Relativity

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Relativity

• Relativity by M.C. Escher

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Types

• Special Relativity Deals with the behavior of
  objects at high speeds (close to the speed of
  light)
• General Relativity Deals with how mass and
  energy affect space and time

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Buying In

• To understand special relativity, you have to
  accept two basic ideas
• 1 The laws of Physics work the same in all
  inertial reference frames
• 2 The speed of light has the same value in all
  inertial reference frames

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Inertial Reference Frames?

• This is just a fancy way of describing a place
  that isnt pushed around
• Example A car moving at 60 mph in a straight
  line, but not a car changing speeds

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Pushing the Issue

• Why does pushing and pulling matter?
• Imagine that youre riding in your car and you
  throw a ball into the air
• If the car is moving at constant speed, the ball
  drops back in your lap
• If you hit the brakes, the ball goes flying into
  the windshield

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Weird Stuff in Special Relativity

• Time-Dilation (the Twin Paradox)
• Length Contraction
• Relativistic Quantities (the ever so famous Emc2)

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Time Dilation
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Twin Paradox

• Suppose you have two twins, one of which is
  placed in a ship and rockets away towards a
  nearby start, the other remains on Earth.
• What will happen when the traveling twin returns?

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• The clock in Twin 1s ship physically moves
  slower than Twin 2s clock on Earth
• This means time is moving slower in the ship than
  on Earth (if Twin 2 could look inside the ship,
  she would see everything happening slower)
• But Twin 1 still experiences a normal flow of
  time (for her, 1 second might represent a couple
  minutes back on Earth)

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Time as a Substance?

• So now were left with a situation in which time
  is no longer just a measurement, completely
  independent from space
• Time in inevitably linked with space
• To cope with this, Einstein came up with a
  mathematical construct called space-time, a 4
  dimensional representation of the universe in
  which time and space are combined

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Length Contraction

• Proof runs the same as that of time dilation
• The faster you move, the shorter an object
  appears

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Applications of This

• Could you fit a 10ft car in an 8 ft garage?
• Possibly for a minute, but when the car slows
  down it stretches to its original length and
  either breaks the garage or gets compressed
• In a relativistic situation, the acceleration is
  where the magic happens (time slows down,
  length contracts)

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Consequences of This Ideology

• We are now left with a theory in which two
  people, witnessing two entirely different things,
  can be correct
• This almost compromises the idea of absolute
  right and wrong what you see and experience
  depends on your reference frame
• Analogs w/ moral relativity?

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Mix of Cause and Effect

• Imagine a situation where you have a light bulb
  triggering a clock when the clock receives light
  from the bulb it starts ticking. Say the clock
  turns on at time (t) 0

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The clock and bulb are separated by distance x.
B/c light has a finite speed, and observer at
rest will see the clock triggered a time t (x/c)
after the bulb turns on.
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A Moving Observer

• Suppose you are an observer flying by at speed v.
  What would you see in this situation?

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Lorrentz Transforms

• You can translate between quantities (time,
  distance) in a reference at rest and a moving
  reference frame by using a few equations called
  Lorrentz Transforms

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• In the light bulb situation, wed use the
  following equation
• t g(t (v/c2)x)
• t is the time measured by the moving observer t
  is at rest observers time
• x is the distance between the bulb and clock v
  is the moving observers speed
• g is a factor that increases the faster you go
• g 1/(1-(v/c)2)1/2

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• You can see from this equation that if v and x
  are big enough, t will be negative
• What does this mean?
• If you set your light bulb/clock configuration up
  right, you will see the clock turn on before the
  light bulb turns on!

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• In this sense, you lose the relationship between
  cause and effect

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Relativistic Quantities

• -Einstein Discovered that mass and energy are
  interchangeable, related by the famous
  equation
• Emc2
• -Besides simply tweaking our notions of what mass
  and energy really are, there are some other
  consequences of this

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• When you speed something up, you have to put
  energy into it
• But relativity says that nothing can be
  accelerated faster the speed of light
• So if you have a particle moving very near c,
  what if you keep putting energy into it?

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• Quite simply, as an object gets closer to the
  speed of light it gets heavier (gains momentum)

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Applications of This

• Nuclear Reactions
• Particle-Antiparticle Interactions

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Pair-Antiparticle Pairs

• Every known particle has an antiparticle
• It is possible for a photon to give up its energy
  to the formation of a particle-antiparticle pair
• In a sense, mass and energy are interchangeable
  mass is just concentrated energy

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Nuclear Reactions

• When you split or fuse atoms (fission and fusion,
  respectively), you get a mass change in the
  nucleus
• This is why so much powers involved (according
  to Einsteins equation, even a tiny amount of
  mass can generate a lot of energy b/c c2 is
  such a big number)

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• The mass of a nucleus is always less than the sum
  of particle masses
• This mass loss comes from a difference in
  arrangement of particles in the nucleus (nuclear
  binding energy)
• In a nuclear reaction, this binding energy is
  released

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Relativistic Doppler Shifts

• As an object moves towards you, it has a higher
  frequency/pitch (blue-shifted)
• As it moves away from you, the frequency is lower
  (red-shifted)

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Basics of General Relativity

• A person in a closed box cannot distinguish
  whether or not the box is in a gravitational
  field or is accelerating
• Einstein proposed that space-time was curved

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Einsteins Equivalence Principle

• An observer cannot tell the difference between an
  accelerated reference frame and one in a
  gravitational field

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• To an observer at rest to the frame, light
  appears to follow a curved path
• However, we know light always travels the
  shortest possible path
• Therefore, the space through which the light is
  moving must be bent
• I.e, gravitational fields bend space-time

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Curving of Space-Time

• Mass and Energy warp space-time
• Objects move in straight lines through
  space-time, but their paths bent because of the
  curvature of space itself
• Certain objects are massive enough to infinitely
  curve space (black holes, quasars)

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• Massive objects bend the path of light traveling
  by, creating an effect known as gravitational
  lensing

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Black Holes
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• Light is trapped in a black hole (hence the name)
  because of the infinite curvature of space time

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So Youve Decided to Fall into a Black Hole.

• Assuming you could survive the many death traps a
  black hole has to offer (jets of intense
  radiation, strong tidal forces that could tear
  you apart, etc), you might witness some pretty
  neat stuff.

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The Photon Sphere

• At a certain distance out from a black hole,
  gravity is strong enough to force light emitted
  by your body into a circular orbit
• In other words, if you looked in front of
  yourself, you would see the back of your head

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Redshifts/Final Image
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Event Horizon
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Once Inside.