Question 1

Which of the following correctly describes what we mean by a great circle on the surface of Earth?
A)any circle on the surface whose center is at the center of Earth
B)any circle of latitude
C)any circle on the surface that intersects the equator
D)any circle larger than 10,000 km in diameter
E)any circle found on an English farm that happens to have been created by aliens

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?
A)Gravity is the same thing as curvature of spacetime.
B)The effects of gravity are exactly equivalent to the effects of acceleration.
C)You cannot distinguish between motion at constant velocity and weight in a gravitational field.
D)The effects of relativity are exactly equivalent to those predicted by Newton's laws of motion.
E)All observers must always measure the same (equivalent)weights for moving objects.

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?
A)within a year
B)in about 10 to 20 years
C)in about 50 years
D)We still wouldn't know about it today.
E)If Einstein hadn't lived,space and time would be very different,and the theory would have been discovered by the ancient Greeks.

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?
A)Earth is following the straightest path possible,but spacetime is curved in such a way that this path goes around the Sun.
B)The mysterious force that we call gravity holds Earth in orbit.
C)Earth and the Sun are connected by a "ropelike" set of invisible,subatomic particles.

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?
A)You will be floating weightlessly.
B)You will feel weight,but less than on Earth.
C)You will feel weight,but more than on Earth.
D)You will feel the same weight as you do on Earth.
E)You will feel yourself pressed against the back of your spaceship with great force,making it difficult to move.

Accepted Answer

The answer of How will you feel in your spacecraft?
A)You...

Question 6

What evidence supports the predicted existence of gravitational waves?
A)Gravitational waves are frequently and easily detected by large telescopes.
B)Gravitational waves have been detected by observing their effect on large masses suspended on Earth.
C)The orbit of a star system consisting of two neutron stars is slowly decaying,suggesting that energy is being carried away by gravitational waves.
D)The energy generated by gravitational waves from the Sun can be seen as it is absorbed by Jupiter.
E)Photographs of spacetime show the gravitational waves as ripples that are clearly visible.

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?
A)Time runs slightly slower on the surface of the Sun than on the surface of Earth.
B)The Universe has no boundaries and no center.
C)The curvature of spacetime can distort the appearance of distant objects.
D)Different observers can disagree about the fundamental structure of spacetime.
E)A binary star system with two stars orbiting each other rapidly emits gravitational waves.

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?
A)any time you are traveling through space at constant speed
B)any time your worldline is perfectly straight
C)any time your worldline is following the straightest possible path through spacetime
D)any time you are very far from any planet
E)You can never be truly weightless.

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?
A)flat geometry
B)spherical geometry
C)saddle-shaped geometry
D)Euclidean geometry
E)This situation can never occur.

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
A)vertical.
B)horizontal.
C)slanted.
D)curved.
E)a circle.

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
A)vertical.
B)horizontal.
C)slanted.
D)curved.
E)a circle.

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?
A)Gravity makes light heavy,causing it to appear redder.
B)Because of gravity,the Sun is always moving away from us,so we see a redshift.
C)Time runs slower on the Sun than on Earth,making lines in the solar spectrum have lower frequency and hence longer wavelength than normal.
D)Spacetime curvature allows red photons of light to escape the Sun more easily than blue photons,leading to an apparent redshift.

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
A)an object that cannot be seen.
B)a hole in the observable universe.
C)a place where light travels slower than the normal speed of light.
D)a place where light travels faster than the normal speed of light.
E)a place where there is no gravity.

Accepted Answer

The answer of According to general relativity,a black hole is
A)an...

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?
A)She is weightless because she is moving at constant velocity.
B)She is weightless because she is in a free-float frame.
C)She is weightless because she is in free-fall.
D)If you are in a gravitational field,then she cannot be 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
A)vertical.
B)horizontal.
C)slanted.
D)curved.
E)a circle.

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?
A)the size of an object
B)the number of independent directions in which movement is possible
C)the letter used to represent length mathematically
D)the number of sides that we can see when we look at an object
E)the height of an object

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?
A)You won't feel any change and will have no way to know that you've left Earth.
B)You'll feel a force that will cause your head to repeatedly bang into the ceiling.
C)You'll know that you left Earth because when you drop a ball it will fall sideways.
D)You'll know that you left Earth because you'll be floating weightlessly in your room.

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?
A)Time is not affected by gravity.
B)Time is affected by gravity,but not in a predictable way.
C)Time is stopped by any gravitational field.
D)Time runs faster in stronger gravitational fields.
E)Time runs slower in stronger gravitational fields.

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?
A)a path that actually is a perfectly straight line
B)a path that follows a circle of latitude
C)a path that follows a circle of longitude
D)a path that crosses the equator
E)the shortest path between the two points

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?
A)If you observe someone moving by you,you'll see their time running slowly.
B)Gravity is curvature of spacetime.
C)E = mc²
D)Time runs slower on the surface of the Sun than on Earth.
E)Space is different for different observers.Time is different for different observers.Spacetime is the same for everyone.

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

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

What does the equivalence principle say?

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?

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

How will you feel in your spacecraft?

What evidence supports the predicted existence of gravitational waves?

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

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

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

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

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

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

According to general relativity,a black hole is

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

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

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

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?

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

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

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?