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?**