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## Spring 2021 ASTR 3740 Black Holes: Clicker Questions

Fri 2021 Jan 15 (no credit)

1. Will you get an A in this class?
A. Yes, I am at least 90% sure of it.
B. I think I have a better than 50% chance.
C. Probably not.

2. In this class, I am most interested in learning about:
A. Relativity.
B. Black Holes.
C. Cosmology.
D. Mathematics.
E. All of the above.
3. Wed 2021 Jan 20:

4. Does spacetime have an existence independent of objects in it? (No right answer).
A. Yes.
B. No.
C. Something else.
5. Which of the following is an inertial frame (a frame with respect to which objects move in straight lines in the absence of forces)? (No right answer).
A. The frame of an object in free-fall.
B. The frame of an object at rest in this room.
C. The frame of a person on a roller coaster.
D. The frame of an electron in an atom.
E. All of the above.
6. Which conservation law is not associated with a symmetry of spacetime?
A. Conservation of energy.
B. Conservation of momentum.
C. Conservation of angular momentum.
D. Conservation of velocity of center of mass.
E. Conservation of electric charge.
7. Fri 2021 Jan 22:

8. The north-pointing jet in the radio galaxy Centaurus A appears brighter than the south-pointing jet. The north-pointing jet appears:
A. Blueshifted, brighter, and speeded up.
B. Redshifted, dimmer, and slowed down.
9. On this spacetime diagram, how fast is Cerulean moving relative to Vermilion, in units of the speed of light?
A. 0.
B. 1/2.
C. 1.
D. 2.
E. The information on the diagram is insufficient to answer the question.
10. If the postulates of special relativity are correct, would the light have moved differently if Cerulean, not Vermilion, had emitted the light?
A. Yes.
B. No.
11. Mon 2021 Jan 25:

12. What is the solution to the challenge problem? (How can Vermilion and Cerulean both be at the center of the lightcone?)
A. In special relativity, reality depends on the observer, and it is possible for two logically inconsistent things to occur.
B. Light moves differently depending on who emits it.
C. Clocks run at different rates depending on velocity.
D. Observers moving at different velocities have different notions of simultaneity.
13. Two circular hoops of the same size start at rest. Hoop A starts moving at near the speed of light towards hoop B. Which hoop passes inside the other?
A. A.
B. B.
C. Neither.
14. If Cerulean were moving as shown relative to Vermilion, which line would be a “now line” for Cerulean?
A.
B.
C.
D.
E.
15. Wed 2021 Jan 27:

16. A cube. Are the lengths of its sides all equal?
A. Yes.
B. No.
17. In the Lorentz transformation movie, what is being varied?
A. The speed $$c$$ of light.
B. The position $$x(t)$$ as a function of time $$t$$ of Cerulean relative to Vermilion.
C. The velocity $$v$$ of Cerulean relative to Vermilion.
18. Fri 2021 Jan 29:

19. On your way out to Alpha Cen, you appear to me, watching you through a telescope on Earth, to move at what speed?
A. 0;
B. ½ c;
C. Near c;
D. 2 c;
E. Near infinite speed.
20. On your way back from Alpha Cen, you appear to me, watching you through a telescope on Earth, to move at what speed?
A. 0;
B. ½ c;
C. Near c;
D. 2 c;
E. Near infinite speed.
21. If round-trip time is 8 years from my (Earth) perspective, then the round-trip time from your (traveler's) perspective is:
A. Practically no time.
B. Less than 8 years.
C. 8 years.
D. More than 8 years.
22. Wed 2021 Feb 3:

23. “The Lorentz Transformation, which is considered as constitutive for the Special Relativity Theory, was invented by Voigt in 1887 [who mistakenly thought the transformations applied to all waves, including sound as well as light], adopted by Lorentz in 1904, and baptized by Poincaré in 1906. Einstein probably picked it up from Voigt directly.” — W. Engelhardt. Why does Einstein, not Lorentz, get credit for discovering special relativity?
A. Lorentz derived the equations, but did not attempt to apply them to reality.
B. Lorentz made some mathematical mistakes, which Einstein corrected.
C. Lorentz thought that matter (electrons) contracts as it moves through the aether, whereas Einstein said there is no aether.
D. Nowadays physicists do in fact attribute special relativity to Lorentz, not Einstein.
E. History is unfair.
24. On a spacetime diagram, the worldline of a person must point:
A. vertically upward;
B. at less than 45° from vertical;
C. at 45° from vertical;
D. horizontally;
E. in any direction.
25. What is a 4-vector?
A. Any set $$\{ t , x , y , z \}$$ of 4 quantities.
B. A set $$\{ t , x , y , z \}$$ of 4 quantities that transform in a certain way under Lorentz transformations.
C. Something else.
26. How does the rest mass m of a spacecraft change with its velocity v?
A. It increases.
B. It stays the same.
C. It decreases.
27. Is the energy-momentum $$p^i \equiv E ( 1 , \pmb{n} )$$ of a photon a 4-vector?
A. Yes.
B. No.
28. Mon 2021 Feb 8:

29. You pass through a scene at near the speed of light. Clocks on objects ahead of you appear speeded by exactly the same amount as the frequencies of photons of light from those objects appear increased. True or false?
A. True.
B. False.
30. The Earth moves at 30 km/s, or 10−4c, in its annual orbit around the Sun. Does the Earth's motion around the Sun cause special relativistic aberration that is observable at 1 arcsecond resolution?
A. Yes.
B. No.
31. Hubble Space Telescope observations of the jet in M87 show blobs emerging at 6c. This suggests that:
A. The jet is moving faster than c.
B. Special Relativity is wrong.
C. The blobs are not parcels of matter, but rather waves of brightness passing along the jet.
D. The jet is pointed almost towards us, and is moving at close to c.
E. The jet is pointed away from us, and is moving at close to c.
32. Why is a second jet not observed in M87?
A. There is no second jet.
B. Aberration bends the second jet out of view.
C. The second jet is relativistically dimmed out of view.
D. The second jet is relativistically redshifted out of view.
E. The second jet is behind the quasar, which obscures it.
33. Wed 2021 Feb 10:

34. In George Gamow's classic book “Mr. Tomkins in Wonderland,” Mr. Tomkins has a dream that the speed of light is 30mph. In the dream, passing bicyclists appear Lorentz contracted along the direction of their motion. Does Mr. Tomkins' dream portray correctly the appearance of objects moving relativistically?
A. Yes.
B. No.
35. In the twin paradox, you and your twin start at the same place, recede from each other at some velocity, then return at the same velocity. The situation seems symmetrical. What breaks the symmetry, that allows the twin to be younger than you on return?
A. The velocities at which you and your twin see each other move are different.
B. The situation is in fact symmetrical, so in fact you must both age the same.
C. The twin moves through space, whereas you do not.
D. The twin accelerates at the turnaround point, whereas you do not accelerate.
E. The twin experiences a sudden loss of time at the turnaround point.
36. Your twin watches you on Earth through a telescope. At the moment that the twin accelerates at Alpha, the twin sees your clock:
A. Run at the same slowed-down rate both before and after accelerating.
B. Suddenly change from 2 years to 8 years.
C. Suddenly speed up.
D. Suddenly slow down.
E. Change from running forward to runing backward.
37. Which would you most like to review (which do you understand least well)?
A. The postulates of special relativity.
B. The paradoxes of special relativity.
C. 4-vectors and Lorentz transformations.
D. Energy-momentum in special relativity.
E. Something else.
38. Pole-in-the-barn paradox: Will the spaceship fit inside the space station?
A. Yes.
B. No.
39. Mon 2021 Feb 15:

40. To observe the most energetic phenomena in the Universe, what spectral band of light would be most promising?
B. Infrared.
C. Optical.
D. Ultraviolet.
E. X-rays.
41. The Newtonian gravitational potential satisfies $$\phi = - \frac{G M}{r^2}$$ at distance $$r$$ from a point or spherical mass $$M$$. Why can't that be correct, in special relativity?
42. Gravity is a $$1/r^2$$ force like the electromagnetic force. Why was it not possible to modify gravity to behave like electromagnetism?
A. Like masses attract, whereas like charges repel.
B. A wave of gravity carries energy (and momentum), so must interact with itself, whereas a wave of electromagnetism carries no charge, so does not interact with itself.
C. Electromagnetism is based on a $$U(1)$$ symmetry, implying only a single conserved quantity (charge), whereas gravity is associated with all symmetries of spacetime, implying several conserved quantities (energy, momentum, angular momentum...).
D. The many symmetries of gravity imply that it is a more complicated force than electromagnetism.
43. The weak Principle of Equivalence states that gravitational mass = inertial mass. Does Newtonian gravity satisfy the weak Principle of Equivalence?
A. Yes.
B. No.
C. Partially.
44. Fri 2021 Feb 19:

45. Suppose you watch this scene while falling freely. According to the Principle of Equivalence, what kind of trajectory will the cannonball follow from your perspective (relative to you)?
A. A vertical line.
B. A straight line.
C. A curved (parabolic) line.
46. Standing on the surface of the Earth, you hold a negative mass object in your hand. According to the Principle of Equivalence, which way does the negative mass object fall when you drop it?
A. Down to the floor.
B. It justs hangs there in mid-air, falling neither down nor up.
C. Up to the ceiling.
D. None of the above.
47. You are in flat space. You swing a clock on a rope in a circle around you, so that the clock is moving at near the speed of light relative to you. According to Special Relativity, the clock will appear to you to tick:
A. Slow;
B. At the same rate as your own clock;
C. Fast;
D. None of the above.
48. In the situation of the previous question 37, the object therefore appears to you (according to Special Relativity):
A. Redshifted;
B. Neither redshifted nor blueshifted;
C. Blueshifted.
49. In this situation, according to Special Relativity, does B see the light from A to be redshifted or blueshifted?
A. B sees the light to be redshifted (lower energy) compared to A.
B. B sees the light to have the same energy as A.
C. B sees the light to be blueshifted (higher energy) compared to A.
50. Mon 2021 Feb 22:

51. What evidence most convincingly suggests that there is a supermassive black hole at the center of our own Milky Way?
A. The black hole causes gravitational lensing.
B. The supermassive black hole is in an x-ray binary star system.
C. Hubble Space Telescope observations show gas swirling down a vortex.
D. A relativistic jet is seen coming out of the core of the Milky Way.
E. Measurements of the velocities of stars at the center of the Milky Way indicate a large mass in a small space.
52. The shortest distance between Boulder (40oN 105.25oW) and Dushanbe, Tajikstan (38.5oN 68.75oE) over the Earth's surface is:
A. A straight line on this map;
B. A curved line on this map.
53. The distance squared $$d r^2$$ between points separated by vertical distance $$d z$$ and angle $$d \phi$$ on the surface of a 2D cylinder of radius $$R$$ is given by ($$z$$, $$\phi$$ are called cylindrical coordinates):
A.  $$d r^2 = d z^2 + d \phi^2$$
B.  $$d r^2 = R^2 ( d z^2 + d \phi^2 )$$
C.  $$d r^2 = ( d z + R \, d \phi )^2$$
D.  $$d r^2 = d z^2 + R^2 \, d \phi^2$$
E.  $$d r^2 = - d z^2 + R^2 \, d \phi^2$$
54. In the previous question 42, the metric $$g_{ij}$$ of the cylindrical spacetime with respect to cylindrical coordinates $$z$$, $$\phi$$ is:
A.  $$\left(\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right)$$
B.  $$\left(\begin{array}{cc} R & 0 \\ 0 & R \end{array}\right)$$
C.  $$\left(\begin{array}{cc} R^2 & 0 \\ 0 & R^2 \end{array}\right)$$
D.  $$\left(\begin{array}{cc} 1 & 0 \\ 0 & R \end{array}\right)$$
E.  $$\left(\begin{array}{cc} 1 & 0 \\ 0 & R^2 \end{array}\right)$$
55. In general, does the metric have to be symmetric ($$g_{ij} = g_{ji}$$)?
A. Yes.
B. No.
56. In general, does the metric $$g_{ij}$$ have to be diagonal ($$g_{ij} \neq 0$$ only if $$i = j$$)?
A. Yes.
B. No.
57. Wed 2021 Feb 24:

58. Will the probe fall into the black hole?
A. Yes.
B. No.
59. How do you know that a spacetime is globally flat?
A. In free fall, all spacetimes are globally flat.
B. Geodesics are straight lines.
C. Geodesics that are initially parallel remain parallel.
D. The spacetime is embedded in a higher dimensional spacetime.
60. Can spacetime be curved inside a region where there is no mass (but there may be mass outside the region)?
A. Yes.
B. No.
61. What aspect of the Schwarzschild metric tells you that the geometry is stationary (independent of Schwarzschild time $$t$$)?
A. All metric components $$g_{\mu\nu}$$ are independent of time $$t$$.
B. The metric is diagonal.
C. The metric is spherical.
D. The spacetime is empty (a vacuum).
62.  The Schwarzschild metric is $d s^2 = - ( 1 - r_s/r ) \, dt^2 + {dr^2 \over 1 - r_s/r} + r^2 ( d\theta^2 + \sin^2\!\theta \, d\phi^2 )$ where $$r_s = 2 G M / c^2$$ is the Schwarzschild radius, the horizon radius.

63. What aspect of this metric tells you that the geometry is spherically symmetric?
64. What is the proper circumference of a circle at radius $$r$$ in the Schwarzschild geometry?
A. $$r$$.
B. $$\pi r$$.
C. $$2\pi r$$.
D. The proper circumference depends on the choice of coordinates.
65. Fri 2021 Feb 26:

66. On this unstable circular orbit, if we accelerate forwards, we will:
A. Fall into the black hole;
B. Remain on the unstable circular orbit;
C. Leave the black hole, going far away from it.
67. Will the probe fall into the black hole?
A. Yes.
B. No.
68. Does it make sense to talk about (massive) observers at rest at the horizon, $$r = r_s$$, of a Schwarzschild black hole?
A. Yes.
B. No.
69. Which of the Schwarzschild coordinates $$t , r , \theta , \phi$$, if any, is timelike inside the horizon, $$r < r_s$$?
A. $$t$$;
B. $$r$$;
C. $$\theta$$;
D. $$\phi$$;
E. None of the above.
70. Mon 2021 Mar 1:

 The Schwarzschild metric is $d s^2 = - ( 1 - r_s/r ) \, dt^2 + {dr^2 \over 1 - r_s/r} + r^2 ( d\theta^2 + \sin^2\!\theta \, d\phi^2 )$ where $$r_s = 2 G M / c^2$$ is the Schwarzschild radius, the horizon radius.

71. How would you solve for the evolution of the radius $$r ( t )$$ as a function of Schwarzschild time $$t$$ for radial $$(d \theta = d \phi = 0)$$ geodesics of light in the Schwarzschild geometry?
A. Set $$d s^2 = 0$$ and solve for $$d r / d t$$.
B. Since $$d s^2 = 0$$ for light, no proper time goes by on a lightwave, so there are no geodesics.
C. Solve Einstein's equations.
D. The geodesic depends on the frequency of the photon.
E. It depends on the choice of coordinates.
72. What will happen at the horizon of the Schwarzschild black hole at the moment you free-fall through it?
A. You will freeze at the horizon, your time slowing infinitely.
B. You will be engulfed in blackness.
C. You will be tidally torn apart.
D. You will encounter an infinitely bright light.
E. Nothing special.
73. You free-fall radially into a Schwarzschild black hole, starting from rest far from the black hole. The sky vertically above you appears:
A. Redshifted;
B. Blueshifted;
C. Neither redshifted or blueshifted;
D. It depends on the choice of coordinates.
74. Wed 2021 Mar 3:

75. Vote for your favorite quiz question.
76. You and a friend are falling toward a Schwarzschild black hole at the same time, though at different locations in longitude and latitude. As you both continue to approach the singularity, will you ever meet?
A. Yes.
B. No.
77. What lies on the other side of the antihorizon (red line)?
A. Nothing.
B. A white hole and another “parallel” universe.
C. The invisible interior of the star that collapsed to a black hole long ago.
78. How to get to the Parallel Universe? (No right answer.)
A. Accelerate towards the Parallel Universe.
B. Accelerate away from the Parallel Universe.
C. A, then go backwards in time.
D. B, then go backwards in time.
E. It's impossible.
79. Mon 2021 Mar 8:

80. From a safe distance, you watch a spherical, pressureless star collapse to a black hole. What will you see?
A. The star will appear to freeze when at the horizon radius, and never collapse.
B. The star will appear to branch into a wormhole and white hole, before becoming a black hole.
C. The star will appear to collapse to a singularity.
81. When the mass of a black hole increases, its horizon expands. Does the horizon appear to engulf stuff that previously fell through the horizon?
A. Yes, stuff that previously fell into the black hole disappears.
B. No, stuff that previously fell into the black hole remains frozen at the horizon, appearing to expand with the horizon.
82. If, as seen by an outside observer, a star collapsing to a black hole appears never to collapse through its horizon, even unto the end of the Universe, does the star ever actually collapse?
A. Yes.
B. No.
83. If a collapsing star somehow stopped collapsing before falling inside its horizon, would it have a horizon?
A. Yes.
B. No.
84. If nothing can escape from a black hole, how can its gravity escape?
A. Gravity is a curvature of space, and does not need to escape.
B. The gravity does not escape, but the tidal force does escape.
C. Gravity does not escape from a black hole: a person outside the BH experiences the gravity of the matter that long ago collapsed to, or fell into, the BH.
D. Gravity travels faster than light.
85. Wed 2021 Mar 10:

86. Which are the most common point sources detected by the Fermi Gamma-ray Space Telescope (≥ GeV)?
A. Pulsar (rotating neutron star).
B. Supernova remnant.
C. High-mass X-ray binary system (containing a high-mass star accreting on to a white dwarf, neutron star, or black hole).
D. Active Galactic Nucleus.
E. Blazar (type of Active Galactic Nucleus in which the jet from the supermassive black hole is pointed directly at us).
87. What happens when we reach the inner horizon of a real astronomical black hole?
A. Nothing special.
B. We will be tidally torn apart.
C. The outside Universe will appear redshifted and dimmed to invisibility.
D. The outside Universe will appear exponentially blueshifted, bright, and speeded up.
E. We will enter a wormhole.
88. Is the singularity of the ideal mathematical solution for a Reissner-Nordström black hole gravitationally attractive or repulsive (what does the river model for RN black holes say)?
A. Attractive.
B. Repulsive.
C. Neither.
89. From the point of view of an observer outside the outer horizon of a white hole, is the white hole gravitationally attractive or gravitationally repulsive (what does the river model for RN black holes say)?
A. Attractive.
B. Repulsive.
C. Neither.
90. Fri 2021 Mar 12:

91. When the Black Hole Flight Simulator is running, does audio work better on the phone or on the computer/Crestron?
A. Better on phone.
B. Better on computer/Crestron.
C. Neither work well.
D. No opinion.
92. Is the ring singularity of the ideal mathematical solution for a Kerr black hole gravitationally attractive or repulsive?
A. Attractive.
B. Repulsive.
C. Neither.
93. The horizons of a rotating (Kerr) black hole are at $$r_\pm = M \pm \sqrt{M^2 - a^2}$$, where $$a$$ is the angular momentum per unit mass of the black hole. What is the maximum possible value of $$a$$?
A. 0.
B. 1.
C. $$M$$.
D. $$\infty$$.
94. What happens if $$a > M$$, in the exact mathematical solution? Can this happen in a real astronomical black hole?
A. The horizons disappear, revealing a repulsive singularity inside.
B. It can't happen.
95. What will happen if you pass through the X-point at the intersection of ingoing and outgoing horizons, in the exact mathematical solution? Can this happen in a real astronomical black hole?
A. You get skewered by infinitely bright beams of energy in both directions.
B. It can't happen.
96. Wed 2021 Mar 17:

97. In the first ever detected merger of two black holes, GW150914, the starting masses of the black hole pair were 29M and 36M, but the mass of the resulting single black hole was 62M, which is less than the sum 65M of the original pair. Where did the energy in the missing 3M go to?
A. A supernova.
B. A jet.
C. Gravitational waves.
D. They disappeared inside the black hole.
E. In general relativity, mass-energy is not conserved.
98. If a gravitional wave is a wave of spacetime that changes distances between things, including the lengths of rulers that measure distances, how can gravitational waves be measured?
99. As GW150914 approached the merger climax, the separation between wave peaks was a bit less than 0.01 seconds. What was the approximate wavelength of the gravitational waves detected?
A. About 10–3 times the size of a proton nucleus.
B. About the size of a proton nucleus.
C. About the size of an atom.
D. About the wavelength of visible light.
E. About the size of the merging black hole system (about 0.01 lightseconds, or 1000 km).
100. Why does the detection of a burst of gamma rays 2 seconds after the gravitational wave signal in GW170817 imply that the speed of gravitational waves is the speed of light?
A. Because gamma-rays are a kind of gravitational wave.
B. Because general relativity predicts that gravitational waves move at the speed of light.
C. Because the signal travelled the same distance, 130 million lightyears, in the same time.
D. Because extremely energetic particles must move at the speed of light.
E. Actually, the fact that the gamma-ray signal was delayed by 2 seconds implies that gravity moves slightly faster than light.
101. Mon 2021 Mar 22:

Watch the Event Horizon Telescope video, the 33 minutes from 5.30 to 38.00.

102. What aspect of the EHT observations points to a confirmation of general relativity?
A. Angular size.
B. Hole in the middle.
C. Brighter on one side.
D. Variability.
E. Redshifted.
Silhouette of a black hole
103. Observations by EHT were made at 1.3mm. Why this wavelength and not a longer one? Why not a shorter wavelength?
A. Higher resolution.
B. Brighter.
C. Penetrates dust and gas.
D. Limitations of atomic clocks.
E. Something else?
EHT Simulations gallery (click on Varying Wavelength)
104. On what timescale should the image of the M87 black hole show intrinsic variation?
A. A second.
B. A minute.
C. A day.
D. A year.
E. Millions of years.
105. The EHT team used atomic clocks to phase up the light seen by different telescopes. Why was that necessary?
106. On what timescale should the image of the Milky Way black hole Sgr A* show intrinsic variation? EHT data on Sgr A* have already been taken, but not yet published. Why not?
107. Wed 2021 Mar 24:

108. A more massive black hole produces Hawking radiation with longer wavelength. Therefore a more massive black hole produces Hawking radiation that is _____ energetic, and therefore has a _____ Hawking temperature.
A. Equally, equal.
B. Less, lower.
C. More, lower.
D. Less, higher.
E. More, higher.
109. Wien's law is $$\lambda_{\rm peak} T = 3 ~{\rm mm}~{\rm K}$$. A 10 solar mass black hole has a Schwarzschild radius of 30 km. Approximately what is the Hawking temperature of a 10 solar mass black hole?
A. $$10^{-7}~{\rm K}$$.
B. $$3~{\rm K}$$.
C. $$10~{\rm K}$$.
D. $$30~{\rm K}$$.
E. $$10^{7}~{\rm K}$$.
110. What is the Hawking entropy of the 4 million solar mass black hole at the center of the Milky Way? How does this compare to the entropy in the CMB (the number of photons in the observable Universe)?
A. The entropy of the Milky Way black hole is larger.
B. The entropy of the CMB is larger.
C. The entropies are comparable.
111. Does an infaller continue to see Hawking radiation when they fall through the horizon?
A. Yes, from the (true, event) horizon.
B. Yes, from the illusory horizon (the redshifted, dimming surface of the star that collapsed long ago).
C. B, and also from the sky above.
D. No.
112. What will Hawking radiation look like (a) at the horizon, (b) near the singularity? Will the temperature (the characteristic frequency of Hawking radiation) be:
B. Similar to the Hawking temperature seen from outside.
C. Somewhat higher than the Hawking temperature seen from outside.
D. Huge.
113. Mon 2021 Mar 29:

114. What are the units (time, length, mass) of the Hubble constant $$H_0$$? What fundamental property of the Universe does $$H_0$$ measure? Why might the measurement of that property not be exact?
115. Does the Universe have a center?
A. Yes (why?).
B. No (why?).
116. What is the Universe expanding into?
A. Nothing (then what does expansion mean?).
B. Something (specifically?).
117. Wed 2021 Mar 31:

118. What does thermodynamic equilibrium mean? (Answer: A state in which there are no macroscopic flows of energy, momentum, number, or other conserved quantities.) What thing in the room you are sitting in is closest to thermodynamic equilibrium?
D. The window.
E. The air.
119. How can the Cosmic Microwave Background (CMB) be construed as evidence for homogeneity and isotropy given that it provides information only over a 2D surface on the sky?
A. If our Galaxy is typical, then observers everywhere in our Universe should see a uniform CMB.
B. The blackbody spectrum of the CMB implies that the Universe was simple and uniform.
C. Actually, it is the 3D distribution of galaxies that provides the strongest evidence.
D. The CMB can not be construed as evidence for homogeneity and isotropy.
120. Wed 2021 Apr 2

121. Does the CMB show a characteristic scale?
A. Yes.
B. No.
122. If there is a characteristic scale, what sets that scale?

123. Does galaxy clustering show a characteristic scale?
A. Yes.
B. No.
124. If there is a characteristic scale, what sets that scale?

Mon 2021 Apr 5

125. What is the length of this line in terms of the radius $$R$$ of the hypersphere, and the angle $$\chi$$?
A. $$R$$.
B. $$\chi$$.
C. $$R \chi$$.
D. $$R \sin\chi$$.
E. $$2\pi R$$.
126. Where is the observer in this embedding diagram of the FLRW geometry?
A. At the center of the sphere.
B. At the north pole of the sphere.
C. At the end of the $$r_\parallel = R \chi$$ line.
D. Anywhere on the surface of the sphere.
E. There is no observer in this diagram.
127. Why do astronomers use the cosmic scale factor $$a(t)$$ rather than the radius $$R(t)$$ of the Universe as a measure of the size of the Universe?
A. The radius $$R$$ is defined only for a closed Universe.
B. Relative scales can be measured without knowing an absolute scale.
C. The Einstein equations determine the evolution only of $$a$$, not $$R$$.
D. Something else.
128. Wed 2021 Apr 7

129. What is something new you learned in the virtual Fiske presentation?
130. Fri 2021 Apr 9

131. What is name of the local region of the Universe that has just turned around from the general Hubble expansion and is beginning to collapse under its own gravitational attraction?
A. The Solar System.
B. The Milky Way.
C. The Local Group of Galaxies.
D. The Local Supercluster of Galaxies.
E. The Cosmic Microwave Background.
132. According to the 2nd Friedmann equation $$\ddot{a} / a = \frac{4}{3} \pi G ( \rho + 3 p )$$, what type of energy-momentum is at the borderline between attraction and repulsion?
A. Radiation ($$p / \rho = 1/3$$).
B. Matter ($$p / \rho = 0$$).
C. Curvature ($$p / \rho = -1/3$$).
D. Vacuum ($$p / \rho = -1$$).
133. If wavelengths expand with the Universe, $$\lambda \propto a$$, how does the temperature $$T$$ of the CMB change with scale factor $$a$$?
A. $$T \propto a$$.
B. $$T \propto a^{-1}$$.
C. $$T \propto a^{-2}$$.
D. $$T \propto a^{-3}$$.
E. $$T \propto a^{-4}$$.
134. In cosmology, the redshift $$z$$ is related to cosmic scale factor $$a$$ by $$1 + z \equiv \lambda_{\rm obs} / \lambda_{\rm emit} = a_0 / a$$. The CMB was released at Recombination, when H transition from ionized (opaque) to neutral (transparent) at $$T \approx 3{,}000 ~{\rm K}$$. The temperature of the CMB today is $$T \approx 3~{\rm K}$$. At approximately what redshift did Recombination occur?
A. $$10^{-3}$$.
B. 1.
C. 1000.
D. $$10^{12}$$.
E. It depends on cosmological parameters such as $$\Omega_{\rm m}$$ and $$\Omega_\Lambda$$.
135. Mon 2021 Apr 12:

136. Observations indicate $$\Omega_{\rm m} \approx 0.3$$ and $$\Omega_{\rm rad} = \Omega_\gamma + \Omega_\nu \approx 10^{-4}$$ (note that $$\Omega_\nu / \Omega_\gamma = \tfrac{7}{8} \times \tfrac{4}{11} \times 3 = 0.95$$ for relativistic neutrinos). At approximately what redshift $$1 + z$$ did the Universe change from radiation-dominated to matter-dominated?
A. 3.
B. 30.
C. 300.
D. 3000.
137. The horizon problem is: How can parts of the CMB more than about 1° apart have almost the same temperature? Why is this a problem?
138. Wed 2021 Apr 14:

139. The Universe just prior to Recombination at $$1 + z \approx 1000$$ and 400,000 years old is best described as:
A. A Big Bang.
B. Dominated by a dense, gravitationally repulsive, GUT-scale vacuum energy.
C. A dark, transparent void, dominated by non-baryonic cold dark matter.
D. An opaque, ionized, photon-baryon fluid close to thermodynamic equilibrium, with sound speed about $$c / \sqrt{3}$$.
E. Stars were forming vigorously, and galaxies were beginning to cluster.
140. Fluctuations in the CMB show a characteristic scale of 1°. What sets this scale?
A. Random fluctuations of vacuum energy.
B. It's the GUT scale (the scale of Grand Unification of forces), enlarged by the expansion of the Universe.
C. It's the sound horizon size $$c_s t_{\rm Rec}$$ with $$c_s \approx c / \sqrt{3}$$ at the time $$t_{\rm Rec} \approx 400{,}000$$ years at Recombination.
D. It's the scale of galaxy clustering.
E. Actually it's just noise; there is no scale imprinted in the CMB.
141. Normally (that is, except during inflation when the Universe was dominated by vacuum energy), the Hubble parameter $$H$$ given by $$H^2 = \frac{8}{3}\pi G \rho$$ evolved with cosmic time $$t$$ as:
A. $$H \propto t^{-2}$$.
B. $$H \propto t^{-1}$$.
C. $$H$$ was constant.
D. $$H \propto t$$.
E. $$H \propto t^2$$.
142. During inflation when the Universe is dominated by vacuum energy, the Hubble parameter $$H$$ given by $$H^2 = \frac{8}{3}\pi G \rho$$ evolved as:
A. $$H \propto t^{-1}$$.
B. $$H$$ was constant.
C. $$H \propto a^{-1}$$.
143. Does the theoretically expected characteristic angular scale of fluctuations in the CMB depend on cosmological parameters $$\Omega_{\rm m}$$ and $$\Omega_\Lambda$$?
A. Yes.
B. No.
144. Mon 2021 Apr 19:

145. Low-$$\ell$$ harmonic peaks in the CMB power spectrum are spaced further apart than higher-$$\ell$$ harmonics. Why?
A. Because lower harmonics are at larger scales where the curvature of the Universe is more apparent.
B. Because dark energy causes more acceleration at larger scales.
C. Because lower harmonics exited the horizon later, when the Universe was more matter-dominated, so the sound speed was lower.
146. The expansion problem is: Why is the Universe expanding? Why is this a problem?
147. The flatness problem is: How come the Universe is so spatially flat? Why is this a problem?
148. At the end of inflation, vacuum energy transforms into particle energy in a burst of entropy creation called “reheating”. But if an FLRW universe conserves entropy according to the Friedmann equation $$dE + p dV = T dS = 0$$, how can the entropy of the Universe increase?
A. The Friedmann equation $$dE + p dV = 0$$ in an FLRW Universe represents conservation of energy, not conservation of entropy.
B. Vacuum energy contains lots of entropy.
C. The concept of entropy cannot be applied to the Universe at large.
149. Wed 2021 Apr 21:

150. What happened before inflation?
A. There was no before: time itself began (the Hawking-Hartle “no boundary condition” proposal).
B. No one knows, but there must have been a time before inflation (before vacuum domination), because vacuum defines no preferred frame, whereas the Universe has a preferred frame (the frame in which the CMB is at rest).
C. “Eternal inflation”: an even higher density vacuum, the Planck density or more, so high that the vacuum expanded faster than pieces of it could decay, producing a multiverse of Universes.
151. What do cosmologists refer to as “non-baryonic cold dark matter”?
A. Matter made from atoms and nuclei.
B. Gravitationally attractive dark matter that interacts by gravity, but not electromagnetically.
C. Gravitationally repulsive vacuum energy.
E. Neutrinos.
152. What do you see in this image?
A. Stars, the bright points with cross-hair diffraction spikes indicating that they are unresolved.
B. Yellowish blobs, which are are galaxies in the galaxy cluster.
C. Bluish arcs, which are background galaxies lensed by the galaxy cluster.
D. Darkness between the bright stars and galaxies.
E. All of the above.
153. What is the best astronomical evidence for non-baryonic dark matter?
A. Laboratory detection of dark matter.
B. Galaxy rotation curves.
C. The Bullet cluster.
D. Dark matter in clusters of galaxies deduced from gravitational lensing.
E. The CMB power spectrum requires non-baryonic cold dark matter.
154. Fri 2021 Apr 23:

155. What essay question(s) would you like to see on the final? Please email me before Monday's in-class Review Session.
156. Temperature is a measure of the mean energy per particle of a system in thermodynamic equilibrium. It is associated with the law of conservation of energy that follows from time translation symmetry of the laws of physics. When can an object be described by a temperature?
A. When all particles have the same energy.
B. When it is in thermodynamic equilibrium.
C. When energy is conserved.
D. When the laws of physics satisfy time translation symmetry.
E. When it has a blackbody distribution.
157. You fire a rocket from Earth. Which rocket wins the orbital race (which rocket returns first to the starting point)?
A. The rocket that stays on Earth;
B. The rocket that fires forwards;
C. The rocket that fires outwards;
D. The rocket that fires backwards;
E. The rocket that fires inwards.

158. Which of the following is not driven by gravity power?
A. Interstellar gas cools, contracts, heats up, forming protostars.
B. A protostar cools, contracts, heats up to the point that it ignites nuclear fusion.
C. A star burns by nuclear fusion.
D. The Fe core of an evolved massive star collapses to a neutron star or black hole, driving a supernova explosion.
E. An accretion disk around a stellar-sized or supermassive black hole heats to x-ray emitting temperatures as it spirals inward.
159. Mon 2021 Apr 26:

160. Breakout session:
What essay question(s) would you like to see on the final?
What would you like to cover in the review today?
161. Wed 2021 Apr 28:

162. Would you vote in favor of making a baby Universe?
3 A. I think that it is immoral to attempt to make a baby Universe. I vote no.
8 B. If this is the only way that our Universe can reproduce, then I think society has a moral duty to make it happen. I vote yes.
2 C. I don't think society should waste resources attempting to make a baby Universe. I vote no.
18 D. I don't have a strong moral opinion, but I support the notion that society should attempt to make a baby Universe. I vote yes.
0 E. I don't really care either way. I probably won't bother to vote.
163. If society were presented with the one-time opportunity to make a baby Universe, what do you think the eventual outcome would be?
8 A. All out war between the yes and no factions.
5 B. Fierce political discussion, resolved by the democractic process.
6 D. Nothing. Society would not care, and would just go about its business.
6 E. C, but the hero and heroine wade in and break the deadlock.
164. You are the leader of the “No-baby-Universe” faction. You believe deeply that your cause is right. You strive for right. But your faction has lost the vote. What do you do?
5 A. Continue to argue non-violently for your cause.
19 B. Fight for right. Start a guerilla war.