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

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?

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) OKSpacelike trajectory: distance (lt-yrs) > time (yrs) IMPOSSIBLE

“Closed timelike curve” : allowed (timelike) trajectory that returns to same point in spacetime

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)

THE GRANDFATHER PARADOXaka 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 paradox Thorne’s resolutions: which is it?

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?

HAWKING’S CHRONOLOGY PROTECTION CONJECTURE

The laws of physics forbid time machines.

“… to keep the world safe for historians”

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

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 1030

– 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

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