Assignment 2

 

Let the vertical axis be time and the horizontal axis space for all diagrams.

 

1. Draw the world line of a stationary object. Label it X.

 

2. Draw a beam of light moving to the right of X.

 

3. Draw the world line of an object moving to the right of X at 1/2 the speed of light.

 

4.  (a) Start with the stationary object X and draw another event (E1) about 1 inch to the right of X about in the middle of the page. Find the event (E2) on X that X would observe to be simultaneous with E1. That is, determine when on X's world line E1 occurred. You will have to send a light pulse from X to E1 and then back again to determine this. Explain your answer briefly. (Hint: draw your lines from E1 to X not the other way around.)

 

(b) Find another event (E3) that would be simultaneous for X with E1. Use these points to draw a simultaneity slice for X for the moment E2. Explain what this means.

 

5. Start with the diagram for 4b. (make a copy)

 

(a) Add the world line of an object Y moving to the right at about 1/3 the speed of light and intersecting X at E2.

 

(b) Determine when on Y's world line E1 would be observed to occur. Again you will need to send out a light impulse from Y to E1 and back again.

 

(c) Repeat part b for E3. Are E1 and E3 simultaneous with E2 for Y? Explain. What does this show?

 

(6) Start with 5a (or just Y)

Find two events not on Y that are simultaneous from Y's point of view. Use these to draw a simultaneity slice for Y.

 

(7) Using a diagram explain why moving clocks appear to move more slowly to stationary observers. Explain!

 

(8) If time slows down for moving objects explain why length would contract from the point of view of a stationary observer. Use a space time diagram and explain.

 

(9) (a) Imagine a momentary flash of light that moves outward from its origin in all directions. Draw the space time diagram of the pulse of light moving off from its origin A in both directions.

 

(b) This diagram divides the universe into two sections: inside the cone and outside. if nothing can move faster than the speed of light and no causal effect can be transmitted faster than the speed of light, then what can you say about everything in the cone? What about outside it?

 

(c) draw another cone originating from a point  B simultaneous for a stationary observer with the origin of the first one. What do these cones tell you about the causal relationship of simultaneous events?

 

10. (extra credit) Imagine that the origin of the cone of light in 9a is the intersection of  X and Y world lines from the questions above. That is, that at the point where X and Y meet in space and time a flash of light is emitted. Draw this. Will both X and Y observe a circle of light moving outward from their point of view as they move away, or just X, just Y, or neither? Explain?