# Problems for Chapter S3

1.) In Einstein's theory of general relativity, the notion of gravity is obsolete.
So, how does he explain the acceleration that we have gotten accustomed to
attributing to gravity (for example, an apple falling from a tree)? Please explain
in 50 words or more.

2.) See figure S3.19 in the textbook (it is the same as one of the figures on the Chapter S3
webpage -- look in the section on Gravitational lensing and click the "diagram" link).
If you were talking with a friend who already believed that spacetime is curved
near massive objects but who had never heard of gravitational lensing, how would
you explain gravitational lensing (using this figure) to your friend (in 100 words or more).

3.) According to Einstein's Equivalence Principle, if you were in a windowless space capsule and you felt weightless,
a.) You could be floating freely, far from any massive objects
b.) You could be in free-fall, falling into a massive object
c.) Both of the above
d.) None of the above

4.) Imagine a flat spacetime diagram in which distance east is plotted on the x axis and time is plotted on the y axis. If someone is stationary, how would that look on the spacetime diagram?
a.) His/her "worldline" would be straight and horizontal
b.) His/her "worldline" would be straight and vertical
c.) His/her "worldline" would curve to the right
d.) His/her "worldline" would curve to the left

5.) A straight line on a flat section of spacetime is equivalent to
a.) The shortest possible path on a curved section of spacetime
b.) A straight line that intersects the surface of the curved section of spacetime
c.) A point on a curved section of spacetime
d.) None of the above

6.) According to Einstein, being in free fall around a massive object is equivalent to
a.) Following the shortest path between two points in curved spacetime
b.) Traveling at a constant velocity far from any massive objects
c.) Both of the above
d.) None of the above

7.) According to Einstein, if an object does not follow the straightest possible path as it travels between 2 points in spacetime, it
a.) "feels weighty"
b.) could be accelerating
c.) could be being held up against the force of gravity
d.) All of the above
e.) None of the above

8.) Einstein's theories say that the curvature of spacetime causes
a.) What we perceive as gravity
b.) What we perceive as time
c.) What we perceive as energy
d.) None of the above

9.) Suppose that you and your friend, Jackie, are in a spacecraft. The spacecraft is accelerating (in the forward direction). You are at the front end of the spacecraft; Jackie is at the back end.
a.) Both you and Jackie would perceive time to move at the same rate
b.) You think that time runs faster for you and Jackie also thinks that time runs faster for you
c.) You think that time runs slower for Jackie and Jackie thinks that time runs slower for you
d.) None of the above

10.) Suppose that you and your friend, Jackie, are in a spacecraft. Your spacecraft is standing in its launch pad on Earth. You are at the front end of the spacecraft (further from the Earth's surface); Jackie is at the back end (closer to the Earth's surface).
a.) Both you and Jackie would perceive time to move at the same rate
b.) You think that time runs faster for you and Jackie also thinks that time runs faster for you
c.) You think that time runs slower for Jackie and Jackie thinks that time runs slower for you
d.) None of the above