Physics
Special Relativity
Special relativity is a fundamental theory in physics developed by Albert Einstein. It describes the behavior of objects moving at high speeds and the relationship between space and time. Key concepts include time dilation, length contraction, and the famous equation E=mc^2, which relates energy and mass. This theory revolutionized our understanding of the universe and has numerous practical applications.
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9 Key excerpts on "Special Relativity"
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...
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...
eBook - PDF- David J. Griffiths(Author)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
2 Special Relativity Classical physics, 1 some aspects of which we discussed in Chapter 1, is – for the most part – comforting to our intuitions. You probably wouldn’t have come up with Newton’s second law (F D ma) on your own (after all, nobody did before Newton), but once it is on the table it feels right. It seems consistent with our everyday experience. Classical physics refines and perfects our intuitions, but it doesn’t upset them. By contrast, the four revolutions in twentieth-century physics are wildly counterintuitive; they seem to contradict everything we thought we understood – everything we took for granted about the world. That is, in part, what makes them so interesting. But it also raises a recurring question: “If this is really true, how come I never noticed it before?” I hope you will keep a skeptical eye on that subtext, as we go along. 2.1 Einstein’s postulates Einstein published his Special Theory of Relativity in 1905. The special theory is not an account of any particular physical phenomenon; rather, it is a description of the arena in which all phenomena occur. It is a theory of space and time themselves. As such, it takes precedence over all other theories. If you were to propose a new model of elementary particles, say, the first thing to ask would be, “Is it consistent with Special Relativity?” If not, you have some fast talking to do. As Kant would say, Special Relativity is a prolegomenon to any future physics. Einstein based the theory on two postulates. Postulate 1: The principle of relativity. Postulate 2: The universal speed of light. 1 Roughly speaking, “classical” physics is the subject as it stood in the year 1900. 39 40 Special Relativity In the following sections I’ll explain these postulates. After that we’ll consider their implications. 2.1.1 The principle of relativity The principle of relativity says that the ordinary laws of physics apply just as well in a system moving at constant velocity as they do in one at rest.
eBook - PDF- Kenneth S. Krane(Author)
- 2020(Publication Date)
- Wiley(Publisher)
Chapter 2 THE SPECIAL THEORY OF RELATIVITY This 12-foot tall statue of Albert Einstein is located at the headquarters of the National Academy of Sciences in Washington DC. The page in his hand shows three equations that he discovered: the fundamental equation of general relativity, which revolutionized our understanding of gravity; the equation for the photoelectric effect, which opened the path to the development of quantum mechanics; and the equation for mass–energy equivalence, which is the cornerstone of his special theory of relativity. ROGER L. WOLLENBERG / UPI / Newscom 26 Chapter 2 The Special Theory of Relativity Einstein’s special theory of relativity and Planck’s quantum theory burst forth on the physics scene almost simultaneously during the first decade of the 20th century. Both theories caused profound changes in the way we view our universe at its most fundamental level. In this chapter, we study the special theory of relativity. ∗ This theory has a completely undeserved reputation as being so exotic that few people can under- stand it. On the contrary, Special Relativity is basically a system of kinematics and dynamics, based on a set of postulates that are different from those of classical physics. The resulting formalism is not much more complicated than Newton’s laws, but it does lead to several predictions that seem to go against our common sense. Even so, the special theory of relativity has been carefully and thoroughly tested by experiment and found to be correct in all its predictions. We first review the classical relativity of Galileo and Newton, and then we show why Einstein proposed to replace it. We then discuss the mathematical aspects of Special Relativity, the predictions of the theory, and finally some experimental tests. 2.1 CLASSICAL RELATIVITY A “theory of relativity” is in effect a way for observers in different frames of reference to compare the results of their observations.
eBook - PDFRelativity: The Theory and Its Philosophy
Foundations & Philosophy of Science & Technology
- Roger B. Angel, Mario Bunge(Authors)
- 2014(Publication Date)
- Pergamon(Publisher)
3 The Principle of Special Relativity The Breakdown of Classical Relativity WE have seen that Newton postulated as a background for his theory of mechanics an absolute space and an absolute time. Although we found ourselves obliged to question the necessity for the introduction of absolute space, it is indeed true that his theory required that an absolute significance be given to the concept of length or distance. For example, the force that chiefly interested Newton is that of gravity. The gravitational force is inversely proportional to the square of the distance between the gravitationally interacting bodies. Now if distance were a frame or coordinate dependent quantity, the law of gravitation would be ambiguous. Since the acceleration produced by a gravitational field is the same in all inertial frames of reference, it follows that, assuming constancy of mass, the distance between two bodies at a given time must be the same in all inertial frames. In fact, one is entitled to make the stronger mathematical claim that distance is invariant with respect to all frames of reference, since the definition s 2 = 6 ij X l X j is independent of time, and hence of velocity and acceleration. In the mid-nineteenth century, a new development in physical theory arose which would eventually place the presupposition of Newtonian mechanics in crucial jeopardy. We refer to the theory of electrodynamics of Maxwell. The crisis was only satisfactorily resolved in 1905 in the first of Einstein's papers on Special Relativity, entitled On the Electrodynamics of Moving Bodies. The title of this paper deserves to be emphasized since philosophical discussions of Einstein's first theory of relativity have too frequently conveyed the impression that it is simply a new theory of kinematics, whereas, in fact, it is as intimitately connected with electrodynamics as the principle of classical relativity is connected with classical mechanics.
eBook - PDFThe Sciences
An Integrated Approach
- James Trefil, Robert M. Hazen(Authors)
- 2016(Publication Date)
- Wiley(Publisher)
Thus Newton’s laws represent an extremely important special case of Einstein’s more general theory. Science often progresses in this way, with one theory encom- passing previous valid ideas. Newton, for example, merged dis- coveries by Galileo of Earth-based motions and Kepler’s laws of planetary motion into his unified theory of gravity. And someday Einstein’s theory of relativity may be incorporated into an even grander view of the universe. Can a human ever travel faster than the speed of light, at “warp speed”? • he speed of light, denoted by the symbol c, is nearly 300,000 kilometers per second. It is one of the best-known physical con- stants in science. • In 1905, Einstein published his theory of Special Relativity, which asserts that the speed of light is a fundamental constant of na- ture. It appears the same to all observers in all frames of refer- ence anywhere in space. • Special Relativity asserts that mass is not a constant; as an object increases in speed, it also increases in mass. • As the mass of an object increases, the energy required to in- crease its speed also increases. • herefore, as an object approaches the speed of light its mass would approach ininity and the energy required to accelerate an ininite mass beyond the speed of light would be ininite. • Consequently, no physical object such as a human being or spaceship that is moving at less than the sped of light will ever exceed that speed. RETURN TO THE INTEGRATED QUESTION Every observer sees the world from a diferent frame of reference. Descriptions of actual physical events are diferent for diferent ob- servers, but the theory of relativity states that all observers must see the universe operating according to the same laws. Because the speed of light is built into Maxwell’s equations, this principle requires that all observers must see the same speed of light in their frames of reference.
eBook - PDFUnderstanding Space-Time
The Philosophical Development of Physics from Newton to Einstein
- Robert DiSalle(Author)
- 2006(Publication Date)
- Cambridge University Press(Publisher)
100 The origins and significance of relativity theory his own view for granted. Rather, they began with the spatio-temporal presuppositions of the Newtonian views, and showed how their inade- quacies revealed the principles on which an entirely new theory could be built. It is sometimes said that Special Relativity overthrew the concepts of absolute space and time. This is only half true; by the time Einstein began his work on electrodynamics, the concept of inertial frame was already widely known, and absolute space was already widely understood to be superfluous (see DiSalle, 1991). Thomson (1884) introduced the notions of “reference-frame” and “reference-dial-traveller,” i.e. a spatial frame and a temporal standard relative to which motion may be measured, so that the laws of motion may be stated thus: for any system of particles moving anyhow, there exists a frame and a time-scale with respect to which every acceleration is proportional to and in the direction of an applied force, and every such force belongs to an action–reaction pair. Moreover, any frame in uniform rectilinear motion relative to such a frame is also an inertial frame. Independently, Lange (1885) offered an essentially equivalent conception, the “inertial system” and “inertial time-scale,” and Lange’s version (and terminology) was more prominently discussed in the German-language literature that Einstein might have read. It was especially emphasized by Mach, in the second (1889) and later editions of Die Mechanik. 2 How much Einstein absorbed of all of these discussions is not clear. It is clear, however, that by 1905 he must have thought it completely uncontroversial that mechanics has no need of absolute space, but needs only “a coordinate system in which the equations of mechanics are valid” (1905, p. 892); by the relativity principle, any system that is in uniform motion relative to such a system is physically equivalent to it.
eBook - PDF- Delo E. Mook, Thomas Vargish(Authors)
- 2018(Publication Date)
- Princeton University Press(Publisher)
2 There are numerous biographies of Einstein that deal with this period in his life. We can suggest the brief but very readable one by Bernstein, Einstein; for a more thorough biography see Clark, Einstein: The Life and Times; for a scientific biography (much of it requiring con-siderable mathematical sophistication) see Pais, Subtle Is the Lord. 54 SPECIAL THEORY OF RELATIVITY for at least the start of our discussion, although later on we will depart from the order in which Einstein presented certain topics. 3 . 2 EINSTEIN'S SEARCH: OPERATIONAL DEFINITIONS Albert Einstein's work on relativity was guided by a series of simple, even childlike questions. He pursued the answers to these questions re-morselessly, and in answering them he began to demolish the Newtonian foundations of physical science. His questions were fundamental: they were questions of definition—indeed, definition of some of the basic terms used by scientists and others to describe the world, terms such as space or time. Einstein sought definitions that contained implicit instructions for mak-ing physical measurements in order to determine the meaning of the terms; that is, his definitions were so-called operational definitions, 3 state-ments providing guidelines for setting up and carrying out protocols of data collection. Curiously, his definitions were not stated in mathematical sym-bols or even in mathematical terms, but as verbalizations. In fact, the first six pages of Einstein's relativity paper boast no mathematics more complex than the simple statement that Any object's speed equals the distance traveled by the object di-vided by the time required to travel that distance, or, in algebraic terms, S P E E D = D I S T A N C E / T I M E , an equation that is really a definition of the concept of speed. Such operational definitions, because they lead to recipes for making measurements, are at the foundation of modern physical science.
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