Chapter S3: Spacetime And Gravity

24 July 2022
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question
Einstein's general theory of relativity suggests that gravity is ______.
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caused by curvature of spacetime
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Which of the following is not a major idea of Einstein's general theory of relativity?
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It is possible to travel through wormholes.
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Einstein's equivalence principle says that ______.
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the number of independent directions in which movement is possible
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What do we mean by dimension in the context of relativity?
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the number of independent directions in which movement is possible
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What do we mean by hyperspace?
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Any space with more than three dimensions.
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What is spacetime?
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The inseparable combination of space and time.
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If two straight lines start out parallel but eventually cross, then they must be in a _______.
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spherical geometry
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Which of the following correctly describes what we mean by a great circle on the surface of the Earth?
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any circle whose center is at the center of the Earth
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What do we mean by the event horizon of a black hole?
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It is the boundary within which events in the black hole cannot influence events in the outside universe.
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What do we mean by gravitational time dilation?
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It is the idea that time runs slower in places where gravity is stronger.
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In what way do observations of Mercury support Einstein's general theory of relativity?
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Mercury's orbit slowly precesses in a way that matches the prediction of general relativity but disagrees with the prediction based on Newton's universal law of gravitation.
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Why do we see a gravitational redshift in the spectrum of the Sun?
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Time runs slower on the Sun than on Earth, making lines in the solar spectrum have lower frequency and hence longer wavelength than normal.
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Which of the following best describes what we mean by a worm hole?
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A hypothesized but unproven type of "tunnel" through hyperspace that connects distant points in the real universe.
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Which of the following correctly describes the relationship between Newton's theory of gravity and general relativity?
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Newton's theory of gravity is an approximation to general relativity that works when gravity is relatively weak but breaks down when gravity is strong.
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Suppose you launch two probes in opposite directions from the Space Station and they meet as they orbit Earth. According to general relativity, why does this happen?
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They are following the straightest possible paths through spacetime, and those paths curve so that the probes meet.
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Suppose the room in which you are sitting was magically transported off the Earth, and sent accelerating through the universe at 9.8 m/s2. Assuming your doors and windows are sealed and closed, how could you tell that you'd left the Earth?
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You couldn't; the equivalence principle tells us that you won't be able to tell the difference.
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Suppose you are in a spaceship accelerating away from Earth at 9.8 m/s2 (1 g), so that you can walk on the floor of your spaceship as though experiencing normal gravity on Earth. Is it possible for you to consider yourself to be at rest? Why or why not?
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Yes, by assuming you are feeling effects of gravity and that Earth is accelerating away from you because it is in freefall.
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In special relativity, we learned that people in different reference frames will measure time differently. According to general relativity, why does this happen?
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they are experiencing the same spacetime reality, but from different perspectives.
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Assuming you are sitting still as you take this quiz, how would you draw your own worldline on a spacetime diagram?
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A straight, vertical line.
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Planes traveling between Seattle and Tokyo often go near Alaska because ______.
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the distance is shorter
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If your worldline is following the straightest possible path through spacetime, then ______.
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you will be weightless
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According to general relativity, why does Earth orbit the Sun?
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Earth is following the straightest path possible through spacetime, but this path happens to go around and around the Sun.
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According to general relativity, what is a black hole?
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A hole in the observable universe.
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According to general relativity, how is time affected by gravity?
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time runs slower in places where gravity is stronger.
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Suppose you and a friend have precise clocks. You are on the ground floor of a tall building and your friend is on the roof. Which of the following statements is true?
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You will see your friend's clock ticking faster than yours, and she will see your clock ticking slower than hers.
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What evidence supports the predicted existence of gravitational waves?
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The orbit of a star system consisting of two neutron stars is slowly decaying, suggesting that energy is being carried away by gravitational waves.
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Each of the following is a prediction of the theory of relativity (special or general). Which one is crucial to understanding how the Sun provides light and heat to the Earth?
answer
E = mc2
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Suppose that a ship is accelerating through space in such a way that the passengers are experiencing a constant force (resulting from the thrust of the ship) equivalent to the total weight of the ship and passengers on Earth. From the point of view of observers on Earth, how does the ship accelerate?
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At first, it has a nearly constant acceleration of 9.8 m/s2. But as it approaches the speed of light, its acceleration gradually slows in such a way that it never stops accelerating, but it never reaches the speed of light either.
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Which of the following best describes the current scientific view of possibilities of travel to distant parts of our galaxy (or universe) with such things as hyperspace, wormholes, or warp drive?
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We do not know if travel in any of these ways is really possible, but they do not contradict any known laws of physics.