Final Exam. Sunday, 5/12, 7:45 am Van Vleck B115

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2 Final Exam Sunday, 5/12, 7:45 am Van Vleck B115 Should take ~1 hour (you ll have up to 2) Similar format, probably at least one longer essay question, more open ended Focused on last 3 rd of class, but everything is fair game I ll hand out review sheet next time

3 Biofuel How many Calories per day do all the cars in the US consume? How many Calories per day do all the people on Earth consume? Oils have about 9 Calories per gram

4 Outline Black holes as wormholes Stabilizing a wormhole Where does the wormhole connect to? Time machines

5 Singularity Rotating BH Ring singularity Also an inner horizon where flow of space slows down to speed of light

6 Rotating BH Falling through inner horizon you see infinitely blueshifted light You can miss the singularity and are push back out through another horizon Black hole connects to a white hole somewhere else Another universe? Pocket universe? Another part of the same universe?

7 Falling into a Rotating BH

8 See description and movies at: rn.html

9 Rotating BH as Wormhole You can miss the singularity and fall back out through another horizon You can see another universe and escape through the white hole In reality, the connection will be unstable and collapse once anything ties to go through it.

10 Black Hole Wormhole

11 Stabilizing a Wormhole Mathematically, can make a 2-way wormhole with no singularity A matter or radiation falls into a wormhole, it will try to pinch off before anything can make it through To stabilize it, need something that give an outward pressure more than its mass

12 Stabilizing a Wormhole A matter or radiation falls into a wormhole, it will try to pinch off before anything can make it through To stabilize it, need something that give an outward pressure more than its mass Need Exotic Matter: something with negative mass but outward positive pressure

13 Exotic Matter Negative mass but positive pressure Avoids having a singularity Pressure keeps mouth of wormhole open

14 Exotic Matter Does anything like exotic matter exist? Dark Energy: Universe is expanding and accelerating Something pushing Universe to make it accelerate Vacuum energy negative pressure in a vacuum

15 Exotic Matter Does anything like exotic matter exist? Quantum Foam: Near a black hole, quantum fluctuation make BH evaporate Act like negative mass as seen by the radiation coming out Act like exotic matter in curved space

16 Wormholes Assuming you could make a stable wormhole: Where does it connect to?

17 Pocket Universe Wormholes Everything that falls into a black hole gets spit out into a new baby universe White hole creates is but quickly pinches off Our Universe could be an example

18 Parallel universe Connects to another universe rather than our own Wormholes Many universe hypothesis: Every possible outcome happens in some universe Might be reachable by wormhole

19 Wormholes Another part of the same universe Shortcut through space Space is stretched inside the wormhole Travel is faster than light on a normal route, but slower than light through wormhole

20 Wormholes Another part of the same universe

21 Time Machines If you have a traversable wormhole, you can build a time machine:

22 Time Machines If you have a traversable wormhole, you can build a time machine: Start with a wormhole with two ends near each other Keep one end fixed Put the other on a spaceship, accelerate to relativistic speed for some time, turn around an bring it back

23 Time Machines If you have a traversable wormhole, you can build a time machine: Start with a wormhole with two ends near each other Keep one end fixed Put the other on a spaceship, accelerate to relativistic speed for some time, turn around an bring it back End that travelled will be younger than stationary end

24 Time Machines If you have a traversable wormhole, you can build a time machine: End that travelled will be younger than stationary end Going from the stationary end to the travelled end will take you forwar in time Going from the travelled end to the stationary end will take you back in time

25 Wormhole Time Machine Can t travel back to before the time machine was created

26 Wormhole Time Machine Can t travel back to before the time machine was created Existence of time machines messes up causality Example: billiard balls

27 Wormhole Time Machine Even if wormholes exist, can time machines really exist? Don t really want them to Radiation traveling through the wormhole build up and destroys it? Wormhole only takes you to a parallel universe, so you can t mess up history?

28 Problem: You create a time machine You travel 10 years into the future and find a statue of yourself at the Capitol labeled World s First Time Traveller You steal the statue and take it back with you in time to prove you went to the future To celebrate, the statue is put up at the Capitol in the spot you found it 10 years later

29 Problem: You create a time machine You travel 10 years into the future and find a statue of yourself at the Capitol labeled World s First Time Traveller You steal the statue and take it back with you in time to prove you went to the future To celebrate, the statue is put up at the Capitol in the spot you found it 10 years later Who carved the statue?

30 Problem: You create a time machine You travel 10 years into the future and find a statue of yourself at the Capitol labeled World s First Time Traveller You steal the statue and take it back with you in time to prove you went to the future To celebrate, the statue is put up at the Capitol in the spot you found it 10 years later Who carved the statue? How old is it?