explain the consequences of the postulates of special relativity

The timing will be more accurate if some sort of electronic detection is used, avoiding human reaction times and other complications. It seems to me unbelievable that the course of any process (e.g., that of the propagation of light in a vacuum) could be conceived of as independent of all other events in the world.")[13]. This total distance should equal \( c\Delta t_{right}\), so we get \( \Delta t_{right} = L/(c-v) \). 27.4: Implications of Special Relativity - Physics LibreTexts Since these seem to be correct to a great extent, ")[2], 1. You can measure the wavelength. 28.1: Einstein's Postulates - Physics LibreTexts By the end of this section, you will be able to do the following: The learning objectives in this section will help your students master the following student standards: [AL] Discuss the history of the concept of the ether. , Second Postulate (Invariance of C): The speed of light in a vacuum or empty space is equal for all the observers in any inertial frame of reference. The original material is available at: x If light speed is a constant and the two frames of reference are both valid, then simultaneity is not the same for all observers. 2 If A and B correspond to the clocks striking in Los Angeles and New York respectively, then it is clear that B must occur at an earlier time in the primed frame if indeed A and C are simultaneous in that frame. { "10.01:_An_Old_and_a_New_Axiom" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10.02:_Consequences_of_Einstein\'s_Postulates" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10.E:_Einstein\'s_Postulates_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Introduction_to_Classical_Mechanics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Forces" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Energy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Momentum" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Rotational_Motion_Torque_and_Angular_Momentum" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_General_Planar_Motion" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_General_Rotational_Motion" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Oscillations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Waves" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Einstein\'s_Postulates" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_Lorentz_Transformations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12:_Spacetime_Diagrams" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "13:_Position_Energy_and_Momentum_in_Special_Relativity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "14:_Relativistic_Collisions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "15:_Relativistic_Forces_and_Waves" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "16:_Appendices" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 10.2: Consequences of Einstein's Postulates, [ "article:topic", "Michelson-Morley experiment", "license:ccbyncsa", "showtoc:no", "authorname:tidema", "Lorentz contraction", "licenseversion:40", "source@https://textbooks.open.tudelft.nl/textbooks/catalog/book/14" ], https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_Mechanics_and_Relativity_(Idema)%2F10%253A_Einstein's_Postulates%2F10.02%253A_Consequences_of_Einstein's_Postulates, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), source@https://textbooks.open.tudelft.nl/textbooks/catalog/book/14. . When astronomers witness an event on the sun, such as a sunspot, it actually happened minutes earlier. In addition, Einsteins theory shows that if you were moving forward relative to Earth at nearly c (the speed of light) and could throw a ball forward at c, an observer at rest on the earth would not see the ball moving at nearly twice the speed of light. The speed of light in a vacuum is c in all inertial frames of reference. Because light speed in air is slower than in a vacuum, light is refracted as it enters Earths atmosphere. There is an interesting symmetry between time dilation and Lorentz contraction, which gives an alternative way of getting equation (\(\ref{eq:1}\)) once the effect of time dilation is known. To see what Michelson and Morley expected to find when they measured the speed of light in two directions, watch this animation. However, as noted above, it is inconsistent with our notions as to how velocities add, or alternatively, how we think the world should look from reference frames moving at different speeds. Another is Newton's first law. For instance, if two clocks, one in New York and one in Los Angeles, strike the hour at the same time in the earth reference frame, then in Galilean relativity these events also appear to be simultaneous to instruments in the space shuttle as it flies over the United States. Abstract. In addition to events and physical objects, there are a class of inertial frames of reference. It is just something you decide is a fixed point or group of connected points. A typical example is Maxwell's equations. 10.2 Consequences of Special Relativity - Physics | OpenStax When the speed of an object becomes the speed of light, its length appears to shorten when viewed by a stationary observer. E [BL][OL] Explain the geometry of the MichelsonMorley experiment. Three (very sensitive) Michelson interferometers have recently been used to detect small vibrations in spacetime itself, the gravitational waves predicted by Einsteins general theory of relativity. Special Theory of Relativity - BYJU'S 1 Postulates of special relativity [ edit] 1. 10.2: Consequences of Einstein's Postulates - Physics LibreTexts When this happens, time measurements are the same in both frames of reference. are not subject to the Creative Commons license and may not be reproduced without the prior and express written The speed of light in vacuum is less than 3.0010. [3] Also Hermann Minkowski implicitly used both postulates when he introduced the Minkowski space formulation, even though he showed that c can be seen as a space-time constant, and the identification with the speed of light is derived from optics. , Einstein began with two simple postulates based on the two things we have discussed so far in this chapter. It might be better to let the students do the experiment at home so they can get more of a hands-on experience. Lesson 1 - Consequences of Special Relativity Postulates; After going through this module, you are expected to: Explain the consequences of Einstein's Theory of Special Relativity postulates; Analyze situations and calculate problems involving the consequences of the postulates of Einstein's Theory of Special Relativity; and In Galilean relativity it is fairly obvious what we mean by two events being simultaneous it all boils down to coordinating portable clocks which are sitting next to each other, and then moving them to the desired locations. where we have the expression for the joule (J) in terms of its SI base units of kg, m, and s. The student knows and applies the laws governing motion in a variety of situations. All of the observed facts about spacetime can be derived from two postulates: where \(X\), \(T\), and \(I\) are defined in figure 4.4. A theory along the lines of that proposed by Heinrich Hertz (in 1890)[17] allows for light to be fully dragged by all objects, giving local c-constancy for all physical observers. 4.3: Postulates of Special Relativity - Physics LibreTexts 10 Special relativity is a theory in physics that concerns the relationship between space and time and says that they're two sides of the same coin: spacetime. for an electromagnetic field, and so forth. A dark fringe appears where the crest of one wave coincides with a trough of the other, so that the two cancel. Changes were made to the original material, including updates to art, structure, and other content updates. x A more modern example of deriving the Lorentz transformation from electrodynamics (without using the historical aether concept at all), was given by Richard Feynman. On the way back, we get a traveled distance of \(L\) minus \( v\Delta t_{left} \), which should equal \(c\Delta t_{left}\), so we get \( \Delta t_{left} = L/(c+v) \). Use the Check Your Understanding questions to assess students achievement of the sections learning objectives. If you did everything correctly, you will get a number very close to the speed of light. Fortunately, there is an event that both observers agree on: the fact that the two light beams, once reflected, return to the person in the middle of the train at the same time. However, collocation is a concept that depends on the reference frame. Consequently the aether should affect the speed of light for a beam traveling in the same direction as the wind, but not one traveling perpendicular to this direction. Here, a relative velocity between observers affects whether two events at well-separated locations are observed to be simultaneous. Ask students if they can think of other examples from the history of science. The main consequence of the minus sign in equation (\ref{4.3}) is that \(\mathrm{I}^{2}\) can be negative and therefore I can be imaginary. 2 Explain what is meant by a frame of reference. First, the vertical side of the triangle is multiplied by c. This is a trivial scale factor that gives time the same units as space. When the speed of one frame of reference past another becomes comparable to the speed of light, a time interval between two events at the same location in one frame appears shorter when measured from the second frame. [OL] If students are struggling with this explanation of simultaneity, let them know that there will be an animation in the next section that should make it clearer. [AL]Be sure students understand that this animation does not explain how light behaves. If you designate a point as being fixed and use that point to measure the motion of surrounding objects, what is the point called? The line passing through these two events, A and B, defines a line of simultaneity for both stationary and moving observers. Light is involved in the discussion of relativity because theories related to electromagnetism are inconsistent with Galileos and Newtons explanation of relativity. 1 Special relativity - Simple English Wikipedia, the free encyclopedia How long does it take light to travel from the sun to Earth in minutes and seconds? The classical way of thinking about simultaneity is so ingrained in our everyday habits that we have a great deal of difficulty adjusting to what special relativity has to say about this subject. A frame of reference is not a complicated concept. 27.2: Consequences of Special Relativity - Physics LibreTexts

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