Special Relativity = Relatively Weird

Special Relativity Postulate 1: The laws of physics are the same for all observers moving with constant velocity There is no test that can be done in a closed room that will determine if the room is sitting still or moving with a constant speed, or what that speed is.

Special Relativity Postulate 2: v = c Special Relativity Postulate 2: The speed of light is the same for all observers v = 0.8c No matter how fast an observer is moving, or in what direction, she will always measure the speed of light to be 3.00 x 108 m/s. v = 0.9c

Special Relativity - Weird Results Time Dilation v = 0.9c Earth’s Reference Frame (Observer on Earth) The clocks on the moving spaceship will appear to run more slowly than clocks on the stationary Earth. v = 0

Special Relativity - Weird Results Time Dilation Ship’s Reference Frame The clocks on the moving Earth will appear to move more slowly than clocks on the stationary spaceship. v = 0.9c

Special Relativity - Weird Results Time Dilation t0 = time on stationary (observer’s) clock t = time on moving clock Ship’s Reference Frame The clocks on the moving Earth will appear to move more slowly than clocks on the stationary spaceship. v = 0.9c

Special Relativity - Weird Results Time Dilation Example A spaceship is zipping by Earth at 96% of the speed of light. Mission controllers on Earth watch as the pilot of the spaceship starts water boiling for his tea. 15 minutes later (by mission control’s clocks), he’s drinking it. How much time elapsed on the ship’s clock? t0 = time on stationary (observer’s) clock t = time on moving clock v = 0.96c

Special Relativity - Weird Results Time Dilation Example A spaceship is zipping by Earth at 96% of the speed of light. Mission controllers on Earth watch as the pilot of the spaceship starts water boiling for his tea. 15 minutes later (by mission control’s clocks), he’s drinking it. How much time elapsed on the ship’s clock? t0 = time on stationary (observer’s) clock t = time on moving clock v = 0.96c

Special Relativity - Weird Results Time Dilation How are we to understand this? “Normal” experience A ball tossed up and then caught moves straight up and down in the train’s reference frame From another reference frame, the ball travels further, and must therefore be going faster. The faster the train appears to be moving, the faster the ball must be moving

Special Relativity - Weird Results Time Dilation How are we to understand this? “Normal” experience Relativistic weirdness A similar experiment done with light: Clock pulses are counted when the light pulse has gone up and down in a spaceship. When the spaceship is moving, the light appears to travel a longer path – but light always travels at the same speed! The clock must run slow. But this is not just clocks slowing down. Time itself actually slows down in that frame.

Special Relativity - Weird Results Length Contraction v = 0.9c Earth’s Reference Frame The moving spaceship will be shorter (when measured by Earth’s meter sticks) than when it is not moving with respect to the Earth. v = 0

Special Relativity - Weird Results Length Contraction Ship’s Reference Frame The moving Earth will be shorter (when measured by the ship’s meter sticks) than when it is not moving with respect to the ship. v = 0.9c

Special Relativity - Weird Results Length Contraction L0 = length when measuring stationary object L = length when measuring moving object Ship’s Reference Frame The moving Earth will be shorter (when measured by the ship’s meter sticks) than when it is not moving with respect to the ship. v = 0.9c

Special Relativity - Weird Results Length Contraction Example When my spaceship is at rest on Earth, it measures 100 m long. When it is screaming by the Earth at 99% of the speed of light, how long do Earth observers measure it to be? L0 = length when measuring stationary object L = length when measuring moving object v = 0.99c

Special Relativity - Weird Results Length Contraction Example When my spaceship is at rest on Earth, it measures 100 m long. When it is screaming by the Earth at 99% of the speed of light, how long do Earth observers measure it to be? L0 = length when measuring stationary object L = length when measuring moving object v = 0.99c

Special Relativity - Weird Results Length Contraction Can lead to an even weirder result Billy Bob rides his bike through town at 0.99c. To observers on the sidewalk, he and his bike appear shortened along the direction of motion: Billy Bob There is no time in which his bicycle wheels straddle an entire city block.

Special Relativity - Weird Results Length Contraction Can lead to an even weirder result Billy Bob rides his bike through town at 0.99c. To Billy Bob, it’s the city blocks that appear shortened along the direction of motion: Billy Bob His front and back wheel do straddle an entire city block. So who’s right?

Special Relativity - Weird Results Relativity of Simultaneity Two events seen as simultaneous from one reference frame may not appear simultaneous when observed from another.

E = m c2 Special Relativity - Weird Results Energy – Mass conversion c = 3.00 x 108 m/s This describes the conversion of mass to energy in the Sun, in the process we call nuclear fusion.

Tommy and Timmy are twins Tommy and Timmy are twins. Tommy becomes an astronaut, and spends a year on the International Space Station. While in Earth orbit, moving at 17,500 mph, … A) Tommy ages more slowly than Timmy B) Tommy ages more quickly than Timmy C) Tommy and Timmy age at the same rate

Astro-Cash Cab! Adrianna Derek Mariah Corey

1) When astronaut Bob cruises by Earth at 97% of the speed of light, his clocks appear to us on Earth to be running slow. What does Bob see when he looks at our clocks? They appear to be running fast. They appear to be running slow. They are running normally.

2) Before Bob left Earth we measured his ship to be 35 feet long 2) Before Bob left Earth we measured his ship to be 35 feet long. As he cruises by Earth at 97% of the speed of light, how long do we measure his ship to be? 35 feet Longer than 35 feet Shorter than 35 feet

the lights to flash simultaneously. 3) When your friend flies by you in a spaceship at half the speed of light, with lights that are simultaneously flashing in your frame, she observes the lights to flash simultaneously. the light in front of her to flash first. the light behind her to flash first.

4) Your friend travels by you in a spaceship at 90% the speed of light 4) Your friend travels by you in a spaceship at 90% the speed of light. Which of the following is not true? You will see time running more slowly for your friend than for you. Your friend will see time running more slowly for you than for her. If you each perform the same experiment to measure the time for an atom to decay, you will each get the same result. Your friend will measure the length of your spaceship to be shorter than what you measure it to be. none of the above (all are true)