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# Length Contraction

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1. Length Contraction

2. 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.

3. Contraction • Light traveling the length of B’s ruler takes less time as A sees B. • Time dilation • Constant light speed

4. Gamma Again • Each observer sees the other stick contracted.

5. 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, • So, L’ = 8.94 ly.

6. Doppler Shift • The classical Doppler shift for sound is due to relative motion between source and observer. • Depend on specific motion • Relativity changes this for light. • Constant speed of light • Only relative velocity

7. Relativistic Shift • The relativistic Doppler shift uses length contraction (or time dilation). • Both the wavelength and frequency are shifted.

8. Redshift • Objects that move rapidly away have wavelengths shifted longer. • Visible light shifts towards the red, and the effect is the redshift. next