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Astronomy 10: Lecture 15 Confusing Physics: Relativity

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Extra Credit Assignment Write a 5 to 10 page paper going into detail on a single aspect of astronomy (currents events, a type of object, etc.). Be concise. Don’t pick too broad a subject. Will be accepted up until the final. Worth up to 5% of your grade If you are more than 5% away from a boundary, I won’t grade it. Plagiarism earns a course grade of F, regardless.

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Exam #3 1 week from today Bring #2 pencil and a scantron form! If you need to schedule a make up contact me today Make ups will need to be finished PRIOR to the final. I have to turn in final grades 1 week from tomorrow.

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Parable #1: Einstein's Cows Farmer plugs in the battery for the electric fence Farmer Einstein

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Parable #1: Einstein's Cows First cow jumps Farmer Einstein

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Parable #1: Einstein's Cows Second cow jumps Farmer sees first cow jump Farmer Einstein

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Parable #1: Einstein's Cows Third cow jumps Farmer Einstein

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Parable #1: Einstein's Cows Einstein sees all three cows jump Farmer sees second cow jump Farmer Einstein

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Parable #1: Einstein's Cows Farmer Einstein

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Parable #1: Einstein's Cows Farmer sees third cow jump. This isn’t really relativity, just a result of the finite speed of light Farmer Einstein

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Relativity Principle #1 The speed of light is the same for all observers regardless of their relative motions. Picture a runner racing a light beam at half the speed of light

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Relativity Principle #1 The speed of light is the same for all observers regardless of their relative motions. After 1 second.

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Relativity Principle #1 The speed of light is the same for all observers regardless of their relative motions. After 2 seconds

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Relativity Principle #1 The speed of light is the same for all observers regardless of their relative motions. After 3 seconds

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Relativity Principle #1 The speed of light is the same for all observers regardless of their relative motions. After 4 seconds

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Relativity Principle #1 But hold on a second! After 4 seconds, isn’t the runner twice as close to where the light beam is as the stationary observer? How could he get the same answer when measuring the speed of light? –Three possibilities… Either the moving observer doesn’t think that 4 seconds have gone by, or he thinks the light beam is farther away than we perceive it as being, or both….

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Parable #2: Follow the bouncing light How do we tell which is the case? Picture a clock that tells time by measuring how light bounces between two mirrors, 1/2 light-nanosecond apart (15 cm).

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Parable #2: Follow the bouncing light How do we tell which is the case? Picture a clock that tells time by measuring how light bounces between two mirrors, 1/2 light-nanosecond apart (15 cm).

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Parable #2: Follow the bouncing light What if our clock is moving at high speed? Then the light has farther to travel. So it take longer to make the journey

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Parable #2: Follow the bouncing light Compare to a stationary clock But what if you are traveling with the clock? –In that case the clock is stationary (with respect to you, so it seems to take 1 nanosecond

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Relativity Principle #2 Time Dilation A moving clock runs slower than a stationary one. –Moving relative to what? Relative to the observer! –If you are on earth and you look at a space ship traveling at near the speed of light, you will see clocks on the space ship running slower –If you are on a space ship traveling at near the speed of light, you will see clocks on the earth are running slower. –Which clock is right?

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Back to our runner Using simple geometry we can determine that for our runner moving at half the speed of light sqrt(1-0.5^2)=0.866 seconds pass for every second we experience. So 4 seconds for us was only 3.464 seconds for our runner, so for him the light should have only moved 3.464 light seconds. But to us it appears that the light is 2 light-seconds from him. The change in time isn’t enough to explain the difference! Our runner’s perception of distance must be different as well.

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Relatvity Principle #3 Lorenz contraction Lengths of moving object appear shorter by a factor of 1/sqrt(1-v 2 /c 2 ) Our distance measures look shorter to the runner. His look shorter to us. He is shrunk by a factor of 0.866. The two light seconds we see appears to be 2.31 light seconds if we use his ruler...

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What time is it? But wait! We just said that after 4 of our seconds he sees that the light is 3.464 light seconds away, but we think he should see it 2.31 light seconds away! That means we’re still missing something….

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Relativity Principle #4 Simultaneity Things can only be said to happen at the same time if they also happen in the same place. What time you think it is somewhere else depends upon how you are moving.

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Relativity Principle #4 Simultaneity Our runner disagrees with us about where the light beam is at any given time. Suppose the beam hits an asteroid after 3 seconds (for us). 3 seconds for us would be 2.598 seconds for the runner. Our runner thinks he has been traveling for 2.598 seconds and is 1.229 light seconds from the asteroid, so he calculates that the asteroid got hit 3.897 seconds after the race started. That’s 3.375 seconds of time for the stationary observer. The two disagree about what time the asteroid got hit!

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Relativity Principle #5 Causality Events separated in time by more time than it takes light to travel between the them could cause one another –All observers, regardless of how they are moving will see the same order of events. If events are separated in time by less than the light travel time one cannot cause the other –Observers may disagree about the order in which they occur.

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Causality: Light Cone

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Parable #3: Fast Car Suppose you have a car 30 feet long and your garage is only 15 feet long with doors at both ends. By moving the car fast enough, can you get the car in the garage and close both doors simultaneously?

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Parable #3: Fast Car How it appears to a stationary observer

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Parable #3: Fast Car How it appears to a stationary observer

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Parable #3: Fast Car How it appears to a stationary observer

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Parable #3: Fast Car How it appears to a stationary observer

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Parable #3: Fast Car How it appears to a stationary observer

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Parable #3: Fast Car How it appears to a stationary observer

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Parable #3: Fast Car How it appears to a stationary observer

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Parable #3: Fast Car How it appears to a stationary observer

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Parable #3: Fast Car How it appears to a stationary observer

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Parable #3: Fast Car How it appears to a stationary observer

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Parable #3: Fast Car How it appears to the driver of the car

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Parable #3: Fast Car How it appears to the driver of the car

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Parable #3: Fast Car How it appears to the driver of the car

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Parable #3: Fast Car How it appears to the driver of the car

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Parable #3: Fast Car How it appears to the driver of the car

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Parable #3: Fast Car How it appears to the driver of the car

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Parable #3: Fast Car How it appears to the driver of the car

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Parable #3: Fast Car How it appears to the driver of the car

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Parable #3: Fast Car How it appears to the driver of the car

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Parable #3: Fast Car How it appears to the driver of the car

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Parable #3: Fast Car How it appears to the driver of the car Were both doors closed at the same time? Stationary observer says yes, driver says no. Both are right.

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Parable #3: Fast Car How it appears to the driver of the car Were both doors closed at the same time? Stationary observer says yes, driver says no. Both are right.

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Relativity Principle #5 Time can be treated like a dimension. For two events all observers will measure the same value for… –DS 2 =(distance between the events) 2 -(c*time difference) 2 If we see two events in the same place, but at different times, someone else may see them in different places, but farther apart in time.

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Relativity Principle #5 Everything moves through space-time at the speed of light. For something to move faster through space it must move slower through time. (Velocity=rotation of your coordinate system.)

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Relativity Principle #5 But everyone perceive themselves as not moving, and therefore moving only through time

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Relativity Principle #5 But everyone perceive themselves as not moving, and therefore moving only through time. You should never see anyone else’s clock moving faster than yours.

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Parable #4: The twin paradox. But what about round trips? Can’t either side say the other’s clock is running slower? Suppose Betty and Barney are twins and one of them travels to a star 4 light years away at a speed that would result in a time and length contraction of a factor of two (0.866*c)

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Parable #4: The twin paradox. Suppose Betty and Barney are twins and Betty of them travels to a star 4 light years away at a speed that would result in a time and length contraction of a factor of two (0.866c) Betty sees the distance as 2 light years, so the round trip will take 4.62 years. During the trip she calculates Barney’s clock is running at half the rate of hers. Barney sees the distance as 4 light years so the round trip will take 9.24 years. During the trip he calculates Betty’s clock is running at half the rate of his. Barney will be 4.62 years older than Betty when she gets back, but where did the extra clock ticks come from? (Think Doppler shift!) On the way out, Betty sees (with light) ticks from Barney’s clock every 3.231 seconds. On the way back, every 0.232 seconds.

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