Time Travel in Physics

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Time Travel in Physics

• Edward Teo
• Department of Physics

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History would become an experimental science.
Carl Sagan (1934-96)
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The fundamental theory of physics that deals
with time is Einsteins theory of special
relativity.
Albert Einstein (1879-1955)
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Time is the Fourth Dimension
In this graph, time is vertical and space is
horizontal.The z-axis has been suppressed.
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Worldline of a Particle
Every particle traces out a worldline in
space-time. If its velocity is constant, its
worldline would be straight.
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The Lightcone
By definition, light traces out a 45 worldline.
The set of all light rays passing through the
point forms the light cone.
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A Timelike Particle lies within the Lightcone
The worldline of a particle lies within the
lightcone,since no particle can travel faster
than light.
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Summary of Time in Special Relativity

• Time is the fourth dimension
• time exists as a block, quite unlike our
  psychological perception of time
• Time is relative
• time slows down for moving particles
• Events simultaneous to one observer need not be
  simultaneous to another
• Causality is preserved

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A Closed Timelike Curve (CTC)
A CTC is a worldline that loops back onto itself.
At some stage, the particle has to travel
faster than light.
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In special relativity, if one could travel
faster than light, one could also go back in
time. But faster-than-light travel is
forbidden.
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To explain the force of gravity in terms of
curvature of space-time, Einstein cameup with
the theory of general relativity.
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Light cones may tip over to form a CTC
because of gravity or rotation of the space-time
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In fact, there are many solutions with CTCs in
general relativity

• Gödel universe (1949)
• Kerr black hole (1963)
• Tiplers rotating cylinder (1976)
• Traversable wormholes (1988)
• Gotts cosmic string time machine (1991)

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Tiplers Rotating Cylinder
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Traversable Wormholes
Kip S. Thorne (b1940) deve-loped the idea of
traversable wormholes for the movie Contact
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Paradoxes in Backward Time Travel

• Grandfather paradox
• Information creation in a causal loop
• Hawkings paradoxWhere are all the time
  travellers from the future?

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Grandfather Paradox (in BTTF)
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The Principle of Self-Consistency
The only solutions to the laws of physicsthat
can occur locally in the universe, arethose
which are globally self-consistent.
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Consider playing billiards near the mouthsof a
wormhole time machine...
(This is a version of the Grandfather paradox
phrased in terms of a physics experiment)
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A Self-Inconsistent Solution
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A Self-Consistent Solution
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Is there a conflict between self-consistencyand
free will??
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Will history really become an experimentalscience
?
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A Causal Loop Creating Information(Where does
the name Marty come from?)
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Similarly, one could use causal loops to ...

• Find out next weeks winning Toto numbers
• Decide who to marry
• Discover a new theory, prove an unsolved
  theorem, compose music, create works of art,
  etc.

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Hawkings Paradox
Why dont we observe tourists, souvenir hunters,
historians, archeologists, fugitives and
criminals visiting us from the future?
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So far we have only considered relativity.
What about the other major building block of
physics - quantum theory ?
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Quantum Theory
is the theory which describes the behaviour of
elementary particles and their interactions.
Quantum theory is both good and bad news for
time travel.
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Bad News

• Hawkings Chronology Protection Conjecture
• because calculations seem to imply that
  quantum fluctuations become infinite near a CTC,
  thus destroying it

The laws of physics do not allow time machines
to be made
Stephen W. Hawking (b1942)
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Good News

• Quantum theory allows the existence of so-called
  exotic matter
• which could be used to construct
  traversablewormholes and other time machines
• However, they would be extremely small or
  short-lived

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Many-worlds Interpretation of Quantum Theory
(Everett, Deutsch)

• Whenever a quantum process occurs, the outcome is
  determined by probability
• For every possible outcome, a new universe is
  created and branches off
• Our universe is bifurcating endlessly like
  branches and twigs of an infinite tree

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Many-worlds and the Grandfather Paradox

• When a traveller goes back in time and changes
  the past, a new universe is immediately created
  and branches off from the original one
• Thus, history in the original universe cannot be
  changed. Instead, a new history is created in the
  new universe
• This is a possible resolution of the Grandfather
  paradox

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Antiparticles (Feynman)
Antiparticles can be regarded as particles going
backwards in time.
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Space-time diagram of antiparticle
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Could the same happen for a person?
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Further Reading

• Paul J. Nahin, Time machines 2nd
  ed.(Springer-Verlag, New York)
• Kip S. Thorne, Black holes and time warps(W.W.
  Norton, New York)
• J. Al-Khalili, Black holes, wormholes time
  machines (Institute of Physics Pub.,
  Philadelphia)