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Modern Physics

Modern Physics. Chapter 2. Companion Website. http://wps.aw.com/aw_harris_mp_2/69/17800/4556992.cw/index.html. Online Flash demos. Constant Speed of Light. c = 3 x 10 8 m/s Why did it take so long to figure this out?. Constant Speed of Light. Think about everyday speeds. Helios.

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Modern Physics

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  1. Modern Physics Chapter 2

  2. Companion Website http://wps.aw.com/aw_harris_mp_2/69/17800/4556992.cw/index.html • 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. 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 c Constancy 1884 – J. C. Maxwell formulated four equations to describe light, which depend on c being constant

  7. Michelson-Morley • 1887-1907: Find the velocity of the Aether

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

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

  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.

  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.

  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. Planet X Earth 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 appearsto 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 DecayEvidence 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 = 0.994 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 v

  36. Lorentzian Relativity v

  37. Lorentzian Relativity S S’ Light flash occurs on amoving train x x’ vt x’ x

  38. Lorentzian Relativity S S’ Light flash occurs on amoving 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

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

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

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

  47. Momentum

  48. Momentum

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