Chapter 29: Relativity

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Chapter 29 Relativity

• Brent Royuk
• Phys-111Concordia University

2
Introduction

• Classical vs. Modern

3
Introduction

• Whats relative about relativity?

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Relativity

• Billy-Bobs Pickup Truck
• Galilean Relativity
• Inertial Rest Frames
• A place where Newtons Laws work.
• A lab on a pickup truck?
• A boxcar? The space shuttle? Earths surface?
• What is lights reference frame?
• c 3 x 108 m/s
• The search for the luminiferous ether.

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Relativity
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Michelson-Morley Experiment
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Einsteins Two Postulates

• The Principle of Relativity The laws of physics
  are the same in all inertial frames of reference.
• Galilean relativity
• Theres no way you can tell youre moving.
• The Invariance of c The speed of light is the
  same in all IRFs, independent of relative motion.
• This is the surprising one.
• Justification? Maxwell and experiment.
• Herman Bondi The irrelevance of motion and the
  uniqueness of light.
• Special vs. General
• Any objections?

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Gedanken

• Billy-Bob again.
• Figure 29-4, p. 972
• So if Sammy the Spaceman flies past you at a
  speed of c/2 and turns on his laser (shooting
  straight ahead) just as he passes, to what
  position has it traveled 1 microsecond later?
• Simultaneity

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Gedanken

• The Relativity of Simultaneity

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Time Dilation

• The Light Clock Derivation
• Notation ? v/c
• Result ?t ? ?to

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Time Dilation

• Calculating Gamma

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Time Dilation

• Why dilation?
• Is this a change in measured time or actual time?
• So which observer is right?

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Time Dilation

• Example Given ? .8, Sammy the Spacemans watch
  tics off 10 s. What do our watches say during
  that interval?
• Proper time the moving clock
• Events and spacetime
• Four Possible Permutations for Time dilation
• Sammys says 10, what do ours say?
• Ours say 10, what does Sammys say?
• Sammy sees ours say 10, what does his say?
• During ten of Sammys, how much time does he see
  pass on ours?
• Remember the first postulate?

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Time Dilation

• The proverbial atmospheric muon
• 0.99,
• ?to 2.20 ?s, h 5 km.

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Time Dilation

• Example Hafele and Keating, 1972 atomic
  clocks on commercial airplanes
• Time dilation was verified within 5-10
• Observed time differences east -40 ns, west
  275 ns. (compared to ground)
• When atomic clocks are transported, they get out
  of sync.
• GPS satellites have to be synchronized with time
  dilation effects accounted for
• NOVA Episode 2612 On a plane trip to London, a
  clock gained 40 ns.
• Joe Hafele Suppose you were to live for 100
  years and you would spend your entire life on one
  of these aircraft, flying around the world, you
  could expect to be younger than people who did
  not do that by about one ten-thousandth of a
  second.

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Length Contraction

• Measured lengths shrink by the gamma factor for
  different reference frames.
• This occurs only along the direction of relative
  motion.
• This is not just something that happens to fast
  meter sticks. Length is really relative to the
  observer.
• Equation L Lo/?
• Example At what speed would a flying meter
  stick appear to be half a meter long?

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Length Contractionhttp//www.glenbrook.k12.il.us/
gbssci/phys/mmedia/specrel/lc.html
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Length Contraction

• Visual Appearance Figure 29-11, p. 980

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Length Contraction

• Visual Appearance Figure 29-11, p. 980

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Length Contraction

• Visual Appearance Antony Searle,
  http//www.anu.edu.au/Physics/Searle/

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Length Contraction

• Visual Appearance Antony Searle,
  http//www.anu.edu.au/Physics/Searle/

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Velocity Addition

• Lets think about three objects, where we
  consider v21, v13 and v23.
• v13 means the velocity of object 1 relative to
  object 3.
• Object 2 is the bullet.
• Classically, v23 v21 v13.
• Relativistically, we get

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Relativistic Time Travel

• How long would it take to go 100 ly at v 0.9
  c?
• The Twin Paradox
• Bobby and Ricky are twins. When they are 20
  years old, Bobby leaves on a space flight to a
  star that is 20 light years away, traveling very
  close to the speed of light. At this extreme
  speed, the gamma factor for time dilation is
  equal to 20. What happens?

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The Pole in a Barn Paradox
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ZPi Labs Geriatric Migration Time
Dilationhttp//zapatopi.net/labs/geriatric_migrat
ion.html

• A Sociological Mystery
• An unresolved question in sociology is why
  elderly Americans so often wish to spend the
  latter years of their lives in places such as
  Florida and the Southwest. Many theories have
  been put forth, including geriatric preference
  for hot temperatures and the increased
  availability of rubber for elastic waistbands in
  beltless pants, but all have been found lacking
  in evidence. An important fact that has either
  been down-played or gone unnoticed by researchers
  in this field is that there is a definite trend
  in the patterns of geriatric migration
  retirement communities tend to concentrate more
  towards the Earth's equator than towards its
  poles. It is from this observation that I have
  discovered the answer to this pressing
  sociological mystery.

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ZPi Labs Geriatric Migration Time
Dilationhttp//zapatopi.net/labs/geriatric_migrat
ion.html

• Although a person living on the equator may not
  notice that time is moving more slowly for him
  than it is for someone in New York, it still is.
  If these two people are in contact with each
  other, the person at the equator will get more
  raw interaction over, to him, the same amount of
  time than he would have if he too lived in New
  York. This is like living more life in less time.
  And if his life was the same length of (local)
  time as it normally would be, then he would
  perceive it as a longer life. Plus, from the
  point of view of the person in New York, it was a
  longer life. What this means to our Senior
  Citizen is more relative time to pass on wisdom,
  enjoy family and friends, help better the future,
  and experience the satisfaction of seeing the
  future start to blossom. Time dilation becomes
  time compression, allowing our Senior Citizen to
  do more with what time he or she has left, to do
  the things that need to get done to insure his or
  her legacy.

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• xkcd.com