1. by Robert Nemiroff Michigan Tech
Time Travel II by
Robert Nemiroff
Michigan Tech

2. Physics X: About This Course
Officially "Extraordinary Concepts in Physics"
Being taught for credit at Michigan Tech
Light on math, heavy on concepts
Anyone anywhere is welcome
No textbook required
Wikipedia, web links, and lectures only
Find all the lectures with Google at:
"Starship Asterisk" then "Physics X" 

3. Time Travel: Machines Extending Conventional Physics
Time travel might be allowed using:
Faster than light (FTL) movement or information transfer
Unusual cosmologies
Black Holes
Cosmic Strings
Wormholes
Alcubierre drive

4. Time Travel Mechanism: Faster than Light Travel (FTL)
Alice flashes her light.  When Bob sees that light, he flashes his light.  
All observers moving slower than the speed of light will agree that Alice flashed her light first. 

5. Time Travel Mechanism: Faster than Light Travel (FTL)
Alice flashes her light again.  Before Bob sees that light, Bob flashes his light.  Although no information was transferred, a flash signal went from Alice to Bob faster than light.
Some observers will think that Bob flashed first.
Some observers nearer Bob, for example.
This "signal" would appear to them to move backward in time. 
Cause and effect cannot be universally established.

6. Time Travel Ideas: Faster than Light Travel (FTL)
Alice flashes her light again.  Before Bob sees that light, Bob flashes his light.  
Extending this scenario, it appears possible, somehow, that Alice sees Bob's light flash BEFORE Alice was going to flash her light.
This shows that FTL communication allows backwards time travel.

7. Time Travel Ideas: Faster than Light Travel (FTL)
Mass cannot be accelerated from slower than light to faster than light.  That would take an infinite amount of energy.  Perhaps, though, mass can be created moving FTL and always remain such.

8. Tachyons particles that move faster than light (FTL).
violate causality
can no longer know what causes what
will strike you before you see them.
will see two images of a tachyon that just passed you
one moving away from you in the direction that the tachyon approached
one moving away from you in the direction that the tachyon is moving away

9. General Relativity: Spacetime Intervals
Two events happen in spacetime.  They are separated in space by dr and in time by dt.
 Time-like interval
One event can affect the other
c dt > dr 
Space-like interval
One event cannot affect the other (without backwards time travel)
c dt < dr
Light-like interval
Light from one could affect the other
c dt = dr   

10. General Relativity: Spacetime Motion
Two events happen in spacetime.  They are separated in space by dr and in time by dt.
 Closed timelike curve (dr = 0; dt < 0)
A curve that comes back to the same spatial point at an earlier time 
closed timelike curves allowed in GR
allows (backwards) time travel
need other physics to disallow?   

11. Time Travel: Cosmologies with closed time-like curves
Godel gave Einstein a "present" of a cosmological solution to General Relativity that admits simple time-like curves.  Objects traveling on these curves would go back in time, and could arrive at their starting points before they left.

12. Time Travel: Wormholes
Generic example: a black hole connected to a white hole through a "shortcut" in space.  
Generic simple wormholes would kill anyone who entered by compressing them to infinite density.
Traversable wormholes might exist but are controversial.  They would have two ends -- a traveler goes in one end and appears "instantly" on the other end.  Some type of dark energy is thought needed.  This also allows FTL communication.

13. Time Travel: Wormholes
Moreover , were one end of the wormhole brought near a black hole (for example), then
time would run more slowly for the black hole end than for the non-black-hole end.   
As time (as measured by an observer far away) progresses, the two ends could get years out of synch.  
The two ends could then be brought close together.
Going in the non-black hole end of the wormhole and coming out the once black-hole end would take an observer only a brief time on the traveler's watch.
But they would come out years in their own past -- time travel!

14. Wormholes
A "shortcut" through spacetime.  Also known as an Einstein-Rosen Bridge. 

15. Time Travel: Tipler Cylinder
A solution to GR near an infinitely long massive cylinder.
If spun fast enough, the cylinder will cause frame-dragging in such a way that accelerating through that region allows a closed time-like curve, and hence time travel.
No singularlities or black holes are involved!  
Unfortunately, the cylinder must be infinitely long (in present understanding.

16. Time Travel: Alcubierre drive
A GR attempt to create a real "warp drive."
A GR metric is envisioned that describes a bubble of spacetime that moves with a ship.  Time dilation acts around this bubble, which could make it move faster than light when compared to distant observers.  Inside the bubble, motion is slow, and nothing moves FTL.
Physics is controversial.  One might need negative-energy like localized dark energy.  At best, one might need a tremendous amount of mass to get this to work.  At worst, one could not communicate with the front of the bubble, and the hot Hawking radiation would be deadly.