WORMHOLE as shortcut

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 dont 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 gtgt 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
• Travelers POV time is later
• Local POV time is earlier
• Rules
• Arrow of time
• Travelers 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) lt time
(yrs) OK Spacelike trajectory distance
(lt-yrs) gt time (yrs) IMPOSSIBLE Closed
timelike curve allowed (timelike) trajectory
that returns to same point in spacetime
4

5
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
• Travelers 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 (Thornes analogy of
  holding hands across wormhole)
• can simply pass through wormhole to go
  back/forward in time
• Cant travel back to time earlier than departure
  of traveler (time the wormhole first became a
  time machine)

6
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

Polchinskis paradox
Thornes resolutions which is it?
7
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?

8
HAWKINGS CHRONOLOGY PROTECTION CONJECTURE
The laws of physics forbid time machines.
to keep the world safe for historians
9
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

10
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

11
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