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A great science story is like a great Seinfeld episode. By the end, seemingly unrelated things all fit together and make the whole thing work as a whole.
Pick up a pinch of salt and drop it into a candle flame, or the burner on a gas stove. You’ll see a flash of yellow as the the salt heats up in the flame. That flash is one of the most profoundly mysterious events in the universe. Why should salt burn yellow? For hundreds of years, no one knew.
Now flash to 1914. Ernest Rutherford has just made his most important scientific contribution, in a lifetime of breathtaking contributions. He’s just discovered, as he said “what the atom looks like.” Rutherford blew apart the old plum pudding model of his mentor JJ Thomson, and showed that the atom is more like a miniature solar system, with a massive nucleus in the center surrounded by bits of fluff called electrons.
There was only one problem. The solar system model couldn’t work. In fact, it would cause every atom in the universe to collapse on itself in less than a second.
Here’s why: electrons have an electric charge. When things with an electric charge accelerate, they give off radiation. That’s what makes radio work – vibrating electrons at the transmitter send radio signals into space. The radio signals vibrate electrons in your metal antenna, and those vibrating electrons make the signal that turns into the sound you hear.
In a solar system atom, the electron would have to be spinning around the nucleus. Otherwise the negative electron would fall right into the positive nucleus like a bird that stops flying. But if the electrons are spinning, they’re also accelerating. If they’re accelerating, they’re giving off radiation, and if they’re giving off radiation, they’re losing energy. A quick calculation showed that if the electrons were accelerating like this, they’d lose so much radiation they’d fall into the nucleus in less than a second.
Since that hasn’t yet happened, despite plenty of seconds to do so, something must be screwy somewhere.
A student of Rutherford’s named Niels Bohr went to work on the screwiness. Bohr knew he had two mysteries. First, why do things like salt give off certain colors when they’re heated in a flame? Second, why don’t electrons collapse into the nucleus? Could Bohr make like a Seinfeld writer and bring it all together?
Bohr had a few tools. Albert Einstein had nine years earlier discovered that light is lumpy. The color of the lump tells you the energy of the lump. Blue lumps have more energy than yellow lumps, and yellow lumps more energy than red. Bohr also knew that the energy of an electron depended on how far it was from the nucleus, just as the energy of a brick depends on how far above your head it is when it’s dropped.
So Bohr took a guess. What if electrons could only “orbit” the nucleus at certain, regular energies? If “A” is the base energy, then the electron could orbit at 1 times A, 2 times A, and so on. (Actually Bohr based the allowed orbits on angular momentum, not energy. But the heart of the idea is still there.) Bohr tried this for the simplest atom, hydrogen, and when he did, out popped the lumps of light that came from heated-up hydrogen atoms! It all came together.
The important thing to remember is that this was screwy physics. No one knew any reason why an electron orbiting a nucleus at only certain, specific distances should not give off radiation. No one knew why, when an electron went from one of these allowed orbits down to a lower one that it should give off radiation in one lump (other than Einstein’s equally screwy idea that, well, it just did). This was physics with no basis in anything anyone had ever seen in the real world. But, for hydrogen at least, it worked.
Sadly for Bohr, nature wasn’t so simple when it came to other atoms like sodium. It took a long while before scientists could work out the rules of how electrons jump in complicated atoms like sodium. But when they did, sure enough, the yellow color of heated salt came jumping out, just as the colors of heated hydrogen came jumping out for Bohr.
Bohr’s discovery not only explained why atoms didn’t collapse. It also helped solve an ancient mystery – a mystery you can recreate yourself with just a pinch of salt and an open flame. Where does the yellow come from?
This is something I wrote last year, but I didn’t have a blog then. Merry Christmas to all those Santas out there.
I’m an atheist. I was born an atheist, and then various people talked me out of it. As a child, with a relatively non-religious immediate family but a deeply religious, southern Baptist extended family (who by the way were and are all warm, loving, and amazingly tolerant and easygoing people), I was eventually sucked in to various bits of the church scene, including being “saved” at one point.
Deep down, though, I knew it was all nonsense. There was a little voice inside me all the time saying, “Come on, really? People actually buy this stuff?” It was a lot like a belief in Santa Claus, the Easter Bunny, the Tooth Fairy, and so on.
Such a comparison inevitably offends religious people, but I think it is important to understand that in a child’s mind these are all big, weighty issues, and it isn’t really clear which ones carry the most weight. I think I have a skill that sets me apart from many people. That skill is that I still remember what it was like to be a kid, even though I’ll soon be – well, not a kid.
The Tooth Fairy and the Easter Bunny are minor players, so I’ll leave them out. Santa is the big guy, and we all know it. As a child, I went through the gamut with Santa, at the same time I was going through thoughts about God. First there’s belief. Sure Santa exists, where else did all the toys come from? Then there’s doubt. Wait a minute, I saw my parents buy that. Wait a minute, I saw that toy under their bed. Wait a minute, there’s no snow, how does the sled work? Wait a minute, our chimney is blocked, how’d he get in? Wait a minute, I couldn’t sleep and got up and found my parents putting toys together.
But there’s still a chance. You hear explanations, rationalizations. The sled doesn’t need snow, of course. Santa brings some of the toys and your parents buy the rest. Santa uses time dilation, the rotation of the Earth, a snap of his magic fingers, etc. etc. etc. You gather scattered bits of evidence, ignoring the rest. I thought I heard sleigh bells. I saw a leg out the basement window that looked like a reindeer. I heard something go bump in the night. Someone ate all the cookies.
It all sounds pretty implausible, but you say, eh, maybe it could all work. I don’t understand enough about the world yet, so I’m reserving judgment. Besides, what if I’m wrong? What if I don’t believe, and then Santa doesn’t come? A year is a long, long, long time when you’re a kid. Why take a chance?
Then you hear someone say something like “Santa is the spirit of giving” and you start to see. My parents are Santa Claus! It all fits. The secret shopping trips. The bags you’re not allowed to look in. The forbidden closets. The “early to bed and don’t come out of your room” commands. Ah, that’s how they did it!
For me, and I remember this distinctly, there was no anger or resentment. I loved the fact that my parents would go out and buy all these toys, then not take credit for doing the buying. It was about this time that I started to find out how much fun it was to give presents to other people, and Christmas for me started to become much less about getting and much more about giving. I started to realize that I was Santa Claus, too.
Later, all the doubts about God started coming to the fore. I felt like I wanted to hang onto this idea of God; so many people I knew believed, there must be something to it. Again, I started gathering scattered pieces of evidence. All the supposed miracles, all the eyewitness testimony. But then those got pretty thin when you looked close. What about the spark of life itself, though, wasn’t there something about life that made it different from non-life, and was it that spark that required God? And, most notorious, what if I’m wrong? Do I really want to risk eternity in Hell? Is it really too much to ask, to just believe, to give up that little bit of your mind in order to receive a get out of Hell free card?
And yet inside was that little voice. “Oh, come on. You know the truth, just like you knew about Santa Claus. There is no God. You decide your fate. You make the choices that matter. You decide for yourself if you’re going to be a good person or a bad person, and not because of any reward or punishment, but because it’s who you are, who you want to be, who you see yourself as. It’s not outside you. It’s inside you, and it’s been there the whole time. You’re an atheist, and you always have been, really.”
And so I teach my children about Santa Claus. And the Tooth Fairy. And the Easter Bunny. I also teach them to be skeptical, to doubt the things they’re told, to figure out for themselves what kind of person they want to be. I believe (and maybe I’ll be proved wrong, but that’s what experiments are all about) that my girls will follow my own line of questions, use the tools of skepticism I’m giving them, and figure it out for themselves. I hope they’ll see the beauty and joy of giving as opposed to getting, and decide that they want to be Santa themselves.
From there, I hope they see the power within themselves to make the choices regarding their own lives. What kind of person will you be? How will you treat others? How do you want to see yourself? No one else, not me, not your mom, not God nor Santa Claus, can tell you who you will be. Only you can do that. Just as you are your own Santa, you are your own God.
That’s why, in our house, we believe in Santa. For now.
And just for fun, here’s the same idea in much more succinct language:
Yes, I’ve read all the books. Albus Dumbledore is one of my favorite fictional characters. I love his emphasis on choice. “It is the choices we make,” he says, “that show who we truly are, far more than our abilities.”
I have the feeling that I’m going to have to find a fun way to treat the science of the Harry Potter books. It shouldn’t be that hard. I find the science of Christmas by leaning on popular culture – why your tongue sticks to a cold flag pole, why reindeer really fly, how to make an exploding snowball, and so on. There have to be similar silly fun bits of science in Harry Potter.
Flying broomsticks are an obvious choice. Must be something fun there.
Potions, of course.
Maybe make a fire-breathing dragon, similar to the barfing pumpkin demo.
“Nearly headless? How can you be nearly headless?” There’s something fun (and gross) there.
Invisibility? Howlers? The whomping willow? There’s got to be something in there somewhere.
The problem is, so much of the later books are so serious. I need some fun! Ideas?
Listening to Feynman again, and I encountered yet another amazing idea. He already got me excited about the experiment with two holes. Now he describes an even simpler experiment, with only one hole.
Suppose a particle (electron, photon, it doesn’t matter) approaches and passes through a single hole in a wall from a great distance. The distance can be so great that we can say with arbitrary accuracy that the particle can have no up-down momentum. If it did, then the angle would cause the particle to miss the hole and in fact travel right out of the picture. In other words, this particle (or rather a whole group of them) must be traveling along a line perpendicular to the wall.
This realization means that we know precisely the value of the particle’s up-down momentum. It’s exactly zero.
The uncertainty principle says that if we know the momentum precisely, we can know nothing about the position of the particle. But that’s not right, because this particular particle, with zero up-down momentum, has a precise up-down position. We know this because this particular particle passes through the one hole in the wall. So now we have a precise up-down momentum and a precise up-down position. Have we beaten the uncertainty principle?
No! And this fact is demonstrated in a dramatic way, a way that makes the uncertainty principle as real and visible as a light beam passing through a keyhole. We know that light spreads out when it passes through a small opening, in a process called diffraction.
So what happens to this particle when it passes through the hole? It is diffracted! It is diffracted into some (unknown and unknowable) angle. And the smaller we make the hole (the better we know the up-down position, in other words), the greater the likely angle of diffraction.
Importantly, we can’t know the exact angle of diffraction. It might be anywhere from zero to some maximum. Only when we send lots and lots of particles through the same hole do we get a spread of angles that shows us the diffraction pattern.
Diffraction, then, is a direct result of the uncertainty principle. Why is the particle diffracted? Because if it weren’t, we’d know the precise up-down position of the particle (in the hole) and the precise up-down momentum of the particle (zero) at the same time. Since we know the first (the particle is in the hole) we can’t know the second, and so the particle goes flying off at some unknown (and unknowable) angle.
Feynman also makes the point that the uncertainty principle is strictly predictive. Yes, we know the momentum and position precisely the moment before the particle enters the hole. But that does us no good. We can’t use that information to predict anything. Only the forward-going information, where the particle is and what its momentum is right now, is any good for making predictions. And since that’s the “good” information, nature denies it from us, by making the particle diffract. You can’t beat the game.
But it’s very fun to try.
I miss the ocean. My wife Julie and I took the most adventurous trip of either of our lives over the summer, flying to New Providence Island in the Bahamas to spend some time together in paradise.
The Bahamas was a little crass and commercialized, not really our style, but the ocean! We love to walk on the beach, stand in the ocean, feel the Sun and the water and the wind and the sand. I love that line, the line where water meets sky, that amazing, flat horizon that goes on and on and on, where two worlds meet. The ocean is where I belong.
One evening Julie and I stood in the warm water, watching the sunset. The horizon was clear, and as the Earth spun we watched the horizon approach the Sun. We could almost feel the Earth moving under our feet, the way the whole world just seemed to tilt toward the changing Sun. From yellow, to orange, to red, the Sun got lower and lower (or so it seemed), and began to disappear below that beautiful watery line.
And then it happened. Just as the Sun finally disappeared, at the very top of the disappearing Sun, we saw a flash of green. Julie and I both gasped as one. Did you see it? Yes, I saw it, did you? Yes! The green flash. We saw the green flash!
We watched the sky turn from blue to purple to black, then made our way back up the hill to our inn. It was an evening we both will remember for the rest of our lives.
So what is the green flash? It is the perfect Goldilocks effect, a result of something being “just right.” Like Julie. (Sorry, I couldn’t resist.)
The Sun is called a yellow-white star, but really it’s pretty much white when seen in outer space. Here on Earth, on the other hand, the Sun looks yellow for exactly the same reason that the sky is blue.
To understand what that means, first you have to remember what color really is. Color makes life beautiful. Green is my own favorite color – green sea turtles (which aren’t really green, of course), green Christmas trees, green grass on a springtime baseball field. But green is one wavelength, or set of wavelengths, of light. Red is a different wavelength, and blue another. White light doesn’t really exist (I wrote about that here).
Here’s the thing: different wavelengths (different colors) behave differently. Because of the size of pieces of air – molecules like nitrogen and oxygen – blue light, which has a very short wavelength, is scattered. That scattered light makes the sky blue. What’s left? Light from the Sun arrives at our eyes missing some of its blue. That makes the Sun look a little more yellow.
At sunset, light passes through a thick layer of atmosphere, also filled with dust and haze that helps remove even more blue and violet light. By the time that light reaches us, almost all of the blue and violet light has been scattered out. What’s left? Mostly red and orange, with some yellow and green mixed in. When it’s all added together, the Sun looks reddish.
We’re getting closer to the green flash. The light from the Sun passing through that thick layer of atmosphere bends. That’s called refraction. You see refraction all the time over hot pavement in the summer. Light is refracted differently by different-temperature air. That wavy look over hot pavement, a hot grill, etc., is the result of light waves bending through those different temperatures.
OK, we’re almost there. There’s still green in the Sun’s light. Just as in a rainbow, green light bends more than red light. So the red light, orange light, etc, pass over our heads as the Sun dips below the horizon. The green light, on the other hand, for just a moment, bends just enough to follow the curve of the Earth and pass right into our eyes.
The green photons are of long enough wavelength to not be scattered, but of short enough wavelength to bend just the right amount. Like Goldilocks, the photons are just right. For just a moment, those green photons generated in the Sun, 93 million miles away, photons that are normally completely hidden, washed out, or blended in to all the other colors, are able to stand by themselves, enter our eyes, and build a memory that will last forever.
That ocean is still out there. Someday we’ll make it back.
I’m listening to Richard Feynman’s physics lectures in the car, and I just finished what might be the best, his description of the double-slit experiment with electrons. The ideas are so profound and amazing that the audience several times bursts into laughter, I think without Feynman even trying to be funny. No one can describe the double-slit experiment as well as Feynman, but once you understand this experiment, you own a piece of this amazing and bizarre universe that will be yours forever.
Here goes. It will be better with pictures, so hopefully I can find some.
First consider things that are definitely lumpy, like bullets. The bullets are indestructible, they start as a lump and end as a lump. Shoot bullets at a wall with two small holes. Each bullet either goes through the top hole or the bottom hole. They might richochet off the edges or something, so when you’re done you have a distribution that looks like this:
Notice that the bullets gather right behind the slits. A reasonable conclusion is that the bullets behind each slit passed through that slit.
OK, now consider water waves. Immerse the whole experiment in water, and instead of a gun shooting bullets, have a finger or something moving up and down in the water. This makes ripples. When the ripples reach each slit, they start two new sets of ripples, one from each slit. But when the two new sets of ripples meet each other, they interfere, creating a different sort of pattern against the far wall.
Interference can be hard to understand; I always like to think of trampolines. You know how bouncing on a trampoline you can get higher and higher if you match your jumping to the bouncing of the trampoline. But if you hit the trampoline at just the wrong time, your bounce gets “swallowed up” by the trampoline. Your crest met the tramp’s trough, and you lose your bounce. Sad, but that’s destructive interference. Well, sort of. Anyway, if you think of it that way, you’ll see that along some parts of the wall you get even bigger waves (constructive interference) and along other parts you get nothing (destructive interference). It’s a very different pattern than you get from bullets.
What about electrons? Now Feynman springs his beautiful paradox. He states what he calls “Proposition A.” That is, each electron either passes through slit 1 or it passes through slit 2. This makes sense, because everything we know about electrons says they are more like bullets than like water. But when you do the experiment, here’s what you get:
Notice that the electrons, as far as we can tell, as far as we can measure them, are still like bullets. That’s an important point to remember. No one has ever “seen” an electron wave. We don’t know what such a thing would look like. Electrons are bullets, as far as we can tell. We never find half an electron. They’re bullets going in, they’re bullets when we catch them on the other side. And yet . . .
In between, when we’re not looking, the electrons act like water! They create an interference pattern on the far wall.
OK, fine, electrons do this bizarre thing when we’re not looking. But surely proposition A still holds, right? Somehow the electrons must move either through slit 1 or slit 2, right? Let’s see.
We set up an experiment. We shine light on the holes. If an electron comes through, we see the light. And indeed, when we do this, we see that electrons come through one hole or the other hole, never both at the same time, never part of an electron here, another part there. Great. Now we turn around and look at the pattern on the wall. What do we see?
Argh! The electrons form a pattern like bullets! The act of looking at the electrons has disturbed them! When we look the electrons do one thing (and proposition A is upheld, every time). When we don’t look, they do something entirely different, and we can’t say whether proposition A is true or not. We get the sense that nature is playing with us.
Feynman then shows how by using less intense light, or light of a longer wavelength, the bullet pattern gradually, bullet by bullet, morphs into the water pattern. It’s a beautiful thing. Nature has covered all her bases. We can’t catch her in her strange act of doing funny things with electrons. And yet,the pattern we get when we’re not looking at the slits shows us that something funny is, indeed, going on.
For instance, suppose you use longer wavelength light. This light is less energetic, so that it is less likely to knock the electron off its path. But by an exact relationship, when you get light of low enough energy not to knock your electrons silly, that light is of just long enough wavelength that you can’t tell anymore which hole the damn electron went through! And guess what kind of pattern you get?
You get the water wave pattern again! Nature has beaten us once more. We try to look with just enough force to see what’s going on, and she turns the electrons into bullets. We look with just too little force to see what’s going on, and the electrons turn back into water waves again! Argh!
To emphasize the strangeness, consider closing one slit. You get half the bullet pattern. Now open the slit and don’t watch. You get the wave pattern. In the bullet pattern, you get electrons in particular spots, say spot Q, even with one slit closed. If you open the second slit (remember, don’t look!), spot Q has no electrons hitting it! For certain spots, you get fewer electrons with two slits than you get with one. More paths, less electrons!
Now for my favorite part, not something Feynman emphasized in his lecture, but something I find completely mind-blowing. We can shoot electrons as fast or as slow as we want. If we’re really patient (read obsessed), we might shoot one electron a year, or one a decade, or (imagining we will live forever) one every thousand years. As long as we’re not looking at the slits, the electrons will, one by one, fall into just the right places to form an interference pattern! But how did the electron from yesterday know that it can’t land in spot Q, because an electron a thousand years from now will enter the apparatus and interfere with it at that spot? Can electrons know the future?
The answer seems to be that the electrons are not interfering with each other. Rather, each electron interferes with itself. In other words, each electron somehow goes through both slits.
But we know that’s not true! We know it because every time we look, we see an electron going through either slit 1 or slit 2. There’s never any ambiguity. Yes, this act of looking destroys the interference pattern. But still, how can an electron that is always observed to be a lump pass through both slits? When we’re looking, electrons go through one slit or the other. Proposition A holds. When we’re not looking, something strange happens, and we just don’t know what it is.
We don’t know how nature does it. We don’t know why nature does it. We just know she does. And we know that we can’t catch her.
It is a beautiful, frustrating, beautifully frustrating thing. And it makes the world an amazing place.
So I don’t want to change the world. What am I doing writing, then?
Why did Joseph Campbell write? Why didn’t he just make his discoveries about myth and then keep them to himself? For some people, that’s enough, or at least they act as if it is enough. My favorite poet, Emily Dickinson, wrote her poetry and then locked it away, safe from “an admiring bog.” Charles Darwin discovered evolution by natural selection, but kept his discovery hidden for years. Even Isaac Newton, not exactly the picture of humility, had to be cajoled into finally publishing his laws of motion.
Teaching, of course, is a different sort of journey than those sorts of discoveries, because it makes little sense to teach to no one. Aren’t I, through my teaching and through even through this blog, trying to change the world? Maybe I am and maybe I’m not. I think, more than anything, I’m just trying to work out things for myself, and writing makes things more real for me. Teaching makes me understand. Teaching about an idea, especially an idea I’m really excited about, makes the idea more real for me.
And then I think maybe there’s something else, something that I don’t really understand, something I’m unable to describe.
Carl Sagan said this: “Not explaining science seems to me perverse. When you’re in love, you want to tell the world.”
Can love change the world? I don’t know. But whether or not it can, it’s why I keep teaching, why I keep stooping down, picking up starfish, and tossing them into the ocean.
I haven’t written for a long time. I’ve been out of balance for a little while, and it’s time to come back now. Recent events have jarred me back, and I don’t want to forget where I am.
Joseph Campbell said, “The way to find out about happiness is to keep your mind on those moments when you feel most happy, when you are really happy — not excited, not just thrilled, but deeply happy. This requires a little bit of self-analysis. What is it that makes you happy? Stay with it, no matter what people tell you. This is what is called following your bliss.”
Teaching makes me happy. Am I making a difference? Maybe. Am I changing the world? Probably not, but who knows? At any rate, that’s not my goal, not if I’m honest about it. My goal is to teach. The act itself. My goal is moments. I’m after that look, that question, that sense of awe, that amazement, that connection. In that moment, I’m fulfilled. In that moment, all the magic tumblers of the universe have clicked into place and suddenly it all makes sense. Does the learner take anything away from that moment? Maybe she does, maybe she doesn’t. Maybe she walks away and never thinks of the moment again. But I take something away from that moment. Every time. I have to remember, because in that moment, for her and for me, life is worth living because the world is wonder-filled.
Joseph Campbell also said, ““When we talk about settling the world’s problems, we’re barking up the wrong tree. The world is perfect. It’s a mess. It has always been a mess. We are not going to change it. Our job is to straighten out our own lives.”
I recently was reminded of John Horgan’s book “The End of Science.” Horgan argues that great discoveries can only be made once. Therefore, eventually all the great discoveries will be made. Various commentators have attacked Horgan’s idea, saying that there are an infinite number of great discoveries to be made, so science will never be done. Maybe. But I think the mistake Horgan makes is not in the second sentence, but in the first. We all of us are on a journey, a personal journey. The discoveries of evolution, special relativity, the origin of the universe, the nature of matter, the structure of a sand grain, are open and available to us all. We can all learn of these things, discover them for ourselves, again, for the first time. We are all discoverers.
One more from Joseph Campbell. He’s such an amazing character, and I could quote him forever and never exhaust his profound sense of the world. Here he’s talking, as it turns out of Star Wars character Darth Vader. But how many other men could he mean?
“He’s not living in terms of humanity, he’s living in terms of a system. And this is the threat to our lives. We all face it. We all operate in our society in relation to a system. Now is the system going to eat you up and relieve you of your humanity or are you going to be able to use the system to human purposes? … If the person doesn’t listen to the demands of his own spiritual and heart life and insists on a certain program, you’re going to have a schizophrenic crack-up. The person has put himself off center. He has aligned himself with a programmatic life and it’s not the one the body’s interested in at all. And the world’s full of people who have stopped listening to themselves.”
I need to listen.