1. Tue. Jan. 6 – Physics Lecture #17 Relativity – SpaceTime 1) Invariants & Spacetime interval 2) Time-like, Light-like, Space-like intervals 3) Spacetime Diagrams 4) Time-ordering of events, Space-ordering of events

2. 0 0 2 3 1 4 2 5 1 5 4 3 x y In the coordinate system displayed, what is the a) “x-length” of the rod? b) “y-length” of the rod? 0 0 2 3 1 4 2 5 1 5 4 3 x y

3. Invariants and Spacetime Interval

4. Arlo lights and holds a match, and 80 seconds later, it goes out. Rebecca, riding in a rocket past these events at constant speed, notes that, as measured in her frame, the match burned for 100 seconds. Consider the events: match is lit and match goes out What is the distance between these two events in Arlo’s frame? 1. 0 2. 60 lt-sec 3. 80 lt-sec 4. 100 lt-sec 5. 125 lt-sec 6. Not enough information

5. Arlo lights and holds a match, and 80 seconds later, it goes out. Rebecca, riding in a rocket past these events at constant speed, notes that, as measured in her frame, the match burned for 100 seconds. How fast is Rebecca going relative to Arlo? How far apart in Rebecca's frame did these two events (lighting and going out) occur? As measured by Rebecca, how far did the lit match travel, and how fast was it moving? As measured by Arlo, how fast and how far did Rebecca travel during the one minute the match was lit? Did anyone/thing present measure proper time?

6. R2.1 Events A, B, and C are shown on a spacetime diagram. a) What are the coordinates of the three events? b) Calculate the interval for each pair of events. c) Identify each interval as time-like, light-like, or space-like. d) In the frame shown, event A occurs before B, which occurs before C. Which events could have their time-order reversed (switching before and after) by choosing an appropriate reference frame? Which events could have their space-order reversed (switching left and right) by choosing an appropriate reference frame? Which events have their time-order preserved in any reference frame? Which events have their space-order preserved in any reference frame? e) Which events could be a "cause" for which other events?

7. R2.8 The spacetime diagram shows the worldlines of Earth and a rocket, as well as several labeled events. How fast is the rocket moving, relative to the Earth? 1. 0 2. 3/5 c 3. 4/5 c 4. c 5. 5/4 c 6. 5/3 c

8. Order events A, B, and C from earliest to latest in Earth’s reference frame. 1. A B C 2. A C B 3. B C A 4. B A C 5. C A B 6. C B A Concept Check: Order events A, B, and C from earliest to latest in Rocket’s frame.

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10. R2.2 The figure shows a spacetime diagram with seven straight lines through the origin labeled with numbers 1 through 6, as well as “back of card” for the horizontal line. The coordinate system is the Earth’s reference frame. a) Which line is a world line of an object at rest relative to the Earth? b) Which line is a world line of a spaceship traveling at speed +0.25c relative to the Earth? c) Which line is a world line of a light pulse emitted by the spaceship as it passes the Earth?

11. The coordinate system is the Earth’s reference frame. Line 1 is the world line of an object at rest relative to the Earth. Line 2 is the world line of a spaceship moving at speed +0.25c relative to the Earth. 1. a2. b3. d4. e5. f d) Which events happen simultaneously in the Earth frame? e) Which events happen simultaneously in the spaceship frame? Which pairs of events are separated by space-like intervals? by time-like intervals? by light-like intervals?