RELATIVITY. Special Relativity

Transcription

1 RELATIVITY Special Relativity

2 FROM WARMUP How does special relativity differ from general? Special relativity deals with inertial reference frames. General relativity deals with gravity and acceleration When does relativity have physical consequences and when does relativity just make things appear a certain way when that way isn't actually the case? Relativity helps us understand what observations are specific to a particular reference frame and which things are true in all reference frames. More time on. Space-time graphs Proper length/time

3 REVIEW OF LAST LECTURE Einstein s Postulates 1. The laws of physics apply in all inertial reference frames. 2. The speed of light is the same for all inertial observers. Time dilation g v/c

4 FROM WARMUP What exactly does the second postulate of Einstein's special theory of relativity mean? If light has a finite speed that doesn't change according to the velocity of the observer or the source, why can't we define a reference frame that is absolutely stationary? If you shoot two beams of light in opposite directions... well that was Michelson's experiment but I suppose I'm just confused about what the results of that experiment mean.

5 FROM WARMUP Last class period we briefly discussed the famous "twin paradox". What is the seeming paradox, and how is it resolved? We didn't have time to get to that last class period The paradox is that, from the point of both twins, it seems that the other twin is moving away at a speed v. But when twin two returns from his space travels, he is much younger than twin 1. This is resolved because twin 2 accelarates, and therefore experiences different frames of reference, while the first twin remains in the same frame of reference. Truthfully I do not quite know. When does relativity have physical consequences and when does relativity just make things appear a certain way when that way isn't actually the case?

6 SIMULTANEITY Q P (a) Now Q P (b) An instant later

7 CLICKER QUIZ Q P Q P Which light beam hits the train wall first? A. They hit at the same time B. The back one hits first (that is, the left-traveling one) C. The front one hits first (that is, the right-traveling one) D. It depends on the reference frame.

8 CONSIDER SPACE TRAVEL A space traveler takes his rocket (0.9 c, gamma = 2.29) to a planet 1 light year away. Earth frame: how long does it take? Traveler frame: how long does it take? Traveler frame: How much does the traveler age? Earth frame: how much does the traveler age? Traveler frame: how fast is the planet approaching? Do you see a contradiction? x = vt: t = 1.11 year year year year 0.9 c x = vt

9 LENGTH CONTRACTION Which is correct? The space traveler aged so little because. A. Time was slowed down (Earth frame of reference) B. The distance shrank (Traveler frame of reference)

10 MUON DECAY Muons are unstable particles (heavier than electrons and neutrinos, but lighter than all other matter particles). When cosmic rays strike the upper atmosphere, a series of reactions produce muons (gamma rays + atomic nuclei -> pions -> muons). Muons have an average lifetime of about 2.2 micro seconds. Ignoring relativistic effects, how far can muons travel on average, if they move at the speed of light? On earth, about 10,000 muons originating from cosmic ray reactions reach ever square meter of the earth s surface. How does relativity explain this? Including relativistic effects, how far could muons potentially travel?

11 FROM WARMUP What is the rest length of an object? The proper, or rest, length of an object is the length measured by some observer who is stationary, or at rest, with respect to the object. The rest length is the length of the object from its reference frame. Note that the book calls this proper length.

12 FROM WARMUP What is the proper time of a journey? Proper time is the time measured by an observer for whom the two events take place in the same location. Proper time of a journey is measured by someone who remains in the same position when witnessing the beginning and end points of a journey.

13 TIME DILATION AND LENGTH CONTRACTION Two sides of the same coin The space traveler aged so little because A. Time was slowed down for him (Earth view) B. The distance shrank for him (Traveler view) Who measure s the trip s rest length? Who measures the traveler s proper time?

14 THE BARN PARADOX Thought question: does the runner fit inside the barn? Barn Frame: Runner Frame:

15 EVENTS What is an event? When did it happen? Where did it happen?

16 SPACE-TIME DIAGRAMS What is an event on this graph? What do we mean by a worldline? Whiteboard example (Barn paradox)