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Special_Relativity

# Special_Relativity - Special Relativity Chapter 7...

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1/11/10 1 Special Relativity Chapter 7 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 ht p:/ www.phys.unsw.edu.au/einsteinlight/jw/module3_weird_logic.htm for a discussion of the weirdness of the invariance of the speed of light!

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1/11/10 2 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 The postulate that the speed of light is the same in any inertial frame leads immediately to a paradox. Imagine the red dot emits a flash of light and the blue dot is moving away from Red at about half the speed of light. Red thinks she is at the centre of the expanding sphere of light. But, says special relativity, Blue also thinks that the light moves outward at the same speed in all directions from him. So Blue should be at the centre of the expanding light sphere too. But he's not, is he. Paradox! ( http://casa.colorado.edu/~ajsh/sr/paradox.html) Challenge Can you figure out Einstein's solution to the paradox? Somehow you have to arrange that both Red and Blue regard themselves as being in the centre of the expanding 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. the units are such that the speed of light is one, c = 1. Thus light moves upward and outward at 45 degrees from vertical in the spacetime diagram. The lines along which Red and Blue move through spacetime are called their 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. This is a
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Special_Relativity - Special Relativity Chapter 7...

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