Journal 5 /9/14

1. Journal 5/9/14 This is the last warm-up of the year. Summarize the top 5 things you feel you’ve learned in this class this year. Objective Due Today To examine some of the stranger problems in relativity none

2. “Paradoxes” in Relativity When we look at relativity, we can get a few odd situations that seem to be paradoxes – contradictions that just can’t happen. We’re going to look at 3 of them.

3. “Paradoxes” in Relativity The Twin Paradox Two brothers are twins. One of them stays on earth, while the other gets on a spaceship going relativistic speeds to head out to a distant star and back. When the journey starts, the twins are 30 years old and the journey is supposed to take 20 years. A B

4. “Paradoxes” in Relativity The Twin Paradox We see the paradox if we look at things from each brother’s point of view. Brother A looks at B’s spaceship and sees his brother moving slowly. He moves so slowly that by the time B heads out and back, B’s clock has only gone forward 10 years instead of 20. Now A is 50 years old, but B is only 40 due to time dilation. Cool. A B

5. “Paradoxes” in Relativity The Twin Paradox But we get a problem when we look at things from B’s point of view. From his point of view, the earth is speeding away behind him. If he looks at A, he’ll see a moving and aging slowly. By the end of his 20 year journey, he’ll see himself at 50 years old but his brother – A – as only being 40. So both brothers see the other as being younger A B

6. “Paradoxes” in Relativity The Twin Paradox Obviously both can’t age slower. If we do this trip, relativity tells us that something has to happen with time. So what’s the solution? A B

7. “Paradoxes” in Relativity The Twin Paradox Remember how we said that moving at relativistic speeds changes length, too? For brother B, the distance he needs to travel for his trip is actually shorter. This means he can get there and back in less time. In reality, we’ll see that brother B actually ages less than A when everything is said and done. A will be 50 while B is only 40. But what about what B sees? He saw his brother aging slower! A B

8. “Paradoxes” in Relativity The Twin Paradox The way we explain what B sees is actually the point of this little paradox. When B turns around to head back to earth, he’s actually going to see time on earth going extra fast until it looks like 20 years have passed on earth. But why? We said that relativity stuff always makes time go slower when looking out. This is true, but its being outdone by the fact that light from earth is hitting the spaceship a lot more often. A B

9. “Paradoxes” in Relativity The Twin Paradox Think of this like driving in the rain. If you drive away, rain won’t hit your windshield as much because it can’t catch up to your car. If you drive into the rain, it hits your car more because your car is “catching up” to the rain. What makes this problem worth looking at is that we need to note that B wasn’t just another point of view. When he accelerated or decelerated, rules for relativity changed. A B

10. “Paradoxes” in Relativity farmer The Snake Paradox An angry farmer wants to kill a snake that’s speeding towards him at relativistic speeds. (Just go with it.) The snake is 2 meters long and the farmer holds his 2 butcher knives 1 meter apart. When the snake is in right in front of him, he swings his knives down aaaand…. the snake escapes unharmed. Wut. snake

11. “Paradoxes” in Relativity The Snake Paradox Once again, to figure this out we need to look at things from both points of view to see what’s really going on. From the snake’s point of view, everything else rushing towards it and is squished shorter. So the farmer’s knives look even closer together. Now we’re trying to fit a 2 meter snake in-between knives that are only ½ a meter apart! The snake looks extra dead now! snake

12. “Paradoxes” in Relativity The Snake Paradox Alright… so how about things from the farmer’s point of view? From his perspective, the snake is moving fast and is squished. Now the snake is only 1 meter long. When he swings his knives down, the snake just barely fits between them and escapes unharmed. So the snake dies from it’s perspective and lives from the farmer’s perspective. Problem! snake

13. “Paradoxes” in Relativity The Snake Paradox The trick here is all about time. Early on, we said that events in relativity don’t have to be “simultaneous”. This means one person may see things happen at a different time than another. The farmer’s view is what we would consider “normal”. The snake shrinks and lives. From the snake’s point of view, it’s going to live, too, but because of something else. snake

14. “Paradoxes” in Relativity The Snake Paradox The snake keeps moving until it gets right before the farmer’s right side knife.Neither knife has come down yet. Next, the right knife onlycomes down then goes back. The snake keeps going and theleft knife goes down and upright as the snake passes. snake snake snake snake

15. “Paradoxes” in Relativity The Snake Paradox This may seem crazy, but this is totally how the universe actually works. Not only can time slow down, space shrink, and mass increase, but we can have things happen at different times as well. However, you can’t use this to time travel or see the future. It’s complicated. snake