Relativity

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Relativity
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Special vs. General Relativity

• Special Relativity deals with non-accelerated
  motion. Objects moving at a constant speed
  relative to something else.
• General Relativity deals with accelerated motion
  and how it relates to observed gravity

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Relative Motion

• Standard velocity addition
• Ex A friend throws a ball at 5 m/s toward you
  from a vehicle moving 5 m/s toward you.
• Ex If the vehicle were moving 5 m/s away from
  you?
• Video.
• Definition of a Frame of Reference Area in which
  objects are at rest relative to each other.

4
Michelson-Morely Experiment

• Purpose Detect relative motion between the
  Earth and the ether by detecting changes in the
  speed of a light wave.
• Demo Interferometer Experiment
• Outcome
• Possible conclusions?

5
Special Relativity

• First Postulate The laws of physics are the same
  in all frames of reference.
• Second Postulate Speed of Light is always
  measured to be the same (3x108 m/s). Its
  independent of the motion between observer and
  the source.

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Simultaneity

• Events that occur simultaneously in one reference
  frame will not appear simultaneous in another
  reference frame
• When moving toward an event at high speed,
  light from that event will reach you first.

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Time Dilation

• Time Dilation Equation
• Derivation
• T T / v(1-v2/c2)
• Exs
• A space explorer goes on a high speed trip for 1
  year at 99 the speed of light. How much time
  passes by here on earth?
• Evidence?
• Muon Decay, Atomic Clocks on airplanes, GPS

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Examples of Time Dilation (?)
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Practice Question

• Your parents go on a 6 month (.5 yr) space cruise
  at a speed of 99.99 the speed of light.
• How old will you be when they return?
• How will they be when they return?

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Twin Trip

• If one twin travels at a high speed away from
  earth and then returns. The traveled twin will
  now be younger than a stay at home twin.
• Twin Trip Simulation Web Site

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Changes to Length and Mass

• Length of object will contract as observed from a
  different reference frame.
• L L x v(1-v2/c2)
• Mass will increase as well as observed from a
  different reference frame.
• M M / v(1-v2/c2)
• Mechanical Universe Video 42 Lorentz
  Contraction

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Energy Mass Equivalence

• Since nothing can go faster than the speed of
  Light, then the energy transferred to a moving
  object must increase the objects mass.
• KE 1/2 m v2 , if v cant exceed c, then
  energy must end up transferred to the mass
• Evidence
• electrons in a accelerators and cyclotrons become
  heavier as their speed increases.
• Nuclear reactions
• E m c2
• Ex 1 kg is converted into how much energy?

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Practice Questions

• A passenger on a rocket traveling at 98 the
  speed of light says that his trip takes 5 days.
  How long does it take from an outside reference
  frame?
• A meter stick (1 m) is contracted to 20 cm as
  observed from an outside reference frame. How
  fast is the meter stick going?
• An object is lifted up so that it has 1000 Joules
  of PE. How much mass is this PE equivalent to?
• What evidence is there that supports Einsteins
  theory of Special Relativity?
• According to Special Relativity, why cant any
  material object go faster than the speed of light?

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General Relativity

• Principal of Equivalence (Animation)
• Observations made in an accelerating reference
  frame are indistinguishable from those made in a
  gravitational field.
• Exs light falling in a rocket ship
• How far would light fall in one second here on
  earth?
• Space-Time
• We can replace our notion of Gravity with the
  idea that mass warps space and time and all
  objects follow the law of inertia
  (4-Dimensionally)
• http//www.ligo.caltech.edu/LIGO_web/aaas0203/curv
  ature_lan.ram

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3 Tests of General Relativity

• Perihelion shift of Mercurys orbit.
• Newtons Law of Gravitation and Keplers Laws
  failed to explain why Mercurys elliptical orbit
  rotated as observed.
• Einsteins General Relativity accurately predicts
  this shift to within 0.1 error. Not Bad!!
• Light from a distant star should be bent by the
  suns gravitational field
• Tested and verified by Eddington in 1919
• Heavily publicized and made Einstein famous
• Gravitational Redshift
• Clocks in a stronger gravitational field should
  run slower than in a weaker field.
• Verified in 1960 with atomic clocks between the
  top and bottom floors at a building at Harvard.
• Re-verified in 1976 and confirmed Relativity
  predictions to within 0.02! WOW!!

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Gravitational Redshift

• Spinning Turntable Example
• Observers looking at clocks in a stronger
  gravitational field will notices those clocks
  running slower.
• Ex If we could look at a clock near the sun
  we would see it run slow.
• Observers looking at clocks in a weaker
  gravitational field will notice those clocks
  running faster.
• Ex Look at a clock that is on the moon it
  will run faster.
• Where do we age the fastest, on top of
  skyscrapers or at street level?
• Black hole effects?

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Other Consequences of Gen. Relativity

• Black Holes
• Extremely dense objects will bend space-time to a
  point of infinite curvature.
• Radius of a Black Hole 2 GM/c2
• For our sun radius 2,900 m
• For earth (M 6 x 1024 kg) r ?
• Gravitational Waves or 2
• Accelerating masses should produce waves in
  space-time. Two stars (or pulsars) rotating
  around each other (or Binary pulsar) should emit
  waves large enough to detect.
• LIGO or LIGO

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Misc.

• Thinking in 4-D is TOUGH!!
• Calculations using General Relativity require the
  use of 4-D descriptors and operators known as
  Tensors (kinda like matrices)
• Gab (8pG)Tab !!
• In other words The rate at which a small ball of
  freely falling test particles begins to shrink is
  proportional to its volume times the energy
  density at the center of the ball, plus the
  pressure in the x direction at that point, plus
  the pressure in the y direction, plus the
  pressure in the z direction.
• Therefore most illustrations and examples are
  simplified to 2-D or 3-D
• http//archive.ncsa.uiuc.edu/Cyberia/NumRel/Movies
  Edge.htmlWormHolesToWhere?