Deck 18: Relativity and Black Holes

Question 1

You have a 1 kg mass at rest sitting on a lab bench in front of you. You see somebody fly by in a spaceship traveling at 0.2c. That astronaut flying by also has a 1 kg mass sitting on a bench in front of her. She would measure that mass to be 1kg.

Answer 1

True

Question 2

The singularity of a black hole has an infinitely small radius, but its event horizon is finite.

Answer 2

True

Question 3

We can't detect the gravitational redshift coming from the Sun because the Sun has a very small amount of gravity.

Answer 3

False

Question 4

What would happen if mass were continually added to a 2M _$\odot$ neutron star?

A) The star's radius would increase.
B) The star could eventually become a black hole.
C) The star could erupt as a nova.
D) The star could exceed the Chandrasekhar limit and become a Type II supernova.
E) The star could eventually return to the top of the main sequence.

Question 5

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 each frame is accelerating
D) the results of physics experiments performed in each frame
E) whether events are simultaneous or not

Question 6

Einstein's special theory of relativity implies that if a person standing at the front of a train traveling at 0.1 km/s shines a flashlight out in front of the train, the emitted photons will travel at a speed of 300,000.1 km/s.

Question 7

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 the Earth
C) a reference frame that is in motion 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

Question 8

Gravitational lensing allows us to see distant objects brightened and distorted because of massive objects in the path that the light from the object travels.

Question 9

One result of relativity is that an astronaut in a windowless spacecraft could tell the difference between falling freely and the presence of a nearby gravitational source.

Question 10

You observe a distant galaxy apparently moving away at 1/3 the speed of light (v =c/3). If you could measure the speed that this galaxy's light is passing the Earth, you would get:

A) c/3
B) 2c/3
C) c
D) 4c/3
E) 5c/3

Question 11

The aberration of starlight is:

A) a change in the wavelength of light caused by the motion of the light source
B) poor focusing of starlight caused by imperfections in the optics of a telescope
C) a change in the direction of starlight caused by its passage through the earth's atmosphere
D) an increase in the wavelength of light as it leaves the surface of a gravitating body
E) a change in the direction of starlight caused by the orbital motion of the Earth

Question 12

Special relativity says that moving clocks run slower.

Question 13

The Earth orbits the Sun because the Sun changes space around it but not time.

Question 14

A black hole can be produced if the stellar core left over after a supernova is larger than 3 M _$\odot$ .

Question 15

Gamma-ray bursts are probably associated with extremely energetic supernova explosions.

Question 16

Gravity is nothing more than a curvature in the fabric of spacetime.

Question 17

Special relativity says that all observers moving at constant speed will measure the same value of the speed of light.

Question 18

Black holes emit no light whatsoever.

Question 19

The mass of an atomic nucleus is a measure of how much energy is contained therein.

Question 20

The Sun could turn into a black hole at the end of its life.

Question 21

What does gravity mean in relativity?

A) It is a result of mass and energy being two forms of the same thing.
B) It is a consequence of distances getting shorter as objects move faster.
C) It is the result of the mass of falling bodies getting bigger because they are in motion.
D) It is the force that objects with mass exert on a body.
E) It is the result of the distortion in spacetime around an object with any energy density.

Question 22

According to relativity, spacecraft that can travel faster than the speed of light are:

A) impossible, because nothing can travel that fast
B) possible, but not useful since they could not contain living beings
C) impossible, since objects that travel that fast would get shorter and squeeze out space for the astronauts to live
D) possible, if we are clever enough with new technologies
E) impossible, because they would require new energy sources that are not yet invented

Question 23

What is the Lorentz factor for an object moving at 0.85c?

A) 1.00
B) 1.67
C) 1.80
D) 1.90
E) 2.05

Question 24

According to Einstein's 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

Question 25

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 one another
D) when objects have a low mass
E) when objects are moving slowly

Question 26

How fast must a muon be moving if it looks to an observer at rest that it lived for 2 * 10 ^{- 4} seconds before it decayed when, in fact, it lived for only 2 *10 ^{- 6} seconds in its moving reference frame?

A) 0.05c
B) 0.50c
C) 0.95c
D) 0.995c
E) 0.99995c

Question 27

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.

Question 28

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

A) if two events take place at the same time, all observers will see that event simultaneously
B) whether events are seen as simultaneous or not depends on the motion of an observer
C) observers will always disagree on when an event took place
D) it is not possible to know when an event happened
E) moving observers can always know whether they are in motion

Question 29

Why do astronauts in space feel no gravity?

A) There is no gravity out in space.
B) Gravity only happens when objects are accelerating.
C) In space, the gravity from the Moon and the Sun cancels out the Earth's gravity.
D) They and their spaceship are both freely falling at the same rate in the gravitational field.
E) The astronauts do not have any mass when they are out in space.

Question 30

Has relatively ever been tested?

A) No, because it would require us to set up physics experiments in faraway galaxies.
B) Yes, because even ordinary motion in automobiles and airplanes produces easily noticeable effects predicted by relativity.
C) No, because no one has been able to think of experiments that are able to measure the small differences between the predictions of Newtonian physics and relativity.
D) Yes, because (for example) subatomic particles can be accelerated to speeds approaching that of light.
E) No, because the theory of relativity contains paradoxes and contradictions, like the twin paradox.

Question 31

The twin paradox shows that special relativity:

A) explains many things but can't explain everything
B) is accurate but contains some worrisome contradictions
C) is incorrect
D) only explains things in steady motion, but cannot be used to explain objects that accelerate
E) correctly accounts for the results of experiments in different reference frames

Question 32

You measure that an object has a mass of exactly 1 kg by weighing it in the Earth's gravitational field. The equivalence principle says that the mass you would measure by trying to accelerate it would be:

A) 1 kg
B) greater than 1 kg
C) less than 1 kg
D) different from 1kg, depending on what it's made of
E) larger than 1 kg because of the Sun's gravity

Question 33

__________ is the result of mass distorting the fabric of spacetime.

A) Energy
B) Radiation
C) Fusion
D) Gravity
E) Electric charge

Question 34

What is true about muons?

A) They are always moving at high speed, so they test relativity.
B) Relativity explains why we can see short-lived muons that are produced high in the atmosphere from cosmic rays.
C) We can see them being deflected from straight lines by the gravity of black holes.
D) They have a mass that does not increase if they are moving fast.
E) They are examples of Hawking radiation from black holes.

Question 35

Suppose you detect a pulsar that gives us 1,000 radio pulses per second, but the pulsar is in a distant galaxy that is apparently moving away from us at 50 percent of the speed of light. An observer at rest with respect to the pulsar in that faraway galaxy would measure a pulse rate of:

A) 870 per second
B) 1,150 per second
C) 1,250 per second
D) 1,366 per second
E) 1,450 per second

Question 36

The equivalence principle says that:

A) the universe is homogeneous and isotropic
B) being stationary in a gravitational field is the same as being in an accelerated reference frame
C) at any radius inside a star the outward gas pressure must balance the weight of the material on top
D) mass and energy are interchangeable and neither can be destroyed
E) gravity does not exist in space

Question 37

How does relativity compare to Newtonian physics?

A) Relativity gives the same result as Newtonian physics when objects are moving slowly.
B) Relativity gives results that contradict many predictions of Newtonian physics, so we know the latter is incorrect.
C) Relativity must be better because it is a newer theory than Newtonian physics.
D) Newtonian physics and relativity make the same predictions, but it's easier to compute results using relativity.
E) Newtonian physics makes predictions that are at odds with certain observations, whereas relativity is consistent with those observations.

Question 38

If you were to design a spacecraft that could travel to the galactic center fast enough that the astronauts aboard only aged by 25 years during the trip, how fast would the spacecraft have to go? The galactic center is 25,000 light years away.

A) 0.95c
B) 0.995c
C) 0.99995c
D) 0.9999995c
E) 0.999999995c

Question 39

Photons have no mass, and Einstein's theory of general relativity says:

A) their paths through spacetime are curved in the presence of a massive body
B) their apparent speeds depend on the observer's frame of reference
C) they should not be attracted to a massive object
D) their wavelengths must remain the same as they travel through spacetime
E) their wavelengths would grow longer as they travel through empty space

Question 40

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) Distances 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.

Question 41

The event horizon of a black hole is defined as:

A) the point of maximum gravity
B) the radius of the original neutron star before it became a black hole
C) the radius from which shock waves course through spacetime due to the strong gravitational distortion of the black hole
D) the radius at which the escape speed from the black hole equals the speed of light
E) the radius at which the gravitational force is the same as that on the surface of the Sun

Question 42

Gravitational lensing occurs when __________ distorts the fabric of spacetime.

A) a star
B) dark matter
C) a black hole
D) any massive object
E) a white dwarf

Question 43

While traveling the galaxy in a spacecraft, you and a colleague set out to investigate the 10⁶M _$\odot$ black hole at the center of our galaxy. She hops aboard an escape pod and drops into a circular orbit around the black hole, maintaining a distance of 4 *10⁶ km, while you remain much farther away in the spacecraft. After doing some experiments to measure the strength of gravity, your colleague signals her results back to you using a green laser. What would you see? Hint: you will need to calculate the location of the event horizon.

A) You would see her signals unaltered in wavelength because she is orbiting well outside the event horizon of the black hole.
B) You would see her signals shifted to a much redder wavelength because she is close to the event horizon.
C) You would see nothing because your colleague has crossed the event horizon around the black hole.
D) You would see nothing because no light can escape the gravitational pull of a black hole no matter how far she is from it.
E) You would see her signals shifted to a much bluer wavelength because black holes can make highly energetic light.

Question 44

Two observers are on different floors of a building, as shown in the figure below. The observer on the bottom floor shines a light upward, which is reflected from a mirror in an upper floor and sent back downward. Consider the gravitational redshift of the light due to the Earth. If the light has a wavelength of exactly 600 nm when emitted, the observer on the upper floor will measure a wavelength of __________ while the observer on the lower floor will see the light returning with a wavelength of __________.

A) "600 nm, 600 nm"
B) " $\gt$ 600 nm, 600 nm"
C) " $\lt$ 600 nm, $\lt$ 600 nm"
D) "600 nm, $\gt$ 600 nm"
E) " $\gt$ 600 nm, $\gt$ 600 nm"

Question 45

The Schwarzschild radius of a 10M _$\odot$ is __________ the size of the Schwarzschild radius of a 5 M _$\odot$ black hole.

A) 1/5
B) 1/2
C) equal to
D) 2 times
E) 5 times

Question 46

The gravitational redshift of light should be smallest for light emitted from the surface of:

A) a black hole
B) the Sun
C) a white dwarf
D) a planet like the Earth
E) a neutron star

Question 47

As shown in this figure, an observer in a windowless room notices that light from a flashlight does not follow a straight path, but instead seems to be bent downwards as it crosses the room. What does the observer conclude is happening?

A) The room is experiencing an acceleration from gravity.
B) The room is accelerating upward.
C) Both A and B at the same time.
D) Either A or B; it is impossible to tell the difference.
E) Either A or B, depending on whether massive objects in the room fall downward or float upward when released.

Question 48

General relativity predicts that pairs of objects with nonzero masses undergoing accelerations can produce:

A) pulses of electromagnetic radiation
B) gravitational waves
C) high-energy particles
D) a slowing of clocks here on the Earth
E) redshifted light from the surface of the object

Question 49

Light is increasingly redshifted near a black hole because:

A) the photons are moving away from us very quickly as they are sucked into the black hole
B) the photons are moving increasingly faster in order to escape the pull of the black hole
C) the photons lose energy because climbing out of the black hole's gravity makes them tired
D) the curvature of spacetime is increasingly stretched near the black hole, which in turn stretches the wavelengths of the photons
E) time is moving increasingly slower as viewed from the observer's frame of reference

Question 50

If the Sun suddenly turned into a black hole, what would be the radius of its event horizon?

A) 3 m
B) 30 m
C) 300 m
D) 3 km
E) 30 km

Question 51

Name one verified prediction of general relativity.

A) Spacetime is flat except inside the Schwarzschild radius of the Sun.
B) Relativity predicts Mercury has an orbital precession, but Newtonian physics does not.
C) Starlight passing near the Sun should be bent away from the Sun by its gravity.
D) Gravitational lensing should make Mercury brighter than it would otherwise be.
E) Mercury's orbital precession is a little bigger than predicted by Newtonian physics.

Question 52

Compared to a clock on the surface of the Earth, a clock on the International Space Station runs:

A) at approximately the same rate, but slightly slower.
B) significantly slower
C) significantly faster
D) sometimes faster, sometimes slower
E) at an equal rate, except during eclipses

Question 53

While traveling the galaxy in a spacecraft, you and a colleague set out to investigate the 10⁶M _$\odot$ black hole at the center of our galaxy. He hops aboard an escape pod and drops into a circular orbit around the black hole, maintaining a distance of 10,000 km, while you remain much farther away in the spacecraft. After doing some experiments to measure the strength of gravity, your colleague signals his results back to you using a green laser. What would you see? Hint: you will need to calculate the location of the event horizon.

A) You would see his signals unaltered in wavelength because he is orbiting well outside the event horizon of the black hole.
B) You would see his signals shifted to a much redder wavelength because he is close to the event horizon.
C) You would see nothing, because your colleague has crossed the event horizon around the black hole.
D) You would see nothing, because no light can escape the gravitational pull of a black hole no matter how far he is from it.
E) You would see his signals shifted to a much bluer wavelength because black holes can make highly energetic light.

Question 54

What is the meaning of the Schwarzschild radius around a black hole?

A) It is the radius at which an orbiting object would show a precession.
B) It is the radius at which gravitational redshift can be detected.
C) It is the radius at which the black hole's spin equals the speed of light.
D) It is the radius at which the escape velocity equals the speed of light.
E) It is the radius at which a body falling onto the black hole would move at half the speed of light.

Question 55

The bending of light passing near a massive object is called:

A) time dilation
B) the twin paradox
C) gravitational lensing
D) length contraction
E) mass increase

Question 56

A geodesic is the name for:

A) the aberration of starlight
B) the gravitational field of the Earth
C) the solid crust of a terrestrial planet
D) the path followed by a freely-falling object in spacetime
E) the shape of a body that has mass

Question 57

In the rubber-sheet analogy for spacetime, what would you expect for objects (such as golf balls) rolling around in the presence of a massive object that is stretching the rubber sheet?

A) Their paths would be straight if they were moving slowly enough.
B) Their paths would curve more the closer they come to the massive object.
C) Their paths would curve by the same amount no matter how close they come to the mass.
D) Their paths would curve towards the mass if they passed close, but bend away from the mass if they passed far from the mass.
E) Their paths would curve less the closer they come to the massive object.

Question 58

The principle of equivalence states that the gravitational mass is equal to:

A) the mass when moving nearly the speed of light
B) the resistance to acceleration
C) the mass when near a black hole
D) the object's weight
E) the density divided by the volume

Question 59

While traveling the galaxy in a spacecraft, you and a colleague set out to investigate the 10⁶M _$\odot$ black hole at the center of our galaxy. She hops aboard an escape pod and drops into a circular orbit around the black hole, maintaining a distance of 1 AU, while you remain much farther away in the spacecraft. After doing some experiments to measure the strength of gravity, your colleague signals her results back to you using a green laser. What would you see? Hint: you will need to calculate the location of the event horizon.

A) Her signals are shifted only slightly toward the red because she is orbiting well outside the event horizon of the black hole.
B) You would see her signals shifted to a much redder wavelength because she is close to the event horizon.
C) You would see nothing, because your colleague has crossed the event horizon around the black hole.
D) You would see nothing, because no light can escape the gravitational pull of a black hole no matter how far she is from it.
E) You would see her signals shifted to a much bluer wavelength because black holes can make highly energetic light.

Question 60

If the Earth were to shrink in size until it became a black hole, its Schwarzschild radius would be:

A) 1 cm
B) 1 m
C) 1 km
D) 10 km
E) 200 km

Question 61

Gamma-ray bursts are likely to be:

A) the signs of accretion onto black holes
B) the product of merging neutron stars
C) produced by the most energetic supernova explosions
D) the result of neutron stars accreting mass and turning into black holes
E) produced by intelligent life in the universe exploding nuclear bombs

Question 62

Muons are elementary particles that decay into other particles in about 2 microseconds. They are formed in the upper atmosphere of the Earth from high energy cosmic rays, and can be detected on the ground even though they could only travel a few hundred meters before decaying according to Newtonian physics. How does relativity explain how we can detect them on the ground? Explain both in our reference frame and in the frame of the muon.

Question 63

What is the central idea in relativity concerning the speed of light? Describe at least two unusual consequences of this idea.

Question 64

Suppose we discovered radio signals coming from the star Alpha Centauri, whose distance is 4.4 light-years from us, and we sent a crew in a spacecraft to visit it. If the spacecraft used revolutionary technology allowing it to travel at a speed of 0.5 c, how long would it take the spacecraft to get to Alpha Centauri, and how long a time would the astronauts say passed during the trip? (Ignore the time it would take to accelerate the spacecraft to reach a velocity of 0.5
c.)

Question 65

Explain how Newtonian physics is an approximation to relativity.

Question 66

Black holes that are stellar remnants can be found by searching for:

A) dark regions at the centers of galaxies
B) variable X-ray sources
C) extremely luminous infrared objects
D) objects that emit very faint radio emission
E) regular, repeated pulsations at radio wavelengths

Question 67

Hawking radiation is emitted by a black hole when:

A) the black hole rotates quickly
B) the black hole accretes material
C) a supernova explodes and forms a black hole out of its core
D) synchrotron radiation is emitted by infalling charged particles
E) a virtual pair of particles is created from the vacuum of space

Question 68

A red giant star is found to be orbiting an unseen object with a short orbital period. By measuring the speed at which it orbits, astronomers deduce that the object has a mass of 10M _$\odot$ This object is probably a __________ because __________.

A) black hole; the giant star is massive and could only be in orbit about something even more massive
B) black hole; its mass is too large to be a neutron star or a white dwarf
C) neutron star; any supernova that would have made a black hole would have destroyed the red giant
D) M-dwarf star; only such stars would be faint enough to go unseen in this system
E) black hole; most red giants orbit neutron stars, and neutron stars can turn into black holes

Question 69

Describe two possible ways to make a black hole.

Question 70

Explain why no object that has mass can ever move at a speed equal to the speed of light. At what velocity do massless particles (e.g., photons) travel in vacuum?

Question 71

Hawking radiation from black holes refers to:

A) light emitted from matter falling onto a black hole
B) the gravitational redshift of light emitted near the event horizon
C) the radiation of particles created near the event horizon
D) high-energy X-rays and gamma rays from the formation of a black hole
E) the optical and infrared light from an energetic supernova explosion

Question 72

Most black holes are found:

A) by the watching the orbits of nearby stars
B) from the bending of the light from background stars
C) by finding objects that emit no light
D) by the X-rays produced by a surrounding accretion disk
E) by the detection of Hawking radiation

Question 73

If you observed that at the centers of some galaxies there were objects emitting lots of X-rays or there was gas in rapid motion, you might conclude that these galaxies:

A) are very old
B) contain many white dwarfs
C) have different physics than on the Earth
D) are rotating quickly
E) contain black holes

Question 74

A person would feel __________ as he approached the event horizon of a black hole.

A) extremely strong tidal forces
B) intense heating
C) strong Hawking radiation
D) strong infrared radiation
E) nothing

Question 75

Explain what four-dimensional spacetime means.

Question 76

Even if a black hole emitted no light, we can still detect it:

A) from sound waves produced by material falling onto the black hole
B) by tides produced on the Earth's oceans
C) through its Hawking radiation
D) through its gravitational effect on surrounding gas or stars
E) by looking for dark patches on the sky where the black hole swallows background light

Question 77

What is the equivalence principle? Describe a consequence of the equivalence principle for astronauts orbiting in the space station.

Question 78

How would the Newtonian theory explain the orbit of the Earth around the Sun? What would the explanation be in general relativity?

Question 79

If the Sun were to be instantly replaced by a 1M _$\odot$ black hole, the gravitational pull of the black hole on Earth would be:

A) much greater than it is now
B) the same as it is now
C) much smaller than it is now
D) larger or smaller, depending on the location of the Moon
E) irrelevant because Earth would be quickly fall into the Sun and be destroyed

Question 80

What is the meaning of the equation E = mc²?