1. Special Relativity Physics 12

2. Key Terms Postulate: a thing suggested or assumed to be true as the basis for reasoning, discussion, or belief Inertial Frame of Reference: When your frame of reference (ie, how you see the world) where Newton’s First Law of Inertia is correct. This occurs when you are moving (or not moving) at a constant velocity.

3. Key Terms Light year (ly): A measure of distance: the distance that light can travel in one year (in a vacuum). It is roughly 9,461,000,000,000 km. We can write light years as metres by multiplying by c (speed of light in a vacuum): 2 ly = 2c (where c is the speed of light) This allows us to cancel c in many formulae

4. Key Terms- from Grade 11 Electromagnetic Waves: Type of waves that do not require a medium for the energy to travel through. Example: Light waves. However, originally it was believed that all waves needed a medium. (Mechanical waves like sound waves do need medium).

5. Light One theory of light is that it acts as a wave. At one point in time, it was thought that waves needed a medium for the energy carried to travel. However, we now know that light waves (electromagnetic) do not need a medium (only mechanical waves do).

6. Michelson-Morley Experiment Prior to experiments by Michelson and Morley, it was assumed that light needed a medium to propagate (travel) through This medium was called the “luminiferous ether” and Michelson and Morley set out to test for the presence of this substance around Earth They used an interferometer, which is a device designed to measure wavelengths of light

7. Michelson-Morley Experiment Michelson performed an experiment in 1881 that was “unsuccessful” in detecting ether Michelson and Morley performed a refined experiment in 1887 where they tried to find that light moving back and forth parallel to the motion of the Earth took longer to complete the same trip as light moving perpendicular to the motion of Earth

8. Michelson-Morley Results Michelson and Morley set the apparatus so that one beam was travelling parallel to the ether and the other was travelling perpendicular to the ether They then rotated the apparatus and attempted to measure changes in the interference patterns Unfortunately, they were unable to observe a change in interference patterns

9. Confused Yet??? Think about relative velocity from grade 11. Remember how confusing it was to think about? Remember how the actual speed was not what the observer witnessed? This is similar! Let’s watch some videos to help!

10. https://www.youtube.com/watch?v=uMaFB3j M2qs https://www.youtube.com/watch?v=uMaFB3j M2qs https://www.youtube.com/watch?v=7qJoRNs eyLQ https://www.youtube.com/watch?v=7qJoRNs eyLQ http://www.upscale.utoronto.ca/PVB/Harrison /SpecRel/Flash/MichelsonMorley/MichelsonM orley.html http://www.upscale.utoronto.ca/PVB/Harrison /SpecRel/Flash/MichelsonMorley/MichelsonM orley.html

11. Speed of Light Michelson and Morley’s results remained a mystery for about 20 years until Einstein published his special theory of relativity Einstein was attempting to address an inconsistency in Maxwell’s equation for the speed of light:

12. Einstein’s Theory Of Special Relativity Einstein came up with his Special Theory of Relativity in 1905 which helped explain this: He postulated the following: 1) The laws of physics are the same in all inertial frames of reference 2) The speed of light in a vacuum (3.00 x 108 m/s) is the same in all inertial frames of reference, regardless of the motion of the source or the observer.

13. Question: This theory was not well received at the time. If you were alive at the time, would you accept these as truths? Why do you think it was not well received?

14. Special Relativity Implications Because special relativity deals with inertial frames of reference, it restricts its application to systems with no acceleration. It also means that, regardless of your speed relative the source, you will always observe light as moving at 3.00 x 10 8 m/s. This implies that your speed, relative to the speed of light, will determine your speed of passage through time: all things pass through time at the speed of light.

15. Questions to Ponder… What happens as you approach the speed of light then? Time physically slows down. Why doesn’t time slow down or speed up if we are traveling in a car then? The amount that we speed up in a car is not significant enough to effect time. It is so much slower than the speed of light.

16. https://www.youtube.com/watch?v=ttZCKAMpcAo Why doesn’t time travel work? http://www.perimeterinstitute.ca/videos/alice-and- bob-wonderland-can-we-travel-through-time http://www.perimeterinstitute.ca/videos/alice-and- bob-wonderland-can-we-travel-through-time Extras: https://www.youtube.com/watch?v=30KfPtHec4s

17. Time Dilation Time itself is measured differently for the moving object than the unmoving object. Moving at high, relativistic speeds causes time to slow down. It is not just the measurement of time that is affected, but time itself. Chemical and biological processes slow down (and stop if moving at light speed).

18. Time Dilation

19. Example: A spaceship carrying a light clock moves with a speed of 0.500c relative to an observer on Earth. According to the observer, how long does it take for the spaceship’s clock to advance 1.00s?

20. Example 2: Biological Aging Astronaut Benny travels to Vega, the 5th brightest star in the night sky, leaving his 35.0 year old twin sister behind on Earth. Benny travels with a speed of 0.990c, and Vega is 25.3 light years from Earth. How long does the trip take from the point of view of Jenny? (Hint: remember back to grade 11… there is no “relative” velocity in this part) How much has Benny aged when he arrives at Vega?

21. Example 3 Example: An astronaut travelling with a speed, v, relative to Earth takes her pulse and finds that her heart beats once every 0.850s. Mission Control on Earth, which also monitors her heart activity, observes one heart beat every 1.40s. What is the astronaut’s speed relative to Earth?

22. Try this! A rocket speeds past an asteroid at 0.800c. If an observer in the rocket sees 10.0s pass on her watch, how long would that time interval be as seen by an observer on the asteroid? (16.7s) Page 819, Questions 1 to 3

23. Practice Problems Page 819 1-3

24. The Special Theory of Relativity Based on his consideration of Maxwell’s lack of a frame of reference, Einstein proposed his special theory of relativity based on two postulates: 1. All physical laws must be equally valid in all inertial (non-accelerated) frames of reference 2. The speed of light through a vacuum will be measured to be the same in all inertial frames of reference

25. Length Contraction If observers are moving relative to each other, than time dilation from one observer’s point of view will be balanced by a corresponding length contraction from the other’s point of view.

26. Something to think about… A metre stick moving with a speed of 0.5c would appear noticeably shorter than a metre stick at rest. As the speed of an object approaches c (speed of light), its length diminishes to 0. WOW!

28. Jenny and Benny again… From Jenny’s point of view on Earth, Benny’s trip took 25.6 years and covered a distance of 25.3 light years (d = 0.990c x 25.6 years) From Benny’s point of view in the spaceship, the trip took 3.61 years. As far as Benny is concerned, he traveled 3.57 light years (d = 0.990c x 3.61 years) So how did Benny travel so much less distance than what Jenny thinks? How can Earth and Vega be separated by such a small distance (3.57 light years)?

29. Length Contraction!!! A moving object has two measurable lengths: Lo = Its proper length (the length on the moving object). L = its contracted length (seen by outside observer)

30. Length Contraction Formula

31. So what is Benny’s contracted distance traveled? How can both be correct??? Everything is RELATIVE! Both are correct depending on who is the observer.

32. One more thing… Length contraction applies ONLY to lengths measured PARALLEL to the direction of the velocity.

33. Example: A spaceship passes Earth at a speed of 2.00 x 10 8 m/s. If observers on Earth measure the length of the spaceship to be 554m, how long would it be according to its passengers? 743 m

34. Length should be SHORTER (contracted).

35. Questions for You A rocket 75.0m long moves at 0.50c. What would its length be according to an observer at rest? 65.0m

36. Question A spaceship is 98m long. How fast would it have to be going to appear only 49m long? 0.87c

37. Questions page 824 4-6 Page 825 1, 2, 4, 5

38. Questions on Time Dilation and Length Contraction 1) A clock ticks once each second and is 10cm long when at rest. If the clock is moving at 0.80c parallel to its length with respect to an observer, the observer measures the time between ticks to be ______ and the length of the clock to be ______. A) More than 1s, more than 10cm B) Less than 1s, more than 10cm C) More than 1s, less than 10cm D) Less than 1s, less than 10cm E) Equal to 1s, equal to 10cm

39. 2. Before takeoff, an astronaut measures the length of the space shuttle to be 37.24m long. Once aboard the shuttle, while traveling 0.10c, he measures the length again and finds a value of: A) 37.05 m B) 37.24m C) 37.43 m

40. 3. As a spacecraft heads directly to Earth at a velocity of 0.8c, it sends a light signal to Earth. When those light waves arrive on Earth, their velocity relative to Earth is: A) 0.8c B) c C) 1.8c

41. 4. A 30 year old woman takes a trip on a rocket leaving her 20 year old brother behind. She travels at a speed of 0.8c and is gone 20 years, according to the younger brother. When she returns how many years older/younger is she than her brother? A) 2 years younger B) 2 years older C) 3 years older D) 10 years older E) 8 years older

42. So How Fast Can We Go???

43. The Universal Speed Limit When we consider the formulae for time dilation and length contraction, we know that we must be dealing with real numbers so the value under the root must be positive Therefore speed (v) cannot be greater than or equal to the speed of light (c) or the denominator becomes imaginary or zero This speed limit only applies to objects with mass (therefore light and the massless photon can travel at the speed of light)

44. The Universal Speed Limit - Summary Nothing with mass can travel faster than or at the same speed as light. Why can’t we travel at the speed of light? The mass increases and therefore prevents enough acceleration to get to the speed of light (or beyond)

45. Mass and Energy Mass increases as you increase your speed Equation: As the speed of the object increases, the value of the denominator decreases so that m gets larger and larger. If v approaches c, the mass approaches m 0 /0, or infinite.

46. Special Theory of Relativity As you travel at speeds closer and closer to the speed of light… 1) Time dilates 2) Length contracts 3) Mass increases

47. So what about E = mc 2 ? This famous formula surrounds the theory that the total energy of a particle is equal to its mass times the speed of light squared. http://www.universetoday.com/114617/a-fun- way-of-understanding-emc2/ http://www.universetoday.com/114617/a-fun- way-of-understanding-emc2/ Want more info? Read page 830 in text.