Question 1

Which of the following correctly describes what we mean by a great circle on the surface of Earth?

Accepted Answer

A great circle is defined as any circle whose center coincides with the center of the Earth. This means that the circle must divide the Earth into two equal halves, and the circumference of the circle must be the greatest possible for any circle that can be drawn on the surface of the Earth. Examples of great circles are the equator and the meridians that pass through the north and south poles. Any other circle on the surface of the Earth that does not pass through the center of the Earth is known as a small circle.

Question 2

What does the equivalence principle say?

Accepted Answer

The equivalence principle states that the effects of gravity are exactly equivalent to the effects of acceleration. This means that an observer in a spacecraft accelerating through space would feel the same effects as an observer on the surface of the earth, which is being accelerated by gravity.

Question 3

Suppose Einstein had never lived and did not publish the special theory of relativity in 1905.According to most historians of science,when would someone else have discovered the theory?

Accepted Answer

The development of the special theory of relativity was closely tied to the state of physics at the beginning of the 20th century, with several scientists working on problems that this theory addresses. Given the rapid progress in physics at the time and the work of contemporaries like Hendrik Lorentz and Henri Poincaré, it's likely that the theory would have been formulated by someone else within a short period if Einstein had not done so.

Question 4

According to general relativity,why does Earth orbit the Sun?

Accepted Answer

According to general relativity, massive objects like the Sun warp the fabric of spacetime, causing the shortest distance between two points to be curved. Since Earth is following the straightest possible path in curved spacetime, it orbits the Sun.

Question 5

How will you feel in your spacecraft?

Accepted Answer

The answer of How will you feel in your spacecraft?
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Question 6

What evidence supports the predicted existence of gravitational waves?

Accepted Answer

The observed decay in orbit of the neutron star system is a clear indication that energy is being carried away by gravitational waves, thus supporting their predicted existence. A, D and E are incorrect because they either suggest gravitational waves can be easily observed or that they create visible effects when this is not the case. B is not necessarily incorrect but does not provide concrete evidence for the existence of gravitational waves.

Question 7

Which of the following statements is not a prediction of the general theory of relativity?

Accepted Answer

The general theory of relativity predicts phenomena related to the curvature of spacetime, such as time dilation, gravitational lensing, and gravitational waves. However, it does not suggest that different observers can disagree about the fundamental structure of spacetime. Instead, it provides a consistent framework for understanding how spacetime is curved by mass and energy, which applies universally.

Question 8

Which of the following correctly describes the conditions under which you will feel weightless,according to general relativity?

Accepted Answer

According to general relativity, weightlessness is experienced when following the straightest possible path through spacetime. This is known as a geodesic, which is the path an object would follow in the absence of any external forces. Therefore, choice C is the correct answer.

Question 9

Suppose two lines appear to be parallel but eventually meet.What type of geometry are you dealing with?

Accepted Answer

In spherical geometry, two lines that appear parallel from the viewpoint of an observer on the surface of the sphere will eventually intersect. This is because on a curved surface like a sphere, there are no truly parallel lines.

Question 10

If you draw a spacetime diagram,the worldline of an object that is traveling by you at constant speed is

Accepted Answer

The worldline of an object traveling at constant velocity will be slanted in a spacetime diagram. This is because the slope of a worldline represents velocity, and if the object is traveling at a constant velocity, the slope must be constant throughout the object's journey. A vertical line would represent an object at rest, and a horizontal line would represent an object traveling at the speed of light, both of which are not relevant to an object traveling at constant velocity.

Question 11

If you draw a spacetime diagram,the worldline of an object that is stationary in your reference frame is

Accepted Answer

A worldline represents the path of an object in spacetime. If an object is stationary in a particular reference frame, it means that it remains at the same position in space at all points in time. Therefore, its worldline would be a straight line perpendicular to the time axis, i.e., a vertical line.

Question 12

Why do we see a gravitational redshift in the spectrum of the Sun?

Accepted Answer

Gravitational redshift occurs because of the general relativistic effect where time runs slower in stronger gravitational fields. On the Sun, the gravitational field is much stronger than on Earth, causing the emission lines in the solar spectrum to appear at lower frequencies (or longer wavelengths) than they would if observed in a weaker gravitational field. This effect is a direct consequence of the time dilation predicted by Einstein's theory of general relativity.

Question 13

According to general relativity,a black hole is

Accepted Answer

The answer of According to general relativity,a black hole is
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Question 14

Suppose you claim that you are feeling the effects of a gravitational field.How can you explain the fact that Al is weightless?

Accepted Answer

Al is weightless because she is in free-fall, which means that she is falling towards the Earth due to the gravitational force. During free-fall, the person and the object both experience the same acceleration, and hence, the person feels weightless. This does not depend on the velocity or the presence of a gravitational field.

Question 15

If you draw a spacetime diagram,the worldline of an object that is accelerating away from you is

Accepted Answer

The worldline of an accelerating object will curve on a spacetime diagram because its velocity is changing over time.

Question 16

What do we mean by dimension in the context of relativity?

Accepted Answer

In the context of relativity, dimension refers to the number of independent directions in which movement is possible. This means that in a 3-dimensional space, movement can occur in three separate and independent directions. In Einstein's theory of general relativity, space and time are merged into a single four-dimensional space-time, which means that movement can occur in four independent directions.

Question 17

Imagine that you are sitting in a closed room (no windows,no doors)when,magically,it is lifted from Earth and sent accelerating through space with an acceleration of 1g (9.8 m/s²).According to Einstein's equivalence principle,which of the following is true?

Accepted Answer

Einstein's equivalence principle states that the effects of gravity are indistinguishable from the effects of acceleration. Therefore, if the room accelerates at 1g, it would mimic the gravitational pull of Earth, making it impossible to discern that you've left Earth based solely on physical sensations or observations within the room.

Question 18

According to general relativity,how is time affected by gravity?

Accepted Answer

According to the theory of relativity, time runs slower in a stronger gravitational field. This phenomenon is known as time dilation. The stronger the gravitational field, the slower time appears to pass for an observer outside that field. In extreme cases, like near a black hole, time can appear to completely stop for an outside observer. This effect has been measured and observed by scientists.

Question 19

What do we mean by the straightest possible path between two points on Earth's surface?

Accepted Answer

The straightest possible path between two points on Earth's surface is the shortest path between the two points, which is also known as the great circle route. This route is the shortest distance between two points on the surface of a sphere, such as the Earth. It may not appear to be a straight line on a flat map, but it is the straightest possible path between two points when considering the curved surface of the Earth.

Question 20

Each of the following is a prediction of the theory of relativity.Which one is crucial to understanding how the Sun provides light and heat to Earth?

Accepted Answer

E = mc² (mass-energy equivalence) is crucial for understanding how the Sun provides light and heat to Earth, as it explains the process of nuclear fusion in the Sun's core, where mass is converted into energy.

Quiz 27: Spacetime and Gravity