development was a link in a chain of elements with a common logic. The special theory of relativity developed by Albert Einstein in the year 1905 was a fundamental break in this tradition and a point of departure from its predecessors. It challenged the fundamental assumptions of Newtonian theory and replaced them with bold new axioms. It forced us to review and revise our most fundamental notions concerning the nature of time, space, force, mass, momentum and energy. The major difficulty in understanding relativity theory is not mathematical, but rather in coming to terms with its basic abstract ideas. The mathematical equipment required of the reader of the present chapter comprises only basic algebra and differential calculus. The theory of relativity rests on two basic postulates: 1. The velocity of light is independent of the frame of reference of any observer. Therefore, it does not depend on the velocity of the source or that of the observer. 2. The principle of relativity: All fundamental laws of physics are identical for all observers moving with constant velocities with respect to each other. Albert Einstein (1879-1955) Comments: (a) The velocity of light waves in vacuum is c = (299772.5+0.1) km/s. In this book this will be rounded to 3-10 5 km/s = 3-10 8 m/s. (b) Space is assumed to be homogeneous and isotropic, so that the velocity of light is the same in all directions. (c) An observer moving at constant velocity is called an inertial observer. (d) The second postulate embraces all laws of physics, not just mechanics. Its content is the following: All the equations describing physical laws in terms of 432
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
In addition, particle accelerators routinely accelerate and measure the properties of particles moving at near the speed of light, where their behavior is completely consistent with relativity theory and inconsistent with the earlier Newtonian mechanics. These machines would simply not work if they were not engineered according to relativistic principles. General relativity A simulated black hole of ten solar masses as seen from a distance of 600 kilometers with the Milky Way in the background. ________________________ WORLD TECHNOLOGIES ________________________ General relativity or the general theory of relativity is the geometric theory of gravi-tation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. It generalises special relativity and Newton's law of universal gravi-tation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations. Many predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, the gravitational redshift of light, and the gravitational time delay. General relativity's predictions have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
The predictions of special relativity agree well with Newtonian mechanics in their common realm of applicability, specifically in experiments in which all velocities are small compared with the speed of light. Special relativity reveals that c is not just the velocity of a certain phenomenon—namely the propagation of electromagnetic radiation (light)—but rather a fundamental feature of the way space and time are unified as spacetime. One of the consequences of the theory is that it is impossible for any particle that has rest mass to be accelerated to the speed of light. The theory is termed special because it applies the principle of relativity only to the special case of inertial reference frames, i.e. frames of reference in uniform relative motion with respect to each other. Einstein developed general relativity to apply the principle in the more general case, that is, to any frame so as to handle general coordinate transformations, and that theory includes the effects of gravity. From the theory of general relativity it follows that special relativity will still apply locally (i.e., to first order), and hence to any relativistic situation where gravity is not a significant factor. Inertial frames should be identified with non-rotating Cartesian coordinate systems constructed around any free falling trajectory as a time axis. Postulates “ Reflections of this type made it clear to me as long ago as shortly after 1900, i.e., shortly after Planck's trailblazing work, that neither mechanics nor electrodynamics could (except in limiting cases) claim exact validity. Gradually I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more desperately I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results...
eBook - PDF- Wassim M. Haddad(Author)
- 2019(Publication Date)
- Princeton University Press(Publisher)
Chapter Thirteen Relativistic Mechanics 13.1 Introduction Our universe is the quintessential large-scale dynamical system, and classical physics has provided a rigorous underpinning of its governing laws that are consistent with human experience and intuition. Newtonian mechanics and Lagrangian and Hamiltonian dynamics provide a rigorous mathematical framework for classical mechanics—the oldest of the physical sciences. The theory of Newtonian mechanics embodies the science of kinematics and dynamics of moving bodies and embedded within its laws is the Galilean principle of relativity, which states that the laws of mechanics are equally valid for all observers moving uniformly with respect to each other. This invariance principle of mechanics, which was known from the time of Galileo, postulated that the laws of mechanics are equivalent in all inertial (i.e., nonaccelerating) frames. In other words, all inertial observers undergoing uniform relative motion would observe the same laws of mechanics involving the conservation of energy, conservation of linear momentum, conservation of angular momentum, etc., while possibly measuring different values of velocities, energies, momenta, etc. In the late seventeenth century, Newton went on to make his greatest discovery—the law of universal gravitation. He postulated that gravity exists in all bodies universally, and showed that bodies attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation. He maintained that this universal principle pervades the entire universe affecting everything in it, and its influence is direct, immediate , and definitive. With this law of universal gravitation, Newton demonstrated that terrestrial physics and celestial physics can be derived from the same basic principles and are part of the same scientific discipline.
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- 2014(Publication Date)
- White Word Publications(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 1 Special Relativity Special relativity ( SR , also known as the special theory of relativity or STR ) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper On the Electrodynamics of Moving Bodies. It generalizes Galileo's principle of relativity—that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)—from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source. This theory has a wide range of consequences which have been experimentally verified, including counter-intuitive ones such as length contraction, time dilation and relativity of simultaneity, contradicting the classical notion that the duration of the time interval between two events is equal for all observers. (On the other hand, it introduces the space-time interval, which is invariant.) Combined with other laws of physics, the two postulates of special relativity predict the equivalence of matter and energy, as expressed in the mass–energy equivalence formula E = mc 2 , where c is the speed of light in a vacuum. The predictions of special relativity agree well with Newtonian mechanics in their common realm of applicability, specifically in experiments in which all velocities are small compared with the speed of light. Special relativity reveals that c is not just the velocity of a certain phenomenon—namely the propagation of electromagnetic radiation (light)—but rather a fundamental feature of the way space and time are unified as spacetime.
eBook - PDFRelativity: The Theory and Its Philosophy
Foundations & Philosophy of Science & Technology
- Roger B. Angel, Mario Bunge(Authors)
- 2014(Publication Date)
- Pergamon(Publisher)
Relativity and Newtonian Mechanics 49 The Principle of Classical Relativity Although Newton was satisfied that his doctrine of absolute space and time was conceptually adequate, he was, nonetheless, aware of a certain practical problem which it posed. The fundamental goal of science is to provide conceptual representations of objective physical laws. The scientist assumes that nature has an objective, nomic structure that is constant throughout space and time. Consequently, the theoretical laws which depict this structure should have global rather than mere local significance. One implication of this requirement is that the formulation of a law should not be dependent on any local factors; ideally it should be free of contextual reference. We have noted that this ideal of objectivity is partially realized by writing laws in vectorial form. A vectorial law has precisely the same significance with respect to infinitely many coordinate systems and is objective at least to that extent. However, while there are inifinitely many suitable systems of coordinates, there are infinitely many more which are unsuitable. From what was said in the previous section, it follows that if we have one suitable system at our disposal, then we may obtain the rest by a transformation which is an element of O i3 x T. The assumption here is that any such element leads to an admissible coordinatization of absolute space and time, the receptacle of physical processes. Clearly, then, one task of theoretical mechanics is to specify a suitable coordinate system. The reason for this is the following. Let us suppose that a scientist wishes to carry out an experimental test of Newton's second law. Suppose, also, that he sets up the experiment in some moving vehicle, say a train. This is not too far-fetched, since the earth is a type of moving vehicle.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
The predictions of special relativity agree well with Newtonian mechanics in their common realm of applicability, specifically in experiments in which all velocities are small compared with the speed of light. Special relativity reveals that c is not just the velocity of a certain phenomenon—namely the propagation of electromagnetic radiation (light)—but rather a fundamental feature of the way space and time are unified as spacetime. One of the consequences of the theory is that it is impossible for any particle that has rest mass to be accelerated to the speed of light. The theory is termed special because it applies the principle of relativity only to the special case of inertial reference frames, i.e. frames of reference in uniform relative motion with respect to each other. Einstein developed general relativity to apply the principle in the more general case, that is, to any frame so as to handle general coordinate transformations, and that theory includes the effects of gravity. From the theory of general relativity it follows that special relativity will still apply locally (i.e., to first order), and hence to any relativistic situation where gravity is not a significant factor. Inertial frames should be identified with non-rotating Cartesian coordinate systems constructed around any free falling trajectory as a time axis. Postulates “ Reflections of this type made it clear to me as long ago as shortly after 1900, i.e., shortly after Planck's trailblazing work, that neither mechanics nor electrodynamics could (except in limiting cases) claim exact validity. Gradually I despaired of the ” ________________________ WORLD TECHNOLOGIES ________________________ possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more desperately I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results...
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
The predictions of special relativity agree well with Newtonian mechanics in their common realm of applicability, specifically in experiments in which all velocities are small compared with the speed of light. Special relativity reveals that c is not just the velocity of a certain phenomenon—namely the propagation of electromagnetic radiation (light)—but rather a fundamental feature of the way space and time are unified as spacetime. One of the consequences of the theory is that it is impossible for any particle that has rest mass to be accelerated to the speed of light. The theory is termed special because it applies the principle of relativity only to the special case of inertial reference frames, i.e. frames of reference in uniform relative motion with respect to each other. Einstein developed general relativity to apply the principle in the more general case, that is, to any frame so as to handle general coordinate transformations, and that theory includes the effects of gravity. From the theory of general relativity it follows that special relativity will still apply locally (i.e., to first order), and hence to any relativistic situation where gravity is not a significant factor. Inertial frames should be identified with non-rotating Cartesian coordinate systems constructed around any free falling trajectory as a time axis. Postulates “ Reflections of this type made it clear to me as long ago as shortly after 1900, i.e., shortly after Planck's trailblazing work, that neither mechanics nor electrodynamics could (except in limiting cases) claim exact validity. Gradually I despaired of the possibility of ” ________________________ WORLD TECHNOLOGIES ________________________ discovering the true laws by means of constructive efforts based on known facts. The longer and the more desperately I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results...
No longer available |Learn more- (Author)
- 2014(Publication Date)
- College Publishing House(Publisher)
The predictions of special relativity agree well with Newtonian mechanics in ________________________ WORLD TECHNOLOGIES ________________________ their common realm of applicability, specifically in experiments in which all velocities are small compared with the speed of light. Special relativity reveals that c is not just the velocity of a certain phenomenon—namely the propagation of electromagnetic radiation (light)—but rather a fundamental feature of the way space and time are unified as spacetime. One of the consequences of the theory is that it is impossible for any particle that has rest mass to be accelerated to the speed of light. The theory is termed special because it applies the principle of relativity only to the special case of inertial reference frames, i.e. frames of reference in uniform relative motion with respect to each other. Einstein developed general relativity to apply the principle in the more general case, that is, to any frame so as to handle general coordinate transformations, and that theory includes the effects of gravity. From the theory of general relativity it follows that special relativity will still apply locally (i.e., to first order), and hence to any relativistic situation where gravity is not a significant factor. Inertial frames should be identified with non-rotating Cartesian coordinate systems constructed around any free falling trajectory as a time axis. Postulates “ Reflections of this type made it clear to me as long ago as shortly after 1900, i.e., shortly after Planck's trailblazing work, that neither mechanics nor electrodynamics could (except in limiting cases) claim exact validity. Gradually I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The ”
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