Deck 18: Relativity and Black Holes

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.

Answer 1

the astronaut will measure a shorter distance than 4.3 light-years.

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.

Answer 2

It is the combined treatment of space and time in the theory of relativity.

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.

Answer 3

Stationary lengths are shorter for objects traveling close to the speed of light.

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.

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.

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

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.

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.

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

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

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

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.

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

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

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

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.

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.

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.

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.

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

Question 21

You measure that an object has a mass of exactly 1 kg.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 the object is made of.
E) larger than 1 kg, because of the Sun's gravity.

Question 22

According to special relativity, spacecraft that would travel faster than the speed of light are

A) impossible, because nothing can travel that fast.
B) possible, but not useful because they could not contain living beings.
C) impossible, because objects that travel that fast would get shorter and squeeze out space in which the astronauts could 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

Suppose you were to travel to the brightest star in Earth's sky, Sirius, 8.6 light-years away, in a spaceship that traveled very close to the speed of light, so that the trip there took only a week for you.During the trip, though, your friends back on Earth would say that around ________ had passed.

A) 1 week
B) 8.6 weeks
C) 17.2 weeks
D) 4.3 years
E) 8.6 years

Question 24

Assume that a group of explorers traveled to the Orion Nebula, which is the nearest star-forming cloud and is at a distance of 1,300 light-years, using revolutionary technology that allowed them to travel at a speed of 0.99c.Observers back on Earth using Earth-bound clocks would say it took the explorers ________ to get there, but the explorers with their moving clocks would say it took them only ________ to get there.

A) 1,310 years; 185 years
B) 1,440 years; 630 years
C) 1,310 years; 390 years
D) 1,440 years; 425 years
E) 1,310 years; 1,300 years

Question 25

To travel at a tenth the speed of light (0.1c), a spacecraft carrying humans would require

A) little effort.
B) technology that does not yet exist.
C) human physiology to evolve further, first.
D) an enormous amount of energy.
E) a way to protect the humans from being crushed by length contraction.

Question 26

If the Lorentz factor is 2, what is the corresponding speed?

A) 0.86c
B) 1.55c
C) 0.27c
D) 0.52c
E) 0.9999c

Question 27

At what fraction of the speed of light would the $\gamma$ factor lead to a tenfold time dilation?

A) 0.5
B) 0.95
C) 0.75
D) 0.995
E) 0.9999995

Question 28

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

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

Question 29

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

A) 1.00
B) 1.67
C) 1.89
D) 0.99
E) 2.05

Question 30

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 31

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

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

Question 32

If you were to design a spacecraft that could travel to the galactic center fast enough that the astronauts aboard aged by only 25 years during the trip, how fast would the spacecraft have to go? (Note: 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 33

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 34

The Large Hadron Collider at CERN in Switzerland can accelerate protons to amazing kinetic energies of the order of 1.6 * 10 ^{- 7} J.What would be the Lorentz factor for a proton of mass 1.67 * 10 ^{- 27} kg at such speed?

A) 133
B) 1,065
C) 70.79
D) 2
E) 999

Question 35

As measured from Earth, a second of time marked by a clock aboard a fast (hypothetical) interstellar ship moving at v = 0.95c would be ________ compared with the second marked by a clock at rest on Earth.

A) 70.71 times shorter
B) 70.71 times longer
C) 7.09 times shorter
D) 3.20 times longer
E) 3.20 times shorter

Question 36

A geodesic is the name for

A) the aberration of starlight.
B) one of Earth's magnetic field lines.
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 37

In the figure below, the astronaut cannot tell the difference between the two situations due to

A) conservation of energy.
B) equivalence of inertial reference.
C) conservation of angular momentum.
D) the equivalence principle.
E) gravitational lensing.

Question 38

Why do astronauts in space appear to feel no pull of gravity?

A) There is no gravity in space.
B) Gravity happens only when objects are accelerating.
C) In space, the gravity from the Moon and the Sun cancels out 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 in space.

Question 39

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 will be straight if they are moving slowly enough.
B) Their paths will curve more the closer they come to the massive object.
C) Their paths will curve by the same amount no matter how close they come to the massive object.
D) Their paths will curve toward the massive object if they pass close but bend away from the massive object if they pass far from it.
E) Their paths will curve less the closer they come to the massive object.

Question 40

A fast-moving muon decays in 2 *10 ^{- 4} seconds, as measured by an observer at rest.In the reference frame of the muon itself, its lifetime is in fact only 2 *10 ^{- 6} seconds.What is the muon's speed?

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

Question 41

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 42

What is the significance 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 43

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 similar to Earth.
E) a neutron star.

Question 44

Which of the following are the only observable properties of black holes?

A) mass, angular momentum, and electrical charge
B) mass, electrical charge, and fraction of heavy nuclei
C) electrical charge, density, and dark matter content
D) angular momentum, mass, and elasticity
E) mass, density of dark matter, and temperature of Hawking radiation

Question 45

The phenomenon pictured in the figure below is an example of

A) a supernova remnant.
B) a black hole.
C) gravitational lensing.
D) a gamma-ray burst.
E) gravitational waves.

Question 46

The bending of light paths near a massive object is the essence of

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

Question 47

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 near the event horizon.

Question 48

Light that is emitted by an object near a black hole is redshifted 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) photons must "borrow" energy in order to escape the black hole.
D) the object is heating up due to gravitational tidal forces.
E) of gravitational time dilation.

Question 49

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 50

How does relativity compare with 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 is well accepted by scientists, whereas relativity is still controversial.

Question 51

According to the theory of general relativity, a clock on top of Mount Everest would run ________ compared with a clock at sea level because ________.

A) faster; of the high altitude, which means a slightly weaker gravity
B) faster; the air is a lot thinner and there is less friction within the clock
C) faster; it is closer to the Moon and thus experiences stronger tidal forces
D) slower; of the low pressure at that altitude
E) identically; time is the same for all clocks in the universe

Question 52

If the Sun were to be instantly replaced by a 1 M_SUN 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 quickly fall into the Sun and be destroyed.

Question 53

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 54

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 55

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 56

The Sun's mass would affect the spacetime in its nearby space and photons from distant stars would follow curved geodesics rather than straight paths when passing close to our star, as in the figure shown below.According to general relativity, an observer on Earth would also expect the "apparent stars" to appear

A) farther apart.
B) hotter.
C) closer together.
D) brighter.
E) more massive.

Question 57

A person would experience ________ as he or she approached the event horizon of a Solar-mass black hole.

A) extremely strong tidal forces
B) flash freezing
C) strong Hawking radiation
D) strong infrared radiation
E) nothing

Question 58

We still use Newton's law of gravitation, even though Einstein's relativity is more correct, because

A) there's not enough evidence for relativity to justify using it.
B) Newton's laws are exact enough except in extreme situations.
C) relativity does not apply to gravitation.
D) inertia mass and gravitational mass are different, and Newton's law accounts for that.
E) Newton was wrong, but the math is much easier.

Question 59

If you were to fall to within the event horizon of a black hole, you would

A) never be able to escape.
B) get stuck at that location forever.
C) get burned up by Hawking radiation.
D) not be able to see light.
E) be destroyed instantly.

Question 60

Which of the following applications could not have been achieved without implementing necessary relativistic effects and corrections?

A) fast-moving automobiles
B) GPS technology
C) interstellar travel
D) radio technology
E) neutrino detectors

Question 61

What is the meaning of the equation E=mc²?

Question 62

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

Question 63

Suppose we discovered radio signals coming from the star Alpha Centauri, which 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 0.5c, how long would it take the spacecraft to get to Alpha Centauri, and how much time would the astronauts say passed during the trip? (Ignore the time it would take to accelerate the spacecraft to reach a velocity of 0.5c.)

Question 64

The detection of gravitational waves is important evidence for

A) the existence of neutron stars.
B) general relativity.
C) the Big Bang.
D) Type II supernovae.
E) Newton's law of gravitation.

Question 65

What is the equivalence principle? Describe a consequence of the equivalence principle for astronauts orbiting in the International Space Station.

Question 66

Muons are elementary particles that decay into other particles in about 2.2 microseconds.They are formed in the upper atmosphere of Earth from high-energy cosmic rays and can be detected on the ground even though they could travel only a few hundred meters before decaying, according to Newtonian physics.How does relativity explain that we can detect them on the ground? Explain both in our reference frame and in the frame of the muon.

Question 67

Explain the relativistic effects on clocks aboard the International Space Station compared with synchronized clocks here on Earth.

Question 68

A gamma-ray burst (GRB), such as the one in the figure below, may be responsible for some of Earth's mass extinctions.GRBs are hard to study because they

A) can only happen in distant galaxies.
B) are rare, of short duration, and very narrow.
C) emit very few gamma rays.
D) only generate gravitational waves.
E) are long-lived but rotating.

Question 69

General relativity predicts that coalescing (merging) massive objects would trigger

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

Question 70

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 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 71

The GPS system requires time accuracy of the order of a few tens of nanoseconds (ns) for the clocks aboard the satellites.At the high altitudes where the satellites are deployed, their orbital speeds are about 20,000 km/h.Show, considering special relativity alone, that corrections are needed in order to keep the surface of Earth and orbiting satellites synchronized to within the required accuracy.

Question 72

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 73

What is the "rubber sheet" analogy for spacetime, and why is it useful for explaining gravity and gravitational waves?

Question 74

A 3-M_SUN star is seen orbiting with an unseen object with a period of 36 days and a semimajor axis of 1 AU.The mass of the unseen object is closest to

A) 150 M_SUN
B) 103 M_SUN
C) 42 M_SUN
D) 21 M_SUN
E) 1 M_SUN

Question 75

Explain how mass and compactness (that is, size and density) would affect the way an object distorts the fabric of spacetime.

Question 76

An external observer watches a spacecraft accelerate.In the spaceship's frame of reference, it is accelerating at a constant acceleration of
g.Which of the situations shown in the figure below will the external observer see for the spaceship's velocity with time, and why?

Question 77

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 with very faint radio emission.
E) regular, repeated pulsations at radio wavelengths.

Question 78

Explain what four-dimensional spacetime means.

Question 79

The laws of physics are the same in all inertial frames of reference, but the "twin paradox" says that the traveling twin will be the one that experiences time dilation and will be younger than the other twin on return to Earth.How are both of these statements correct?

Question 80

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 unseen object has a mass of 10 M_SUN.This object is probably a ________ because ________.

A) black hole; the giant star is massive and could be in orbit only 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