1. WORMHOLE as shortcut Travel through hyperspace is like travel through middle of Earth vs. travel along surface Could travel long distances in short time without violating speed limit

2. STABILIZING WORMHOLES Ordinary matter: stable wormholes don’t exist –no static solutions –throwing matter or radiation in makes it worse Work backward from desired spacetime curvature –Wormhole must be held open by “exotic” matter negative energy from POV of light-ray traversing wormhole tensile energy >> material energy, from POV of stationary observer (matter poised to release huge energy if it expands) –Vacuum fluctuations in curved space can behave as exotic matter –Can vacuum fluctuations stabilize wormholes?

3. TIME MACHINES Definition: Leave and arrive in same place –Traveler’s POV: time is later –Local POV: time is earlier Rules: –“Arrow of time”: Traveler’s time must always move forward Local time must always move forward –Speed limit: nothing can be measured to travel faster than light Timelike trajectory : distance (lt-yrs) < time (yrs) OK Spacelike trajectory : distance (lt-yrs) > time (yrs) IMPOSSIBLE “Closed timelike curve” : allowed (timelike) trajectory that returns to same point in spacetime

4. WORMHOLE AS TIME MACHINE Each mouth opens to local patch of Universe But flow of time is the same across the wormhole Keep one mouth stationary, let other travel out and back at close to c –Exploit twin paradox –Traveler’s end of wormhole: returns to find world has aged much more than she has –Stationary end: everything has aged at the same rate as the traveler (Thorne’s analogy of “holding hands across wormhole”) –can simply pass through wormhole to go back/forward in time Can’t travel back to time earlier than departure of traveler (time the wormhole first became a time machine)

5. THE GRANDFATHER PARADOX aka VIOLATION OF CAUSALITY Can you go back in time and kill your grandfather before your parents are born? –Obviously not … but what stops you? –Thorne proposes self-consistency condition for inanimate objects Polchinski’s paradoxThorne’s resolutions: which is it?

6. Unfortunately, there are an infinity of self-consistent trajectories... Which is the real trajectory? Or are they all possible, with different probabilities? –quantum wavefunction But will quantum effects destroy the time machine? –circulation of vacuum fluctuations back and forth in time –runaway reinforcement destroys time machine?

7. HAWKING’S CHRONOLOGY PROTECTION CONJECTURE The laws of physics forbid time machines. “… to keep the world safe for historians”

8. DOES ‘EXOTIC MATTER” EXIST? Vacuum behaves in “exotic” fashion near an event horizon –basis for Hawking evaporation –does not work if horizon is not present no good for holding wormholes open Believed that vacuum (and all forces of nature) behave differently at high energies (i.e., high temperatures) –e.g., conditions just after Big Bang –fundamental idea in grand unified theories Observations suggest that the matter/energy of the Universe was exotic just after Big Bang

9. INFLATION of the EARLY UNIVERSE Basic idea: Expansion of Universe tremendously accelerated shortly after Big Bang –occurred at ~10 -36 sec (Planck time was 10 -44 sec) –Universe “inflated” by factor 10 30 –requires matter to have repulsive gravity exotic matter Proposed by Alan Guth (1980) to explain: – “flatness” problem Problem: expansion of universe “just right” Solution: curvature “stretched out” by inflation –“horizon” problem Problem: Universe uniform in all directions and locations, but different regions could not have communicated Solution: regions were in contact before inflation started

10. AN ACCELERATING UNIVERSE? Negative vacuum energy would accelerate the expansion of the Universe –ordinary matter/energy would decelerate it –this is what Einstein called the “cosmological constant” introduced to explain how Universe could remain stationary later called it his “biggest blunder” Direct evidence that Universe was expanding more slowly in the past –acceleration more gentle than during era of inflation –increases estimated age of Universe: resolves discrepancy with measured ages of stars