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Length Contraction Relative Space An observer at rest measures a proper time for a clock in the same frame of reference. An object also has a proper length when measured by an observer in the same frame of reference. If other observers are moving the apparent length will change in the direction of motion. Contraction Light traveling the length of B’s ruler takes less time as A sees B. • Time dilation • Constant light speed L L c t t Gamma Again Each observer sees the other stick contracted. 2 L v L 1 L c Distant Star A starship cruises at 0.999c towards a star that is 200. ly away. What is the apparent distance to a traveler on the ship? The speed given is in units of c so v/c=0.999. For the moving observer, L L L 1 0.999 2 So, L’ = 8.94 ly. Doppler Shift The classical Doppler shift for sound is due to relative motion between source and observer. • Depend on specific motion cs vo f f cs vs Relativity changes this for light. • Constant speed of light • Only relative velocity Relativistic Shift The relativistic Doppler shift uses length contraction (or time dilation). Both the wavelength and frequency are shifted. c/ f 1 v / c 1 v / c 1 v / c f f 1 v / c Redshift Objects that move rapidly away have wavelengths shifted longer. Visible light shifts towards the red, and the effect is the redshift. next