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 3rd of class, but everything

is fair game •  I’ll hand out review sheet next time

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

Outline

•  Black holes as wormholes

•  Stabilizing a wormhole

•  Where does the wormhole connect to?

•  Time machines

Singularity – Rotating BH

•  Ring singularity •  Also an inner horizon where flow of space

slows down to speed of light

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?

Falling into a Rotating BH

See description and movies at:

•  http://jila.colorado.edu/~ajsh/insidebh/rn.html

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.

Black Hole Wormhole

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

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

Exotic Matter

•  Negative mass but positive pressure

•  Avoids having a singularity

•  Pressure keeps mouth of wormhole open

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

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

Wormholes

•  Assuming you could make a stable wormhole:

•  Where does it connect to?

Wormholes •  Pocket Universe

– 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

Wormholes •  Parallel universe

– Connects to another universe rather than our own

– Many universe hypothesis: Every possible outcome happens in some universe

– Might be reachable by wormhole

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

Wormholes •  Another part of the same universe

Time Machines

•  If you have a traversable wormhole, you can build a time machine:

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

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

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

Wormhole Time Machine

•  Can’t travel back to before the time machine was created

Wormhole Time Machine

•  Can’t travel back to before the time machine was created

•  Existence of time machines messes up causality

•  Example: billiard balls

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?

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

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?

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?