Information about Midterm

1
Information about Midterm 2

• Grades are now posted on course website
• Average 107/160, s.d. 27, (compare with first
  midterm 111/160, s.d. 21)
  
• Highest 154/160, (1st 148/160)
• Scores below 70 serious concerns
• To estimate course grade, sum all scores so far,
  compare percentage to approximate grade scale
  given in the course syllabus
  
• Final exam Saturday, May 12, 8-10 am
• Pick up midterm exams in class (before lecture)

2
Analysis of an exam question

• Question 49, 2nd midterm
• What is the ultimate fate of an isolated white
  dwarf?
  
• (a) It will cool down and become a cold black
  dwarf
  
• (b) As gravity overwhelms the electron degeneracy
  pressure, it will explode as a supernova
  
• (c ) As gravity overwhelms the electron
  degeneracy pressure, it will explode as a nova
  
• (d) The electron degeneracy pressure will
  eventually overwhelm gravity and the white dwarf
  will slowly evaporate
  
• (e) As gravity overwhelms the electron degeneracy
  pressure, it will become a neutron star

3
Analysis of an exam question

• Question 49, 2nd midterm
• What is the ultimate fate of an isolated white
  dwarf?
  
• (a) 36 (correct)
• (b) 24 (distractor)
• (c ) 21 (distractor)
• (d) 13 (distractor)
• (e) 7 (distractor)
• Point biserial correlation 0.46 (range 0.10 -
  0.59)
  
• Exam Reliability coefficient 0.89

4
Chapter S2Space and Time
5
What are the major ideas of special relativity?
6
Einsteins Theories of Relativity

• Special Theory of Relativity (1905)
• Usual notions of space and time must be revised
  for speeds approaching light speed (c)
  
• E mc2
• General Theory of Relativity (1915)
• Expands the ideas of special theory to include a
  surprising new view of gravity

7
Key Ideas of Special Relativity

• No material object can travel faster than light
• If you observe something moving near light
  speed
  
• Its time slows down
• Its length contracts in direction of motion
• Its mass increases
• Whether or not two events are simultaneous
  depends on your perspective
  

8
Whats relative about relativity?
9
Relativity of Motion

• Motion is not absolutewe must measure speed of
  one object relative to another
  
• Example Plane moving at 1,670 km/hr from E to W
  would appear from space to be standing still

10
Absolutes of Relativity

• The laws of nature are the same for everyone
• The speed of light is the same for everyone
• All of relativity follows from these two ideas!

11
Making Sense of Relativity

• As children, we revised our ideas of up and
  down when we learned that Earth is round
  
• Relativity forces us to revise how we think of
  space and time

12
How did Einstein think about motion?
13
Reference Frames
Ball moves at 10 km/hr in reference frame of plane
Ball moves at 910 km/hr in reference frame of
someone on ground

• Motion can be defined with respect to a
  particular frame of reference

14
Absoluteness of Light Speed
Light moves at exactly speed c
Light moves at exactly speed c (not c 900 km/hr)

• Einstein claimed that light should move at
  exactly c in all reference frames (now
  experimentally verified)

15
Whats surprising about the absoluteness of the
speed of light?
Light moves at exactly speed c
Light moves at exactly speed c (not c 900 km/hr)
16
Thought Experiments

• Einstein explored the consequences of the
  absoluteness of light speed using thought
  experiments
  
• The consequences will be easiest for us to
  visualize with thought experiments involving
  spaceships in freely floating reference frames
  (no gravity or acceleration)

17
Relativity of Motion at Low Speeds
18
Relativity of Motion at Low Speeds
19
Relativity of Motion at High Speeds
20
Light Speed is Absolute
c 0.9c c !?!
21
Relativity of Motion
22
Why cant we reach the speed of light?
23
Trying to Catch up to Light

• Suppose you tried to catch up to your own
  headlight beams
  
• Youd always see them moving away at speed c
• Anyone else would also see the light moving ahead
  of you

24
Special Topic What if Light Cant Catch You

• Is there a loophole?
• What if youre somehow moving away from a distant
  planet faster than the speed of light?
  
• In that case you have no way of detecting that
  the planet is there.
  
• Although there are some phenomena that move
  faster than light, no information can be
  communicated faster than the speed of light
  

25
How does relativity affect our view of time and
space?
26
Path of Ball in a Stationary Train

• Thinking about the motion of a ball on a train
  will prepare us for the next thought experiment

27
Path of Ball in a Moving Train

• Someone outside the train would see the ball
  travel a longer path in one up-down cycle
  
• The faster the train is moving, the longer that
  path would be

28
Time Dilation

• We can perform a thought experiment with a light
  beam replacing the ball
  
• The light beam, moving at c, travels a longer
  path in a moving object
  
• Time must be passing more slowly there

29
The Time Dilation Formula
Light path in your reference frame
Light path in frame of other spaceship
30
The Time Dilation Formula

• Time will appear to pass more slowly in a moving
  object by an amount depending on its speed
  
• Time almost halts for objects nearing the speed
  of light

31
Simultaneous Events?

• In your reference frame, red and green lights on
  other spaceship appear to flash simultaneously

32
Simultaneous Events?

• But someone on the other spaceship sees the green
  light flash firstsimultaneity is relative!

33
Length Contraction

• Similar thought experiments tell us that an
  objects length becomes shorter in its direction
  of motion

34
Mass Increase

• A force applied to a rapidly moving object
  produces less acceleration than if the object
  were motionless
  
• This effect can be attributed to a mass increase
  in the moving object

35
Velocity Addition
36
Formulas of Special Relativity
37
Deriving E mc2
Mass-Energy of object at rest
Kinetic Energy
38
Do the effects predicted by relativity really
occur?
39
Tests of Relativity

• First evidence for absoluteness of speed of light
  came from the Michaelson-Morley Experiment
  performed in 1887
  
• Time dilation happens routinely to subatomic
  particles the approach the speed of light in
  accelerators
  
• Time dilation has also been verified through
  precision measurements in airplanes moving at
  much slower speeds
  

40
Tests of Relativity

• Prediction that Emc2 is verified daily in
  nuclear reactors and in the core of the Sun
  

41
Test Relativity for Yourself

• If speed of light were not absolute, binary stars
  would not look like two distinct points of light
  
• You can verify relativity by simply looking
  through a telescope at a binary star system

42
A Paradox of Non-Relativistic Thinking

• If speed of light were not absolute, you would
  see the car coming toward you reach the collision
  point before the car it struck
  
• No paradox if light speed is same for everyone

43
How can we make sense of relativity?
44
Making Sense of Relativity

• According to you, time slows down in a moving
  spaceship
  
• According to someone on that spaceship, your time
  slows down
  
• Who is right?
• You both are, because time is not absolute but
  depends on your perspective
  

45
Toward a New Common Sense

• As children we learned that up and down are
  relative
  
• Relativity tells us that time and space are
  relative

46
How does relativity offer us a ticket to the
stars?
47
A Journey to Vega

• The distance to Vega is about 25 light-years
• But if you could travel to Vega at 0.999c, the
  round trip would seem to take only two years!

48
A Journey to Vega

• At that speed, the distance to Vega contracts to
  only 1 light-year in your reference frame
  
• Going even faster would make the trip seem even
  shorter!

49
A Journey to Vega

• However, your twin on Earth would have aged 50
  years while you aged only 2
  
• Time and space are relative!