1. Modern Physics
Chapter 2

2. Companion Website Online Flash demos
Online Flash demos

3. Constant Speed of Light
c = 3 x 108 m/s
Why did it take so long to figure this out?

4. Constant Speed of Light
Think about everyday speeds
Helios
Galileo

5. Albert Einstein (3/14/1879 – 4/18/1955)
1894 (Age 15)
The Investigation of the State of Aether in Magnetic Fields
Failed entrance exam to ETH (Swiss Fed. Inst. Tech.)
1895
Chasing light idea, Special Relativity
1900
Finished ETH (physics and math)
Swiss patent office clerk (EM devices)
1905 (Annus Mirabelis)
4 papers
Photoelectric Effect
Brownian Motion
Special Relativity
Matter and Energy Equivalence

6. c Constancy
1884 – J. C. Maxwell formulated four equations to describe light, which depend on c being constant
Electric charges cause electric fields
No magnetic monopoles to cause magnetic fields
Changing magnetic fields cause electric fields
Electron currents and changing electric fields cause magnetic fields

7. Michelson-Morley
: Find the velocity of the Aether

8. Michelson-Morley 1887-1907: Find the velocity of the Aether v mirroru c
Light source
Beam splitter
mirror
screen

9. Michelson-Morley 1887-1907: Find the velocity of the Aether mirror
Light source
Beam splitter
mirror
screen

10. Einstein’s Postulates
Physics is the same regardless of inertial frame
Light moves with constant speed in the eyes of all observers

11. Postulate 1
Suppose you are sitting in a soundproof, windowless room aboard a hovercraft moving over flat terrain. Which of the following can you detect from inside the room? May have multiple answers.
1. rotation
2. deviation from the horizontal orientation
3. motion at a steady speed
4. acceleration
5. state of rest with respect to ground
Answer: 1, 2, and 4. There are no experiments that can detect uniform
motion (or rest); we can sense any motion that causes acceleration.

12. Postulate 1
Suppose you are sitting in a soundproof, windowless room aboard a hovercraft moving over flat terrain. Which of the following can you detect from inside the room? May have multiple answers.
1. rotation
2. deviation from the horizontal orientation
3. motion at a steady speed
4. acceleration
5. state of rest with respect to ground
Answer: 1, 2, and 4. There are no experiments that can detect uniform
motion (or rest); we can sense any motion that causes acceleration.
Answer: 1, 2, and 4. There are no experiments that can detect uniform
motion (or rest); we can sense any motion that causes acceleration.

13. Postulate 1
As far as we can tell, we don’t know which frame is actually doing the moving as long as no acceleration is involved.
Answer: 1, 2, and 4. There are no experiments that can detect uniform
motion (or rest); we can sense any motion that causes acceleration.

14. Postulate 2 Sound is longitudinal and has no polarization
Speed of Light : Speed of Sound as Aether : Air
c is constant with respect to source or medium?
Sound depends on both
vs = vsource + vair
Aether?
Can it move radially wrt all sources?

15. Postulate 2
The speed of light is constant as found empirically (Michelson-Morely) and theoretically (Maxwell)

16. Consequences
How do we rectify our conceptual notion of additive velocities?
We have to change our idea of space-time
Space-time is not the same for all inertial frames

17. Consequences
How do we rectify our conceptual notion of additive velocities?
Simultaneous events in one frame that are at different locations will not be simultaneous in a different inertial frame (relative simultaneity)
Two events occuring at the same location in one frame will have different temporal separation in another inertial frame (time dilation)
The length of an object in one inertial frame will be different in a different inertial frame (length contraction)

18. Relative Simultaneity
The train and platform experiment from the reference frame of an observer onboard the train.
The train and platform experiment from the reference frame of an observer on the platform.

19. Space-Time Diagram Stationary frame (on train) Moving frame (platform)
ct’
ct’ ct ct ct
ct’
t = 0
t = 1
t = 2 x’ x’ x x’ x x

20. Relative Simultaneity

21. Time Dilation
Events occur in the same location are denoted with the prime frame, S’.

22. Time Dilation
Events occur in the same location to someone riding along with the timer.
Therefore, on the timer it is the prime frame (t’). Someone off of the timer observes
Events at two different locations. Therefore, a stationary frame is unprimed.
ct’ h ct h x x v

23. Time Dilation From previous slide
Bring c into square root by squaring it
Replace h with ct’
Square both sides to get rid of square root
Cancel c in first term on right
Solve for t by bringing it to left hand side by itself.
Simplify by pulling t out of both terms on the right hand side by.
Square root both sides

24. Time Dilation

25. The Relativistic Correction, g

26. Plot of gn

27. An Example of Time Dilation
1971
U. S. Naval Observatory flew jets around the world
Some East, with Earth’s rotation
Some West, against Earth’s rotation

28. The Twin Paradox
Events occur in the same location to the spaceship. Therefore, it is the prime frame.
Earth
Planet X
t = 0 s
t = ?
20 ly
t’ = 0 s
t’ = ?
v = 0.80 c

29. The Twin Paradox
How do we reconcile that the relative motion between Earth and spaceship should make it impossible to determine which one sees time dilation?

30. The Relativistic Correction, g
Time for those moving at high speed appears to go slower than when stationary.

31. Length Contraction
An object in motion will appear shorter than an object at rest. t1 t2 v
t=t2-t1

32. Muon Decay Evidence of Special Relativity
Muons (μ-) decay to mu neutrino (vμ), electron anti-neutrino (ve), and an electron (e-) in 2.2 μs (2.2 x 10-6 s) in the muon’s rest frame
Feynman diagram

33. Muon Relativity Muon speed
v = c
At the top of a 2 km high mountain we detect 560 muons/hr. How many should reach sea level (2 km below)?
2 km

34. Muon Relativity

35. Classical Galilean Relativity

36. Lorentzian Relativity

37. Lorentzian RelativityS S’
Light flash occurs on a moving train x x’ vt x’ x

38. Lorentzian RelativityS S’
Light flash occurs on a moving train x x’ vt x’ x

39. Lorentzian Relativity

40. Velocity Transformation

41. Velocity Transformation

42. Velocity Transformation

43. Velocity Transformation
S frame
v = 0
S’ frame
meteor
v = 0.8c
u = - 0.6c

45. Velocity Transformation
S frame
v = 0
S’ frame
v = 0.8c
u = -c

47. Mechanics Requirements Expectations Valid in all inertial frames
Physics does not change with relative velocity
Reduce to classical expectations at low speed
Agreement with experiment/observation
Expectations

48. Lorentzian Momentum y y’ 2 2 2 2 2 2 1 1 1 1 1 x x’ S S’ v

49. Momentum

50. Momentum

51. Momentum

52. Mechanics Requirements Expectations Valid in all inertial frames
Physics does not change with relative velocity
Reduce to classical expectations at low speed
Agreement with experiment/observation
Expectations

53. Energy

54. Energy

55. Energy

56. Energy

58. Higgs Boson - LHC
Circumference is 27 km

59. Higgs Boson - LHC mp = 1.6726217 x 10-27 kg c = 2.99792458 x 108 m/s
Each Beam
450 GeV  vp = c
3.5 TeV  vp = c
proton
proton

60. The Neutrino – Neutron Decayp e
Wolfgang Pauli (1930)
Neutron decays don’t conserve energy or momentum
Hypothesized the neutrino
SuperKamiokande
1998-present
Measure the mass of the neutrino
MINOS – Main Injector Neutrino Oscillation Search
2005-present
No neutrino mass (v = c) v

61. The Neutrino – Neutron Decayp e v

62. Energy
Accelerator vs. Collider

63. Energy
Massless Particles

65. Length Contraction

66. Muon Relativity
Muon speed
v = 0.98 c
3 km
? km
t = ? μs
t’ = 2.2 μs