Special_Relativity

Special_Relativity - Special Relativity Chapter 7...

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Special Relativity Chapter 7

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Einstein’s revolution - rethink the meaning of space and time Published “Special Theory of Relativity” in 1905 followed by “General Theory” in 1916 which incorporates gravity He began with the postulate that the laws of physics should be independent of the velocity of the observer Foundations
Apply this to Maxwell’s theory of EM radiation - requires there to be a solution to the equations that is constant in time (for someone moving at speed c ) but sinusoidal in space - not possible! Thus, speed of light must be the same for all observers, independent of their motion (EM waves are different from mechanical waves). How can velocity of light be constant? Velocity measurement depends on distance and time interval - could these quantities depend on the motion of the observer? See http://www.phys.unsw.edu.au/einsteinlight/jw/module3_weird_logic.htm for a discussion of the invariance of the speed of light.

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Simple experiment shows that simultaneity is not absolute. Thus, time is not absolute. Einstein then investigated how different types of situations appear to observers with different velocities (inertial reference frames). Einstein’s postulate could be stated “There is no experiment we can perform to tell us which inertial frame is moving and which is at rest. There is no ‘preferred’ inertial frame.” Absolute time absolute simultaneity
The constancy of the speed of light is paradoxical Imagine a red dot emits a flash of light  while a blue dot is moving away from the  red one at half the speed of light.   The red dot sees itself at the center of  the expanding sphere of light.  SR insists that the blue dot also sees the  light moving outward at the same speed  in all directions.  How can that be so? Paradox! ( http://casa.colorado.edu/~ajsh/sr/paradox.html)

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Find the solution to this paradox (i.e. arrange it so that both Red and Blue regard  themselves as being in the center of the sphere of light). In a spacetime diagram, the units of space and time are chosen so that light goes  one unit of distance in one unit of time (i.e. c = 1). Light moves upward and outward  at 45 degrees in the spacetime diagram. The lines along which Red and Blue move are called  worldlines . Each point in 4- dimensional spacetime is called an event. Light signals converging to or expanding  from an event follow a 3-dimensional hypersurface called the  lightcone . In the  diagram, the sphere of light expanding from the emission event is following the  future lightcone. There is also a past lightcone not shown here.
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This note was uploaded on 07/11/2011 for the course AST 3019 taught by Professor Sarajedini during the Spring '08 term at University of Florida.

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Special_Relativity - Special Relativity Chapter 7...

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