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 0.999 c 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 motionDepend 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