Relativity : Revolution in Physics

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Relativity Revolution in Physics

• Einsteins Triumph

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Special Relativity - 1905

• How motion in space is related to motion in time
• Applies to inertial frames, moving with respect
  to one another at constant velocity
• Does not apply to accelerated motion
• Requires changing Newtons Three Laws of Motion
  for high velocities
• Requires changing definitions of momentum and
  energy

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Strange Predictions

• Stretching (dilation) of time
• Contraction of length
• Existence of rest mass according to E
  mc2

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Basics

• All motion is relative must be defined with
  respect to a particular frame of reference.
  Examples
• The ground
• A moving bus
• Q What is speed of a 30 m/s baseball relative to
  you thrown from a truck traveling at 20 m/s
  toward or away from you?

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Two Postulates

• The laws of physics are the same in any inertial
  (that is, non-accelerated) frame of reference.
• This means that the laws of physics observed by a
  hypothetical observer traveling with a
  relativistic particle must be the same as those
  observed by an observer who is stationary in the
  laboratory
• The speed of light is the same for all observers,
  no matter what their relative speeds.

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First Postulate

• All the laws of nature are the same in all
  uniformly moving frames of reference
• Consequences
• All frames of reference are arbitrary
• Absolute motion does not exist
• No possible experiment confined to a vehicle can
  detect its motion (you can detect motion by
  looking outside)

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Second Postulate The Speed of Light is
Constant, Regardless of the Motion of Source or
Observer

• Light does not behave like the baseball!
• Imagine a flashlight beam directed from a
  spaceship moving with nearly the speed of light.
  All measurements of the speed of this light give
  same answer 300,000 kilometers per second

Courtesy www.cybersurfari.org/images/promos/
fall2k2/spaceship.gif
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Thought Experiments

• Einstein had deep insight into nature
• Remarkable powers of concentration
• Great ability to visualize events
• YOU can improve your powers too
• Excellent Einstein link http//whyfiles.org/052ei
  nstein/genius.html

Courtesy of the Archives, California Institute of
Technology
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Einsteins Thought Experiments

• Imagined riding alongside beam of light
  concluded it was impossible
• Train experiment. Made shocking discovery that
  simultaneity of events depended of motion of the
  observer
• Light clock discovered time dilation and how
  big it is
• Link to Einsteins Thought Experiments
  http//aether.lbl.gov/www/classes/p139/exp/gedanke
  n.html

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Train Experiment
Courtesy homepage.mac.com/ardeshir/
TrainImage.jpg
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Light from each lightning strike does not arrive
at observers position at same time delays
depend on speed of train
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Light Clock Experiment
Light clock moving
Light clock at rest
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Light Clock Experiment
Light path as seen by observer at rest
ct
ct0
vt
Shows three positions of light clock as it moves
to the right at speed v. By Pythagorean theorem
Zero subscript refers to non-moving frame
c2t2 c2t02 v2t2
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Time Dilation Equation

• c2t2 c2t02 v2t2
• c2t2 - v2t2 c2t02
• t21 (v2/c2) t02
• t2 t02 /1 (v2/c2)
• t t0 1 (v2/c2)-1/2

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Interpretation

• Compared to a system at relative rest, time
  passes more slowly in a moving system
• Within a given system (rest frame) no
  relativistic effects are noticed
• Example 30 minute waste basket fire on a
  spaceship traveling at v 0.8 c. How long will
  this fire appear to last when seen from Earth?

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Wastebasket Fire

• t0 30 min
• v/c 0.8
• t t0 1 (v2/c2)-1/2
• t 30min1 - 0.64-1/2
• t 30/0.6
• t 50 minutes

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Variation With v/c

• Complete this table

v/c (v/c)2 1 v2/c2 1 v2/c2 1/2
1
0.8
0.9
0.99
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Variation With v/c

• Complete this table

v/c (v/c)2 1 v2/c2 1 v2/c2 1/2
1 1 0 0
0.8 0.64 0.36 0.6
0.9
0.99
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Variation With v/c

• Complete this table

v/c (v/c)2 1 v2/c2 1 v2/c2 1/2
1 1 0 0
0.8 0.64 0.36 0.6
0.9 .81 .19 0.43
0.99
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Variation With v/c

• Complete this table

v/c (v/c)2 1 v2/c2 1 v2/c2 1/2
1 1 0 0
0.8 0.64 0.36 0.6
0.9 .81 .19 0.43
0.99 .98 .02 0.14
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Twin Trip

• According to time dilation a twin astronaut on a
  high speed trip returns younger than his/her twin
  because time runs more slowly for the moving twin
  compared to the stay-at-home.
• If the trips lasts 30 years at v/c 0.8 and both
  twins are initially 20 years old, what will be
  their ages on earth afterward?

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Paradox

• Since motion is relative why couldnt we look at
  the trip from the point of view of the traveling
  twin (who sees the earth recede when he/she
  leaves). Then wouldnt the traveling twin age
  more?

Courtesy University of New South Wales, Australia
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Resolution of Paradox

• Argument in Hewitt Chapter 15 section 7.
• Trip involves acceleration which special
  relativity does not include. How many times must
  traveling twin accelerate or decelerate (if all
  motion is straight line) before returning? In
  other words problem is not symmetrical because
  traveling twin has several reference frames while
  stay at home has only one
• Using General Relativity, which does include
  acceleration it is also possible to show that
  stay at home twin ages more

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Twin Paradox Resolution, cont

• 3. World Line in spacetime argument
  http//physics.syr.edu/courses/modules/LIGHTCONE/t
  wins.html
• Link to multiple explanations
• http//math.ucr.edu/home/baez/physics/Relativity/S
  R/TwinParadox/twin_paradox.html

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Implications for Space and Time Travel

• Very long space trips are possible within a
  single lifetime
• Require speeds comparable to c
• For v/c 0.999 70 years on Earth elapse in only
  one year of a travelers time.
• Traveler could journey to a star 35 ly from earth
  and return in only one year of travelers time.
• On longer trips would return to a different
  century
• A form of time travel into future

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Brain Teaser

• Viewed from frame of reference of light how much
  time is required for a journey to the center of
  our galaxy, 30,000 ly away?
• Answer None. In frame of reference of a light
  wave time stands still.

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Length Contraction

• Moving objects contract along their direction of
  motion (not perpendicular)
• L L0 1 v2/c2
• What would be the length an Earth observer would
  measure for a spaceship traveling at v/c 0.8 if
  an observer on the ship measures 100 meters?
• Answer 60 meters

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Puzzler

• An observer on earth measures the length of a
  rocket ship traveling at v 0.8c to be 60
  meters. What would be the measured length of
  this ship when at rest on Earth?
• Answer 100 meters

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Mass and Energy

• Mass is a form of energy
• Even object at rest has energy
• Rest energy is E0 mc2
• All exo-energetic (energy producing) reactions,
  chemical and nuclear, get their energy from mass.
  The reaction products have less mass than the
  reactants!
• In chemical burning the difference is less than
  one part in a billion
• In nuclear fission about one part in a thousand

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Rest Energy of a Kilogram

• Problem Calculate the rest energy in joules of
  one Kilogram
• E0 mc2
• E0 1Kg (3.0 x 108 m/s)2
• E0 9 x 1016 Joules

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Amount Available from Burning

• Take the ratio of one in a billion joules
  available from chemical burning and apply to E
  1017 Joules to find the amount available from
  burning 1 kg of coal.
• Answer Approx. 108 J
• Is this reasonable? Make an argument or do some
  research to find out!

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Relativistic Momentum

• Replace mv by
• p mv 1 (v2/c2)-1/2
• As speed approaches speed of light, what happens
  to p?
• Answer approaches infinity
• How much force x time would be required to
  accelerate it further?
• Answer infinite

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Brain Tickler

• Based on relativistic increase in momentum why is
  c the ultimate speed limit in the universe?
• Answer because infinite force is required to get
  there and infinite force cannot exist

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Alternate Interpretation of Relativistic Momentum

• Some physicists write p mv where
• m m0 1 (v2/c2)-1/2
• This is called relativistic increase of mass

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Relativistic Kinetic Energy

• Instead of KE ½ mv2
• KE mc2 1 (v2/c2)-1/2 mc2
• Challenge show that the above expression
  simplifies to ½ mv2 in the limit that v
  approaches zero.

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Correspondence Principle

• Relativity doesnt replace Newtons physics, it
  extends it to high speeds. So all relativistic
  equations must reduce to Newtons when speeds are
  low.
• Examples
• L L0 (1 v2/c2
• t t0 1 (v2/c2)-1/2
• p mv 1 (v2/c2)-1/2

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Unanswered Questions

• What is time?
• Why does it only run forward?
• Could there be universes where it runs backward
  (anti matter particles can be conceived as
  particles running backward in time)
• Was time created by the Big Bang or did it exist
  before?