Time

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Time
Topics Different perspectives of
time Simultaneity What is now? The arrow of time
Motivation Trying to understand this most
slippery of concepts.
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Einstein and time

• Special relativity
• Motion through time and motion through space, are
  linked. High relative velocities produce Lorentz
  time dilation.
• General relativity
• Spacetime can be warped. Massive objects can
  produce gravitational time dilation.
• Time is not a uniform metric that is equable to
  all observers.
• Let us remind ourselves about how special
  relativity
• smashed the concept of simultaneity.

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Simultaneity

• Events are simultaneous if they happen at the
  same instant in time. We see them happen
  simultaneously because the light pulses reach us
  at the same time.
• The finite velocity of light complicates the
  issue slightly, because light from objects
  further away must travel further (i.e., longer).
  However, we can account for this effect.

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Time and the now

• What is now? Events around the Universe that
  happen at the same time share the same now.
• We can make a list of everything that is
  occurring now.
• We are in class now. (t0)
• A lunar probe sends a signal now. (t1.28 s)
• Radiation is leaving the Suns surface now.
  (t500 s)
• Two comets in the Oort cloud collide now. (105
  au, t579 d)
• A star in the Andromeda galaxy ignites He now.
  (t2.5106 y)
• A star explodes in a distant galaxy now. (5 GLY,
  t 5109 y)
• A star explodes in a galaxy on the other side of
  the observable universe now. (47109 LY away, t
  gtgt 47109 y)

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Recall from relativity
L
The trainside observer sees two lightning strikes
share a now.
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But the train passenger observes that the two
strikes do not share a now.
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Relativity and the now

• We see that motion modifies whether or not events
  share a now.
• Shift your frame to one moving, relatively, to
  the right...
• The two stars at the right popped earlier than
  the star on the left.

tt1
tt2
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Relativity and the now

• This is important enough, let us repeat it.
• What does the observer see?
• The events are not simultaneous. They are not in
  the same now.
• Remember you cannot say that the loss of
  simultaneity is because the observer is moving.
  Who is to say who is moving, in empty space?

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Relativity and the now

• How much of an effect is this?
• Suppose an event far away (at distance L)
  happens now (adjusted for light travel time). If
  you shift to a reference frame moving (at a
  velocity v) towards the event, you shift it out
  of that now, by a time interval (?t)
• Approach it, and it happened earlier (at a more
  ancient now).
• Move away from it, and it happened later (at a
  more futuristic now).

L
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How much does velocity shift now?

• Bring back some of the events on our now-list.
• If you move at 2.5 m/s (jogging speed)
• If you move at 885 km/hr (speed of a commercial
  jet)
• Radiation left the Suns surface...
• ?t 410-6 s earlier than now
• Two comets in the Oort cloud collided...
• ?t 0.4 s earlier than now
• A star in the Andromeda galaxy ignited He...
• ?t 7.6 d earlier than now
• A star exploded in a 5 GLY galaxy
• ?t 42 y earlier than now
• A star exploded on the other side of the
  observable universe
• ?t 390 y earlier than now

?t 0.4 ms earlier than now
?t 40 s earlier than now
?t 2.0 y earlier than now
?t 4100 y earlier than now
?t 38000 y earlier than now
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What part of your now?

• Reverse the roles.
• If someone is moving away from us, they would
  include parts of our past in their own now list.
• If they change their direction and move towards
  us, they would include parts of our future in
  their own now list.

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Now and physics

• Think of everything in the now as a frozen
  instant in time.
• As one now transitions to the next, and the next,
  and the next, it is like different frames in a
  film.
• Interestingly, there is nothing in the laws of
  physics that embodies this notionof a slice of
  reality that is illuminated, one now after
  another.
• Even our innate sense of time flow (that now
  flows from one moment to the next) is not
  supported by physics.
• Furthermore, there is nothing in physics that
  says we should be at any specific point in our
  timeline.

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Now and a loaf of bread

• As one now transitions to the next, it is like
  looking at a loaf of bread, one slice at a time.
• The effect of motion is to change the events of
  nowit changes the angle at which you cut the
  bread.
• The faster the speed, the more angled the cut.
• Depending upon your speed, all of time, every
  event in the history of the universe, can be made
  to be happening now.
• Is there even any sense to the concept of now?

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Times arrow

• Let us examine why time seems to move in one
  direction.
• Why cant we remember the future?
• Why cant we change our pasts?
• This one-directionality is called the arrow of
  time.
• Why does time have a direction?

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Time

• A ball fired upwards at an angle, in a vacuum,
  travels in a parabolic trajectory.
• Film the ball in its trajectory, show it in
  reverse, and it would look exactly the same!
• This symmetry indicates that physical laws are
  symmetric in time.
• Indeed, all laws in physics are symmetric in
  time. Film something happening, and it can be
  shown in reverse, with no violation of physical
  laws.

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Explosions?

• Can you even run explosions in reverse?
• Yes! Even though it might be seem contrived, it
  is entirely possible to rig an explosion in
  reverse (an implosion), so that you fire a whole
  set of fragments together, to assemble a bomb, in
  reverse.
• While possible, there is no denying that this
  would be difficult.
• The example of the bouncing ball is similarly
  asymmetric on close inspection. Friction with air
  makes it slower in the way down.
• You could conceivably recreate the bouncing ball
  in reverse by bombarding the ball with carefully
  aimed molecules, so it would rise slowly, and
  then fall more rapidly on the final part of its
  bounce.

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The arrow of time

• The Universe ages in one direction because there
  is an overwhelming tendency for things to become
  more disordered.
• It appears that timewhatever it actually isis
  closely associated with randomness in nature
  (entropy).
• The flow of time IS the same as the drive for
  systems to become more disordered.
• Our Universe began in a highly ordered
  stateuniform, unclumpy energy and matter
  confined by a strong gravitational field. The
  story of the big bang is the story of a Universe
  becoming messy.
• The expansion of the Universe into larger scales
  began the flow of time.

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Ruminations

• I wonder. Does time have meaning in empty space?
  Does time proceed only because the Big Bang
  happened?
• And what about a piece of empty space in our
  Universe. Does time proceed in it? Perhaps,
  because empty space is curved and expanding?

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