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of gravity is obsolete.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.
Einstein would say that the Earth's mass distorts spacetime.
It makes a "dip" in spacetime,
so spacetime near the Earth
is not flat, it is curved. The moon is trying to take
the shortest
(translated as straightest)
route through spacetime. If you use non-relativistic thinking
(i.e. if you
consider 3 dimensional space, rather than 4 dimensional
spacetime) that route looks like a circle
about the Earth.
As for the apple, when it was still attached to the tree,
the Earth's rotation
carried it along. Then, it's stem
detached from the tree and the apple was free to follow
its own path. In the curved 4 dimensional spacetime, the
path carries the apple to the Earth's surface.
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).
I would tell my friend that both light and objects
respond to curved spacetime. Light travels
in the straightest possible path (between 2 places) in a curved spacetime.
In the figure, the light is coming
from the real object,
the blue ball at the top, center of the figure. The
object emits light in all
directions. Two of those
directions are shown on the figure -- they are traced with
yellow lines.
As the photons travel along these paths,
they come somewhat near to a very massive object.
The massive object is drawn in orange. It has caused spacetime
to curve. So, when the photons
from the "real object"
(marked with the blue dot) come near the "massive object"
(marked with the orange dot), they continue to travel
in the straightest possible path,
but from our point of
view, that path seems to be curved. The paths seem
to bend, such that
the left path bends back toward the
right after passing the massive object
and vice verse for the other path.
Neither of these paths come to the Earth
straight-on -- both come to the Earth slightly from
the side.
So, when we detect the photons, we detect
them coming from the side. The figure shows two sets
of dashed lines, these lines represent the perceived
paths of the photons. By that, I mean that
our eyes don't realize that spacetime is curved, so when we
unconsciously trace back the photon's paths,
we assume that the photons made
straight paths through a flat space. So our eyes perceive
the sources of the photons as being "image 1" on the
left of the "real object" and "image 2"
on the right of the real object.
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
Answer: c
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 his/her "worldline" 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
Answer: b
5.)
Imagine two sections of spacetime; the first is perfectly flat
and the second is curved. Also imagine that there is an object
in the flat section and that the object's path is a straight
line between two points.
If there were also an equivalent object in the curved section of
spacetime,
what sort of path in the curved section of spacetime would be most
equivalent to the straight path in the flat section of spacetime?
a.) The shortest possible path between 2 points on the curved
section of spacetime
b.) A straight line that intersects the surface of the curved section of
spacetime
c.) A single point on a curved section of spacetime
d.) None of the above is remotely equivalent to the straight
path in flat spacetime
Answer: a
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
Answer: c
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
Answer: d
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
Answer: a
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
Answer: b
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
Answer: b