Question 1

An astronaut traveling at very high speeds to Proxima Centauri, which is 4.3 light-years from Earth, would arrive in fewer than 4.3 years, from his or her perspective.This is because
A) he or she can travel faster than the speed of light.
B) a light-year is longer than the distance light travels in 1 year.
C) radioactive particles (muons) will interfere with the astronaut's clock.
D) Proxima Centauri appears to be farther than it is due to the travel time of light.
E) the astronaut will measure a shorter distance than 4.3 light-years.

Accepted Answer

Due to the effects of special relativity, specifically length contraction, the astronaut will measure a shorter distance to Proxima Centauri than 4.3 light-years, allowing them to arrive in fewer than 4.3 years from their perspective.

Question 2

What is the meaning of the word spacetime?
A) It is a mental framework for keeping track of numbers in Newtonian physics.
B) Space and time form a two-dimensional region where physics takes place.
C) The term has no special meaning; it's just a fancy way to sound important when talking about physics.
D) It is the combined treatment of space and time in the theory of relativity.
E) It is the idea that observers will always measure the same locations and times of events.

Accepted Answer

Spacetime is the concept in the theory of relativity that combines space and time into a single interwoven continuum.

Question 3

Which of the following is a consequence of Einstein's special theory of relativity?
A) Moving clocks run quicker.
B) The velocity of light depends on the speed of the observer.
C) Stationary lengths are shorter for objects traveling close to the speed of light.
D) Gravity arises because mass distorts spacetime.
E) Faster-moving objects require less force to accelerate them.

Accepted Answer

According to Einstein's special theory of relativity, lengths contract in the direction of motion for objects traveling close to the speed of light, a phenomenon known as length contraction.

Question 4

Compared with a clock on the surface of Earth, a clock on the fast-moving International Space Station runs
A) at approximately the same rate, but slightly slower.
B) significantly slower.
C) significantly faster.
D) sometimes faster and sometimes slower.
E) at an equal rate, except during eclipses.

Accepted Answer

Due to the effects of special relativity, a clock on the International Space Station runs slightly slower compared to a clock on Earth because of its high speed relative to the Earth's surface.

Question 5

In an accelerator, a massive particle may gain a relativistic speed for which its total energy is 1,000 times greater than its rest energy.This implies a Lorentz factor of

A)0.999.	
B)10.	
C)1.
D)1,000.

Accepted Answer

The Lorentz factor (γ) is defined as the ratio of the total energy to the rest energy of a particle. If the total energy is 1,000 times the rest energy, then the Lorentz factor is 1,000.

Question 6

What is the meaning of the phrase inertial frame of reference?
A) a reference frame that is not accelerating
B) a reference frame that is stationary with respect to Earth
C) a reference frame that is rotating at constant speed
D) a reference frame that is accelerating at a constant rate
E) a reference frame in which there are strong gravitational forces

Accepted Answer

An inertial frame of reference is one that is not accelerating, meaning it is either at rest or moving at a constant velocity.

Question 7

In an accelerator, a massive particle may gain a relativistic speed for which its total energy is 1,000 times greater than its rest energy.This implies a Lorentz factor of

A)0.999.	
B)10.	
C)1.
D)1,000.

Accepted Answer

The Lorentz factor (γ) is the ratio of the total energy to the rest energy. If the total energy is 1,000 times the rest energy, then the Lorentz factor is 1,000.

Question 8

Stellar aberration should be distinguished from stellar parallax in that
A) stellar aberration immediately allows for measurements of distances to stars.
B) stellar parallax is easily observable, whereas aberration is impossible to measure.
C) stellar aberration depends on Earth's orbital speed around the Sun.
D) stellar parallax depends on Earth's orbital speed around the Sun.
E) stellar aberration demonstrates that the speed of light is infinite.

Accepted Answer

Stellar aberration is caused by the motion of Earth around the Sun, affecting the apparent position of stars due to the finite speed of light.

Question 9

At what (relativistic) speed does the length of a spacecraft become half of its rest length?
A) 0.40c
B) 0.27c
C) 0.99c
D) 0.87c
E) 0.10c

Accepted Answer

The length contraction formula is L = L0 * sqrt(1 - v^2/c^2). To make L = 0.5 * L0, solve for v: 0.5 = sqrt(1 - v^2/c^2). Solving gives v ≈ 0.87c.

Question 10

You are driving on an interstate at 70 mph and, in the adjacent lane but moving in the opposite direction, another car is zipping by.From your point of view, the other car seems to pass at 150 mph, which would seem crazy.What is the speed that the odometer should indicate inside the other car?
A) 80 mph
B) 55 mph
C) 220 mph
D) 110 mph
E) 150 mph

Accepted Answer

The relative speed between the two cars is 150 mph. Since you are moving at 70 mph, the other car must be moving at 80 mph (150 - 70 = 80).

Question 11

According to Einstein's special theory of relativity, which two quantities are different manifestations of the same thing?
A) mass and gravity
B) light and energy
C) energy and mass
D) temperature and energy
E) distance and time

Accepted Answer

Einstein's special theory of relativity introduced the concept that energy and mass are interchangeable, as expressed in the famous equation E=mc², indicating they are different manifestations of the same physical reality.

Question 12

For a fast (hypothetical) interstellar ship moving at v = 0.95c relative to stars, a distance of 10 ly between neighboring stars would measure
A) 32 ly.
B) 10.5 ly.
C) 3.1 ly.
D) 9.5 ly.
E) 10 ly.

Accepted Answer

Due to length contraction in special relativity, the distance between stars as measured by the ship moving at 0.95c would be shorter than the rest frame distance. The contracted length is calculated using the Lorentz factor, resulting in approximately 3.1 ly.

Question 13

You are driving on an interstate at 70 mph and, in the adjacent lane and moving in the same direction, another car is passing you.From your point of view, the other car seems to advance at 10 mph (i.e., it is only slowly moving ahead of you).What is the speed that the odometer should indicate inside the other car?
A) 70 mph
B) 10 mph
C) 80 mph
D) 60 mph
E) 75 mph

Accepted Answer

The other car is moving 10 mph faster than you, so if you are driving at 70 mph, the other car must be traveling at 80 mph.

Question 14

What will observers in different inertial frames of reference always agree on?
A) how the speed of light varies with the motion of an observer
B) the length of the meter, but not the duration of the second
C) the rate at which each frame is accelerating
D) the laws of physics
E) whether events are simultaneous or not

Accepted Answer

Observers in different inertial frames of reference will always agree on the laws of physics, as stated by the principle of relativity.

Question 15

In the figure below, an observer in the spaceship on the right would observe the light emitted by the spaceship on the left as traveling at ________ and with ________ frequency than which it was emitted. 
A) c; a lower
B) c; a higher
C) 1.5c; the same
D) 1.5c; a lower
E) 1.5c; a higher

Accepted Answer

The answer of In the figure below, an observer in...

Question 16

Suppose that an object is moving and it is emitting light toward you, in vacuum.What would you notice about the light you observe?
A) The wavelength appears longer.
B) The frequency appears lower.
C) The energy appears lower.
D) The speed appears constant.
E) The speed appears to increase.

Accepted Answer

The speed of light in a vacuum is constant and does not change regardless of the motion of the source or observer.

Question 17

One consequence of Einstein's ideas about the speed of light is that
A) if two events take place at the same time for one observer, they will occur simultaneously for all observers.
B) whether events are seen as simultaneous or not depends on the motions of observers.
C) two events cannot happen at the same time for two different observers.
D) it is not possible to know when an event happens.
E) people could design and fly interstellar spaceships moving as fast as light itself.

Accepted Answer

Einstein's theory of relativity suggests that simultaneity is relative and depends on the observer's frame of reference, meaning that two events may be simultaneous for one observer but not for another, depending on their relative motion.

Question 18

Of all four muons produced at 15 km aboveground and schematically shown in the figure below, which one would "see" the distance to the ground as a mere 200 m? 
A) the muon moving at 0.9c
B) the muon moving at 0.99c
C) the muon moving at 0.999c
D) the muon moving at 0.9999c
E) The muons would not experience any relativistic effect because they are too tiny.

Accepted Answer

The answer of Of all four muons produced at 15...

Question 19

Earth's motion results in the apparent phenomenon of
A) aberration of starlight.
B) gravitational waves.
C) special relativity.
D) Newton's law of gravitation.
E) gravitational lensing.

Accepted Answer

The aberration of starlight is an apparent shift in the position of stars due to Earth's motion around the Sun.

Question 20

When do the predictions of special relativity match those of Newtonian physics?
A) in terrestrial laboratories
B) inside our Solar System
C) when different observers are at rest with each other
D) when objects have a low mass
E) when objects are moving slowly

Accepted Answer

The predictions of special relativity match those of Newtonian physics when objects are moving slowly compared to the speed of light, as relativistic effects become negligible at low velocities.

Quiz 18: Relativity and Black Holes

An astronaut traveling at very high speeds to Proxima Centauri, which is 4.3 light-years from Earth, would arrive in fewer than 4.3 years, from his or her perspective.This is because

What is the meaning of the word spacetime?

Which of the following is a consequence of Einstein's special theory of relativity?

Compared with a clock on the surface of Earth, a clock on the fast-moving International Space Station runs

In an accelerator, a massive particle may gain a relativistic speed for which its total energy is 1,000 times greater than its rest energy.This implies a Lorentz factor of

What is the meaning of the phrase inertial frame of reference?

In an accelerator, a massive particle may gain a relativistic speed for which its total energy is 1,000 times greater than its rest energy.This implies a Lorentz factor of

Stellar aberration should be distinguished from stellar parallax in that

At what (relativistic) speed does the length of a spacecraft become half of its rest length?

You are driving on an interstate at 70 mph and, in the adjacent lane but moving in the opposite direction, another car is zipping by.From your point of view, the other car seems to pass at 150 mph, which would seem crazy.What is the speed that the odometer should indicate inside the other car?

According to Einstein's special theory of relativity, which two quantities are different manifestations of the same thing?

For a fast (hypothetical) interstellar ship moving at v = 0.95c relative to stars, a distance of 10 ly between neighboring stars would measure

What will observers in different inertial frames of reference always agree on?

In the figure below, an observer in the spaceship on the right would observe the light emitted by the spaceship on the left as traveling at and with frequency than which it was emitted.

Suppose that an object is moving and it is emitting light toward you, in vacuum.What would you notice about the light you observe?

One consequence of Einstein's ideas about the speed of light is that

Of all four muons produced at 15 km aboveground and schematically shown in the figure below, which one would "see" the distance to the ground as a mere 200 m?

Earth's motion results in the apparent phenomenon of

When do the predictions of special relativity match those of Newtonian physics?