Time Travel

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• Weve seen w/ both special and general relativity
  that time is not completely static
• Given the right situation, time can be
  manipulated in different ways
• The question is, does this include the
  possibility of time travel?

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• As it turns out, time travel could be possible w/
  the right technology
• Unfortunately for us, the right type of
  technology does not include Deloreans and flux
  capacitors

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• Instead, we need a way to both create and
  manipulate wormholes

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• If we can figure out a way to master wormholes,
  we might come up with two strategies for time
  travel
• The first uses special relativity
• The other uses general relativity
• Both rely on the idea of time moving differently
  in different reference frames

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Strategy One Special Relativity

• Remember the twin paradox?
• Recall that the twins clocks move differently
  (hence one is older than the other when he/she
  gets back)

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• So lets say I have a spaceship in my front yard
• This ship is connected, via wormhole to my living
  room

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• This wormhole exists in a higher dimension than
  the space the ship travels through
• Lets also assume that as the space ship travels,
  it stays connected to the wormhole as the ship
  moves, the wormholes length never changes

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• Before the ship leaves, I make sure that the
  clock inside and living room clock read the same
  time
• After this check, the ship blasts off into space
  at 9AM (on January 1st, 2000)
• According to the ships clock, it stays in flight
  for 6 hours (at a speed very close to light
  speed) then turns around and heads back to Earth
• It arrives back on my front lawn at 9PM

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• Sure enough, if I look through the wormhole and
  see my front lawn in the background
• But if I turn around and look at my front lawn,
  the ship isnt there
• Whats going on?

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• From the twin paradox, we know that time travels
  differently inside the ship than it does for me
  in my living room
• 9 hrs of near light speed travel corresponds to a
  much longer time for me
• In fact, Id have to wait 10 years before I see
  the ship arrive back on my front lawn

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• Once the ship arrives, I could go inside, look
  through the wormhole, and see a younger version
  of myself sitting in my living room (if I
  traveled through, I would be moving into the
  past)
• Conversely, I could look through the wormhole in
  2000 and the see the world of 2010 (and again, I
  could travel through the hole into that world)
• In fact, I might see an older version of myself
  peering through

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Strategy Two General Relativity

• Once again, well rely on the use of wormholes
• This time however, we slow time w/ gravity rather
  than speed

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The Setup

• Imagine two regions of space one close by a
  neutron star or black hole(B), the other a
  distance R away (A)

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• We know from GR that the clocks will move at
  different rates B will move slower than A b/c
  its in a higher gravitational field
• If were not convinced, we could actually travel
  from clock A to B and observe the two different
  clock rates (assuming we take travel time into
  account)

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• Heres where it gets interesting Place a
  wormhole between A and B such that a person
  looking through the wormhole at A will be able to
  see B
• The wormhole is effectively reducing the distance
  R between the two clocks by creating a shortcut
  in higher dimensional space

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How Does This Relate to Time?

• We know that if the distance between the two
  clocks is very small, theyre essentially ticking
  at the same rate
• So a person looking through the wormhole will see
  clock A with the same time as clock B

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• Lets imagine a new scenario a person is
  standing at B, decides he wants to check up on
  clock A, comes back, and travels through the
  wormhole to A
• What will happen?

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• By doing this, this person is looking or
  traveling into the past
• In fact, depending on the setup (you pick an R
  big enough or wait around long enough), he could
  see a younger version of himself checking the
  time at clock A

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Limitations of Our Time Machine

• The furthest you can travel back in time is the
  moment the ship blasts off, or the moment you
  place your wormhole near a neutron star
• Both machines rely on the use of wormholes, which
  havent been confirmed or denied

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Two Views of Time

• A line that can branch off, forming new lines
• One continuous line with the occasional
  closed-loop

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Einsteins Views World Lines

• A world line describes where you are and when
• Even when you die, the world lines of individual
  atoms continue
• According to Einstein, they can form loops but
  cannot be cut

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Paradoxes

• The man w/ matricidal tendencies
• Events with no beginning
• The story of Jane

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The Man w/ No Past

• One day, a struggling inventor gets a visit from
  a wealthy, older gentlemen from the future
• The older man gives the young inventor two
  things knowledge of stock market booms, and the
  blueprints for a time machine

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• Using this knowledge, the young inventor gets
  rich off of investments
• In his spare time, he constructs a time machine
• Decades later, he travels back in time to meet
  his former self, thereby completing the process

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• The question is, where did the knowledge on time
  machine construction come from?

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Jane
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Billiard Balls

• Unfortunately, its a bit tough to do
  calculations involving humans
• However, we can calculate what might happen with
  billiard balls in a modified version of the
  matricide paradox

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• Say you have two openings of a wormhole separated
  by a few feet
• You want to fire a billiard ball into one end,
  such that it will come out the other end in the
  past
• But what happens if the billiard ball comes into
  the past, hitting its younger self and preventing
  it from reaching the opening

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• In all these paradoxes, certain things have to
  happen to ensure that world lines are not broken
• Why?
• What stops a person from killing their ancestors
  once in the past?

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• The ability to act according to choice
  constitutes free will
• If you cant act, something is restricting your
  free will
• Some physicists have claimed the laws of physics
  do this during time travel

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