Physics
Einstein's Theory of Special Relativity
Einstein's Theory of Special Relativity, proposed in 1905, revolutionized our understanding of space and time. It states that the laws of physics are the same for all non-accelerating observers and that the speed of light is constant for all observers. This theory led to groundbreaking concepts such as time dilation, length contraction, and the famous equation E=mc^2.
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10 Key excerpts on "Einstein's Theory of Special Relativity"
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.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 3 Special Relativity and General Relativity Special Relativity USSR postage stamp dedicated to Albert Einstein 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. ________________________ WORLD TECHNOLOGIES ________________________ 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.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 4 Special Relativity USSR postage stamp dedicated to Albert Einstein 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. ________________________ WORLD TECHNOLOGIES ________________________ 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.
eBook - PDFThe Sciences
An Integrated Approach
- James Trefil, Robert M. Hazen(Authors)
- 2022(Publication Date)
- Wiley(Publisher)
Maxwell’s equations could be wrong and the speed of light depends on the speed of the source emitting the light (in spite of abundant experimental support for the equations); or, 3. Our intuitions about the addition of velocities could be wrong, in which case the universe might be a very strange place indeed. Einstein focused on the third of these possibilities. The idea that the laws of nature are the same in all frames of reference is called the principle of relativity, and can be stated as follows: • Every observer must experience the same natural laws. This statement is the central assumption of Einstein’s theory of relativity. Hidden beneath this seemingly simple statement lies a view of the universe that is both strange and wonderful. The extraordinary theoretical effort required to understand the conse- quences of this one simple assumption occupied Einstein during much of the first decades of the twentieth century. janeb13/Pixabay FIGURE 7.2 Albert Einstein (1879–1955). 7.2 | Special Relativity 189 THINK! STOP & It may seem obvious that the laws of nature are the same every- where in the universe, but how can we know for sure? How might you test this statement? We can begin to understand Einstein’s work by recalling what Isaac Newton had dem- onstrated three centuries earlier, that all motions fall into one of two categories: uniform motion or acceleration (Chapter 2). Einstein therefore divided his theory of relativity into two parts—one dealing with each of these kinds of motion. The easier part, first pub- lished by Einstein in 1905, is called special relativity and deals with all frames of refer- ence in uniform motion relative to one another—reference frames that do not accelerate. It took Einstein another decade to complete his treatment of general relativity, mathe- matically a much more complex theory, which applies to any reference frame whether or not it is accelerating relative to another.
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.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 2 History of Special Relativity The history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einstein, and subsequent work of Max Planck, Hermann Minkowski and others. Introduction Although Isaac Newton based his theory on absolute space and time, he also adhered to the principle of relativity of Galileo Galilei. This stated that all observers who move uniformly relative to each other are equal and no absolute state of motion can be attributed to any observer. During the 19th century the aether theory was widely accepted, mostly in the form given by James Clerk Maxwell. According to Maxwell all optical and electrical phenomena propagate in a medium. Thus it seemed possible to determine absolute motion relative to the aether and therefore to disprove Galileo's Principle. The failure of any experiment to detect motion through the aether led Hendrik Lorentz in 1892 to develop a theory based on an immobile aether and the Lorentz transformation. Based on Lorentz's aether, Henri Poincaré in 1905 proposed the Relativity Principle as a general law of nature, including electrodynamics and gravitation. In 1905 Albert Einstein published what is now called Special Relativity (SR) – he radically reinterpreted Lorentzian Electrodynamics by changing the concepts of space and time and abolishing the aether. This paved the way to General Relativity. Subsequent work of Hermann Minkowski laid the foundations of Relativistic Field Theories.
Our intuitions about the addition of velocities could be wrong, in which case the universe might be a very strange place indeed. Einstein focused on the third of these possibilities. The idea that the laws of nature are the same in all frames of reference is called the principle of relativity, and can be stated as follows: • • • Every observer must experience the same natural laws. • • • This statement is the central assumption of Einstein’s theory of relativity. Hid- den beneath this seemingly simple statement lies a view of the universe that is both strange and wonderful. The extraordinary theoretical effort required to understand the consequences of this one simple assumption occupied Einstein during much of the first decades of the twentieth century. Stop and Think! It may seem obvious that the laws of nature are the same everywhere in the universe, but how can we know for sure? How might you test this statement? We can begin to understand Einstein’s work by recalling what Isaac Newton had demonstrated three centuries earlier—that all motions fall into one of two categories: uniform motion or acceleration (Chapter 2). Einstein therefore divided his theory of relativity into two parts—one dealing with each of these kinds of motion. The easier part, first published by Einstein in 1905, is called special relativity and deals with all frames of reference in uniform motion relative to one another—reference frames that do not accelerate. It took Einstein another decade to complete his treatment of general relativity, mathematically a much more complex theory, which applies to any reference frame whether or not it is accelerating relative to another. At first glance, the underlying principle of relativity seems obvious, perhaps almost too simple. Of course the laws of nature are the same everywhere—that’s the only way that scientists can explain how the universe behaves in an ordered way.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 9 History of Special Relativity The history of special relativity consists of many theoretical results and empirical findings obtained by Albert Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einstein, and subsequent work of Max Planck, Hermann Minkowski and others. Introduction Although Isaac Newton based his theory on absolute space and time, he also adhered to the principle of relativity of Galileo Galilei. This stated that all observers who move uniformly relative to each other are equal and no absolute state of motion can be attributed to any observer. During the 19th century the aether theory was widely accepted, mostly in the form given by James Clerk Maxwell. According to Maxwell all optical and electrical phenomena propagate in a medium. Thus it seemed possible to determine absolute motion relative to the aether and therefore to disprove Galileo's Principle. The failure of any experiment to detect motion through the aether led Hendrik Lorentz in 1892 to develop a theory based on an immobile aether and the Lorentz transformation. Based on Lorentz's aether, Henri Poincaré in 1905 proposed the Relativity Principle as a general law of nature, including electrodynamics and gravitation. In 1905 Albert Einstein published what is now called Special Relativity (SR) – he radically reinterpreted Lorentzian Electrodynamics by changing the concepts of space and time and abolishing the aether. This paved the way to General Relativity. Subsequent work of Hermann Minkowski laid the foundations of Relativistic Field Theories. Aether and Electrodynamics of Moving Bodies Aether models and Maxwell's equations Following the work of Thomas Young (1804) and Augustin-Jean Fresnel (1816), it was believed that light propagates as a transverse wave within an elastic medium called luminiferous aether.
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.
eBook - PDFEinstein Relatively Simple: Our Universe Revealed In Everyday Language
Our Universe Revealed in Everyday Language
- Ira Mark Egdall(Author)
- 2014(Publication Date)
- World Scientific(Publisher)
E i n s t e i n R e l a t i v e l y S i m p l e 80 Just like in the presidential signing ceremony, events that happen at the same time in one reference frame do not necessarily happen simulta-neously in another reference frame. So the doors are closed and reopened at the same time in the barn reference frame — but at different times in the pole reference frame. Do you see it? From the point of view of the barn, the front and rear doors are closed and reopened when the pole is fully inside the barn — simultaneously. But from the point of view of the pole, first the rear door is closed and reopened and then, after the barn passes over the pole, the front door is closed and reopened — not at the same time! Once again, our oh so clever Albert Einstein is victorious. That a soli-tary young man with virtually no contact with physicists of his day could have thought up such a profound and all encompassing theory as special relativity is nothing short of astounding. Yes, Lorentz and Fitzgerald come up with some of the mathematics, and both they and French physicist Henri Poincaré had suggested some of the ideas of special relativity, but only Einstein made the full leap. He alone was able to cast off the shackles of Newtonian physics with, as physicist Kip Thorne put it, “a clarity of thought that others could not match.” 14 We are awed by Einstein’s fearlessness and humbled by his genius. Perhaps you are still doubtful. Maybe you are asking how space itself can contract? And for that matter, how can time shrink? Einstein thought deeply about the physical implication of his theory. He found his answer in the strict empirical view that reality is only what we measure . What are “Time” and “Space”? It might appear possible to overcome all the difficulties attending the definition of “time” by substituting “the position of the small hand of my watch” for “time”.
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