2. Special Relativity 1 Jack Muryn

3. Albert Michelson In 1638, Galilee Galileo conducted an experiment using covered lanterns separated by one mile, then increasing distances, attempting to see the time the light took to reach the observer one mile or more away from the lantern. He realized the delay between uncovering the lantern to reaching the observer was incidental. The first real breakthrough about this concept was done by Ole Roemer in 1676, which was completely accidental. While he was studying the time for Jupiter’s moon, Io, to complete an eclipse, he noticed that his measurements varied considerably, becoming inaccurate, and then strangely becoming accurate again. At some times, Io’s exit from the shadow would begin later than predicted, and vice versa. But he was able to calculate a very accurate value for c. But many still said that the speed of light (c) was infinite. In 1878, Albert Michelson conducted an experiment on Mt. Wilson in California to precisely determine c. A mirror on Mt. San Antonio 22.5 miles away was used with a high-speed rotating octagon of mirrors. Which increased the accuracy 20 times over previous measurements.

4. In the late 1800s, a serious problem was discovered: Classic wave theory doesn’t work right unless there is a preferred frame of reference - i.e. of motion… Maxwell’s equations do not allow for such. Is there a “material” that light propagates through—the “ether”? 1887 – Michelson & Morley Experiment – conclusive evidence that the speed of light in a “ vacuum ” is independent of the motion of the source! No such ether exists! Consequence: all observers measure the same speed of light, regardless of their motion with respect to the light source!!!!

5. Before Einstein’s “Big Idea” James C. Maxwell had shown that light always travels at the same speed. Albert Michelson developed an experiment to show that the speed of light actually does change, contrary to what Maxwell had hypothesized. Ether theory. (The ether is the dotted-line vectors.) Ether theory was an attempt to explain Michelson’s results, who had expected to show that “c” does actually change in his precise measurements. His experiment actually proved just the opposite!

6. A Theoretical Physicist… what’s that?! The young German scientist began to run “thought experiments,” as he called them. He attempted to explain these controversies by thinking of possibilities that no one had considered before. He did no experimentation. Some said he had his head in the clouds. The man… Albert Einstein.

7. 6 Galileo and Newton: Motion is relative Whenever we talk about motion, we must always specify the vantage point from which motion is being observed and measured. To measure the speed of an object, we first choose a frame of reference and pretend that we are in that frame of reference standing still. Then we measure the speed with which the object moves relative to us—that is, relative to our frame of reference. But the speed of light is the same and does not change depending upon the frame of reference, as in all other cases.

8. 7 Space-time Time… the 4 th dimension. As we travel, we move through space and time. When we are at rest, we only move through time. Light only moves through space… time stands still for light.

9. 8 Postulates of the Special Theory of Relativity All motion is relative, not to any stationary “hitching post” in the universe, but to arbitrary frames of reference. (IOW, there  anywhere in the universe that we can refer to as “home base.”) Imagine a passenger on a train who looks out his window and sees the train on the next track moving by his window. The important point: If you were in a train with no windows, there would be no way to determine whether the train was moving with uniform velocity or was at rest.

10. Einstein first envisioned relativity while watching a clock at 12:00 noon from the back of a trolley with his close friend, Michele Besso. 9

11. 10 First of Einstein's postulates of the special theory of relativity: 1. All laws of nature are the same in all uniformly moving frames of reference. Any number of experiments can be devised to detect accelerated motion, but none can be devised, according to Einstein, to detect a state of uniform motion. Therefore absolute motion has no meaning. No experiment, mechanical or electrical or optical, has ever revealed absolute motion. That is what the first postulate of relativity means.

12. 11 Second postulate in his special theory of relativity: 2. The speed of light in free space has the same measured value for all observers, regardless of the motion of the source or the motion of the observer; that is, the speed of light is a constant.

13. Captain Kirk, pull over! SPEED LIMIT – STRICTLY ENFORCED

14. 13 Einstein’s Postulates 1. The Principle of Relativity (of motion) 2. The Principle of constancy of the speed of light.

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16. 15 To illustrate this statement, consider a rocket ship departing from the space station A flash of light traveling at 300,000 kilometers per second, or c, is emitted from the station. An observer in the rocket sees the flash of light pass her at the same speed c If a flash is sent to the station from the moving rocket, observers on the station will measure the speed of the flash to be c. All observers who measure the speed of light will find it has the same value c.

17. 16 Simultaneity: An interesting consequence of Einstein's second postulate occurs with the concept of simultaneity. Two events are simultaneous if they occur at the same time. Consider, for example, a light source in the exact center of the compartment of a rocket ship…

18. 17 From the point of view of the observer who travels with the compartment, light from the source travels equal distances to both ends of the compartment and therefore strikes both ends simultaneously.

19. 18 Simultaneity The events of light striking the front and back of the compartment are not simultaneous from the point of view of an observer in a different frame of reference. Because of the ship’s motion, light that strikes the back of the compartment doesn’t have as far to go and strikes sooner than light strikes the front of the compartment

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21. 20 Time Dilation: The notion that time can be stretched Suppose this light clock is "0 inside a transparent high- speed spaceship. An observer who travels along with the ship and watches the light clock sees the flash reflecting straight up and down between the two mirrors, just as it would if the spaceship were at rest.

22. 21 Time Dilation: What an outside observer sees

23. 22 Compare inside the space ship and outside the space ship Suppose now that we are standing on the ground as the spaceship whizzes by us at high speed- say, half the speed of light. Things are quite different from our reference frame, for we do not see the light path as being simple up-and-down motion. Because each flash moves horizontally while it moves vertically between the two mirrors, we see the flash follow a diagonal path. In the earthbound frame of reference the flash travels a longer distance round trip between the mirrors.

24. 23 Because the speed of light is the same in all reference frames (Einstein's second postulate) The flash must travel for a correspondingly longer time between the mirrors in our frame than in the reference frame of the on-board observer. The l-o-n-g-e-r diagonal distance must be divided by a correspondingly l-o-n-g-e-r time interval to yield the same value for the speed of light in our frame of reference. This stretching out of time is what is called time dilation.

25. 24 The light clock is shown in three successive positions

26. 25 Three distances make up a right triangle

27. 26 The Lorentz Transformation Einstein needed to find a new transformation (the old one being the Galilean transformation). It must fit both the laws of mechanics and Maxwell’s electrodynamic equations. It must allow c to be a constant and hence for time to be relative.

28. 27 Historical Note The Lorentz transformation was derived in 1890 by Hendrik A. Lorentz (Nobel prize 1902) to explain the null result in the Michelson-Morley experiment of 1887. He proposed that one of the arms of the interferometer would contract by a factor of explaining the null result. Only basis was to fit the experimental data. IOW, Lorentz proposed that “c” DOES change, but that since the length contracts, we don’t detect it. (Not true)

29. 28 Relative time The relationship between the time t o (call it proper time) in the frame of reference moving with the clock and the time t measured in another frame of reference (call it the rel ative time ) is: v =speed of the clock relative to the outside observer (the same as the relative speed of the two observers) c = speed of light

30. 29 Express the time dilation equation more simply:

31. 30 Lorentz factor  (gamma)

32. 31 Reading the Lorentz Curve Substitute 0.5c for v in the time-dilation equation and after some arithmetic find that  = 1.15; so t = 1.15 t o.  = = = = = 1.15 This means that if we viewed a clock on a space- ship traveling at half the speed of light, we would see the second hand take 1.15 minutes to make a revolution, whereas an observer riding with the clock would see it take 1 minute.

33. 32 Reading the Lorentz Curve Cont: If the spaceship passes us at 87% the speed of light,  = 2 and t = 2t o. We would measure time events on the spaceship taking twice the usual intervals, for the hands of a clock on the ship would turn only half as fast as those on our own clock. Events on the ship would seem to take place in slow motion. At 99.5% the speed of light,  = 10 and t = 10 t o ; we would see the second hand of the spaceship's clock take 10 minutes to sweep through a revolution requiring 1 minute on our clock. So then, at 0.995 c, the moving clock would appear to run a tenth of our rate; it would tick only 6 seconds while our clock ticks 60 seconds. At 0.87 c, the moving clock ticks at half rate and shows 30 seconds to our 60 seconds; at 0.50 c, the moving clock ticks 1/1.15 as fast and ticks 52 seconds to our 60 seconds. Moving clocks run slow (as compared to a stationary reference).

34. Does this just seem that way? 33

35. The Twin Paradox 34

36. 35

37. Length contraction 36

38. 37 Length Contraction As objects move through space-time, space as well as time changes In a nutshell, space is contracted, making the objects look shorter when they move by us at relativistic speeds. What contracts is space itself.

39. 38 Lorenz Length Contraction v = relative velocity between the observed object and the observer c = the speed of light L = the measured length of the moving object L o = the measured length of the object at rest.

40. 39 Length Contraction L = L 0 or The length of an object is measured to be shorter when it is moving relative to the observer than when it is at rest. Length - observer is at rest relative to the length being measured. Length - observer is moving relative to the length being measured.

41. 40 We can express this as L = L o At 87% of c, an object would be contracted to half its original length. At 99.5% of c, it would contract to one-tenth its original length. If the object were somehow able to move at c, its length would be zero!

42. 41 Contraction takes place only in the direction of motion. If an object is moving horizontally, no contraction takes place vertically.

43. 42

44. Length Contraction Illustrated 43

45. 44 Length contraction should be of considerable interest to space voyagers. The center of our Milky Way galaxy is 25,000 light-years away. Does this mean that if we traveled in that direction near the speed of light it would take over 25,000 years to get there? From an Earth frame of reference, yes, but to the space voyagers, decidedly not! At the speed of light, the 25,000-light-year distance would be contracted to no distance at all. Space voyagers would arrive there instantly! Of course… minor detail: it is not possible for us to travel at the speed of light. But as we approach the speed of light, the distance greatly shortens, as does the time!

46. Mass expansion 45

47. 46 Total Energy and Rest Energy E  m 0 c 2 (Total Energy) E 0 m 0 c 2 (Rest Energy)

48. 47 Equivalence of Mass and Energy E 0 = m 0 c 2 Even when a particle has no velocity and therefore no kinetic energy, it still has energy by virtue of its mass. The laws of conservation of energy and conservation of mass must now be combined into one law: The law of conservation of mass-energy. Mass and energy are equivalent.

49. Evidence of mass expansion   m 0 48 IOW, because it is more massive when it moves at relativistic speeds, it is not deflected as much by the electromagnets.