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Now I’ve done it. I’ve put the dreaded “God Particle” title on my blog after railing against it in the past. (And yes, I really did write that, even though my identity has been expunged. Another story. Better to be published without credit than to not be published at all, I suppose.)

Here’s my excuse. In his book Smashing Physics, which I just finished listening to, English (very English) physicist Jon Butterworth makes the following statement about the Higgs boson and the Brout-Englert-Higgs (BEH) field that gives mass to matter particles:

 

If you think this BEH mechanism is correct, then every time you measure the mass of something, you are seeing evidence for it. On the other hand, this becomes simply a matter of interpretation, since the BEH theory has explained the mass, but has made no unique prediction for any new phenomena that you can test experimentally. Maybe some other theory could also explain the mass. In fact, this is pretty much why the draft of Peter Higgs’ second paper on the matter was initially rejected by the journal Physics Letters. He then went and added an equation that essentially says something along the lines of, ‘Well, if this field is there, you can also make waves in it, and this will appear as a new scalar, i.e. spinless, particle . . .’

That is the famous Higgs boson, and that is why we have to see whether it’s there or not. It was this prediction that made it possible to demonstrate whether the BEH mechanism was just a neat piece of mathematics, or whether it really operates in nature.

 

It struck me the contrast between this statement and the ubiquitous proof of God given by believers. God, they say, is everywhere. Everything is evidence of Him.

What they fail to consider is that, as in the case of the BEH field theory, some other theory might explain the world just as well as the God theory. What testable prediction does the God theory make?

 

William Lane Craig, who is supposedly the best the apologists can put up, presents a version of the “evidence for God is everywhere” argument on his web site:

 

1. The fine-tuning of the universe is due to either physical necessity, chance, or design.

2. It is not due to physical necessity or chance.

3. Therefore, it is due to design.

 

How does Craig reach point 2, the key point in his argument? I’ll let you read it, but it essentially comes down to, “no one has yet thought of any argument that convinces me. Therefore, design.” That’s just an argument from ignorance, a God of the gaps. I can’t think of anything else, therefore God.

It’s fine to be skeptical of the multiverse, of inflationary cosmology, of the 10^500 possible worlds of String Theory. I certainly am.

Maybe the fine tuning is a physical necessity. Maybe it is chance. Maybe it’s something else, something we haven’t yet considered, including the idea that maybe the fine tuning is an illusion, caused by our incomplete understanding. The best current answer to the fine-tuning problem is, ‘we don’t know yet.”

Yet nowhere does Craig put his concept of God under the same skeptical microscope. And that’s the point I’m making here.

Note the key difference between physicists like Butterworth and theologians like Craig. Physicists are open to the idea they may be wrong. They devise tests that are vulnerable to failure. They don’t make their pet theory the default position.

Imagine if instead the physicists had taken Craig’s angle. They might have said:

 

1. Particle properties are caused by either the BEH mechanism, or by something else.

2. No one’s offered a “something else” that I find compelling.

3. Therefore, particle properties are caused by the BEH mechanism. Done!

 

But this isn’t what happened. Instead, physicists came up with an idea, then put that idea to the test. First, physicists crafted the BEH mechanism, an idea that fit the known data. But they didn’t stop there. Next they found real-world implications of their theory (the Higgs boson). Then they they devised tests. And finally, at the Large Hadron Collider, they performed these tests and examined the outcome.

god-particle

OK, this isn’t nearly funny enough. Somewhere out there is a good God Particle joke. The search goes on.

This is what is so impressive about the discovery of the Higgs. The BEH prediction could have failed. The physicists could have been wrong. At any point the data might have pointed in a different direction. But it didn’t. The Higgs is really there, the BEH field is an accurate representation of reality. We humans have glimpsed something true, and real, and right about the universe. That is what science can do. God particle 1, God (still) 0.

 

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I was recently in Hitchcock Hall at The Ohio State University with my daughter. Displayed in the lobby is a jet engine used in the Boeing 737.

hitchcock hall display

To the left and the right of the jet engine were two mounted flatscreen monitors giving information about the engine and its operation. We started talking about these two inventions, which both in their own ways changed the world. My daughter made the point that in fact the flatscreen and everything it represents might be a more important invention than the jet engine, because it is the flatscreen and the explosion of information technology that has truly opened the world. It’s a good point. They’re both such amazing inventions, though, that I wanted to write a little about each of them.

How does a jet engine work?

What I’ll write here completely ignores the most important parts of a jet engine – the control systems, the sensors, the subtle ways in which we humans get the engine to do our bidding. Just as Wilbur and Orville Wright’s great contribution was not the physics of flight but the control of the airplane, the thing that makes a jet engine work is the way we monitor and control it. But I don’t know nearly enough to write anything about that.

What I do know is the basic physics of the engine. Much like your car’s engine, the jet engine burns fuel. As the fuel burns, heat is released, and gases expand. Unlike your car’s engine, though, the expanding gases in a jet engine don’t push on a piston. Instead, they push on the blades of a turbine, causing the turbine to spin around 1o,000 times a minute. The turbine is connected via a shaft to the huge fan at the front of the engine. This spinning fan pulls in air. Some of this air is compressed and pushed into the combustion chamber to support the burning fuel. Most of it, though, bypasses the combustion chamber and comes flying out the back of the engine, producing most of the engine’s thrust.

Here’s an animation from NASA showing the key pieces:

engineanimated

This air, mixed with burned fuel and air from the combustion chamber, flies out the back of the engine. That’s the action. The reaction is that the engine (and the aircraft it’s attached to) moves forward, into even more air. And the world flies.

OK, what about the flatscreen?

The same caveats apply. Ask me to build, or even fix, a flatscreen, and I’m lost. The true genius of modern flatscreen monitors lies not in the basic physics, but in the control, the logic, the functionality of the screen. And of these details I’m painfully unaware. Again, what I know is the physics.

Not long ago, televisions were electron guns. Electrons produced at the back of the television flew through a tube (the cathode ray tube) and struck the phosphors at the front of the screen, producing light. The technology worked, but the tubes were heavy, expensive, and used a lot of energy.

Today’s flatscreens depend on two technologies that sound similar but are in fact quite different. The light energy emitted from a flatscreen into your eye originates with light-emitting diodes, LEDs. The particular colors produced by the screen come from liquid crystal displays, or LCDs. Here’s a little about each.

LEDs are light bulbs that don’t use a filament. Instead, they use a sort of cliff, over which electrons fall. When electrons move from one material to another inside the LED, they fall into a lower energy state. You can imagine the electrons jumping off a cliff, shouting “cowabunga” or something as they fall, except the “shout” comes out as a piece of light, a photon. The difference in energy between the beginning material and the ending material determines the type of photon released. Phosphors in the LED turn those photons, usually of a very specific type, into a wide spectrum that our eyes see as white light.

band gap cliff

LCDs are completely different. These in a sense reverse the action of the phosphor inside the LED. By absorbing photons of many colors and emitting photons of just one color, each liquid crystal can make a single dot of a single color on the screen.

This is what an LCD flatscreen looks like up close.

This is what an LCD flatscreen looks like up close.

The amazing thing, though, is that each color cell in the screen can be (and is) turned on and off very quickly with just a small electric signal, allowing each tiny piece of the screen to produce a particular color at a particular time. When added together, all these on and off signals add up to the picture. And the world sees.

Two world-changing technologies on display side by side. Ain’t science grand?

 

OK, if you read my last post you maybe think I’m insane. Maybe you thought so anyhow. But consider . . .

My radio really did turn on all by itself. That’s not all that surprising, even though it’s never done that before. It has, on many occasions recently, switched from Aux to broadcast right in the middle of a great audiobook passage, causing me to, well, not be kind to my native tongue. So clearly there’s some electrical trouble a-brewing in my onboard communications system.

So here’s my question: what if that had happened at a different moment? What if, instead of gooey, cheesy, pepperoni-ey 😉 pizza, there was an ad for Jesus? (What, Jesus doesn’t buy radio ads? Doesn’t he believe in free markets?) Or a Billy Graham crusade? (What, he’s retired? Well, his son’s still at it, right?) Or some such thing? Would I have been shaken to my core?

I’d like to think not. I’d like to believe that I’d stick to my ideals. Supernatural explanations are always bad explanations. It has nothing to do with odds. It has to do with the nature of explanation. Unlikely things have to happen sometimes – otherwise they wouldn’t be unlikely, they’d be impossible.

Something caused my radio to turn on. That something certainly has a physics explanation – most likely a pretty boring one. The easiest person for me to fool is myself.

So play on, 97.1 The Fan. Anybody else hungry for pizza?

 

Last night’s Cosmos episode, the twelfth of thirteen, gave a straightforward and understandable explanation of how carbon dioxide warms the Earth. I thought it was very well done.

Naturally, the howling began soon after, as deniers pulled out their favorite misunderstandings and/or misrepresentations of the facts. Everyone is entitled to their own opinion regarding what we should do about carbon dioxide and climate change. Everyone is not entitled to their own facts. The next time a denier goes on about the unsettled science, say this:

 

Fact: the Earth emits much more infrared that it absorbs from the Sun (why? I’ll explain below)

Fact: carbon dioxide absorbs infrared light. (why? I’ll explain that below, too)

Fact: when carbon dioxide absorbs infrared light, it re-emits a large percentage of that light right back to Earth (this is simple geometry – the atmosphere is not very far above the Earth)

Fact: this re-emitted infrared light adds heat energy to the Earth (this is just physics – all light carries energy, E = hf)

Now, the denier must explain in what weird universe adding heat energy to the Earth doesn’t affect temperature. It really is that simple.

 

OK, details, just because they’re great science. First, the Earth emits much more infrared than it absorbs from the Sun. The Sun is quite a bit hotter than the Earth, so hot that it glows white-hot. The Sun sends a great deal of visible light toward the Earth.

The Earth glows, too, but it glows in invisible infrared light. Consider that the Earth needs to radiate away the same amount of energy as it absorbs – otherwise the Earth would get hotter and hotter, until it, like the Sun, glowed white hot. Clearly the Earth is not glowing white-hot. Most of the high-energy light from the Sun is absorbed by the Earth and re-emitted as much lower-energy infrared light.

With no atmosphere, that infrared light would just travel out into space. This is what happens, for instance, on the Moon. On Earth, though, the carbon dioxide (and other gases like water vapor and methane) in the atmosphere redirect some of that infrared light back. Why? It’s because of the shape of carbon dioxide.

Consider an oxygen (O2) or nitrogen (N2) molecule:

oxygen molecule

 

These molecules are made of just two atoms. Suppose someone asked you to bend this molecule. You can’t bend it in the middle, because there’s no atom there, just empty space. The only way to affect its shape is to move the atoms closer together or further apart. It’s like trying to break a baseball bat by pulling it longways. Pretty hard to do. This is why the air is see-through. Not just infrared light, but even visible light is of too low an energy to vibrate oxygen or nitrogen molecules (actually, blue and purple light do have enough energy to affect the molecules somewhat, which is why the sky is blue).

now consider a carbon dioxide molecule (CO2)

carbon dioxide

 

This molecule has three atoms. It can vibrate in a new way. In addition to the really hard direction of pushing and pulling length ways, this molecule can bend in the middle. Just like breaking that baseball bat is a lot easier if you push up in the middle and down on both ends, so the CO2 molecule can vibrate back-and-forth along this shearing direction with a much lower energy input. It turns out that energy level is smack in the middle of the infrared spectrum.

These facts can’t be denied. CO2 does absorb infrared light and send it back to Earth, causing the Earth to heat up. You can have your own opinion regarding what we should do about this extra heat (I have some strange ideas myself), but you’re not entitled to your own facts.

A pendulum swings back and forth.

foucault

Gravity keeps the wire taut. An electromagnet near the pivot at the ceiling gives just the right push, just the right pull, to keep the pendulum swinging. Below the pendulum, the Earth turns.

But wait. Isn’t the pendulum attached to the Earth? Surely the ceiling, connected to the walls, connected to the floor, connected to the ground, all turn with the Earth. You and I turn with the Earth. What makes the pendulum so special?

Let’s try an experiment. A ball is connected to a string. You are the Earth, and the ball and string are your pendulum. Swing the pendulum gently back and forth. Now turn in a circle. You’ll see the pendulum staying in the same plane, swinging back and forth, back and forth despite your rotation.

So it is on the rotating Earth. The pendulum holds its plane as the Earth turns below.

This would be true if we lived on either of our planet’s poles. But the weather is not so good.

Now hold the pendulum horizontally, as if your belt were our planet’s Equator. This time as you turn, you see the pendulum turning with you. Of course, you can’t swing the pendulum this way, but you can see in your minds eye that were it to swing above the equator, it would turn with the Earth.

At my latitude of 40 degrees North, the pendulum acts like two pendulums, each independent of the other. One portion acts as if it is on the North pole, ignoring the Earth’s rotation. The other part behaves as if it is at the equator, tugged along by the Earth’s daily spin.

All this is well-understood, and mathematical models make these descriptions rigorous and exact. We can predict within fractions of seconds just how long a pendulum at any latitude will swing before seeming to return to its starting point on the constantly-spinning Earth.

But the deeper question remains. Why? Why should the pendulum preserve its original plane? The question actually has a more general form: Why should constant-speed straight-line motion be no different than standing still, but motion in any kind of curve, arc, or acceleration be detectable by things like pendulum precession?

einstein with pendulum

The answer is deep and surprising. The universe has a memory. It remembers the path of everything, not through three-dimensional space, but through four-dimensional space-time. The pendulum at the north pole continues to keep its plane because it remembers its former self. Even in a universe in which nothing existed except the pendulum and the gravitational field which keeps it taut, the pendulum would hold the plane established by its own past. Three-dimensional motion through space is relative. Four-dimensional motion through space-time is absolute. What a strange world we find ourselves in.

If you read my last post about light, you know that light of all kinds (visible and invisible) is produced when things with an electric charge (like electrons) are jiggled.

Today the science blogs and even the ordinary news websites are abuzz with the announcement that researchers with an experiment called BICEP2 (what a great name!) have detected gravitational waves in the microwave radiation left over from the Big Bang. Deep, exciting, but still somewhat preliminary, this is a discovery worth watching. It could settle once and for all whether cosmic inflation really happened and may even give us insight into whether or not we live in a multiverse. So what in the world are gravitational waves, and what, if anything, do they have to do with light?

Jiggling electric charge produces electromagnetic waves (radio light, visible light, x-ray light, and so on). Is there such a thing as “gravitational charge”? Yes there is. We call it mass. But since all matter particles have mass, they all possess this “charge.”

We notice gravity every day when we stand up, jump, or try to keep our meatballs from rolling off our plate. Mmm, meatballs. This is because we live on Earth, and Earth has a lot of mass. But everything, not just things with a lot of mass, produces a gravitational pull. It’s just that, for most things, the pull of gravity is incredibly small.

Yet even this small pull has been measured. In 1797-98, English scientist Henry Cavendish measured the gravitational force between two heavy balls. His experiment was so sensitive that Cavendish had to observe it from far away, ensuring that his own movements wouldn’t disturb the delicate equipment. A telescope focused on the apparatus led out of Cavendish’s basement laboratory and to the enraptured scientist stationed far away. He watched as the two balls oh so delicately pulled toward one another. Cavendish had just measured the strength of gravity.

A modern version of Cavendish's experiment, using a light source and a mirror to measure the gravitational pull.

A modern version of Cavendish’s experiment, using a light source and a mirror to measure the gravitational pull between the larger balls, M, and the smaller, m.

Cavendish’s experiment helped us know the value of the gravitational constant, G, that appears in Newton’s equation for gravity. G plays the same role in Newton’s gravity equation that εand µplay in the equations for electric and magnetic fields.

\ F_C = \frac{1} {4 \pi \varepsilon_0} \frac{q_1 q_2} {r^2}

|\boldsymbol{F}_m|={\mu_0\over2\pi}{|\boldsymbol{I}|^2\over|\boldsymbol{r}|}.

F = G \frac{m_1 m_2}{r^2}\

Just as Maxwell’s manipulations showed that electromagnetic waves (i.e. light, both invisible and visible) moved through space with a particular speed c, Albert Einstein’s work with gravity showed that it, too, moved through space with a particular speed. What is that speed? Amazingly, it is that same value c, the speed of light (and, as it turns out, gravitational waves). Einstein’s work showed that, just as jiggling an electron up and down produced electromagnetic waves, jiggling any massive object up and down produces gravitational waves. The catch is that gravitational waves are so incredibly weak that they are extremely difficult to detect.

While the BICEP2 data is not what most scientists would call a direct detection of gravitational waves, it is (if it holds up) excellent evidence for their existence. However, despite what some web stories are claiming, this is not the first indirect gravitational wave detection in history. In 1974, Joseph Taylor and Russell Hulse, using data collected from the Arecibo radio telescope in Puerto Rico, found two neutron stars traveling about one another in tight, fast orbits. These neutron stars are so massive, and are orbiting so quickly, that they produce copious gravitational waves.

The diagram shows how the two neutron stars in the Taylor-Hulse system lose energy to gravitational radiation as they orbit one another.

The diagram shows how the two neutron stars in the Taylor-Hulse system lose energy to gravitational radiation as they orbit one another.

Just like light waves, gravitational waves carry away energy. That energy has to come from somewhere; Einstein’s theory showed that the energy for gravitational waves produced by two such orbiting bodies must come from their orbital energy, causing the bodies to move toward one another and spin even faster (a bit like water getting faster as it spins down a drain). Taylor and Hulse were able to measure this changing rotation rate, and it matched Einstein’s prediction beautifully. While they hadn’t detected gravitational waves directly, Taylor and Hulse had shown that the orbiting neutron stars behaved exactly as if gravitational waves were real.

The lovely and impressive Arecibo radio telescope, where Hulse and Taylor made their observations.

The lovely and impressive Arecibo radio telescope, where Hulse and Taylor made their observations.

There’s a beautiful symmetry between the behavior of electromagnetic waves and gravitational waves. Both are, in an important way, properties of the fabric of spacetime – both are something the universe does. Both move at a particular speed, c. Both come in “colors” determined by their frequency. And, crucially, both give us a window to understand the universe.

When new kinds of electromagnetic waves beyond visible light were discovered, they revolutionized our understanding. Radio light, infrared light, ultraviolet light, x-ray light, and gamma ray light all gave us new insights when they were collected from the sky, including discoveries of pulsars (neutron stars), quasars, black holes, gamma ray bursts, and the cosmic microwave radiation itself. If and when we’re able to not just infer but in fact detect and study gravitational waves, we’ll have an entirely new way of “seeing” the universe. Who knows what discoveries await?

Light is something the universe does.

light

I wanted to use that statement in an article I wrote a long time ago, but the editor didn’t allow it. What ever could I have meant by such an odd statement? Just this.

Light is ubiquitous. We know what happens when we enter a dark room and flip on a light switch. Suddenly (and it does seem to be sudden) objects in the room become visible. A flashlight can do something similar, and we can even direct the beam of the flashlight at particular objects and not at others.

I remember being puzzled by the car’s rearview mirror. I’d ask an adult what the mirror was for and learn that it gave a view behind and outside the car. Not from my vantage point, though. Apparently the light entering another’s eyes could be different than the light entering my own.

I also remember standing outside on a warm summer day, feeling the heat of the Sun on my face, my hands, my back. Light bulbs that had been on were hot to the touch, and a crayon positioned under a lamp would melt into a waxy puddle. Light could do things.

But what was it?

Another early memory is of my dad building for me an electromagnet from a battery and some wire. Pressing on the wire over the battery brought the wire into contact with the button at the top, completing the circuit and allowing the whole thing to pick up paper clips, screws, and so on. How was it that completing a circuit could turn wire and a battery into a magnet?

What I didn’t know was that every time I completed that circuit, I was sending electrons streaming along the wire, and those electrons were sniffing out the space all around. The way that electrons sniff involves spreading electric (if the electrons are still) or both electric and magnetic (if the electrons are moving) fields, and the ability to sniff in a particular medium (air, say, or water, or rubber, or anything else in the space) is called the permittivity (for electric fields) or permeability (for magnetic fields) of the medium.

What if there is no medium? What if the circuit is just surrounded by pure vacuum? Even here there is a permittivity, as well as a permeability. In fact, these are constants of nature, known as ε(read as epsilon zero, the permittivity constant) and µ(read as mu zero, the permeability constant). These values show up in the most interesting places; for instance εappears in the formula stating how strongly two electrically-charged objects feel each other when separated by some distance r:

\ F_C = \frac{1} {4 \pi \varepsilon_0} \frac{q_1 q_2} {r^2}

Meanwhile an analogous formula for magnetic field strength includes µ0

|\boldsymbol{F}_m|={\mu_0\over2\pi}{|\boldsymbol{I}|^2\over|\boldsymbol{r}|}.

(Note that magnetic fields are about electric current I, while electric fields are about electric charge q, indicating that it’s moving electrons that cause magnetic effects).

What does all this have to do with light? Just this. Around 1861 Scottish physicist James Clerk (pronounced “Clark”) Maxwell was fiddling around with the equations for electric and magnetic fields. What happened next changed our understanding of the universe forever. Maxwell found that his equations predicted that electric and magnetic fields could propagate through empty space, one producing the other on and on. That propagation would take the form of a varying electric and magnetic field moving in a particular direction. The speed of that propagation came out as a constant number, dependent only on the electric and magnetic constants εand µ0.

c_0={1\over\sqrt{\mu_0\varepsilon_0}}.

Even more amazing, though, was the number Maxwell got when he plugged those numbers into the equation. The value of c came out suspiciously close to the measured value for the speed of light! Put the equations of electricity and magnetism together, and the speed of light comes flying out of your math, unbidden and unexpected, but undeniably there.

We now know that any time electrons jiggle, whether it’s in the radio transmitter of your cell phone, in the awesome accelerated motion of an x-ray machine, or even in the hot filament of a flashlight, the result is light. Some of that light you can see, like a small portion of the light from a hot light bulb filament. Much of it you can’t see, like the radio light flying away from your cell phone or the x-ray light bouncing off your dental fillings, or the infrared light that does much of the work in heating your face in the Sun or your crayons under a lamp. Yet every bit of it is light, an electrical and magnetic vibration in the very fabric of the universe.

Light is something the universe does.

Special relativity is famous for drawing shocking conclusions from relatively (ha) straightforward math. Yet the derivation of E = Mc2 is often left out of these simple derivations. Science writers need a good way of answering the question “Why does E = Mc2?” and so I’m writing this down, inspired by a discussion in The Universe in the Rearview Mirror by Dave Goldberg.

First comes a qualitative description, which becomes beautifully quantitative with just one additional step. It also mirrors Einstein’s actual derivation of the formula. Ready? Here we go . . .

Begin with two bedrock principles. One, the conservation of energy, which will play a small part in the following, and only toward the end. Two, the conservation of momentum, which will play a larger part right from the beginning.

OK, imagine if you will an atom sitting perfectly still. That atom emits a pair of photons of exactly equal frequency (f) in exactly opposite directions.

(“Ah, ha!” you say, “already you’re violating one of your bedrock principles, or else assuming what you’re setting out to prove, for where did the atom get the energy to emit two photons? Don’t worry about that for now. Just assume that the atom was “energized” somehow. We know that atoms emit photons like this often, so it’s no stretch to begin the thought experiment with an observed phenomenon.)

Since a photon’s momentum is determined by its frequency (see below), and the frequencies are equal, we know that these two photons have identical momentum. Since they also are emitted in exactly opposite directions, their momenta exactly cancel. As predicted by the conservation of momentum, the atom does not move. It is in the same position before and after the emission.

Now imagine that same situation, but think of the atom moving slowly across your field of view (maybe the atom is moving, maybe you are moving. According to the Principle of Relativity, it doesn’t matter.) We specify slow motion to show that this is not an effect of high speed, but rather an effect of any motion at all.

Photons always move at the speed of light (c), so the emitted photons (whether against the direction of the atom’s motion or with the direction of the atom’s motion) will just move at the speed of light, no faster and no slower. Instead of changing speed, they change frequency (f). The photon emitted in the direction of motion is “squashed” into a higher frequency f’, while the photon emitted opposite the direction of motion will be “stretched” into a lower frequency f’’. This is just the Doppler effect for light.

Photons have momentum. We know this because light shining on a surface actually pushes on that surface. However, the momentum of a photon can’t be given by mass times speed, because photons have no rest mass. Instead, we know that the photon’s momentum is given by p = hf/c, where p is the momentum, h is Planck’s constant, and c is the speed of light.

Now we notice something strange. In the non-moving frame, we see that momentum is conserved quite naturally: hf/c = – hf/c as the left and right photon momenta cancel. In the moving frame, though, the atom keeps moving at the same speed before and after the emission (this is necessary by the principle of relativity; we can’t tell if the atom is moving and we’re sitting still or if we’re moving and the atom is sitting still – or even if we’re both moving at the same rate when we think we’re both at rest). This means that in the moving frame the atom’s momentum plays no role if the atom is the same before and after the emission. This is crucial, so hold it in your mind.

In the moving frame the photons are either squashed or stretched. This changes their momentum. In particular, there is suddenly more momentum in the forward direction and less in the backward direction. Uh oh! We said that one of our bedrock principles is that momentum is conserved. How can that be? It appears that in this example momentum is created from nothing.

There’s only one way to save our momentum conservation bedrock. The atom itself has to change. In particular, some of the atom’s mass must have disappeared. Where did it go? The only sensible place is into the photons. But since photons have no mass, that mass must have become energy. Wow!

Now for a more quantitative approach.

In our naïve assumption that the atom doesn’t change in the emission of photons, we ended up with something that made no sense. Here it is

The no sense “equation”:

momentum before  =  momentum after

mv = hf’/c – hf’’/c  + mv

where m is the mass of the atom and v is the atom’s speed. This “equation” tells us that hf’/c – hf’’/c must equal zero. We know that can’t be true, because when the atom is in motion the photons are no longer identical – one is squashed and the other is stretched; this changes their frequencies and therefore their momenta.

We know by the Principle of Relativity that the v’s have to be the same on both sides of the equal sign. This means the two m’s in this equation are not the same.

Let’s call the m before the emission m0. Let’s call the mass after the emission m’.

OK, here’s the equation again; this time it really is an equation:

momentum before = momentum after

m0v = hf’/c – hf’’/c + m’v

now we rearrange a little

(h/c)(f’ – f’’) = (m0 – m’)v                             (1)

This equation (we’ll call it equation 1 because we’ll need to call on it later) tells us that the difference in momentum between the two photons must be equal to the difference in momentum (which comes down to the difference in mass) between the atom before emission and the atom after emission.

So what is the difference in momentum of the two photons? This is something we can know experimentally, or we can use the formula for the Doppler effect for light. We’ll do the latter here.

For the photon emitted in the direction of motion:

f’ = f(1 + v/c + (v/c)2 + (v/c)3 + . . . )    NOTE: frequency gets bigger for the squashed photon

For the photon emitted opposite the direction of motion:

f’’ = f(1 – v/c + (v/c)2 – (v/c)3 + . . . )    NOTE: frequency gets smaller for the stretched photon

Here’s the nice thing about using a very slow atom. v is much, much smaller than c, so for anything bigger than (v/c)2, the number becomes tiny, tiny, tiny. We can ignore such tiny numbers, hooray!

Now let’s go back to equation (1), putting in our new values for f’ and f’’.

Equation 1:

(h/c){ f(1 + v/c + (v/c)2 + (v/c)3 + . . . ) – f(1 – v/c + (v/c)2 – (v/c)3 + . . . ) } = (m0 – m’)v

and simplify:

(h/c){f(2v/c)}  = (m0 – m’)v    NOTE: all the other terms either cancel {f – f and (v/c)2 – (v/c)2} or else are so small that we can ignore them.

And simplify some more (the v terms cancel, the c terms are combined)

2hf/c2 = (m0 – m’)

We’re almost there!

We know that the energy of the two photons is just 2hf (again, the Principle of Relativity tells us that the energy in the rest frame and the energy in the moving frame has to be the same). We also know that the term m0 – m’ is just the change in mass. Let’s call that change in mass M

Then 2hf = E

(m0 – m’)  = M

E/c2 = M

And finally,

E = Mc2

Wow indeed. The energy that came out as two photons is just the mass lost by the atom, multiplied by the speed of light squared.

The Higgs Field is Ugly.

Despite physicists’ tendency to wax eloquently about the beauty and harmony they uncover in their particle accelerators, if you really press them they’ll admit that the Higgs Field is an ugly piece of physics stuck on to our universe for no apparent reason.

Well, maybe for one reason.

But you’re not going to like it.

The Higgs field isn’t even the ugliest piece of physics out there. Far, far uglier is an even more recent discovery, something known as vacuum energy.

But let’s start with the Higgs. It’s ugly enough to get your revulsion meter running.

The Higgs field, we’re now fairly certain, permeates all space. Its tiny, tiny value ensures that matter particles like electrons and quarks interact with it, giving them mass. They don’t interact too much, though, otherwise they’d appear much more massive than they do. The problem is, the Higgs has no business being so small. When we add up all the factors that go into the Higgs field, we find that it ought to be huge, about 1016 times (that’s a 1 followed by 16 zeroes, or about ten million billion times) larger than it is.

So why is the value of the Higgs field so low? You’re not going to like the answer. Keep reading.

In 1999 cosmologists made a shocking discovery. The universe, known for many years to be expanding, is not merely getting bigger. It is accelerating. The acceleration is caused by something that physicists had assumed was zero. We now know that it isn’t zero, but instead is extremely tiny. It’s called the vacuum energy.

Like the measured value for the Higgs field, the measured value for the vacuum energy is too small. Way too small. In fact, the difference between theory and experiment in regards to the vacuum energy has been called “the worst prediction in the history of physics.”

The vacuum energy is smaller than the predicted value by a factor of something like 10120. This is a number so large that it literally defies explanation. Remember that 10120 is already ten times larger than 10119, which is ten times larger than 10118, and so on. Then consider that the total number of particles in the observable universe is something like 1080, which is 1040 times smaller than 10120, and you start to get just a glimmer of just how big that number is – and just how big a problem physicists face.

In a crazy turn of events, though, these two problems, the Higgs problem and the much larger vacuum energy problem, have found a potential solution in two quite separate fields: string theory and cosmology.

In the late 1990s, string theory, the idea that all elementary particles are made of tiny strings, seemed on the verge of a breakthrough. The various forms of string theory looked to be converging, and hopes were high that a single “theory of everything” was just around the corner.

Then disaster struck. String theorists kept finding more and more new versions of string theory. They kept finding more and more ways for strings to form a universe. They kept finding more and more ways that the extra dimensions and other parameters of string theory could fit together mathematically in a coherent description of the world.

No one knows for sure, but it seems likely today that there are at least (ready for this?) 10500 distinct, consistent ways that strings can make a universe. Every one of these 10500 (the number is so big that even 10120 is utterly dwarfed by it) has different laws of physics; in particular different values for the Higgs field and different values for the vacuum energy.

OK, big deal. We only have one universe, right? So who cares if there are 10500 different ways to put a universe together? We live not in 10500 universes, but just the one. Don’t we?

That’s where cosmology comes in. The Big Bang is by now a well-established event in the history of the universe, but the Big Bang all couldn’t explain some very puzzling observations about the early universe. It took an idea called inflation to make the Big Bang universe work. Briefly, inflation is the idea that at the moment of the Big Bang the universe grew by an enormous amount, far faster than the speed of light ordinarily would allow. Inflation explained why the universe looks the way it does today.

But the causes of inflation remained murky. Some researchers realized that if inflation could start once, it could start again. In fact, the real problem wasn’t starting inflation. It was stopping it.

In an inflationary universe, the end of inflation could never be a global phenomenon, but only a local one. In other words, the end of inflation in our piece of the universe would not have spelled the end of inflation in the rest of the universe. Inflation would keep going, on and on, possibly forever. Each time it stopped, a new bubble universe would be created. And (here it comes) each of those bubbles would have its own unique laws of physics.

So where does that leave us? Scientists argue and sputter about what is science, whether these ideas are measurable, testable, have anything to do with our reality. But as spectators we can take the longer view. Many, many different lines of reasoning are now pointing us in the same direction: we are but a single instance in a vast and ancient multiverse.

Tragically, it is entirely possible that we will never be able to prove this idea.

I told you you weren’t going to like it.

I am a realist. I believe there really is a reality out there, whether or not we can always collect evidence related to that reality. As an observer of science but not a scientist, I find it quite likely that we live in a multiverse in which our observable piece is but one tiny bubble, a single instance in a far grander collection of separate universes. It is also likely that these other bubbles have separate values for things like the Higgs field. There are probably many factors that go into determining the Higgs field, and those factors themselves can be scrambled around as new universes come into being.

The Higgs, then, is ugly because it’s parochial. The question, “Why does the Higgs have the value it does?” becomes equivalent to asking why the Earth orbits 93 million miles from the Sun. Sure, there is a proximate answer to that question, having to do with this asteroid nudging that asteroid, this planetoid glomming on to that one, and so on. But such details aren’t very interesting. The ultimate answer, the answer we were really looking for when we asked why in the first place, is that the Earth orbits as it does because while many orbits were possible, in most of those we would not be here to ask.

Similarly, there may be no interesting physics reason explaining why the Higgs field has the value it does. Certainly, the proximate explanation will discuss things like fields, particles, and their interactions, but the ultimate answer will be that the Higgs (and the vacuum energy, and probably many other constants of the universe) have the values they do because we intelligent beings can find ourselves only in that tiny fraction of bubbles in which the laws of physics allow for us. And despite our very best efforts, we may never be able to prove that this is true.

Like I said, ugly.

higgs ugly

This is the photo that came up when I searched for “Higgs ugly”. I’m sure someone out there knows who this is, but I’m thinking she is neither of those search terms.

My new book is now available as an ebook at Barnes and Noble. From the website:

Atoms and Eve is a story of discovery. Born in 19th century America, Eve Dalrymple wants to know everything. She struggles to find her way in the male-dominated field of nuclear physics, but thrills to the amazing discoveries she and her colleagues make about the nature of the atom. Those discoveries will ultimately lead Eve, her heroes, and her colleagues to the most difficult and dangerous moral dilemmas the world has ever faced. Through Eve, we experience the wonders of the hidden, beautiful, and perilous world of the atom.

The cost of the ebook is $1.00. After the ringing success of The Turtle and the Universe (whose title was swiftly changed to “half off” I think), no publisher wanted to commit paper and ink to another effort. After much thought, I decided to go the self-publishing route.

If you don’t have a nook reader, no worries, you can download the free nook reader app for use on your computer or mobile device:

http://www.barnesandnoble.com/u/nook-mobile-apps/379003593

For my COSI friends out there, you’ll recognize that Eve’s story is inspired by the Electric Workshop in Progress. Yes, I changed the spelling of “Dalyrimple” and I changed Eliza to Eve so as to make a weak joke. But I think you’ll enjoy the story behind all those crazy electric machines.

I’d love to know what you think of Atoms and Eve.

My first book, called The Turtle and the Universe, was published by Prometheus Books in July 2008. You can read about it by clicking on the link above.
My second book, Atoms and Eve, is available as an e-book at Barnes and Noble. Click the link above. You can download the free nook e-reader by clicking the link below.
November 2017
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A blog by Stephen Whitt

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