Common Denominator

Back in the summer I wrote a little with a few to the Science and Scripture class I designed and have occasionally taught for Houghton University. This week I'd like to work a bit on Chapter 3 of a book proposal I'd soon like to submit somewhere. Chapter 3 is "Creation and the Big Bang."

Previous writings here on the blog have included:

2.1 Relationships between Science and Faith
2.2 Critical Realism and the Coherence of Truth
2.3 Approaches to Scripture
8.1 Approaches to Genesis 2-3
8.2 Situating Genesis 2-3
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3.1 General and Special Relativity
In 1905, a young patent clerk named Albert Einstein submitted a paper trying to resolve one of the unresolved conundrums of physics at that time. Experiments had shown that the speed of light remained constant no matter how fast or slow the source of the light was moving. This was baffling because it was not how other waves behaved. Scientists expected the speed of light to add to or subtract from the motion of its source, like a train’s headlight shining forward or backward. Yet every test showed that light’s speed never changed. 

Before Einstein, physicists expected light to behave like a projectile. If you shine a flashlight from the front of a moving train, its speed should be the train’s speed plus the speed of light. If you shine it backward, it should be the speed of light minus the train’s speed. But experiments had already shown that no matter how fast the train—or the Earth itself—was moving, the speed of light remained the same. This contradiction is what Einstein set out to resolve in 1905.

Einstein’s proposed solution was that space and time actually appeared to be longer or shorter depending on how something was moving in relation to you. If you were on the ground looking at a spaceship moving quickly in the sky, the length of the spaceship would be shorter to you than if it were sitting next to you (called “length contraction”). Similarly, a clock on the spaceship would move more slowly to you than a clock next to you (called “time dilation”). Mind you, if you were on the spaceship, space and time would appear normally. But they would appear differently to you if you were observing from a framework moving more slowly in relation to the spaceship.

This proposal came to be known as the theory of special relativity. Einstein proposed that space and time were not separate aspects of a particular context or framework. Instead, they were intimately connected to each other – later conceptualized as "spacetime." As an object approached the speed of light, its length in the direction of motion contracted from the standpoint of something moving much more slowly, and time appeared to slow down for it.

The mathematical equation for the contraction of length as something approaches the speed of light is known as the Lorentz contraction formula. Here is the formula.
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Textbox:

L=L0​ * sqrt (1−v^2/c^2​​)

Where:
L = Observed length of the moving object (contracted length)
L0​ = Proper length (length of the object at rest)
v = Velocity of the object relative to the observer
c = Speed of light (≈3.00×10^8 m/s)
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You can see that when something is moving much more slowly than the speed of light, there will be almost no observable difference in length. When the velocity is small, v is much smaller than c, making that part approach 0. The length equals the length proper. But as an object approaches the speed of light, the difference in length becomes very significant. The length of the object approaches zero.

In Einstein’s theory of special relativity, the speed of light becomes the universal speed limit. No object with mass can reach or exceed the speed of light, and the speed of light will be the same no matter how quickly or slowly an object is moving. This idea was counterintuitive. If you stood on top of a train and threw a rock forward, you would expect the speed of the rock from the standpoint of the ground to be the speed of the train plus the speed of the rock. In everyday life, speeds add up or subtract. But if you shine a flashlight forward or backward from the top of a train, the speed of light will measure exactly the same either way. It’s the space and time that changes relative to the ground.

In 1915, Einstein extended his theory to propose the general theory of relativity. The key new element was the impact of mass on spacetime. What Einstein proposed was that mass and energy curve spacetime. When light travels near a sun, it appears to curve because the mass is curving spacetime. This was confirmed in 1919 when Arthur Eddington observed that starlight was displaced passing near the Sun. The curvature of spacetime was altering the light coming past the Sun.

The conclusion, in effect, is that space and time are not rigid but can stretch, curve, and expand. Indeed, it would be confirmed in 1929 by Edwin Hubble that space is expanding. This is not just about the matter in the universe expanding, but the fabric of space itself is getting bigger. The current model sees the universe beginning with a point and then rapidly expanding into the vast universe we know today.

We will ponder these discoveries in relation to creation later in the chapter. It changes our view of creation from one where God puts materials into emptiness to one where God creates the emptiness itself. It may transform our sense of what a creation out of nothing (ex nihilo in Latin) might mean. Apparently, God did not create the universe out of zero but out of an empty set with no elements in it at all.

A little over four years ago, I found a great book on relativity. Peter Collier's A Most Incomprehensible Thing: Notes Toward a Very Gentle Introduction to the Mathematics of Relativity. I've gone through a little less than half of it.

His concept is to introduce all the math needed for special and general relativity in the first 100 pages or so. He tries not to assume that you've had any of the math beyond algebra. He does pretty well although I think you probably need to have done some of it before to get it.

BTW, I first saw an approach something like this in the summer of 1983 at Rose-Hulman. I was given a physics textbook by Marion and Hornyak that interspersed calculus lessons with the physics. I thought it was brilliant--introduce the background math as you need it. It's something like problem-based learning.

I've basically finished Hawking. So on Fridays I hope more or less to alternate between Susskind's book on quantum mechanics and Collier. I don't entirely have down everything from his 58 pages on special relativity. Maybe I'll go back at some point. But I want to move forward through his 180 or so pages on general relativity.

4.1 Introducing the Manifold
a. Special relativity functions on the basis of what is called "Minkowski" space, which is flat.

• 3.2.2 Time for a flashback. In chapter 3, he introduces Minkowski space or spacetime. In Newtonian mechanics, we talk about three-dimensional space, Euclidean space. 
• For special relativity, Einstein drew on the idea of four-dimensional space, with time as the fourth dimension (spacetime). 
• This is named for the German mathematician, Hermann Minkowski (1864-1909).
• In Minkowski space, parallel lines never meet, so it is still flat space.

In general relativity, space curves, so we need some new math. Einstein, with the help of David Hilbert, found this math in the work of the German Bernhard Reimann (1826-66).

b. In general relativity, matter and energy curve spacetime. Gravity is not considered a force but a property of the curvature of spacetime. The idea of a "Riemannian manifold" is used to model this. A manifold is a smoothly curved space that is locally flat.

It would be like an ant walking on an apple. The ant thinks it is walking straight, but it is curving around the apple. Such a path on a sphere or curved surface is called a geodesic.

A circle is a one-dimensional manifold. If you walk on the perimeter and the circle is large enough, it just seems like you are walking straight. A sphere is a two-dimensional manifold. We can speak of a manifold as n-dimensional when locally it can be described by n dimensions.

1. I finished the next chapter of Brian Greene's, The Fabric of the Cosmos, a few days ago. I was excited because he filled in some things about relativity I had never really read about.

My first two summaries were:

a. Overview
b. Spinning Space Buckets

2. Greene begins with a little flashback to James Clerk Maxwell, whose beautiful equations conquered electromagnetism in the 1800s.

Maxwell's Equations

Maxwell, following Faraday, suggested that electric fields and magnetic fields (which are deeply related) spread out through space. Maxwell was the one who suggested that light itself was an electromagnetic wave that acted in space. In the late 1800s, the theory was that there was an "ether" that light moved through, like the water that ocean waves move through or the air that sound waves move through.

The problem was that there was no evidence of such an ether. More importantly, the speed of light seemed to be the same no matter where it was found--coming from something stationary, coming from something moving. Normally, speeds add up. A person walking 3 mph on a train moving 50 mph is moving 53 mph in relation to the ground. But light on the ground is 3 x 10⁸ and light on the train is 3 x 10⁸ and light from a plane is 3 x 10⁸.

3. This is of course where Einstein comes in in 1905. Light can be the universal speed limit if space and time contract relative to speed. So the train is just a wee bit smaller from the perspective of the ground as it moves, to compensate for the speed of a flashlight shined by someone riding on it. You're not contracted on it, but it contracts relative to the person observing on the ground. A plane contracts relative the person on the ground a smidge more, so that the light shining from its wings also comes out exactly at 3 x 10⁸ mps, no matter who is looking from whatever frame of reference, moving or not.

"The combined speed of any object's motion through space and its motion through time is always precisely equal to the speed of light" (49).

4. There were some new insights for me into some of the more precise contours of Einstein's theory in this chapter. So not everything is relative in Einstein's theory. "Spacetime" as a whole is an absolute reference point. It can be sliced up differently, but it is the same loaf. Time is sliced up differently in some cases. Space is sliced up differently in some cases. But it is the same loaf of spacetime, which he concludes by the end of the chapter is a thing. (I didn't fully understand this last part of the chapter, but I feel like I'm making progress)

At one point of the chapter, Greene talks about how there is a totality to motion through spacetime. If something is more or less not moving in space, then all of its motion is through time. But if it has a velocity, then some of its motion through time is diverted to its motion through space and time moves more slowly. It's a fascinating idea (48).

5. The last part of the chapter turns to the question of acceleration. Einstein's special theory of relativity only applied to objects moving with a constant velocity. His general theory in 1915 turned to the question of gravity and acceleration.

The fundamental insight here was that gravity is really only a body following the contours of spacetime, which is warped by mass. So a planet bends spacetime, and gravity is basically our bodies wanting to follow the path of the warp. The ground stops us. Free fall is thus nothing different from weightlessness.

His field equations were the result:

1. I had been reading a book called, Our Mathematical Universe. I got through the part of the book that is generally accepted by physicists of the universe. But I came to realize that most view the rest of the book not only speculative, but perhaps bordering on the irresponsibly speculative.

So I've switched to another book on the current state of physics: Brian Greene's The Fabric of the Cosmos. Now he is also speculative. He obviously likes string theory and the idea of multiple universes. I'm not real fond of either but at least these are well-trodden paths.

So I thought I'd dawdle through this book for a few Fridays. Chapter one is called "Roads to Reality: Space, Time, and Why Things Are as They Are."

2. The progression of the chapter is roughly:

• Classical Reality
• Relativistic Reality
• Quantum Reality
• Cosmological Reality
• Past and Future Reality

The first half of this material will be familiar to the science enthusiast. He starts with Newton's sense that space and time are fixed entities in which we move. Einstein transformed our understanding here, for space and time become adjustable.

Entering the quantum reality apparently requires us to throw all our intuitions out the window. Here we encounter an idea I believe I first saw in Richard Feynman. Human intuitions were formed to help us survive and thrive in the macro-world. (I think you might say so whether you are speaking of how God made us or of how evolution developed us). The implication is that our "common sense" and our intuitions have no point of reference for the quantum world.

So the math seems to work, but no one really knows what it means. There are aspects of math itself that are are like this. Take Euler's famous equation from the 1700s: e^iπ - 1 = 0. What does it mean to raise something to the power of the square root of negative 1? I don't have a clue, but it works.

In the quantum world, at least so far, you cannot predict things. Rather, each event has a probability of happening. The universe is not determined. It is a game of chance.

3. When Greene gets to his section on cosmological reality, he covers some of the bases that I had been reading in Tegmark. One cosmological reality is the fact that the arrow of time only points in one direction. In theory, it would not have to be so. But the current sense of things is that something that happened very early in the history of the universe flipped the switch that makes time unidirectional.

Then he covers the big bang, the idea that the universe expanded rapidly into something like its current form from a much smaller version. He also mentions ideas new to me from Tegmark, which apparently have been around since the 70s and 80s--inflationary cosmology. This is a supposed period before the big bang when space itself expanded a million trillion trillion times in less than a millionth of a trillionth of a trillionth of a second.

4. What's missing is a grand unified theory that can reconcile both quantum mechanics and relativity. He seems to like Superstring theory and M theory. I sense increasing disgruntlement with these theories because there is no experimental data to suggest them whatsoever. They are completely hypothetical. Even Sheldon has given up on string theory. :-)

I'm dawdling through a book called, The Science of Interstellar, by the physicist Kip Thorne. Here's an interesting paragraph on GPS (slightly edited):

"Our smart phones rely on radio signals from a set of 27 satellites at a height of 20,000 kilometers.... Each radio signal... tells the smartphone where the satellite is located and the time the signal was transmitted... The scheme would fail if the signal were the true times measured on the satellite. Time at a 20000 kilometer height flows more rapidly than on earth by 40 microseconds each day and the satellites must correct for this. They measure time with their own clocks, then slow that time down to the rate of time flow on Earth before transmitting it to our phones."

Einstein predicted that time moves more slowly relative to locations close to heavy gravitational objects than it does relative to locations that aren't.

I suppose we all wish we could live several lives. In one of them, I would teach physics.

I finished the last few chapters of The Perfect Theory: A Century of Geniuses and the Battle over General Relativity and enjoyed it immensely. There's rarely a book that holds my attention, but this one pulled me on like a novel. I envy the brilliance of the characters in this story and wish I could even catch a glimpse of their thoughts.

Here are my earlier posts:
Chapter 1: Einstein in 1907
Chapter 2: The General Theory of Relativity Born
Chapters 3-6: Expanding Universes, Collapsing Stars, Cuckoo Einstein, and Steady States
Chapters 7-10: Black Holes and Gravitational Waves

Chapter 11: The Dark Universe
This chapter is dominated by the rise of the notion that the universe is full of dark matter, as well as the rise of the idea of dark energy. The key figure of the chapter is Jim Peebles of Princeton, who is still living at almost 80. He retired in 2000.

Peebles devoted most of his career to trying to figure out how the galaxies of the universe hang together. What role do galaxies play in Einstein's relativity? Basically, he explored the middle part, from the Big Bang to what they look like now. He was scooped trying to find background radiation from the Big Bang but he was a key predictor of it.

Throughout his career, he followed the dictum of his mentor, Bob Dicke--good observations trump mediocre theories. This would lead him and others to conclude that something they eventually called dark matter existed. Space should curve quickly but it is relatively smooth. Why does the universe lean Euclidean rather than non-Euclidean? The "cold dark matter" model or CDM suggested that 96% of the universe's stuff isn't seen because it doesn't interact with light.

Hard not to think of the ether that Einstein disproved... or did he?

At the same time, dark matter doesn't account for why the universe doesn't expand even more quickly. Since Einstein abandoned his constant (lambda), the idea that there might be a number in his equation to keep the universe from expanding had been considered an embarrassment. Einstein invented the possibility of a constant in his equations to keep the universe from expanding and he did it because he didn't like the idea of an expanding universe. It was a classic example of fiddling with the data because you didn't like the conclusion.

But by 1996, at a meeting meant to celebrate Peebles 60th birthday by a series of debates, the constant was brought up again as a possible explanation for why the universe wasn't flying apart. Michael Turner from the University of Chicago argued for it. Reluctantly, many cosmologists have finally accepted it.

Or have they? We are witnessing the rise of speculation about another dark entity--dark energy.

Chapter 12: The End of Spacetime
I've never had the slightest interest in string theory. It's a bizarre thing but the very idea that fundamental reality is a bunch of vibrating strings is really annoying to me. Quite irrational, I know. I side with Leslie Winkle in Big Bang Theory, an episode mentioned in this chapter. :-) As Einstein once said of pure math, I find string theory "superfluous erudition" that is pointless because it's untestable, narcissistic, and self-feeding.

I have a similar reaction to Stephen Hawking too. I admire his genius, of course. From what I can tell, he seems a lot smarter than Einstein ever was. His main contribution seems to be his finding that black holes radiate and ultimately evaporate, that they satisfy the second law of thermodynamics and have a temperature.

He's made and lost other bets. Most recently, he bet against the Higgs boson, which seems to have been discovered. Hawking would rather see confirmation of M-theory with its strings and membranes, multiverses and things popping in and out of nothing. Another book on my shelf is Lee Smolin's The Trouble with Physics, which seems to be part of a wave of "fed-up-ness" with string theory, a theory that has produced nothing of any tangible benefit for physics. I'm thinking it's a colossal waste of two decades.

Smolin is one of the founders of Leslie Winkle's "loop quantum gravity." The notion here is in part that space itself is quantized, that if you get down far enough, space doesn't exist on the quantum level. Now there's a more attractive theory.

Bryce DeWitt summarized the two main approaches to gravity in 1967. The covariant approach is that of the string theories. Gravity is just another force carried by a particle, dubbed the graviton. I'm not sure why I find this approach so annoying, maybe because it was a departure from classical general relativity. The canonical approach sees gravity as a function of the geometry of spacetime. It just seems so much more profound than some dinky particle or vibrating strings.

Chapter 13: A Spectacular Extrapolation
In this chapter Ferreira looks at the minority report, various alternative theories of quantum gravity that simply have not won the day or have been overlooked. The title of the chapter comes from Peebles' sense that while Einstein's general relativity has done well to describe the motion of planets within our solar system, it is quite spectacular to suggest it applies on the level of the universe.

Just as Newtonian physics broke down when things approached the speed of light or the subatomic level, so relativity breaks down on the quantum level and in the farthest reaches of space. Are we really to think that 96% of the universe is "dark matter" or is this as silly a suggestion as the ether was at the end of the 1800s? In Ferreira's words, general relativity is due for a fresh look (211). What about Dirac's work near the end of his life? Was Sakharov right to suggest that gravity emerges from the quantum nature of matter? (214) What of the discarded proposals of Milgrom and Bekenstein?

I wish I were smart enough to grasp all the nuances. I have a strong hunch is that we are in such deep waters here that a lot of the theorists don't even understand each other's proposals. Who will be the new Einstein and Hawking, the person who looks at these questions in completely fresh and different way, one that goes against all our sensibilities?

Chapter 14: Something is Going to Happen
So Ferreira hopes. Meanwhile, the US is falling behind because we aren't willing to spend the kind of money it takes to do this sort of research. We can't even get to the space station now without the help of the Russians--who by the way aren't helping us get there right now. Congress has cut funding to LISA (for measuring gravity waves). But at least the EU is still funding this sort of research.

Meanwhile, we're afraid CERN is going to cause a black hole to swallow up the earth because we saw Dan Brown's Angels and Demons.

The next installment of The Perfect Theory: A Century of Geniuses and the Battle over General Relativity. The book just came out this year but, amazingly, chapter 10 is already outdated!

Here are my earlier posts:
Chapter 1: Einstein in 1907
Chapter 2: The General Theory of Relativity Born
Chapters 3-6 Expanding Universes, Collapsing Stars, Cuckoo Einstein, and Steady States

Chapter 7: Wheelerisms
The namesake of this chapter is John Wheeler, who was known for turns of phrase like, "mass without mass" and "charge without charge." He's the one who popularized the term "black hole." He came up with the notion of a "wormhole" that bypasses space and time.

One of his main contributions to relativity was the way in which he helped rejuvenated interest in it. In the 1950s, physics was far more interested in quantum matters than general relativity. You could experiment with the quantum. General relativity was more a matter of distant space. Wheeler's support helped get some conferences on relativity going.

So there was the Institute of Field Physics, funded by a couple rich guys who were interested in gravity. Wheeler supported them and their appointment of Bryce DeWitt and his wife as the first employees. They set up meetings on gravitation in Chapel Hill, North Carolina, in the late 50s.

When Richard Feynman (quantum man extraordinaire and former student of Wheeler) arrived for the first conference in Chapel Hill not knowing directions, he helped the taxi driver figure out where it was by suggesting there would have been other attendees in the back of the taxi saying "gee mu nu, gee mu nu" (). In the words of Ferreira (author of the book), "The driver knew where to go" (109).  

Another meeting of this sort came out of oil money and the University of Texas at Austin. The result was the Texas Symposium on Relativistic Astrophysics, first held in 1963 in Dallas, just after Kennedy was shot. One of the things discussed at this symposium were "quasi-stellar radio sources" that were being detected by people like Maarten Schmidt. After the conference, they would be called quasars. They were super-massive objects that emitted lots of energy.

Chapter 8: Singularities
The 60s were the "Golden Age of General Relativity," according to Kip Thorne, one of Wheeler's students. Roger Penrose was a player in the decade. He showed that the collapse of stars after they burned out always ended in singularities or black holes, as they would come to be called.

This was also the decade where the background radiation of the universe was discovered. It showed that the steady state theory was false. The universe had a beginning. Stephen Hawking emerged at this time, showing that the universe would not only end with singularities but had also begun with one.

This was also the decade where pulsars were discovered, "pulsating radio stars." These are neutron stars, stars made up almost completely of neutrons. I'm getting a better picture now of what some of the earlier chapters were talking about. There are white dwarfs that Eddington knew of. These are smaller suns that burn out but they are not massive enough to become singularities from which light cannot escape.

There are black holes. These are the super-massive stars that, when they burn out, collapse into a relativistic nightmare from which nothing can ever escape. From our perspective, they become frozen in time. Neutron stars, of which pulsars are an example, are somewhere in between in mass, more massive than white dwarfs but not so massive as a black hole.

Chapter 9: Unification Woes
Relativity and quantum mechanics have always been difficult to fit together. Einstein couldn't do it. Paul Dirac couldn't do it, although he did it with the electron. The Dirac equation had been a landmark in the history of physics. It had predicted the existence of antiparticles, for example.

This chapter takes a bit of a detour into quantum physics, since it is on the continued attempts to fit quantum physics with relativity and gravitation in particular. The 50s and 60s saw the putting together of quantum electrodynamics (QED) and what is now called the "standard model" of physics.

Dirac, like Einstein, never accepted some aspects of quantum physics. He accepted more than Einstein. For example, he showed that the approaches of Heisenberg and Schroedinger really said the same thing in two different ways. In his later career, like Einstein, Dirac became somewhat of a recluse, a celebrated landmark who refused to stay with where the program had gone. In the summer of 1983, while at Boy's State, I touched his office door at Florida State, the year before he died. He had withdrawn from the mainstream and had become a shadowy figure from the past.

In particular, QED leads to a lot of infinities that are ignored. So even though the equations point to an infinite mass for an electron, QED "normalizes" the mass of an electron by substituting the actual measured value for the infinity. Frankly, this bothers me too and surely speaks to some inadequacy in the theory, says the guy who doesn't have a degree in physics.

Hawking did some work to show some additional places where quantum physics and general relativity might come together. Hawking showed that black holes slowly evaporate, "black hole radiation."

Chapter 10: Seeing Gravity
It is amazing to me that this book is already needing to be updated. I bought this book on March 1, 2014 at the IU Memorial Union Bookstore in Bloomington. It just came out in early February of this year. By March 17, chapter 10 was out of date. That was the date that it was announced that gravitational waves had been observed.

Einstein predicted the existence of gravitational waves, ripples in spacetime, as early as 1916. Eddington rejected the idea, and Einstein himself backed off on the idea in 1936. But Hermann Bondi made a compelling case for them at the watershed 1957 meeting at Chapel Hill. Feynman agreed.

A guy named Weber was also there and would spend the rest of his life trying to prove it experimentally. Unfortunately, he saw them everywhere. Eventually he was marginalized by the scientific community and died a bitter man in 2000. He used very imprecise measuring tools, compared with the laser interferometry that is currently used.

The idea that large objects might give off "gravitational radiation," however, was supported indirectly in 1978. Taylor and Hulse used the very equations Einstein created and whose results he then later rejected to examine two neutron stars orbiting each other. The chapter ends with LIGO in North America trying to find gravitational waves using laser interferometry. Unfortunately for them, they do not seem to be the ones that discovered them.

A final feature of interest in this chapter is the rise of "numerical relativity." For decades, attempts to solve Einstein's field equations in relation to colliding black holes, using computers, would break down the computers. The computer power just wasn't powerful enough yet. Frans Pretorius cracked that one in 2005. He solved Einstein's equations for two colliding black holes on a computer without the process shutting down--90 years after Einstein set them out.

As a side note, the drive to do numerical relativity and the need for more computing power apparently played a role in the implementation of the internet, so that multiple computers across distances could collaborate together. That was in the mid-80s when Larry Smarr was convincing the US government to fund a network of supercomputing centers.

It's quite clear that some of these discoveries would not have happened without a willingness on the part of the government to fund scientific research without immediate results. Such funding seems essential to the long term ability of the US to stay ahead of the curve. The problem is that it will not always pay off and, even when it does pay off, it can be a long time later. We just have to have the foresight to commit to scientific research without immediate results.

Alas, it looks like I will leave Florida with only 7 chapters of The Perfect Theory finished. So what else is new. Going by my past record, those last 115 pages may never be read.

Here's a much briefer summary of chapters 3-6.  I've already summarized:

Chapter 1: Einstein in 1907
Chapter 2: The General Theory of Relativity Born

Chapter 3 is called "Correct Mathematics, Abominable Physics"
I feel a bit sorry for Einstein. He had a few very significant "outside the box" thoughts in very early 1900s. He generally seemed to have them bouncing ideas off of genius friends and acquaintances. His college buddy Marcel Grossman helped him bounce his way into special relativity in 1905. Then David Hilbert helped him find his way to general relativity in 1915.

But after that, he pretty much became a celebrity "has been" and eventually a "cuckoo," as Oppenheimer once called him. One of the things I find striking about these chapters is how closed minded the greats were. They rose to fame on thinking outside the box but then became part of the establishment that pretty much ignored new ideas that didn't fit with their sense of things. It's all pretty straightforward Thomas Kuhn stuff.

So, in this chapter, we hear how Einstein and Eddington basically ignored a string of relativity enthusiasts who came to them showing how there were possible solutions to the general relativity functions that might point to an expanding universe. Alexander Friedmann was a Russian who showed that, according to Einstein's functions, the universe had either to expand or contract. Einstein mistakenly corrected him in publication when it was Einstein's mistake.

Einstein and Eddington, for whatever reason, just didn't like the idea of an expanding universe. Georges Lemaître, a Roman Catholic priest, was another who showed this to Einstein. Einstein's response was that his calculations were correct mathematically but that his "physics was abominable."

Eventually, Einstein would have to eat dirt, as would Eddington. In 1925, Hubble showed that there were galaxies beyond our Milky Way galaxy. Then by January of 1929, Hubble and Humason had both shown that the redshifts of these far away nebulae were larger than those closer to us. In other words, the universe was expanding.

Lemaître had been one of Eddington's own students and he had ignored him. But in the end, both Eddington and Einstein would repent and thrust him into center stage. He would become the world's leading cosmologist. Although Lemaître came to his conclusions scientifically, he of course believed that his findings, that the universe expanded from a beginning, fit with his faith in God.

Chapter 4 is called "Collapsing Stars"
Einstein and Eddington also found the idea of a burned out star that might collapse in on itself "absurd." In other words, the idea of a black hole didn't fit with their sensibilities. Eddington had written a classic book in 1926 called The Internal Constitution of Stars, but he couldn't bring himself to see a star becoming so dense that not even light could get out, so much so that the inside of the star became permanently shut off from the outside world.

The work of several "relativists" pointed in this direction. The Russian Karl Schwarzschild died prematurely of illness in 1916, but he had simplified some aspects of Einstein's theory, explained some loose ends in the prediction of Mercury and other planets' orbits. But his work had also curiously predicted the phenomenon of black holes.

Subrahmanyan Chandrasekhar (Chandra for short) integrated some of the developments in quantum mechanics into the relativity of stars and supported Schwarzchild's conclusions from a different angle. But when he presented it, Eddington's clout ruled it out. Mathematically possible but not something that would take place in the elegant universe as he saw it. Chandra would then abandon his research on the subject of white dwarfs, even though he was pretty much correct.

The last part of this chapter is about Robert Oppenheimer, father of the atomic bomb and leader of the Manhattan Project. He set up quite the physics team at Berkeley. He and one of his students published a paper in 1939 arguing for black holes. Of course it came out the day that the Nazi's invaded Poland, and it would disappear for a good while.

Chapter 5 is called, "Completely Cuckoo"
This was Oppenheimer's description of Einstein in his later years at Princeton. Einstein could never reconcile himself with the quantum physics of Heisenburg's uncertainty principle. He spent his last years more or less as a recluse trying to find a grand unified theory that would never come.

These were apparently years when general relativity was viewed somewhat like string theory is today in many circles. Without any clear way experimentally to test it, those who work with it seem to be playing idiosyncratic games with math without any real pay off in the real world.

In the 50s, Princeton played home to a number of famous thinkers, the "Institute for Advanced Study." But before Ferreira, the author of the book, gets there, he reviews how the Nazi's opposed Einstein's theory as "Jewish physics." In the USSR, there was similar opposition by materialists to the seemingly idealized world of Einstein. Of course things like the atomic bomb and the nuclear arms race were too important for the Nazis or the Soviets in the end to let these "fundamentalists" win.

One friend Einstein did have at Princeton in these years was Kurt Gödel. He played with Einsteins general relativity equations and asked what would the universe be like if it were rotating on a central axis. The result? Spacetime would loop back on itself and you could actually travel back in time. Einstein's reaction to his friend's work was predictable--mathematically interesting but completely unrelated to the real world.

Oppenheimer would eventually move from Berkeley to Princeton to head the Institute. He and Einstein had a cordial relationship. Oppenheimer respected Einstein even if he considered him cuckoo and more of a landmark than a beacon in the story of physics. He would later say that Einstein "did no good" in his later life. However, Einstein supported Oppenheimer when he hit on hard times for being opposed to the Hydrogen bomb. Oppie would come to regret the Manhatten project and, in time, he lost his national security clearance. But Einstein supported him and was untouchable in the public eye. Einstein was a pacifist.

Chapter 6: "Radio Days"
This chapter has to do with the discovery of the quasar, which gives off massive radio waves. A lot of the chapter deals with the charismatic Fred Hoyle, who pioneered the "steady state" theory of the universe. Hoyle found the idea that the universe had a beginning and started with a "big bang" a detestable idea. He suggested that the universe was constantly generating enough matter to keep going. It thus wouldn't need a beginning.

Because Hoyle was able to get the idea out to the public, it was taken quite seriously by the British masses, even though few scientists thought the data supported him at all. Suffice it to say, they repaid him by refusing to publish his papers for two or three years.

Hoyle's theory would eventually be shown incorrect.

I don't know if I'll get around to blogging any more from this book. I do hope to finish it in the next couple months. If I find anything I think is really interesting, I may be back...

I continue my Spring Break posts on The Perfect Theory, a book on the general theory of relativity and its footprint on the last century.  So far:

1. Einstein in 1907

1. I might have titled these thoughts on the second chapter, "Einstein in 1915." That is the year that Einstein delivered a short four page paper to the Prussian Academy of Sciences explaining how gravity fit with relativity and thus truly gave birth to the general theory of relativity (as opposed to the special theory he set out in 1905). The paper consisted of 10 field equations.

There is some debate whether Einstein actually put these equations in their final form first or whether David Hilbert did. Einstein was not a math-lover, particularly. To be sure, he was way ahead of most of us, but he considered math "superfluous erudition."

I have a hunch I know where he was coming from. He did not mean the calculus or algebra that we find so useful in engineering. I suspect he meant the drive to prove things that seem obvious. From what I can tell, Einstein was more of an intuitive soul, and the drive to mathematical minutia probably did not suit him well.

David Hilbert (University of Göttingen) was quite the opposite, with an agenda to solve 23 problems in the twentieth century. A quick perusal of the list and you might agree with Einstein. Hilbert wanted to "reduce every single mathematical fact in the universe from no more than half a dozen axioms" (76). Kurt Gödel would later demolish Hilbert's goal in 1931 with his incompleteness theorem.

Hilbert was extraordinarily more gifted at math than Einstein and Einstein ended up turning to him to help with non-Euclidean geometry, which was less than 100 years old. Euclid was Greek and had proposed, using common sense, that two parallel lines never meet.  In the 1820s, Carl Friedrich Gauss had explored the rules of geometry on, say, curved sheets of paper, where Euclid's assumptions don't hold. On a sphere, parallel lines intersect and the angles of a triangle add up to 270 degrees. Bernhard Riemann in the 1850s had explored the rules of geometry into all sorts of non-Euclidean obscurity.

So in 1915, Einstein and Hilbert mailed back and forth, as Einstein tried to use Riemann's math to express gravity as a result of the curvature of space rather than as a force per se. It's still debated whether Hilbert beat Einstein, although Hilbert yielded to Einstein and Einstein usually gets the ultimate credit. It might be fair to say that neither would have come up with the answer without the other.

Einstein came up with 10 equations of 10 functions of the geometry of space and time in which "gravity is nothing more than objects moving in the geometry of spacetime. Massive objects affect the geometry, curving space and time" (21).

2. There is a second part to the chapter that relates to Arthur Eddington. There is often a politics and a history to science, as to any discipline, and it is seen in this book. In 1915, Europe was at war. In World War I, the Germans were fighting the English. Both many English scientists and German scientists went irrational, as war tends to make all of us. 93 German scientists (not Einstein) signed "An Appeal to the Cultured World" in support of the German government and rather bad on its facts. Meanwhile, Eddington's colleagues in England wanted to dismiss all German scientific thought as obviously inferior.

Eddington managed to convince the right people to let him head to the island of Principe in 1918 instead of to the war. His task? To measure where a certain set of stars appeared to be as their light passed by the sun during an eclipse. As Einstein's theory had predicted, their apparent position was off approximately what Einstein's theory said it would be due to the effect of the sun curving space because of its great mass.

In 1919 Eddington presented the results to the Royal Astronomical Society, "the most important result obtained in connection with the theory of gravitation since Newton's day," J. J. Thompson said (discoverer of the electron). Einstein was now a celebrity and Eddington the foremost authority on Einstein's theory in the English-speaking world.

The general theory of relativity has been substantiated time and time again ever since. Without taking such things into account, things like GPS wouldn't work.

There are two items on my life's bucket list that I fear I will never attain--a general understanding of quantum mechanics and relativity. There's nothing more humbling to me than my repeated attempts to start up these mountains.

I came across a book a few weeks ago, The Perfect Theory, that I'm giving a little time to this week on vacation. It's about Einstein's theory of general relativity. I doubt I'll get too far into it but I thought I might blog a little to jog the memory when I retire at 70 and return to that bucket list with all that free time. :-)

The first chapter starts interestingly enough in 1907. That's further than I've ever gotten before. Einstein came up with his theory of special relativity in 1905. That was the year he published his paper arguing that clocks move more slowly and objects appear to shrink as they approach the speed of light.

He was working as a patent clerk from 8-6 every day at the time and talking through the problems of modern physics with his old friend Marcel Grossman on the side. Einstein didn't play the game of academics very well. He did what he wanted and didn't accept the principle that professors assign grades which have something to do with getting jobs. So patent office it was, a mercy job even at that.

Einstein set out to resolve the consequent contradictions from two claims of the physics of his day: 1) the laws of physics work the same in any inertial frame and 2) the speed of light always has the same value. These two principles contradicted each other because if you shine a light from the front of a moving train, you would think that light would move faster than some light you shined from a flashlight on the ground in the same direction.

If I have it right, Einstein's famous solution was to suggest that, from your perspective standing on the ground, the time for the light shining from the front of the train moves more slowly than it does for you with the light shining from you the ground. But on the train, time moves the same as always.

Thus the grandfather paradox. If I am on a train moving close to the speed of light, time proceeds normally for me. But if my son does not get on that train. He may grow up and have children who, by the time I return to the speed he is moving, are older than I am.

In 1907, Einstein was asked to summarize his theory and give implications, which he did in the Yearbook of Electronics and Radioactivity. His series was called, "On the Relativity Principle and the Conclusions Drawn from It." There was one very significant addition.

The Special Theory of Relativity only works for frames of reference that are moving at a constant speed in relation to each other. It does not apply to frames of reference that are speeding up in relation to other frames of reference. In other words, it only works if the train is moving at a constant speed in relation to the ground.

Meanwhile, gravity involves acceleration. Einstein didn't have it all figured out (and he would need help), but he had an insight in 1907 that would later bear the appropriate fruit. "If a person falls freely he will not feel his own weight." What I take this insight to be is that, in the frame of reference of the person falling, there is a constancy that is different from that perceived by a person looking on, much as that experienced by a person on a train who does not feel the speed an observer on the ground observes.

With a little help, this seed would lead to a general theory in 1915 that could accommodate gravity and accelerating frames of reference.

Albert Einstein, Relativity: The Special and the General Theory, trans. by R. W. Lawson (New York: Bonanza, 1961).

Part 1: The Special Theory of Relativity
I. Physical Meaning of Geometrical Propositions
Geometry reduces to assumptions, "axioms."  Propositions are built out of these axioms.  We prove things based on whether they proceed logically from the axioms.

At the same time, the basic ideas of geometry undoubtedly derived from nature originally. "Geometrical ideas correspond to more or less exact objects in nature, and these last are undoubtedly the exclusive cause of the genesis of those ideas" (2).

In fact, we can turn geometry into physics if we add the following proposition: "Two points on a practically rigid body always correspond to the same distance..., independently of any changes in position" (3).  So Einstein has now connected abstract geometry to physical objects.  We have connected what was an idea (geometry) to the real world (physics).

As the book continues, Einstein will go on to show that the "truth" of this proposition is actually limited.
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Note: The idea that the ideas of math originate in nature seems sound.  Pythagoras believed that numbers were the greatest reality, and that the world played them out in some way. Plato believed that the physical world was a copy of an ideal original. They had it backwards.  Aristotle probably came closer: numbers and mathematical "realities" are simply abstractions of the "real world."
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II. The System of Coordinates
We can identify the location of something with reference to the body it is on or we can take a rigid measuring rod from a body to it.  So we can locate a place on the earth by measuring off how many of the units on this rod it takes to get to it from some reference point or we can use a measuring pole to get to a point in a cloud above that point on the earth.

So we imagine locating any point by a number of units of some rigid measuring body to get to it from some point of reference. We don't always have to use a physical pole, since we can use other means to measure.  The Cartesian system of reference imagines three planes (x, y, z) from which we can construct perpendiculars to any point in space.

So in Euclidean geometry, "Every description of events in space involves the use of a rigid body to which such events have to be referred" (8).

III. Space and Time in Classical Mechanics
"The purpose of mechanics is to describe how bodies change their position in space with 'time'" (9). But the concepts of "position" and "space" are somewhat ambiguous. If I drop a rock straight down from a train, it looks like it falls in a straight line to me, but it looks likes it falls in the shape of a parabola to someone sitting on the ground.

First, let's do away with the notion of space ("of which, we must honestly acknowledge, we cannot form the slightest conception," 9) and replace it with "motion relative to a practically rigid body of reference." And by "rigid body of reference," we are thinking of a "system of coordinates" such as was defined in the previous chapter.

There is thus "no such thing as an independently existing trajectory... but only a trajectory relative to a particular body of reference" (10).

A complete description of the motion of a body includes how its position relative that frame of reference changes in relation to time.  The person dropping the rock off the train has a clock and the observer on the ground both have identical clocks measuring "ticks" on the clock as the rock drops.

IV. The Galilean System of Coordinates
The fundamental law of mechanics in physics is the law of inertia set down by Galileo and Newton.  A body at rest tends to stay at rest, and body in motion tends to stay in motion.  This law, however, only relates to a particular frame of reference, an "inertial frame of reference."  [A body at rest on the earth stays at rest on the earth, but it is constantly accelerating in relation to the sun because the earth is spinning.]

"A system of co-ordinates of which the state of motion is such that the law of inertia holds relative to it is called 'a Galilean system of co-ordinates'" (11).

V. The Principle of Relativity (in the restricted sense)
A "uniform translation" is when something is moving at a constant velocity and direction in relation to some frame of reference.  It is not rotating, for example.

"If K is a Galilean co-ordinate system, then every other co-ordinate system K' is a Galilean one, when, in relation to K, it is in a condition of uniform motion of translation" (13).  Accordingly, the mechanical laws of Galileo and Newton will hold good in K' just like they do in K.  In other words, the same physical laws work in K and K'.  This is the principle of relativity (in its restricted sense).

Developments in the study of electrodynamics in the late 1800s had called into question the principle of relativity. [Einstein's work would demonstrate that it could still hold.] But there were strong reasons to think it might hold. For example, "it supplies us with the actual motions of the heavenly bodies with a delicacy of detail little short of wonderful" (13). Why would it work in mechanics but not in electrodynamics?

Another complication if the principle of relativity didn't hold would be that we would have to have some basic frame of reference where the laws of mechanics hold most simply, but the rules would change somewhat in other frames of reference moving in relation to it.  So the laws of motion would apply straightforwardly in coordinate system K but they would be complicated by the motion of K' in relation to K.

Take the earth, for example, rotating around the sun.  Because it is moving in a circle, we would expect its movement to alter its velocity in relation to some absolute frame of reference throughout the course of the year.  Accordingly, we would expect the laws of motion to change in some way throughout the year as we moved in relation to the "absolute state of rest."

"The most careful observations have never revealed such anisotropic [different properties when something is moving in a different direction] properties in terrestrial physical space" (15). For Einstein, this was a very powerful argument for the principle of relativity, that the laws of motion apply the same way in every inertial frame of reference.
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Note: It would be very interesting to trace the history of rhetoric against relativism.  I've never heard anyone in Christian circles speak against relativity, but I can imagine some preachers in the early 20th century doing so.  Although the notion of relativism in ethics has been around forever, I have wondered if rhetoric against relativism in any way was affected or triggered by Einstein's theory of relativity at the turn of the twentieth century.

On Fridays, I'm working through Einstein's groundbreaking 1905 essay where he proposed his special theory of relativity.

Introduction

I. Kinematical Part
The essay is divided into two parts, the "kinematical" part is the part that has to do with bodies in motion.  The second part is the "electrodynamical" part, which has to do with charges in motion.

1. Definition of Simultaneity
Einstein's purpose in this section is to come up with a definition for simultaneous events in a "stationary" system. [To call it a "stationary" system is a bit of a misnomer, since movement is really relative, as Galileo indicated three hundred years earlier. Any "system" moving at a constant velocity might be considered stationary in terms of all the elements in that system. Such a system constitutes an "inertial frame of reference."]

If something is at rest relative to a stationary system, you can identify its location easily using x, y, z coordinates that you locate from some point of origin in that system.  It gets a little more complicated if you want to describe the motion of some material object in that system, its change in location in relation to time.  Then you will have to be clear about what you mean by "time."

If we say the velocity of an object means that it is at one point at time A and another point at time B, we are assuming, in effect, that if there were clocks at both points A and B, they would be moving forward in sync with each other. [After all, what is time, really, at this point, other than to say that 7 o'clock means that the small hand on my watch is pointing toward the 7?]

How can we make sure the clocks are in sync?  Einstein defines synchronous and simultaneous in the following way, namely, that the amount of time it takes for light to get from stationary point A to stationary point B is the same as the amount of time it takes for light to get back from B to A.  Since the speed of light is constant in any medium, the time should be the same given that the distance is fixed in this system.

[Since Einstein is defining simultaneity here, rather than demonstrating it, I still find this move on his part a little puzzling.  Is he saying that these two clocks are synchronized if the hands on clock A read twice the amount of time when the light reflects back as the hands on clock B read when the light arrived there from clock A?  That would satisfy his definition.]

Einstein further mentions two truths that follow from this assumed definition.  1) If the clock at B synchronizes with the clock at A, then the clock at A will synchronize with the clock at B. 2) If there is some other clock C that synchronizes with A, then it will also synchronize with B.

Finally, we can express the speed of light as the distance traveled per time.  The distance from A to B and back is 2AB.  The time passed is the time it took from when the the light began at point A (ta) till its return back to point A (t'a).  Thus c (the speed of light) = 2AB/(t'a - ta).

One of the things on my bucket list is to understand an equation in quantum physics called Schrödinger's equation before I die.  For anyone who thinks Wikipedia is for lightweights, tell me what you think of this page.

Off and on for years I have tried to find an entry point, but I usually don't even get through the starting point of quantum physics, Max Planck in 1900.  Schrödinger proposed his equation in 1925. I would love to grasp those 25 years in physics, let alone get beyond them. Dare I share one of my novel starts (I've started dozens)--a quantum physicist who has an accident in which his brain damage leads him to struggle to relearn some of what he formerly knew so well, only to achieve the barest of success.

I found a delightful book recently by Alan Lightman called, The Discoveries. Not that I have made much progress in it either. But he has some of the most groundbreaking scientific essays of the twentieth century in it, and he gives nice introductory essays.

I feel almost ready to write one "chapter" in those groundbreaking first 25 years.  In 1905, Einstein published four groundbreaking papers, including one that introduced his idea of special relativity. I thought perhaps I could summarize that paper slowly here.
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"On the Electrodynamics of Moving Bodies," Albert Einstein, 1905.

Introduction
Einstein starts by noticing that the famous theories of James Clerk Maxwell (1831-79) lead to some inconsistencies. Maxwell was a Scottish physicist who seemed to establish that light was a wave and at least established that electricity and magnetism were manifestations of the same basic phenomenon. His "electromagnetic theory" was the greatest achievement in physics since Isaac Newton (1642-1727) and paved the way for the developments of twentieth century physics (not to mention the radio, television, and cell phones).

The first paragraph of Einstein's essay points out some of the problems Maxwell's theory had left. For example, science at that time had two different explanations for the current created in a wire around a magnet, depending on whether you moved the magnet through the wire or the wire over the magnet. If you moved the magnet through the wire, science said that the magnet generated an electric field around it that caused current in the wire. But if you moved the wire over the magnet, science did not say there was an electric field over the magnet. Instead, it said that an electromagnetic force was created in the wire. The current generated, however, was exactly the same.

[Note: I do not really grasp the relevance of this particular example at this point]

In the second paragraph of the introduction, Einstein sees a solution to these sorts of anomalies in the reconciling of two principles that were already accepted but that seemed contradictory.

First, there was the "principle of relativity" that had been established three hundred years earlier by Galileo.  Physical laws operate the same in any "inertial frame of reference," that is, in any collection of items moving together at a constant velocity. The recent laws of electromagnetism set down by Maxwell were no exception: "the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good." (72).

The second postulate on which Einstein will base his theory is the "theory of light constancy."  "Light is always propagated in empty space with a definite velocity c which is independent of the state of motion  of the emitting body" (72). In other words, light will move at 300,000,000 meters per second whether it shines from a spaceship moving 100,000 meters per second or from someone with a flashlight in your back yard. Einstein himself was not the first to suggest this constancy.

Einstein was keen to resolve the apparent contradiction between these two postulates. How is it that light does not move faster off a moving truck than it does from someone standing on the side of the road? They are two different inertial frames of reference and so, relative to each other, the velocity of the truck should add on to the velocity of light relative the ground.

Maxwell's equations worked for "stationary bodies." That is to say, they worked within the framework of a single inertial frame of reference. Einstein's goal in this essay is to present a "simple and consistent theory" that will work for bodies moving in relation to each other, to present a theory relating to the "electrodynamics of moving bodies."

As a side benefit, he aims to show that the notion of a "luminiferous ether" is superfluous. Since Maxwell had seemed to show that light was a wave, the question had arisen as to what sort of a medium the wave moved through.  Water waves moved through water.  What did light waves move through?  At the time, physicists assumed there must surely be some sort of invisible medium through which light moved, something they called the "ether."

But experiments had failed to show any ether (e.g., the Michelson-Morley experiments). The ether gave a sense of absolute space--there would be something at rest at every point of the universe. Einstein's theory ends up negating the notion of "absolute stationary space" or absolute rest in space.