Friday Science: Hawking 10 (Unification)

It always feels good to finish a book. Here is the last review of Stephen Hawking's A Brief History of Time.

Chapter 1: Heliocentric
Chapter 2: Spacetime
Chapter 3: Expansion of the Universe
Chapter 4: Uncertainty Principle
Chapter 5: Elementary Particles and the Forces of Nature
Chapter 6: Black Holes
Chapter 7: Black Holes Ain't So Black
Chapter 8: The Origin and Fate of the Universe
Chapter 9: The Arrow of Time

Chapter 10: The Unification of Physics
As the title suggests, Hawking in this chapter is looking for a grand unification theory (GUT). He spends a little time on string theory, which is probably where he put his bet at one point. My sense is, however, that enthusiasm for string theory has waned these last few years as some of the particles it predicts have not been discovered during tests that should have produced some.

• The difficulty is to combine general relativity with quantum mechanics.
• He mentions old problem of renormalization. The math says "infinity," but we know what it should be from experiment. So you just substitute the experimental value and keep going.
• String theory: open string, closed string, two strings join. Two strings separate. Graviton's cross. Strings, strings, strings.
• String theory suggests there may be either ten or twenty-six dimensions. We don't see the others because they're two small.
• He goes into the anthropic principle again. Life can only exist when three dimensions predominate, so we're just lucky.
• It would take too much energy to find out what it would have been like near the big bang.
• Even a GUT would not predict everything about the future--uncertainty principle, some equations are just too hard to solve.

Here endeth Hawking.

Friday Science: Hawking 9 (The Arrow of Time)

Friday reviews of Stephen Hawking's A Brief History of Time so far.
Chapter 1: Heliocentric
Chapter 2: Spacetime
Chapter 3: Expansion of the Universe
Chapter 4: Uncertainty Principle
Chapter 5: Elementary Particles and the Forces of Nature
Chapter 6: Black Holes
Chapter 7: Black Holes Ain't So Black
Chapter 8: The Origin and Fate of the Universe

Chapter 9: The Arrow of Time
Getting close to the end. The problem we are dealing with in this chapter is the fact that, on the quantum level, nothing prevents a forward or backward movement in time. In the macro-universe, time only can move in one direction. In the micro-universe, this simply is not the case.

The first reason for this is what Hawking calls the "thermodynamic" arrow of time. We easily identify with a cup shattering on the floor. We do not identify with a cup unfalling and unshattering.

Another arrow is the "cosmological" arrow. The universe is expanding. My sense is that Hawking, writing this book in the late 80s, hoped that eventually this expansion would stop and recontract, making possible an oscillating big bang of sorts. That view has largely been eliminated in the last twenty years

A third arrow he mentions is the "psychological" arrow. This one I am less convinced of. It seems to be related to the anthropic principle. Basically, he argues that our brains are just wired to see time moving in only one direction.

Short chapter. I'm sure I don't fully know the depth of some of what he is saying. But I think I know enough to know that subsequent developments have trashed some of what he said.

The universe has a prevailing arrow of time, based on the second law of thermodynamics and its expansion. On the micro-level, this may not always be the case.

Friday Science: Hawking 8 (Universe Origins)

Friday reviews of Stephen Hawking's A Brief History of Time so far.
Chapter 1: Heliocentric
Chapter 2: Spacetime
Chapter 3: Expansion of the Universe
Chapter 4: Uncertainty Principle
Chapter 5: Elementary Particles and the Forces of Nature
Chapter 6: Black Holes
Chapter 7: Black Holes Ain't So Black

Chapter 8: The Origin and Fate of the Universe
Here are some points of interest in this chapter:

• Hawking presented a paper at the Vatican in 1981 apparently arguing that the universe was finite but had no boundary, meaning no beginning.
• He recounts the path I've been trodding a lot lately. The universe started at a point, virtually infinitely hot. Then it cooled a little to where there were mostly electrons, photons, and neutrinos. About a hundred seconds protons and neutrons would start binding into deuterium and helium...
• George Gamow suggested in 1948 that we should be able to detect background radiation from this beginning. This was discovered in 1965.
• Then he builds to Alan Guth's idea of inflation. Why is the universe so uniform, but with significant fluctuations?
• He mentions two versions of the anthropic principle. He does not like the strong one, although I find it hard to distinguish the two versions. What he calls the strong one basically argues that the universe is the way we see it because otherwise we would not be here. The weak one seems more to say that in a universe there is bound to be life developing somewhere.
• He gets to Guth and inflation. In the hottest time of the universe, all the forces would have coalesced into a grand unification. Then gravity would separate out, then the strong force, then the weak force leaving the electromagnetic force working.
• He shares a little about some papers in Moscow. He's reminiscing. Aww.
• He ends the chapter with some suggestions toward a grand unified theory. This was in the late eighties so I'm not sure how helpful they are. Mainly, they have to do with imaginary time. I don't know enough to follow completely.
• "If Euclidean space-time stretches back to infinite imaginary time... One could say, 'The boundary condition of the universe is that it has no boundary' It would neither be created nor destroyed" (136).
• Hawking suggests that the imaginary time may actually be the real time. He suggests that while this universe looks like it had a beginning and will have an end, maybe this is an illusion. 
• Of course he ends the chapter asking then why we would need God.
• He seems to look to a big crunch. He was wrong.

Friday Science: Hawking 7 (Black Holes Evaporating)

Friday reviews of Stephen Hawking's A Brief History of Time so far.
Chapter 1: Heliocentric
Chapter 2: Spacetime
Chapter 3: Expansion of the Universe
Chapter 4: Uncertainty Principle
Chapter 5: Elementary Particles and the Forces of Nature
Chapter 6: Black Holes

Chapter 7: Black Holes Ain't So Black
Here we get quite a bit of Stephen Hawking's distinctive work. Some points of interest:

• Black holes are defined as the set of events from which it is not possible to escape, which basically begins the black hole at the event horizon.
• The paths of light at the event horizon must be parallel to each other but never meet. That also means a black hole can never decrease in area.
• This non-decreasing property is similar to entropy. Jacob Bekenstein in fact suggested that the area of the event horizon was a measure of the entropy of the black hole.
• Entropy has to do with the second law of thermodynamics. The entropy of an isolated system always increases. That is, disorder increases.
• If a black hole has entropy, it should have a temperature and it ought to emit radiation. But a black hole can't omit anything.
• So space isn't really empty. Particles and antiparticles emerge and annihilate. Near the edge of the event horizon, some get separated before they annihilated and go into the black hole. This gives the appearance of a black hole emitting a particle. 
• Meanwhile, a flow of negative energy into the black hole would reduce its mass. The universe is too young, but this process could eventually disintegrate a black hole into nothing.
• There may be some primordial black holes (very small). Some of them might be disintegrating about now. Some scientists are looking for final bursts of their disappearance.

Friday Science: Hawking 6 (Black Holes)

Friday reviews of Stephen Hawking's A Brief History of Time so far.
Chapter 1: Heliocentric
Chapter 2: Spacetime
Chapter 3: Expansion of the Universe
Chapter 4: Uncertainty Principle
Chapter 5: Elementary Particles and the Forces of Nature

Chapter 6: Black Holes
I hate it when I don't finish things. I'm about half way through Hawking's book but got sidetracked by the end of the semester.

• "Black hole" is a term coined by John Wheeler in 1969.
• The concept goes back even further. In 1783 John Mitchell suggested a sufficiently massive and compact star would not allow light to escape its gravitational pull.
• The Marquis de Laplace suggested the same thing just a few years later.
• In 1928 Subrahmanyan Chandrasekhar, on a boat to Cambridge to study with Sir Arthur Eddington, calculated how big a star could get after burning out.
• The principle here is the balance between the Pauli exclusion principle and the fact that nothing can move faster than the speed of light. When a star gets sufficiently dense, the repulsion of the exclusion principle becomes less than the gravitational attraction and the cold star would collapse in on itself.
• A cold star about 1.5 times the size of our sun would do so, a mass now known as the Chandrasekhar limit. (Lev Davidovich Landau came to similar conclusion about about the same time.)
• Stars less than the limit become white dwarfs, with a radius of a few thousand miles.
• Slightly more massive neutron stars can be supported by the exclusion repulsion between neutrons and protons. Radius of about 10 miles. 
• A pulsar is a special kind of neutron star that emits regular pulses of radio waves. Pulsars were discovered in 1967 by Jocelyn Bell at Cambridge.
• Above the Chandrasekhar limit, might such stars reduce to a singularity, a point. Chandresekhar faced strong opposition to the idea from people like Eddington and Einstein. 
• Oppenheimer before WW2 did some work on this in relation to light. At a boundary known as the event horizon, light cannot escape the black hole.
• "God abhors a naked singularity." In cosmic censorship, we can't see what goes on inside a black hole (Penrose).
• Roger Penrose and Stephen Hawking did a lot of work on black holes between 1965-1970, which are a little like space before the Big Bang. 
• Some solutions to the general relativity equations suggest wormholes through black holes to the other side of the universe or perhaps even passage back in time. But a human probably wouldn't survive.
• In 1967, Werner Israel, some non-rotating black holes end up spherical (a solution Karl Schwarzchild suggested in 1917). Penrose and Hawking showed that all non-rotating stars collapsing into a black hole end up spherical.
• In 1963 Roy Kerr postulated Kerr black holes, rotating black holes that end up in various shapes.
• "A black hole has no hair." Their final shape depends only on mass and rate of rotation, not on the shape the star had before collapse. As they collapse, they give off gravitational waves until they settle down.
• Black holes are detected by the gravitational pull they have on other visible stars under certain conditions (e.g., the emission of massive amounts of energy from the nearby star). Cygnus X-1 is a system that seems to have such a black hole. There's probably one at the center of our galaxy as well.
• Quasars are systems that emit enormous amounts of energy and may have massive black holes at their center.
• There could be some primordial black holes out there, formed in the early universe, smaller than our sun.
• Hawking discovered that black holes glow like a hot body. See next chapter.

Friday Science: Hawking 5 (Particles)

Friday reviews of Stephen Hawking's A Brief History of Time so far.
Chapter 1: Heliocentric
Chapter 2: Spacetime
Chapter 3: Expansion of the Universe
Chapter 4: Uncertainty Principle

Chapter 5: Elementary Particles and the Forces of Nature

Particle Discoveries

• Aristotle--matter can be divided endlessly (300s BC)
• Democritus--matter is made up of atoms (400s BC)
• John Dalton--revived atomic theory (1800s)
• Albert Einstein--Brownian motion confirms atoms (1905)
• J. J. Thomson--demonstrated electrons (late 1800s)
• Ernest Rutherford--atoms have a nucleus (1911)
• James Chadwick--discovered the neutron (1932)
• Murray Gell-Mann--Discovered protons and neutrons made up of quarks (1964)
• Six flavors of quark: up, down, strange, charmed, bottom, and top.
• P. A. M. Dirac--antiparticles and combined with special relativity (1928)
• Four categories of force carrying particles:
• The graviton is proposed as the basis for gravity, and gravitational waves have been discovered since Hawking wrote this book. Personally not sure that gravity is based on particles. Einstein didn't look at it that way.
• The photon is the basis for the second force, the electromagnetic force. It is much stronger than the gravitational force but can be either attractive or repulsive and works over smaller distances.
• The particles known as the W and Z mediate what is called the weak nuclear force, which is the basis of radiation. Abdus Salam and Steven Weinburg worked out a way to unify the electromagnetic and weak force into an electroweak force, moving toward grand unification.
• The gluon is the basis for the final force, the strong nuclear force. I believe that the unification of this force with the electroweak force has also been achieved since Hawking wrote his book. Gravity is what is left to unify.

Other Nuclear Characteristics

• Particles have spin. The options are 1/2, 0, 1, and 2. Particles of matter are particles of spin 1/2. Particles of 0, 1, and 2 give rise to the forces between matter particles.
• Pauli's exclusion principle says that two particles cannot be in the same state at the same time.

Friday Science: Hawking 4 (Uncertainty Principle)

Chapter 4 is fairly short and titled, "The Uncertainty Principle." I continue to be pleasantly surprised that, while I have never pushed through this book these last 25 years, I have basically covered all this ground elsewhere. Here are some bullet points on the chapter.

The Uncertainty Principle

• At the beginning of the 1800s, Laplace thought that science indicated a deterministic world. Hawking suggested this was resisted by people who believed God was involved in the world.
• He must mean scientific determinism, since there are plenty of theists who believe in divine determinism. 
• I have always found Hume and others to be the thickest of imbeciles on this point. Even if the universe were rigidly and mechanistically deterministic, that would not logically preclude God acting from the outside. This relates to my contention that both theist and atheist often do not understand the implications of ex nihilo creation, making a whole lot of analytic Christian philosophers look like idiots to me.
• 1900, Max Planck suggests that energy exists in quanta rather than in a continuous spectrum of energy.
• In 1926, Werner Heisenburg recognizes the uncertainty principle. The better you know the position of a particle, the less determined the momentum of a particle is and vice versa.
• Hawking was a positivist idiot, leading to a lot of confusion over the years as to what exactly the Uncertainty Principle might mean. He presented it in a moronic way.
• The way he presented it was as if it is because we cannot observe its position without messing up the momentum and vice versa. In other words, he went fallacy of ignorance on us. If we can't know it, it doesn't exist. Moron.
• The interpretation of the uncertainty I prefer is that these things do not have a specific state in the first place. When you observe a position or a momentum, you cause it to take on a specific state. In this sense, it is not indefinite because we cannot know it. We cannot know it because it is indefinite.

The Double Slit Experiment

• The second quantum paradigm shift he presents is the double-slit experiment. If you randomly shoot electrons at a grid with two slits, an interference pattern will emerge on a screen behind the grid, as if the electrons are a wave that goes through the two slits like water would and then adds and subtracts on the other side as the two emerging waves collide ("interference").
• But if you remove one of the slits, the emergence won't be like one wave. It will be like shooting particles through a slit.
• This is the idea that a particle is both a particle and a wave. de Broglie famously suggested that particles had pilot waves and thus that particles very literally were both particles and waves.
• Feynman suggested that the particle goes through both slits at the same time. 
• I don't have time to review, but to me the best explanation of this phenomenon is again, probabilistic. We cannot determine where any individual particle might go, but with one or two slits, the resultant average is what we observe with one or two slits. The probability is certain. The individual path is not.

Friday Science: Hawking 3 (Expansion of Universe)

I started Friday reviews of Stephen Hawking's A Brief History of Time.
Chapter 1
Chapter 2

Chapter 3: The Expanding Universe
1. I'm trying to figure out why I found this book so hard to read back in the nineties. My brain is a strange thing. Sometimes nothing will go in and then at other times a mess of complicated stuff goes right through. My breakthrough book was The Perfect Theory.

So chapter 1 talks about the earth at the center of the universe. We hear about Copernicus and Newton. He mentions relativity and quantum mechanics. Chapter 2 then gives Einstein's special and general theories of relativity. Chapter 3 is about the Big Bang.

2. This chapter makes it clear that Hawking sees how the Big Bang theory could play into belief in God but of course he rejects that. I'm always a little puzzled by Christians who have a really negative view of a big bang, because it seems to serve in strong support of the cosmological argument for the existence of God.

It must be the fact that most scientists think it took place a little less than 14 billion years ago. But that's not the same as evolution. John Piper, for example, is very open to an old earth even though he does not believe in evolution.

3. He talks a little about the process of discovering that we are inside a galaxy of stars and that there are millions of other galaxies of stars. Edwin Hubble in 1924 was the first to discover other galaxies. The two factors in the brightness of a star are its luminosity and its distance from us. Hubble's logic went like this:

• If we know the luminosity of what we're observing, we can figure the distance from us.
• We know the distance of some stars near us using geometry. Since we know the distance, we can determine the luminosity of various type of stars.
• [We can type them by analysis of the light they emit, their spectra.]
• Now, knowing the luminosity of these types, we can figure out the distances of distant ones.

4. Hubble discovered that the spectra of all the stars everywhere was shifted to the red end of the spectrum. That is to say, using the Doppler effect, they were moving away from us. In short, every point, everywhere in the universe, is moving away from every other part of the universe. The universe is expanding.

Indeed, the farther away a galaxy is, the faster it is moving away! The speed of expansion suggests whether 1) it will eventually slow down and pull back in on itself (cosmic crunch), 2) it will continue at a steady speed, or 3) it will expand faster and faster until there is a cosmic rip. The third seems to be the case. Alexander Friedmann in 1922, four years before Hubble, had predicted the expansion.

Einstein hated the idea of cosmic expansion, actually introduced a "cosmological constant" into his formulas to make it stop. :-) Ironically, he was right about the constant, but wrong about expansion.

5. In 1965, two men working for Bell Labs picked up a background radiation that was theoretically explained by a big bang. If the universe was infinitely old, it would have already dissipated. The universe must have been fantastically hot to begin with, but it has been cooling down ever since. If we extrapolate back, the universe would have begun as something like a "singularity," a single point.

"Dark matter" has also been proposed to explain why galaxies swirl as they do. The outer rims of the galaxies swirl at the same basic speed as other parts.

A lot of people didn't like the idea of an expanding universe. It played too easily into an argument for God. Fred Hoyle in England was a very charismatic propagator of a "steady state" theory, where matter is constantly being created. He's a study in how people believe as much because of the person selling stuff as on the basis of truth. He was wrong. Go away, charmer.

6. The chapter ends with Roger Penrose's discovery of the probability of black holes, and of course Hawking's work built off of him. Together they proposed that the universe had begun with such a singularity that then expanded in a big bang. Again, this idea faced a lot of resistance but, in the end, the math was the math.

The problem--still unsolved--is that general relativity and quantum mechanics don't fit together. This is no problem today because the cosmos is really big and the atom is really small. But before the big bang, the universe was immensely dense and immensely small. This is the biggest problem in modern physics.

Friday Science: Hawking 2 (Spacetime)

Last week I started Friday reviews of Stephen Hawking's A Brief History of Time.

Today I want to do a brief overview of the second chapter. The second chapter basically introduces spacetime, the theories of relativity. Here are some salient points:

• So Aristotle thought that you had to push a body in motion for it to stay in motion. Rest was the preferred state. This makes sense because friction slows down ordinary motion.
• But Galileo and Newton in the 1600s formulated a different law--a body in motion tends to stay in motion and a body at rest wants to stay at rest. This fact doesn't undermine God at all, but it does undermine one of Aquinas' arguments for God--God as the "prime mover," a concept Thomas Aquinas took from Aristotle.
• Another principle that Galileo and Newton formulated was the principle of relativity. Speeds are relative to each other. If I am going 30 mph on a train in relation to the ground and I throw a baseball forward at 30 mph, the baseball will be going 60 mph in relation to the ground.
• In the late 1600s, it was discovered that light moves very fast. 
• In the 1800s, it was discovered that light moves at a fixed speed. At first they thought that everything was moving through some sort of ether, but Michelson-Morley showed apparently not.
• So there was a problem. A light shone from the front of a moving train proves not to move faster than a light shone from the ground or from a space ship. The principle of relativity was in danger.
• Einstein solved this with his special theory of relativity (1905). Space contracts as you approach the speed of light, and nothing can move faster than the speed of light.
• Einstein came up with spacetime diagrams--time on the y axis, one dimension of space on the x-axis.
• This suggests that cause-effect relationships can only take place within a "light-cone" that could emerge from an event at a point in time. Say light moves out from a point at a time. It spreads out in a sphere from the point. But if we diagram this light's progress with time as the z axis and two dimensions as space, the light spreads out in a cone on our diagram.
• If you take that same concept and play it backwards in time, there is a cone of light that could arrive at this location at the time of the event. 
• These two light cones suggest the locations that could cause an event or be caused by an event. Because nothing can move faster than the speed of light, anything outside the cone in time or space could not have affected or be affected by the event at that point in spacetime.
• This theory messed up Newton's theory of gravity, because it connects force to distance. So if the distance changes, the gravity presumably would too.
• This problem eventually led to Einstein's general theory of relativity (1915). He supposed that gravity was not a force at all but rather a bending of space caused by mass. So what would normally be a straight line of motion looks like it curves because space itself curves. This made it possible to explain why Mercury's motion around the sun is a little different than Newton's theory would have predicted.

So this is all stuff I've read elsewhere.

Friday Science: Hawking 1

1. I can't say that I am a big Stephen Hawking fan. Obviously I never met him. I enjoyed the movie based on his life. I like a lot of the same stuff he did. He was funny on the Big Bang Theory.

I always got the impression that he was a bit of a donkey. Perhaps that's unfair. I imagine it must be hard when you're that much smarter than everyone else not to think that everyone else is an idiot. Of course so much smartness in one area can also entail immense density in other areas. I'll let God handle all that.

2. I bought A Brief History of Time a long time ago, probably from Joseph Beth Bookstore in Lexington, Kentucky in the early nineties. It came out in 1988. For some reason, I just couldn't get into it. I never made it out of the first chapter. It neither grabbed my attention nor did it get past the atrium of my thick head.

One of the benefits of a slowing metabolism is that I can read more and more. And with the death of Hawking this week, I sense it's time for me to buckle down and read this thing. There was a second edition in 1998 with an extra chapter, which I downloaded on Kindle to be able to get any revised thoughts he might have had.

The last ten years have not smiled on Hawking's intuitions. He had bet against the Higgs boson. He lost. In fact, he made one big discovery that, in retrospect, doesn't seem so startling at all. He was just the one to put it together. He concluded that black holes "evaporate" as it were. Yeah Hawking.

3. The first chapter is called, "Our Picture of the Universe." Some in this chapter is well known to those who are interested in these things. But there are a few surprises.

Here are the main points:

• Aristotle (300s BC) and Ptolemy (200s AD) both thought the world was a sphere, but they thought that the sun, stars, and planets revolved around the earth.
• Copernicus, Galileo, Kepler, and finally Newton came up with equations that worked a whole lot better, supposing that all these things revolved around the sun, with the moon only going around the earth.
• No one seems to have asked if the universe was expanding until the twentieth century. There was an assumption of a static universe. Why then did the universe not collapse under gravity? Newton thought by supposing an infinite universe, the pull would be equal in every direction. But this apparently is not how infinity works in this instance.
• Heinrich Olbers in 1823 then asked the question about line of sight. In a static universe, there should be stars everywhere we look, a completely lit sky.
• In 1929, Edwin Hubble discovered that the universe everywhere was moving away from us (red shift). This brought the question of the universe's beginning into science.
• The beginning had always been there in religion. Augustine suggested that God created time when he created the world. So it makes no sense to talk about time before the creation. As a side-note, this is the current convergence between science and faith--both believe that the universe had a beginning.
• The last part of the first chapter has two main points of interest. The first is the incompatibility of general relativity with quantum mechanics, the physics of the very large and the very little. Hawking longed for a "grand unified theory" or, as his biographical movie was titled, "a theory of everything."
• He also endorses Karl Popper's philosophy of science. Science should be oriented around falsifiability. A good theory is one that has not yet been falsified. You can never finally prove a scientific theory. A good scientific theory thus has two characteristics: 1) it must accurately describe a large class of observations and 2) it must make definite predictions about future observations that are not falsified.