The Eötvös Experiment. Galileo’s result that all objects fall to Earth with the same acceleration (neglecting air resistance) is very important to general relativity—if it were not true, general relativity would be in serious trouble. Describe the experiments of Baron Roland von Eötvös, who tested Galileo’s conclusions in the late 19th century. How did the results of these experiments influence Einstein as he worked on general relativity? Write a one- to two-page summary.

Suppose the Sun were magically replaced by a black hole of precisely the same mass.
a. How would the curvature of spacetime change in the region where the Sun used to be located?
b. How would the curvature of spacetime change in the region of Earth’s orbit?
c. What effect would the change have on Earth’s orbit?

Many people have seen rubber sheet diagrams that show black holes looking like funnels, and therefore they assume that black holes really are funnel shaped. Imagine that you are talking to a person who believes this misconception to be true. Write a one- or two-paragraph explanation in words the person would understand that explains how the misconception arises and what a black hole would really look like if we could see one.

Find an everyday object that obeys the rules of each of the three basic types of geometry—flat, spherical, and saddle shaped. Describe the object and explain how you know which geometry it has.

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?

Suppose two people start out traveling due north from the same latitude, one near Denver and one near San Francisco. Are their paths parallel when they start? Will their paths stay parallel, or will they meet? If they will meet, where will they meet? Summarize your answers with a one- or two-paragraph description of the people’s journey, and explain what the results tell us about the geometry of Earth.

Roles: Scribe (takes notes on the group’s discussions), Proposer (proposes key points on each side of the debate), Skeptic (points out weaknesses in proposed arguments), Moderator (leads group discussion and makes sure the group works as a team).
Activity: Discuss the quote from Einstein at the very end of the chapter, and debate whether the distinction among past, present, and future is real or an illusion.

General relativity has been extensively tested in many different ways and has passed every test with flying colors. Yet scientists continue to test it with sensitive measurements and attempts to detect gravitational waves. Why do scientists keep testing a theory that works so well? What would happen if it failed some future test? Explain.

Hallmarks of Science. Chapter 3 discusses both the idealized scientific method and a set of hallmarks by which you can distinguish science from nonscience. Did Einstein follow the idealized scientific method in his work on general relativity? Does general relativity satisfy the hallmarks of science? Explain.

Choose the best answer for following question. Explain your reasoning with one or more complete sentence.
If wormholes are real, which of the following best describes what one is?
(a) a place where it is possible to travel faster than light
(b) a shortcut between distant parts of the universe
(c) a black hole with a wormlike shape

Choose the best answer for following question. Explain your reasoning with one or more complete sentence.
Why do we think that gravitational waves really exist?
(a) We have observed them with telescopes in space.
(b) We have observed orbiting objects that are losing precisely the amount of energy we expect them to be losing to gravitational waves.
(c) They are predicted to exist by the general theory of relativity.

Choose the best answer for following question. Explain your reasoning with one or more complete sentence.
Gravitational lensing occurs because
(a) gravity causes light to slow down.
(b) gravity curves space and light always follows the straightest possible path through space.
(c) the effects of gravity are indistinguishable from the effects of glass lenses.

Choose the best answer for following question. Explain your reasoning with one or more complete sentence.
On the surface of which of the following objects would time run most slowly?
(a) the Sun
(b) an object with the same mass as the Sun but twice the radius
(c) an object with the same mass as the Sun but only half the radius

Choose the best answer for following question. Explain your reasoning with one or more complete sentence.
According to general relativity, Earth goes around the Sun rather than flying straight off into space because
(a) gravity creates an invisible bond holding Earth and the Sun together.
(b) Earth is going as straight as possible, but the shape of spacetime makes this path go round and round.
(c) in its own reference frame, Earth can consider itself to be stationary