MP07SpecialRelativity1

MP07SpecialRelativity1 - CHAPTER 2 Special Theory of...

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2.1 The Need for Aether 2.2 The Michelson-Morley Experiment 2.3 Einstein’s Postulates 2.4 The Lorentz Transformation 2.5 Time Dilation and Length Contraction 2.6 Addition of Velocities 2.7 Experimental Verification 2.8 Twin Paradox 2.9 Space-time 2.10 Doppler Effect 2.11 Relativistic Momentum 2.12 Relativistic Energy 2.13 Computations in Modern Physics 2.14 Electromagnetism and Relativity CHAPTER 2 Special Theory of Relativity 1 It was found that there was no displacement of the interference fringes, so that the result of the experiment was negative and would, therefore, show that there is still a difficulty in the theory itself… - Albert Michelson, 1907 Albert Michelson (1852-1931)
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Newtonian (Classical) Relativity Newton’s laws of motion must be implemented with respect to (relative to) some reference frame. x z y A reference frame is called an inertial frame if Newton’s laws are valid in that frame. Such a frame is established when a body, not subjected to net external forces, moves in rectilinear motion at constant velocity .
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Newtonian Principle of Relativity If Newton’s laws are valid in one reference frame, then they are also valid in another reference frame moving at a uniform velocity relative to the first system. This is referred to as the Newtonian principle of relativity or Galilean invariance . x z y
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The Galilean Transformation For a point P: In one frame K : P = ( x, y, z, t ) In another frame K : P = ( x , y , z , t ) x z y K P = ( x, y, z, t ) P = ( x , y , z , t )
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Conditions of the Galilean Transformation 1. Parallel axes 2. K’ has a constant relative velocity (here in the x -direction) with respect to K. 3. Time ( t ) for all observers is a Fundamental invariant , i.e., it’s the same for all inertial observers. v x x t yy zz tt
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The Inverse Relations Step 1. Replace -v with +v. Step 2. Replace “primed” quantities with “unprimed” and “unprimed” with “primed.” v x x t yy zz tt
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2.1: The Need for Aether The wave nature of light seemed to require a propagation medium. It was called the luminiferous ether or just ether (or aether ) . Aether had to have such a low density that the planets could move through it without loss of energy. It had to have an elasticity to support the high velocity of light waves. And somehow, it could not support longitudinal waves. And (it goes without saying…) light waves in the aether obeyed the Galilean transformation for moving frames.
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Maxwell’s Equations & Absolute Reference Systems In Maxwell’s theory, the speed of light, in terms of the permeability and permittivity of free space, was given by: Aether was proposed as an absolute reference system in which the speed of light was this constant and from which other measurements could be made.
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MP07SpecialRelativity1 - CHAPTER 2 Special Theory of...

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