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Special Relativity

Special Relativity. Starter: A spaceship moving at ½ the speed of light has a headlight that sends out light at the speed of light (naturally). The space ship is moving towards a planet where a person

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Special Relativity

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  1. Special Relativity Starter: A spaceship moving at ½ the speed of light has a headlight that sends out light at the speed of light (naturally). The space ship is moving towards a planet where a person measures the incoming speed of the light from the spaceship. What speed does the person on the planet measure the light to be? ( speed of light = c) a. .5 c b. c c. 1.5 c d. none of these

  2. Special Relativity Starter According to Special Relativity, a material object cannot obtain the speed of light. What would happen to gamma, if v equaled c? g

  3. Light is a wave – what is the medium? Answer: The Magical Aether.

  4. The Michelson–Morley experiment was performed in 1887. Result: There is no Aether.

  5. Einstein’s Interpretation There is no Aether – Light moves at the same speed regardless of the motion of the source or the observer. If the speed of light is invariant – time and distance depend on the observer’s motion.

  6. Time Dilation T = g To g If the clock is at rest with respect to a person, the time the person reads is labeled To.

  7. Length Contraction L = Lo / g g If the length is at rest with respect to a person, the length the person reads is labeled Lo.

  8. Practice / Example A rocket ship, 200m long ,moves by an observer at .95c. Calculate gamma. g = = 3.20 2. How long is the ship according to the observer? L = Lo / g = 200m/3.20 = 62.5m An astronaut on the ship sees 1 second ticks off on his clock. What time interval does the observer measure? T = g To = 3.20 (1 sec) = 3.20 seconds

  9. Application Complete the time dilation, length contraction problem set.

  10. Connection Muons are created in the upper atmosphere and have a very short lifetime. They move toward Earth at around 95%c. They shouldn’t live long enough to make it to the surface of the Earth, but they do. Why do they make it to the surface? Hint: What happens to their internal clock that governs their lifetime?

  11. EXIT Exit: A spaceship moving at 95 % the speed of light is 100m long. What length does an observer on a stationary platform measure the ship to be?

  12. EXIT Exit: A spaceship moving at 3/4 the speed of light has a headlight that sends out light to a planet it is moving towards. Before Einstein, what was the expected speed of light as measured on the planet? After Einstein, what is the expected measured speed of light?

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