1. Albert Einstein and 100 Years of Relativity
Christopher M. Johns-Krull
Rice University, Dept. of Physics and Astronomy
October 17, 2016

2. The eternal mystery of the word is its comprehensibility
The eternal mystery of the word is its comprehensibility. The fact that it is comprehensible is a miracle.
-- Albert Einstein
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3. The laws of physics are the same for all observers
Special Relativity’s Postulates
The laws of physics are the same for all observers
The speed of light is the same for all observes
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4. The Laws of Physics
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5. Is the Speed of Sound Constant?
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6. Is the Speed of Sound Constant?
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7. The Speed of Light He actually first tried an offset circle. 7
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8. Relative Speeds Change How They Add
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9. Special Relativity

10. Faster than Light Travel – NO!
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11. Time Dilation: Normal Objects Moving – Speed Changes
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12. Time Dilation: Light Moving
D = T x V
V = D/T
c = D/T
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13. Time Dilation – Leads to Length Contraction
Can measure distance with speed and velocity:
D = T x V
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14. Length Contraction

15. When Simultaneous Things Aren’t
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16. And Mass Goes Up
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17. Some Formulas
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18. E = m c2
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19. Experimental Tests He actually first tried an offset circle. 19
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20. Experimental Tests
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21. Experimental Tests
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22. We Can Kind of Do It!
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23. Twin Paradox
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24. But Motion is Relative
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25. Working Through the Paradox
6.0 lyr away
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26. Working Through the Paradox
6.0 lyr away
At the start of the journey, your clocks are the same. Han Solo then accelerates to 0.6c and travels to the distant star at this speed. We will not worry about the details of acceleration or deceleration. On Earth you have a telescope that allows you to see Han’s closk, and he has one that allows him to see yours.
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27. On the Way…
6.0 lyr away
Han uses the length contraction formula and finds that the distance he has to travel is 4.8 lyr.
γ = 0.8 and 6 * 0.8 = 4.8
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28. Han Arrives
6.0 lyr away
Han traveled for 4.8 lyr at 0.6c and took 4.8/0.6 = 8 years
You observe that he traveled 6.0 lyr at 0.6c and it took 6/0.6 = 10 years
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29. Han’s Clock When He Arrives
6.0 lyr away
Han records 8 years.
You see 8 years on Han’s clock but 16 on yours – 10 to get there plus 6 for the light to get back to you. Han’s clock is running at ½ the speed of yours
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30. Your Clock When Han Arrives
6.0 lyr away
Han sees 8 years on his clock.
Han sees 4 years on your clock because he is seeing yours as it was 6 years ago when he gets there. Your clock is running ½ the speed of Han’s.
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31. Now Han Comes Home 6.0 lyr away Han’s clock goes from 8 to 16.
Your clock goes from 10 to 20.
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32. Now Han Comes Home 6.0 lyr away
But you see Han’s clock go from 8 to 16 while yours went from 16 to 20, so you see Han’s clock running twice as fast as yours.
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33. Now Han Comes Home 6.0 lyr away
But Han sees your clock go from 4 to 20 while his went from 8 to 16, so Han sees your clock running twice as fast as his.
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34. Working Through the Paradox
6.0 lyr away
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35. Superluminal Motion
M 87
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36. Simple Measure of Speed
v = d/t

37. Superluminal Motion Explained
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38. Moving to General Relativity
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39. In Essence GR Works with Geometry
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40. Is All Motion Relative?
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41. It Can be Made to be!
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42. The Equivalence Principle
The effects of gravity are exactly equivalent to the effects of accelerations
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43. The Equivalence Principle
And its corollary
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44. Spacetime instead of Space & Time
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45. A Spacetime Diagram
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46. A Spacetime Diagram
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47. More Worldlines
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48. More Worldlines
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49. Shortest Distance – Straight Lines
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50. Shortest Distance – Straight Lines
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51. Shortest Distance on a Sphere
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52. Shortest Distance on a Sphere
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53. The Geometry of the Universe
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54. “Straight” Lines in Curved Spacetime
If you are floating freely, then your worldline is following the straightest possible path through spacetime. If you feel weight, then you are not on the straightest possible path.
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55. What is an Orbit?
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56. A New Understanding of Gravity

57. An Orbit is a Straight Path Through Curved Spacetime
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58. A New Understanding of Gravity