# Chapter S3

## Unlock all answers in this set

question
What do we mean by the straightest possible path between two points on Earth's surface?
The shortest path between the two points
question
List five major ideas that come directly from the general theory of relativity.
1. Gravity arises from distortions of spacetime. It is not a mysterious force that acts at a distance. The presence of mass causes the distortions and the resulting distortions determine how other objects move through spacetime. 2. Time runs slowly in gravitational fields. The stronger the gravity, the more slowly time runs. 3. Black holes can exist in spacetime, and falling into a black hole means leaving the observable universe. 4. The universe has no boundaries and no center, yet it might still have a finite volume 5. Large masses that undergo rapid changes in motion or structure emit gravitational waves that travel at the speed of light.
question
What is the equivalence principle? Give an example.
Equivalence principle is the fundamental starting point for general relativity, which states that the effects of gravity are exactly equivalent to the effects of acceleration. The effects of gravity are exactly equivalent to the effects of acceleration. For example, you cannot tell the different between being in a closed room on Earth and being in a closed room accelerating through space at 1g.
question
What do we mean by dimension? Describe a point, a line, a plane, a three-dimensional space, and a four-dimensional space. What does hyperspace mean?
Dimension (mathematical) describes the number independent directions in which movement is possible. Hyperspace is any space with more than three dimensions. A point has 0 dimensions. Sweeping a point back and forth along one direction generates a 1-dementional line . Sweeping a line back and forth generates a 2-dimensional plane . Sweeping a plane up and down generates a 3-dimensional space . Sweeping space back and forth in some "other" direction generates a four-dimensional space.
question
Explain the meaning of the statement "Space is different for different observers. Time is different for different observers. Spacetime is the same for everyone."
These different "pictures" are the differing perceptions of time and space of observers in different reference frames. Thus, different observers will get different results when they measure time, length, or mass, even though they are all actually looking at the same spacetime reality.
question
What is a spacetime diagram? What is a worldline? What is an event?
Spacetime diagram is a graph that plots a spatial dimension on one axis and time on another axis. Worldline is a line that represents an object on a p=spacetime diagram. Event is any particular point along a worldline; all observers will agree on the reality of an event but may disagree about its time and location.
question
Explain how the idea of spacetime geometry means that the universe has no center and no edges.
This overall shape must be one of the three general types of geometry. This fact explains how it is possible for the universe to have no center and no edges.
question
How can you tell whether you are following the straightest possible path through spacetime?
If you are floating freely, then your worldline is following the straightest possible path through spacetime. If you feel weight, then you are not on the straightest possible path.
question
According to general relativity, what is gravity? With this view, why does the Earth orbit the Sun?
Gravity is one of the four fundamental forces; it is the force that dominates on large scales. The fact that Earth goes around the Sun tells us that spacetime itself is curved near the Sun. in other words, what we perceive as gravity arises from the curvature of spacetime.
question
Describe the idea behind the "rubber sheet" analogy to spacetime and the limitations of the analogy. In the analogy, what does mean? Why does the curvature of spacetime near a star depend on both the star's mass and its size?
In flat regions of spacetime, freely moving objects move in straight lines. The mass of the Sun causes spacetime to curve, so freely moving objects (such as planets and comets) follow the straightest possible paths allowed by the curvature of spacetime. Circles that were evenly spaced in flat spacetime become more widely spaced near the central mass. A mass like the Sun causes spacetime to curve, and the curvature of spacetime determines the paths of freely moving masses like the planets.
question
Explain how the idea of spacetime geometry means that the universe has no center and no edges.
If the Universe began in an explosion and is expanding, is it or is it not required to have a center? No. Once the Universe began to expand, it became like an expanding surface. Space itself was expanding. Once objects began to appear in the Universe, we had some "markers", if you will, against which to establish coordinate locations. Try as we might, however, we have never been able to use these galaxies to establish a spatial preference in the Universe. There is no center, and all of space seems to be expanding away from all of the rest of space. No matter where you are.
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What is a black hole? What do we mean by the event horizon of a black hole?
If we shrank the Sun enough, we could eventually curve spacetime so much that it would become a bottomless pit - a hole in the observable universe, which is called the black hole . The boundary that marks the "point of no return" is called the event horizon.
question
According to general relativity, how is time affected by gravity? According to general relativity, why does Earth orbit the Sun? Describe the use and limitations of the rubber sheet analogy.
Time runs slower in places where gravity is stronger. Earth is following the straightest path possible through spacetime, but this path happens to go around and around the Sun. we use it to represent spacetime. The issue is it is 2D and we have to ignore any effects of friction bc there is no friction in space.
question
What is gravitational time dilation? What determines how much time is slowed in a gravitational field?