From Eternity to Here
The Quest for the Ultimate Theory of Time
Sean M. Carroll, Penguin Group, 2010About the author
Sean Carroll is a theoretical physicist at the California Institute of Technology. He received his Ph.D. from Harvard in 1993, and worked at MIT, the Institute for Theoretical Physics at UC Santa Barbara, and the University of Chicago before moving to Caltech. His research involves theoretical physics and astrophysics, focusing on issues in cosmology, field theory, and gravitation. He is the author of "Spacetime and Geometry", a graduate-level textbook on general relativity; has produced a set of introductory lectures for The Teaching Company entitled "Dark Matter and Dark Energy: The Dark Side of the Universe"; and blogs regularly at "Cosmic Variance". His lives in Los Angeles with his wife, writer Jennifer Ouellette.
Prologue: The nature of time, the importance of entropy, and the role of cosmology
p1 Definition of time from Wikipedia
p2 "Arrow of time" introduced
p2 You can make an omelet out of an egg, but not an egg from an omelet - part of his collection of examples of irreversible phenomena. Another was stirring a spoonful of milk into your coffee.
p2 His description of entropy
p3 The beginning of the universe was a low entropy state
p3 Role of entropy in our view of cause and effect. Actually, having read the rest of the book and having heard his comments at the Greer-Heard Forum in Feb 2014, it is clear that he associates cause and effect with the increase in entropy and indeed attaches time itself to the increase in entropy, which places the increase in entropy in our universe in a far more fundamental role than I am willing to give it. It does explain why he was willing to say in the Greer-Heard Forum that cause and effect do not apply to the universe as a whole. I'm guessing that he meant that he didn't see cause and effect applying to the multiverse, but he hadn't developed that topic there. This does seem like a rather extreme position of scientism - that something like cause and effect is merely an accident of our "comoving frame" within the multiverse that exists only because entropy must increase. I see cause and effect as a fundamental aspect of reality and one of the things that points to a reality transcendent to the material universe that we see.
p3 Boltzmann, Maxwell, Gibbs - developed description of the macroscopic from the microscopic and the role of entropy in irreversible processes. They didn't know about general relativity and quantum mechanics
p4 Introduces the multiverse idea with the Big Bang not being the beginning.
p5 Interesting story of the objections of an older physics professor to one of his talks on cosmology.
p5 "If our universe began at the Big Bang, it is burdened with a finely tuned boundary condition for which we have no good explanation. But if the observe universe is part of a bigger ensemble - the multiverse - then we might be able to explain why a tiny part of that ensemble witnesses such a dramatic change in entropy from one end of time to the other."
Part I: Time, Experience and the Universe
1. The Past is Present Memory
p9 Augustine "What is time? If no one asks me, I know. If I wish to explain it to one that asketh, I know not."
p10 Three approaches to time
p11-14 builds concept of space-time
p16 Galileo story - in church, watches chandelier move as pendulum, finds that larger amplitude gave same period.
p16"In 1581, a young Galileo Galilei reportedly made a breakthrough discovery while he sat bored during a church service in Pisa. The chandelier overhead would swing gently back and forth, but it seemed to move more quickly when it was swinging widely (after a gust of wind, for example) and more slowly when it wasn't moving as far. Intrigued, Galileo decided to measure how much time it took for each swing, using the only approximately periodic event to which he had ready access: the beating of his own pulse. He found something interesting: The number of heartbeats between swings of the chandelier was roughly the same, regardless of whether the swings were wide or narrow. The size of the oscillations - how far the pendulum swung back and forth - didn't affect the frequency of those oscillations."
p19 Conceptual intro to relativity and distinction between time as a "location" in space-time and as an interval between events.
p23 view from "nowhere"
p24 Augustine's discussion of time. Carroll calls Augustine's view "presentism" whereas he points to "eternalism"
p25 Last paragraph - returns to 3 views of time like p10.
2. The Heavy Hand of Entropy
p29 "there seems to be an allowed order that is somehow built into t he very fabric of the world."
p29 "Like energy or temperature, entropy tells us something about the particular state of a physical system; specifically, it measures how disorderly the system is."
p30 "A big part of our task in this book will be to explain how the single idea of entropy ties together such a disparate set of phenomena, and then to dig more deeply into what exactly this stuff called 'entropy' really is, and why it tends to increase. The final task - still a profound open question in contemporary physics - is to ask why the entropy was so low in the past, so that it could be increasing every since."
p31 "The arrow of time, therefore, is not a feature of the underlying laws of physics, at least as far as we know. Rather, like the up/down orientation space picked out by the Earth, the preferred direction of time is also a consequence of features of our environment. In the case of time, its not that we live in the spatial vicinity of an influential object; it's that we live in the temporal vicinity of an influential event: the birth of the universe. The beginning of our observable universe, the hot dense state known as the Big Bang, had a very low entropy. The influence of that event orients us in time, just as the presence of the Earth orients us in space."
p32 Section "Nature's Most Reliable Law", the second law of thermodynamics. Eddington quote "if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation."
p32 C P Snow "A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics, the law of entropy. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: 'Have you read a work of Shakespeare?'."
p33 Story of Boltzmann, Clausius and Carnot and their proposals regarding entropy starting 1877. At this time
p33 Clausius in 1850 understood that a law of nature was involved and formulated it as "heat does not spontaneously flow from cold bodies to warm ones."
p34 Clausius coined the term entropy in 1865 and expressed it in the Q/T form. He showed that the tendency for heat to flow from a hot object to a cold one is equivalent to saying that the entropy of a closed system would only go up or remain the same, never go down.
p37 Boltzmann had atoms now, and formulated a quantitative expression for entropy.
p37 "Entropy is a measure of the number of particular microscopic arrangements of atoms that appear indistinguishable from a macroscopic perspective."
p37 "In an isolated system entropy tends to increase, because there are more ways to be high entropy than to be low entropy."
Carroll gives a good concise history of the development of the concept of entropy. Part of it is summarized in the graphic above.
p38 "Entropy, quite literally, makes life possible." There are a lot of valid points surrounding this extraordinary statement, but in my mind not enough to justify such an extreme statement. He rightly points out that at or near equilibrium, life would not be possible since nothing much of a creative nature could happen.
p39 Introduces Lord Kelvin and the idea of the heat death of the universe.
p40 Thomas Pynchon short story "Entropy".
p41 "Ultimately, the reason why we can form a reliable memory of the past is because the entropy was lower then." ?! I think the top paragraph diverges from the evidence, but concludes that the universe was ordered in a certain way. That I'll buy, and I think it was because it was created that way.
p41 Last paragraph discussion of cause and effect as related to an increase in entropy.
p42 Discussion of "possibilism": the current moment exists, and the past exists, but the future does not (yet) exist. Contrasts with "block time" where entire space-time manifold exists, past, present and future being equally real.
p43 "If we knew the precise state of every particle int he universe, we could deduce the future as well as the past." I doubt that! This theoretical physicist is not taking as fact the probabilistic view of the wave function? And he talks about vacuum fluctuations later?
p43 "The punch line is that our notion of free will, the ability to change the future by making choices in a way that is not available to us as far as the past is concerned, is only possible because the past has a low entropy and the future has a high entropy. The future seems open to us, while the past seems closed, even though the laws of physics treat them on an equal footing." Interesting that he seems to be accepting the possibility of free will, when the thoroughgoing philosophical materialists conclude like Mlodinow that "our thoughts are as determined as the orbits of atoms."
p43 "treatment of the future as different from the past has no basis in the laws of physics" - he has stated this many times already, but it seems rooted in classical determinism.
3.The Beginning and End of Time
p45 Pooh-poohs both balloon and raisin bread pictures of the expansion of the universe.
p45-49 Surveys the expanding universe
p49 Starts Big Bang discussion
p50 Pooh-poohs the beginning of time and space at the Big Bang, a reasonable discussion of our ignorance back past a certain point where physical laws break down and we need quantum gravity.
p51 Prefers view of the Big Bang as a phase transition. Big Bang: that moment just before our current cosmology becomes relevant.
p53 Uses 1 part in 100,000 anisotropy in CMB WMAP image. He says that even smaller scales were very smooth, gravity having turned up the contrast knob.
p54 Mentions Lemaitre - no special place, but a special time at the Big Bang
p56 1998 dark energy and the acceleration of the expansion, Saul Perlmutter and Brian Schmidt - Carroll was office mate of Schmidt at Harvard in the early 1990s.
p58 Claims dark energy is approximately constant in space and time. Associates it with "vacuum energy" which he equates to a "cosmological constant" "a minimum amount of energy inherent in the fabric of space-time itself."
p59 Vacuum is "alive with virtual particles"
p59 "These virtual particles are not especially mysterious or hypothetical - they are definitely there, and they have measurable effects in particle physics that have been observed many times over."
p60 We can examine the contributions to the vacuum energy of virtual particles up the the energy where quantum gravity becomes important, the Planck energy of about a billion joules, and "The result is a complete fiasco." It's larger than the experimental value by 10120! The "cosmological constant problem".
p60 At the recombination time the energy density in matter was about a billion times larger than the vacuum energy. Today they are somewhat comparable.
p61 The density of vacuum energy is unchanging as the universe expands.
p61-62 Black holes evaporate - Hawking.
p62 The entropy of the universe. There are some keys to his thinking here - can't quite pin down his thinking.
p62 "Given perfect knowledge of the laws of physics, the question "Why has the universe evolved in the fashion it has?" is equivalent to "Why were the initial conditions of the universe arranged in the way that they were?" But that latter formulation is already sneaking in an implicit notion of time asymmetry, by privileging past conditions over future conditions. If our understanding of the fundamental, microscopic laws of nature is correct, we can specify the state of the universe at any time, and from there derive both the past and the future. It would be better to characterize our task as that of understanding what would count as a natural history of the universe as a whole."
p62 "cosmologists have underappreciated the importance of the arrow of time, since it is arguably the single most blatant fact about the evolution of the universe."
p63 Puts relative numbers to the entropy of the universe.
p64 The low entropy of our universe near the Big Bang leaves us with two basic possibilities:
He makes clear that his preference is #2 "I think it would be more elegant - nearly inevitable result of a set of dynamical laws." This brings him to the point of attributing "agency" to the laws, but the laws I know about don't create anything, they just describe what happens in the system that has already been initiated.
Part II: Time in Einstein's Universe
4. Time is Personal
p67-72 General conceptual introduction to relativity
p81 E=mc2 doesn't apply to light or dark energy
5. Time Is Flexible
p83 Newtonian mechanics and Maxwell's equations incompatible
p84 Gravity not really a "force" at all but a feature of space-time itself - the curvature of space-time.
p85 "deflected by force of gravity" really just following a space-time line. Straight line in space-time maximized time on clock.
p86 38 microseconds per day effect on GPS, actually they make the clocks run appropriately more slowly according to Carroll.
p87-88 "In general relativity, energy is not conserved." Spends a page defending that assertion.
p88 Discusses black holes
p89 interesting discussion of black hole event horizon. Light cones tilted so that you have to travel faster than c to escape.
p90 For black hole of 1 solar mass, time from event horizon to singularity is about a microsecond.
p90 Bottom paragraph I don't understand. Need to think about Figure 20.
p92 "It's the same reason why we believe in free will." Interesting that he believes in free will without theism. "Black holes turn out to provide the strongest connection we have between gravitation and entropy."
6. Looping Through Time
p97 Story of Godel and Einstein.
p104 After discussion of time travel and closed timelike paths, returns to the discussion of free will. Interesting, his commitment to free will. Closed timelike curves seem to him to imply predestination, which he is unwilling to accept.
p106 Closed timelike curves - probably don't (and can't) exist.
p106 Flatland - handful of solutions to Einstein's equations that feature timelike curves.
p106 Equations of space-time enormously difficult to solve in any real world situation.
p107 Discusses Abbot's Flatland, Gott's model of a closed timelike path in flatland.
p108 Talks about Guth and Farhi and the group's calculations about timelike loops.
p116 Hawking's "Chronology Protection Conjecture", laws of physics prohibit the creation of closed timelike curves.
p116 Absence of time machines necessary for a consistent arrow of time.
Part Three: Entropy and Time's Arrow
7. Running Time Backward
p120 Story of LaPlace, LaPlace's statement on determinism
p121 Brings up conservation of information
p112-135 Conditions for time reversal
p136 Kaon - antikaon
p138 Lee, Yang & Wu on non-conservation of parity
p139 Cronin & Fitch Kaon experiment
p140 Return to conservation of information
p142 Reversible underlying laws give rise to macroscopic irreversibility
8. Entropy and Disorder
p143 Irreversible processes - egg to omelet is my favorite.
p144 Clausius, Maxwell and Thomson worked on determining the macroscopic from the microscopic
p145 Boltzmann's work in 1780s
p146 Models gas diffusion throughout hole in partition and gives numbers for 2000 particles.
p150 Entropy - number of ways to rearrange and leave macroscopically the same - not quite right. Entropies of two systems which are merged is the sum of the individual entropies. The logarithm has this property. Boltzmann sought to derive the entropy and finally reaches the S=klnW expression.
p153 Shows approach to equilibrium. Has table for 2000 particles.
p154 Feynmann's wet towel story and "wetness equilibrium".
p157 Pool balls - any configuration equally unlikely. Boltzmann's W "the number of ways we can rearrange the microscopic constituents of a system without changing its macroscopic appearance". Introduces microstates and macrostates. W is the "number of microstates corresponding to a particular macrostate."
p163 Uses Benjamin Button story and White Queen in Alice.
p164 "We often say that entropy measures disorder. That's a shorthand translation of a very specific concept into somewhat sloppy language - perfectly adequate as a quick gloss, but there are ways in which it can occasionally go wrong. Now that we know the real definition of entropy given by Boltzmann, we can understand how close this informal idea comes to the truth."
"The question is, what do you mean by "order"? Thats not a concept that can easily be made rigorous, as we have done with entropy. In our minds, we associate 'order' with a condition of purposeful arrangement, as opposed to a state of randomness. That certainly bears a family resemblance to the way we've been talking about entropy. An egg that has not been broken seems more orderly than one that we have split apart and whisked into a smooth consistency."
"Entropy seems naturally associated with disorder because, more often than not, there are more ways to be disordered than to be ordered. A classic example of the growth of entropy is the distribution of papers on your desk. You can put them into neat piles - orderly, low entropy - and over time they will tend to get scattered across the desktop - disorderly, high entropy. Your desk is not a closed system, but the basic idea is on the right track."
"But if we push too hard on the association, it doesn't quite hold up. " This whole discussion through p166 is quite good, I think.
p167 A recurring theme: "The real laws of physics seem to be reversible at a fundamental level." Comes out of example of pool table with a sticky wall on one side.
p167 "reversibility is based on conservation of information." Joseph Liouville and "Liouville's theorem".
p166-169 Principle of indifference - we assume all microstates equally probable.
p169 "the real reason we use the principle of indifference is that we don't know any better. And, of course, because it seems to work." In this discussion he brings up systems that are "ergodic" and pass through every possible state - many have tried to prove such systems.
p170 Josiah Willard Gibbs defined entropy in terms of what we don't know.
p172 Section on "Proving the Second Law" In 1872 at the age of 28, Boltzmann put forward the "H-Theorem" But his theorem about entropy inevitably increasing gets to an irreversible result, when the laws of physics seem to be time reversible. Objection raised in 1876 by Josef Loschmidt (Loschmidt's reversibility objection) after comments to the same effect by William Thomson (Lord Kelvin) and James Clerk Maxwell. I need to read this again to really get the point. Has to do with Boltzmann's assumption of molecular chaos - assumed uncorrelated before a collision, but that introduces a time asymmetry.
p174 Boltzmann: "He proved that entropy would never decrease, if we neglect the circumstances under which entropy would decrease."
p174 In section "When the laws of physics aren't enough" argues that the entropy has to be at least partially a consequence of the initial conditions.
p176 "The Past Hypothesis" "is the one profound exception to the Principle of Indifference that we alluded to above." Must assume that the universe began in a state of very low entropy.
p176 "The Principle of Indifference would have us imagine that, once we know a system is in some certain macrostate, we should consider every possible microstate within that macrostate to have an equal probability. This assumption turns out to do a great job of predicting the future on the basis of statistical mechanics. But it would do a terrible job of reconstructing the past, if we really took it seriously."
"Boltzmann has told us a compelling story about why entropy increases: There are more ways to be high entropy than low entropy, so most microstates in a low-entropy macrostate will evolve toward higher-entropy macrostates. But that argument makes no reference to the direction of time. Following that logic, most microstates within some macrostate will increase in entropy toward the future but will also have evolved from a higher-entropy state in the past."
Sorry, I'm just not getting that. If you took a sequence of states at different times, you would find that those before would have lower entropy, those later higher entropy, with no expectation that this pattern would change as you proceeded either direction in time.
p177 Has diagram of a cusp in a time curve with a low entropy point, which proceeds toward higher entropy both past and future, approaching an equilibrium in both directions. But I certainly don't know of any system like that.
p178 "Why is the Past Hypothesis true?" "Why did the universe have a low entropy near the Big Bang?"
9. Information and Life
p180 Ties memory to low entropy in the past or the Second Law. "all the important ways in which the past differs from the future can be traced to a single underlying principle, the Seccond Law of Thermodynamics. This implies that our ability to remember the past but not the future must ultimately be explained in terms of entropy, and in particular by recourse to the Past Hypothesis that the early universe was in a very low-entropy state. Examining how that works will launch us on an exploration of the relationship between entropy, information and life."
This seems to me to be am extraordinary philosophical stance. Certainly I see that in certain ways, entropy can be described as "time's arrow", but I have never entertained the idea that the whole idea of time could be subsumed by entropy and the second law. It seems to me that the Second Law does indeed describe the processes by which systems evolve in time, but space-time seems more fundamental.
p182 Expresses confidence in a memory dependent upon the Past Hypothesis - a very low entropy from past to here.
p183 Waxes philosophical about the "Past Hypothesis" as completely necessary.
p184 Interesting Cause and Effect section
p186 Story of Maxwell's demon with a diagram. Rolf Landauer in 1961 and Charles Bennett in 1982 answered the paradox.
p189 Information as physical. Szilard approach to Maxwell's demon. 1940's Shannon
p191 Information is the difference between the maximum possible entropy and the actual entropy of a macrostate.
p191 Comments about creationists and some of their statements about the second law of thermodynamics.
p192-193 For every high energy photon received from the Sun, the Earth emits 20 low energy photons. The temperature of the Sun is about 20 times the temperature of the Earth. 20 times as many photons translates to 20 times the entropy, so the Earth emits the same amount of energy that it receives, but with 20 times the entropy.
p194 Schrodinger "What is Life?" where he posited some kind of "aperiodic crystal" to contain the information of life. "This insight helped inspire Francis Crick to leave physics in favor of molecular biology"
p195 Schrodinger suggested that the "essence of life: staving off the natural tendency toward equilibrium with one's surroundings."
p196 Section on free energy
p200 Kolmogorov complexity algorithm
10. Recurrent Nightmares
p202-206 Nietzsche, Poincare, theories of recurrent universe, chaos
p207 Zermelo recurrence objection
p209 Back to the conclusion that the "past hypothesis" is necessary in context of Boltzmann and Zermelo. Boltzmann's "assumption A" which is really the past hypothesis.
p210 Why do we find ourselves living in the part of history of the universe in the relatively recent aftermath of the low entropy state? Dilemma of infinite age. Boltzmann's three ways, one of which with the Big Bang implies a low entropy state.
p212 Begins to produce a picture of the fluctuations from equilibrium which will provide a way to treat present universe as the return from a fluctuation.
p213 The anthropic appeal
p214 Are we on the return from a giant entropy fluctuation?
p214 His summary of the anthropic principle. He is very skeptical of its value, even resistive to it. You can see him turning away from the anthropic principle toward the multiverse. It is a good discussion, but emerges from a prior commitment to philosophical materialism.
p215 Invokes Boltzmann in support of the multiverse. Good long quote of Boltzmann who envisions the universe as much larger than our observation and comes to a picture of our observable universe as an extraordinary improbable state.
p216 "We live in the aftermath of one exceptionally large fluctuation." We will call the direction toward lower entropy "past" and the direction toward greater entropy "future".
p217 Democritus and Leucipus atomists and materialists. Also invokes Lucretius, all arguing against purpose.
p218 Quote of Lucretius which sounds almost Job-like "surely the atoms did not hold council, assigning order to each, flexing their keen minds with Questions of place and motion and who goes where." good quote on what Carroll calls "the swerve".
p218 "the task was to explain the emergence of the apparent complexity we see around us without appealing to an overall design, but simply by considering the essentially random motions of atoms." The Boltzmann-Lucretius scenario.
p221 Section on "Boltzmann Brains". He begins to assert his strong feelings against the anthropic principle. He writes confidently and aggressively here, without much real evidence that I can see to support the assertions.
p222 Cites Eddington. OK, I think he is revealing his true feelings here. He sees our existence and a whole universe that started far from equilibrium as unthinkable. Departures from equilibrium would be localized and floating in a vast sea of near equilibrium.
p222 Does conclude that the idea of our universe as a random fluctuation about equilibrium in eternal space-time is falsified. The concept of the "Boltzmann Brain". They talked a good bit about Boltzmann Brains in the Feb 2014 Greer-Heard Forum, but I felt it was mostly a dialog between Carroll and Craig which went over the heads of most of the rest of us. But p222 does give a succinct summary of what is meant.
p223 Curious that he introduces the term "warrant" like he may have read the philosophy of Plantinga and others.
p224 Feynman quote is a great summary of his past several pages. "From the hypothesis that the world is a fluctuation, all of the predictions are that if we look at a part of the world we have never seen before, we will find it mixed up, and not like the piece we just looked at. If our order were due to a fluctuation, we would not expect order anywhere but where we have just noticed it .."
"We therefore conclude that the universe is not a fluctuation, and that the order is a memory of conditions when things started. This is not to say that we understand the logic of it. For some reason, the universe at one time had a very low entropy for its energy content, and since then the entropy has increased. So that is the way toward the future. That is the origin of all irreversibility, that is what makes the processes of growth and decay, that makes us remember the past and not the future, remember the things which are closer to that moment in history of the universe when the order was higher than now, and why we are not able to remember things where the disorder is higher than now, which we call the future."
This statement by Feynman has elements of what appears to be Carroll's view of time, that it is just the progress from low entropy to high.
p226 "The universe we see is not a fluctuation - at least, to be more careful, a statistical fluctuation in an eternal universe that spends most of its time in equilibrium. So that's what the universe is not; what it is, we still have to work out."
Interesting quote, since back on p213 and p216 he has discussion and illustrations that seem to be favorable to our universe being a relatively localized fluctuation in an otherwise high entropy multiverse. I had presumed that this was the way he was going to explain why our universe had such a low entropy near the Big Bang.
p226 A paragraph on Boltzmannn and his suicide. A tribute to Boltzmann's brilliance, far ahead of his time.
"When it comes to explaining the low entropy of our early universe, we won't ever be able to say, 'Boltzmann was right', because he suggested a number of different possibilities without ever settling on one in particular. But the terms of the debate were set by him, and we're still arguing over the questions that puzzled him more than a century ago."
11 Quantum Time
p228 View of classical physics and leadup to quantum.
p230 "In the classical world, it might be difficult to obtain a precise measurement of some quantity; we need to be very careful not to disturb the system we're looking at. But there is nothing in the classical world that prevents us from being careful. In quantum mechanics, on the other hand, there is an unavoidable obstacle to making complete and nondisruptive observations of a physical system. It simply can't be done, in general. What actually happens when you try to observe something, and what actually counts as a 'measurement' - those are the locus of the mystery. This what is helpfully known as the 'measurement problem', much as having an automobile roll off a cliff and smash into pieces on the rocks hundreds of feet below might be known as 'car trouble'. Successful physical theories aren't supposed to have ambiguities like this; the first thing we ask about them is that they be clearly defined. Quantum mechanics, despite all its undeniable successes, isn't there yet."
p231 measurement in quantum mechanics is an irreversible process
p231-232 good overview of classical and quantum mechanical differences
p232-238 discusses wavefunction with a cat as the observable. Shades of Schrodinger's cat.
p238 Starts discussion of Copenhagen and "many worlds" approaches to quantum mechanical measurement. Expresses his dissatisfaction with the Copenhagen view.
p242 moves to the uncertainty principle
p244-246 Discusses "many worlds" approach and quantum entanglement.
p251 Brief history of the many worlds approach.
Part Four: From the Kitchen to the Multiverse
12 Black Holes: The Ends of Time
p259 Introduction to Stephen Hawking
p261 Excellent section "Black Holes are For Real". Responding to the question about how you can see a black hole, he has an excellent sentence "But we can see what happens to things around them, and the environment near a black hole is sufficiently unique that we can often be confident that we have located one." Good general information resource on black holes.
p266 Bekenstein's entropy, some history about Wheeler.
p268 Hawking radiation. Work of Hawking and Penrose. Event horizon rips apart virtual particle pairs with one trapped, the other escaping as real particle.
p273 Surface gravity greater for smaller mass black holes.
p274 Black hole information loss paradox.
p278 The holographic principle. Gerard t'Hooft, Leonard Susskind and Raphael Bousso.
p284 String theory surprise
13 The Life of the Universe
p288 "A truly closed physical system with a very low entropy is surprising and suggests that something bigger is going on." I would guess that this is the kind of reasoning that inclines him toward the multiverse, and I would have to agree that this is one of the strongest arguments for the multiverse.
p295 Discussion of Penrose
p299 Evolution of entropy following Penrose
p301 After looking at some of the probabilistic arguments: "The conclusion is perfectly clear: The state of the early universe was not chosen randomly among all possible states. Everyone in the world who has thought about the problem agrees with that. What they don't agree on is why the early universe was so special - what is the mechanism that put it in that state?"
p302 Penrose thinks early state was a black hole.
p308 More on vacuum energy.
14 Inflation and the Multiverse
p315 Story of Guth and his "double box" note, the proposal of inflation.
p317 "But as a matter of observational fact, the universe looks very flat. As far as anyone can tell, there is no measurable curvature in the universe today at all." This is the "flatness problem".
p318 " The flatness problem bears a family resemblance to the entropy problem we discussed in the last chapter. In both cases, it's not that there is some blatant disagreement between theory and observation - all we have to do is posit that the early universe had some particular form, and everything follows nicely from there. The problem is that the 'particular form' seems to be incredibly unnatural and finely tuned, for no obvious reason. We could say that both the entropy and the spatial curvature of the early universe were just small, and there's no explanation beyond that. But these apparently unnatural features of the universe might be a clue to something important, so it behooves us to take them seriously."
p318-319 More of the interesting story of Guth and his inflation proposal. He was pursuing ideas of magnetic monopoles, grand unified theories.
p320 More about inflation.
p322 Inflation and the horizon problem
p322-323 Discussion of the transparency point.
p324 Excellent paragraph on the horizon problem: "The horizon problem is this: How did those widely separated points know to have almost the same conditions? Even though they are all within our cosmological horizon, their own cosmological horizons are much smaller, since they are much closer to the Big Bang. These days it's a standard exercise for graduate students studying cosmology to calculate the size of the cosmological horizons for such points, under the assumptions of the standard Big Bang model; the answer is that points separated by more than about one degree of the sky have horizons that don't overlap at all. In other words, there is no event in space-time that is in the past of all these different points, and there is no way that any signal could be communicated to each of them. Nevertheless, they are all share nearly identical physical conditions. How did they know?"
He adds a note, p407, that I need to think about some more. "You might think that, because the Big Bang itself is a point, the past light cones of any event in the universe must necessarily meet at the Big Bang. But that's misleading. For one thing, the Big Bang is not a point in space - it's a moment in time. More important, the Big Bang in classical general relativity is a singularity and shouldn't even be included in the space-time; we should talk only about what happens after the Big Bang. And even if we included moments immediately after the Big Bang, the past light cones would not overlap."
p324 Points out that the horizon problem is closely connected to the entropy problem. "Having the entire early universe share very similar conditions is a low-entropy configuration, as there are only a limited number of ways it can happen."
p324 Excellent paragraph on inflation as well. He really hit a homerun with this particular page in the book.
"Inflation seems to provide a neat solution to the horizon problem. During the era of inflation, space expands by an enormous amount; points that were initially quite close get pushed very far apart. In particular, points that were widely separated when the microwave background was formed were right next to each other before inflation began - thereby answering the 'How did they know to have similar conditions?' question. More important, during inflation the universe is dominated by dark super-energy, which - like any form of dark energy - has essentially the same density everywhere. There might be other forms of energy in the patch of space where inflation begins, but they are quickly diluted away; inflation stretches space flat, like pulling the edges of a wrinkled bedsheet. The natural outcome of inflation is a universe that is very uniform on large scales."
While this paragraph gives some neat explanation for the inflation concept, it seems to have some highly speculative content. This is the first time I have seen inflation explained as a result of "dark super-energy", although it has some plausibility.
p328 "Besides offering a solution to the horizon, flatness and monopole problems, inflation comes with a completely unanticipated bonus: it can explain the origin of the small fluctuations in the density of the early universe, which later grew into stars and galaxies." He attributes this to "simple, and inevitable: quantum fluctuations" The simple I don't get and the 'inevitable' is a really weird philosophical statement!
p330 His version of the multiverse.
p333 "What good is inflation?" with a summary paragraph. That summary paragraph is wildly speculative and envisions our universe as a small patch of a larger manifold that suddenly begins to inflate, so that the properties of the inflated patch become our universe with very uniform properties. That gets him around the fine-tuning requirement, which explains his aversion to fine-tuning arguments.
He further comments on this page "the goal is to explain why a universe like the one we find ourselves in would arise naturally as a result of dynamical processes in the early universe." So there is a clear philosophical commitment to philosophical naturalism, demanding a mindless and purposeless process for producing the universe and us.
p334-338 Further discussion of the inflationary scenario that I need to think about more. He is clearly proceeding from a "scientistic" a priori philosophical bias which is quite alien to me, but he suggests that the majority of contemporary cosmologists are even more extreme in that philosophy, taking the presumption that our universe is but a small "comoving patch" in a much more vast multiverse as a given.
p334 More on the "dark super-energy". "Our patch finds itself in a configuration where it is very small, and dominated by dark super-energy; other parts of the universe might look dramatically different, but who cares?" Later he comments "clearly there is more to the story", but which he means something very different that I would mean by such a statement. It looks like he takes the extremely low entropy of our universe near the Big Bang as something near to a proof that our universe is but a tiny part of the whole. He models the entropy of our "patch" just prior to inflation. Although my philosophical bias is profoundly different from his, he does seem to honestly bang his head against the many problems and unknowns attendant to the early universe or multiverse.
15 The Past Through Tomorrow
p339 Overall summary
p340 States the hypothesis: "Deep down, the fundamental laws of physics simply aren't reversible." Remarkable in that throughout the book he has hammered on the reversibility of the laws of physics.
p341 "Space of states" not clear to me. Comments about possible eternal time parameter.
p343 Possibility that the irreversibility of the laws of physics explains the arrow of time?
p371 "Here we are, claiming to be engaged in the practice of science, attempting to 'explain' the observed arrow of time in our universe by invoking an infinite plethora of unobservable other universes."
p374 As close as he comes to a statement of his personal philosophy. Scientism it is, but not as outrageous as the scientism of Atkins. Presumes the Copernican principle and complete purposelessness of the universe.
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