The Saga of Light, Part 1: Electromagnetic… RADIATION!!!

Bremsstrahlung

Bremsstrahlung is German for “braking radiation” (braking, as in “car brakes”, not breaking like “it broke my heart when they cancelled Ash vs. Evil Dead”). Based on the name you can probably get an idea of what it’s all about: it’s the emission of electromagnetic radiation that must necessarily result when a charged object is brought to a halt. Though a particle doesn’t really have to fully come to a “stop” to still be called Bremsstrahlung. In fact, it is most commonly used to refer to what happens when two charged particles scatter off one another, like an electron scattering off an atomic nucleus.

The scattering of particles can conceptually be thought of in a very simple way: two particles, with speeds and directions of motion v1 and v2, go into a little black-box, which is the scattering event itself, and then trade some energy and momentum in the hidden, nonjudgmental secrecy of the black box (salacious!) before emerging with some new direction and speed (v1,new and v2,new).

Bremsstrahlung2

Generally there are rules for what kind of hanky-panky can transpire, such as the total energy and momentum of the system must be conserved and such. In fact, figuring out exactly what happens in such a scattering event is a super advanced topic in physics, but thankfully we really don’t need to care about any of that. All we care about is that they go into the mystery conceptual box and “something” happens and when they come out we expect the speed and direction of the particles to change during the scattering.

If we want to get fancy here, Newton’s First Law says: “an object in motion remains in motion with a constant speed and in the same direction unless acted upon by an external applied force”, Newton’s Second Law says: “applied forces produce accelerations, with the resulting acceleration being in-step with the strength of the applied force”. Yes, that is a super dense couple of statements but really all that means is that if its speed is changed OR its path is simply deflected in direction, then it has experienced an acceleration/deceleration event. Often both happen (both direction and speed are changed), but – as we’ll see – not always. Put another way, the literal definition of acceleration is the amount that velocity changes in a given amount of time. Velocity has a speed and direction and thus when you have a change in speed or direction you have had acceleration (or deceleration) occur. Because that’s so important to understand let me repeat that yet again: if a particle’s direction of motion is changed, even if it maintains the same speed, then acceleration has occurred and there will be emission of light.

So charged particles, bonking against charged particles give off electromagnetic radiation. This will be super important in just a moment when we talk about black-body radiation. However, Bremsstrahlung can be more generally conceptualized as any EM emission resulting from the “braking” or slowing-down of charged particles. For example, if you launch high speed electrons at a large chunk of material, they’ll penetrate into the material some distance as they are brought to a stop (well, within the material they’ll still have thermal motion but they’ll have lost all their “shooting” motion they initially had). This is in fact exactly how we make X-rays.

In an X-ray tube, like those used in medical X-rays and CT scanners as well as airport luggage scanners (ugh!) and in certain scientific apparatus(es), like X-ray crystallography machines, electrons are accelerated to very high speeds using basically an electron particle accelerator and fired at a metal target. As the electrons hit the metal target and bleed off their excess speed by repeated collisions with the atoms of the metal, X-rays are produced. Like a high diver penetrating into a pool at high speeds and being suddenly brought to a stop over a very short distance/depth by the water.

Now of course, when one says “electron particle accelerator”, one might be thinking of some super fancy device, like the big particle accelerators at CERN in Geneva (like the Large Hadron Collider). But no, to make an electron particle accelerator you just need two pieces of metal and a power source in a glass evacuated chamber. Such “cathode ray tubes” (CRT) were also how old CRT televisions worked. Though in a CRT television screen the accelerated electrons are being shot at a phosphor coated screen rather than a metal target as the goal is to create visible light rather than X-rays, however such screens were actually made with thick lead glass so that any unintentionally created X-rays never left the tube. This, by the way, is why you should always dispose of CRT screens in the “e-waste” bin and not send them to regular landfills (well, the lead and some other toxic elements used in their manufacturing).

Fixed_anode_x-ray_tube
[Source: https://en.wikipedia.org/wiki/File:Fixed_anode_x-ray_tube.jpg]

Anyways, that was a bit of an aside on electron accelerators. Of course, there’s tons of engineering that goes into making a very good X-ray tube that is very efficient and reliable, but my point is just that such devices, at their core, are really fairly straightforward and not at all as complex or large as the phrase “electron particle accelerator” would have you think.

It’s also worth pointing out that Bremsstrahlung doesn’t technically have to occur in such fancy atomic-and-subatomic-particles scenarios. Like if Marty McFly in Back to the Future had not reached the 88 MPH he needed to go back in time but the DeLorean was still struck by lightning and became charged and then it smashed into the town hall and suddenly came to a stop… you would get Bremsstrahlung… and Marty would probably be dead. And if you don’t have any idea what I’m talking about… well… you should watch better movies!

In the case of a DeLorean, it wouldn’t be X-rays, mind you, because electrons shot from an accelerator have speeds near that of the speed of light, and are decelerated to essential a stop (or no net motion in the same direction) where the DeLorean is going from 88 MPH to 0 MPH in a split second, which is… ya know… a lot slower, so you’d get more radio light (more on this in the next post). But it’d be there; you have a charge and it’s being decelerated.

Black-Body Radiation, Our First Look

Let’s now make our first attempt (we’ll have much more to say about this in later posts) at understanding why you and everything around you is glowing… all the time, even if you don’t think you are. This has to do with what is called ”black-body” radiation.

Ok so to start off, what’s with the name “black-body radiation”? That kind of sounds ominous. But what it means is pretty straightforward. The light that a detector like our eyes detects could come to us through a number of different routes. One of the key ones is reflection off an object and the other is through an object’s own emission of light. We’ll have a lot more to say about this later but for now we just need to understand that when I look at a real object, the light that I get is a combination – or a sum – of these two. I receive light that it is reflecting from an external source and light that is being emitted by the body itself. And what we want to do is sort of conceptually separate the two (emission and reflection) and ignore reflection and only talk about light that is being emitted by a body.

So what the phrase “black-body” refers to is a hypothetical, magical material that reflects absolutely zero light. Blacker than black, blackest night, like that Green Lantern arc. So black-body radiation is basically “the light that you would see, even if you had a black-body which reflects nothing”. And that’s all the term “black-body” means. It means if we separate reflection and emission then, conceptually, black-body radiation is the emission-only part that I’d get regardless of whatever reflection is happening.

And what we’re about to learn is that everything and anything emits black-body radiation, no matter its material properties or whether it’s gas, solid, or a quark-gluon soup (which would not be as tasty as it sounds). Everything emits this light all the time. There’s only one condition, that it have a temperature above absolute zero. If it’s warmer than the coldest possible temperature, which is about -273 degrees Celsius (or -460 degree Fahrenheit in Freedom Units), be it you, your desk, my cat staring at me creepily right now, it’s glowing. Constantly. Of course you don’t seem to be glowing. Your eyes don’t see you or your desk as glowing, and the fact that my cat is glowing is an entirely unrelated coincidence. But we do see hotter objects, like the Sun or an incandescent light-bulb or a camp-fire as glowing and they are glowing exactly because of this black-body radiation. But we’ll get to that. First let’s look at why you’re glowing, – and trust me for now that you really are – and where this “black-body radiation” comes from.

But, Why?

So, why? Let’s keep this qualitative. There’s two key ingredients here. The first is one we’ve already talked about. Accelerating or decelerating charges, which is to say charges that are speeding up or slowing down, give off light; electromagnetic radiation. And what are atoms? They’re clouds of electrons (which are negative charges) and atomic nuclei (which are positive charges). They’re charges. They may be present in equal numbers, thus the atom as a whole may have no net charge, but they’re still charges individually. And if something has a temperature above absolute zero, what are they doing? They’re moving. In a sense, temperature is the average amount of motion the particles in a system – gas, liquid, solid, whatever – have. The higher the temperature, the higher the average speed.

But this thermal motion is a bit of a random chaos. Atoms or molecules (or sub-atomic particles, or a plasma of ions or whatever, like I said, all states of matter emit this black-body light) are flinging about and colliding with one another, and transferring energy and momentum (we talked about this) and their life isn’t terribly unlike that of a pinball. And as we learned with Bremsstrahlung, a collision of charges results in emission of light.

Furthermore, the amount and energy of the light emitted isn’t random. Just as the temperature of a substance reflects the average particle speed, the average particle speed reflects the average deceleration or acceleration characteristic of a collision that most frequently occurs at that temperature. So random thermal collisions generate a constant output of light, but the varieties of energies or wavelengths of that light have a distinct spread that is also related to the temperature. We’ll learn more about the exact spread and variety of light that is emitted by black-body radiation in a later post, but all we care about now is that you have this constant emission.

So that’s the first part, thermal random motion constantly generates light.

The second part that makes black-body radiation possible is something I’m actually not going to talk about (sorry). And that’s because it relates to that dastardly thing called quantum mechanics. All I want to say is that, if you just take the first part of the story and cranked out the math just sort of treating atoms like little charged billiard balls, you’ll predict the wrong mix of light. Not only that, you’ll get an alarmingly wrong prediction. Specifically, if you use those Maxwell’s equations I mentioned previously (which don’t include any quantum effects) alone you’d predict that any and all objects are giving off an infinite amount of light in a given moment.

In fact this exact problem – back around the year 1900 – was one of the original reasons for the development of quantum mechanics in the first place. On top of this issue, there were other issues, such as one we’ll talk about in just a moment dealing with the emission due to orbiting electrons and issues we’ll talk about in later posts of the photoelectric effect and absorption spectra. Resolving this issue with black-body radiation involved big names like Max Planck, Albert Einstein, and… an oven. Actually not a joke. If you’re curious, just look up “the Ultraviolet Catastrophe!”. So-called because people in the early 20th century were super dramatic.

However, quantum mechanics only comes in to our understanding of black-body radiation if you want to figure out the exact right mixture of light you expect to get. But the reason for the light is entirely a result of the (pre-quantum) physics of electromagnetic radiation that we’ve already discussed. There’s just a lot of charges colliding and those collisions basically cause deceleration/acceleration that leads to constant emission of light.

Later in these posts we will come to understand in great detail that light actually carries energy. However, for right now just trust me that it does with the promise of justification to come. So, if electric and magnetic fields carry energy then these EM fields which radiate away have energy and must get that energy FROM somewhere. They get it from the motion of the particle themselves, which are then slowed down. This, by the way, is another reason why Bremsstrahlung is called “braking” radiation, because emitting this radiation always leaves the particle moving slower. I honestly don’t know which meaning really inspired the name (i.e. is it named after the emission that occurs when a charge slows down, or the fact that a charge slows down when it emits… these are the questions of our time!)

We talked about how temperature is in essence average speed. So if emission of electromagnetic radiation results in a particle slowing down then when a system emits black-body radiation it cools down. This is why another term for black-body radiation is “thermal radiation”, as it’s bleeding thermal energy to light/electromagnetic energy.

Common Misconceptions by Physics Students (Skip if you’ve never taken a physics class)

I also just want to take a moment to dispel a common misconception about black-body radiation and Bremsstrahlung and the upcoming discussions of other ways light occurs. However, in talking about this misconception I’m going to talk about some concepts that we won’t talk about until later posts. So if the next few paragraphs have a lot of jargon and concepts you’ve never heard of, just skip ahead to the next section. You don’t have the misconception I want to correct so you’re good to go!

As we move on in these blog posts we’ll come to understand more of the quantum mechanical side of light with photons and quantized electron levels and so on. It is a very, very common misconception I see, when people learn about this aspect or perspective on light, that they think that light can only come in certain “quantized” frequencies or wavelengths. They get the erroneous idea that only certain wavelength and frequencies can exist because they learn about these precise electron transition. As we’ll learn in later posts, it is true that electron transitions can be a source of light (like in neon signs or sodium-vapor lamps), but they often aren’t and in fact even they can be continuous.

The things we’re discussing now, like black-body radiation and Bremsstrahlung, occur in both quantum and classical physics and they can produce any wavelength of light. They produce continuous spectra. The energy for the light isn’t coming from some quantized electron transition, it’s coming from the kinetic energy of motion of particles and in free systems (i.e. not bound), even in quantum mechanics, kinetic energy is a continuous quantity. So if you look at the spectrum of black-body radiation (given by Planck’s Law, which we’ll learn about later) you see a continuous spectrum of wavelengths. This DOESN’T change in quantum mechanics. All wavelengths can and are emitted by such light sources.

Antennae

Let me now show you another very common situation where this acceleration and declaration of charge happens. Consider a sort of funny bent wire like the following:

Dipole_Antenna2

and imagine at the center meeting point of these wires there’s a source of electric current that at one moment can pull electric current in from the right and push it out to the left, or switch its polarity and push to the right and pull from the left. Of course it may seem like I’ve gotten very complicated very quickly but the reason I want to consider such a set-up, is because such a set-up is actually quite important to your everyday life.

The net result of this scenario is that as the current source switches, electric current is pushed and pulled down the wire. As this current is pushed and pulled, because at the end of the wire there’s no place for the electrical charges to go, you get positive and negative charges that pile up at the ends of the wires, like this:

Dipole_receiving_antenna_animation_6_800x394x150ms
[Source: https://en.wikipedia.org/wiki/File:Dipole_receiving_antenna_animation_6_800x394x150ms.gif]

And we see what happens with the green arrows which represents the electric field associated with these charges. What we have is a cycle of charges accelerating into the edge of the wire, then they decelerate as they come to the end of the wire, then they come to a stop, then accelerating them again (but in the opposite direction) as we pull them out again and so on, ad nauseum. It’s very similar to my animation of “flicking” a charge except doing it in a continual periodic way. And looking at the animation we see the clear result of this, a sinusoidally varying electric field (there’s also a magnetic field, as we’ll see, but it’s not shown in this animation.) Here’s another animation:

Dipole_xmting_antenna_animation_4_408x318x150ms
[Source: https://en.wikipedia.org/wiki/File:Dipole_xmting_antenna_animation_4_408x318x150ms.gif]

what we have just designed is called a “dipole antenna”. You might also know them as “rabbit ears” antennae.

Rabbit_Ears

Hearing this description of a dipole antenna, with its two prongs designed to push and pull (i.e. accelerate and decelerate) charges, you might wonder why it is necessary to have two prongs. Why can’t you just have a single wire and push and pull a time-varying current up and down it? Well, you totally can, that’s called a “monopole antenna” (in contrast to our “dipole” antenna) for fancy people or often just a “whip” antenna. That’s what the antenna that comes out of your car is, and it’s also the kind you find in, for example, old radios that have a single telescoping rod for an antenna.

In fact there are many, many, many ways of making antennae and each has subtle advantages and disadvantages. However, I chose to focus on dipole antennae because they’re amongst the most common forms of antennae for radio and television applications.

Now let’s look at one last scenario, before ending this post, where light should be emitted but in this special case it actually isn’t

Cyclotron Radiation and the Instability of Atoms

An important point I hammered home when discussing Bremsstrahlung was that a change in speed or direction represents an acceleration. This is something that is not often appreciated. This means that if I have a charged particle going in a circle with constant speed, I still have acceleration because even though its speed isn’t changing, its direction is at all moments.

There are two common scenarios where a charged particle will do this. The first is if it is in a constant magnetic field. It’s really not the goal of these posts to get deep into electrodynamics – beyond understanding electromagnetic radiation, obviously – and we would need to do that in order to really understand why a charged particle will make loop-de-loops if trapped in a region of constant magnetic field. So let’s just take it as a given, here, that it does do this. But, thus, because of this circular motion it must constantly emit light. This is called ”cyclotron radiation”.

A very interesting tangent on this is actually flipping the story on its head: by inputting electromagnetic radiation in a specific way it’s actually possible to accelerate a particle doing loops because it’s in a magnetic field. This is the basis of how the cyclotron particle accelerators of the 1930s worked. Perhaps this might be a good topic for a later entry (vote on the page off the side-menu if this interests you!). But this cyclotron emission of light by charges that are doing loops because they’re in a magnetic field absolutely does happen and isn’t what I want to talk about.

The second common way where we find a charge going in a circle is if I have a very light (as in doesn’t weigh much) negative charge, like an electron, orbiting around a much heavier positive charge like a nucleus. This orbit results from an inward force of electrostatic attraction between unlike (i.e. positive and negative) charges. So it’s much like the orbiting of planets around a star except the force of attraction is from electromagnetism, not gravity and its strength is determined by their charge rather than their mass.

At the turn of the 20th century this picture of a heavy positive nuclei being orbited, like a little planet, by a negatively charged light-weight electron was believed to exactly be what happened in atoms, that you had little electrons orbiting atomic nuclei like the Earth orbiting the Sun. However, this was deeply troubling to the physics of the time and especially to the new rock-star of Maxwell’s equations that had been developed just 30-50 years previously. The issue was this emission that must occur.

Cyclotron_Atom2.jpg

As we talked about with black-body radiation, when this orbiting charge emits light that light must carry away energy and that energy must come from somewhere, namely, from its motional/kinetic energy. Thus, this unavoidable emission must slow down the electron.

But then this idea of an atom being like a little solar system was impossible. Assuming the electron was in a stable orbit, that orbit must decay as it bleeds away energy of motion and converts it to cyclotron-esque electromagnetic radiation and eventually the electron must spiral into the nucleus. But that doesn’t happen. According to the physics of the day, atoms shouldn’t be stable. In fact, if you actually do the math, atoms should decay in less than a few billionths of a seconds. After that, the electron will spiral into the nucleus. So, what gives?

Well, that simple question ended up being only the tip of the iceberg (the Ultraviolet catastrophe was also part of this iceberg). The iceberg that we now call “quantum mechanics” and it turns out that the world of atoms is far, far, far different than any naive picture of orbiting bodies. The reason I’ve brought it up here is so we can see how this simple effect of pre-quantum electromagnetism (accelerating charges must give off electromagnetic radiation) laid at the heart of an open question at the beginning of the 20th century that would eventually rip open all of physics.

Optional Note for Advanced Readers

This apocryphal history I gave of the failure of classical physics is actually a bit lazy in an interesting way. After this discrepancy was discovered but before Bohr put forward his model, much focus was put by people like Paul Ehrenfest on actually finding classical charge distribution that don’t radiate when accelerated. Such distributions actually exist within Maxwell’s equations. If you’d like to learn more about these attempts to save classical physics I’d Google the phrase “nonradiation condition”, one of the very interesting dead-ends that they often drop from physics history books.

Of course, the final realization after the dust settled was that atoms are nothing like little solar systems and, in fact, in something like a hydrogen atom (the simplest possible atom) electrons actually have no orbital rotation at all, quantized or otherwise. And yet, this view of the atom as a rotating electron about a nucleus is still used throughout Hollywood CGI and even in science textbooks despite being thrown out over a century ago. C’est la vie. Though, in their defense I suppose any more accurate attempt would look less visually interesting and at this point it’s more cultural iconography than an actual diagram.

You might then ask, well why is the Earth-Sun system stable? Well, although the Earth is most definitely in a constant state of acceleration as it orbits the Sun (or, “more correctly” the Earth and Sun orbit each other), some rough calculations by me show that its acceleration is 15,000,000,000,000,000,000,000,000 times less than what an electron’s would need to be in that original, pre-quantum notion of an atom. So, suuuuppppeeerrrrr insignificant.

Optional Note for Advanced Readers

My argument here is admittedly a bit shaky as I do not believe it is so straightforward to figure out what the entire Larmor emission is for a neutral body like the Earth. However, it is simple enough to show that an electron in circular orbit with charge q and a radius of the Bohr radius and mass of an electron must have an acceleration of kq^2/(a_0^2 m_0) \approx 9 \times 10^{22} \textrm{ m/s}^2 where the Earth makes a rotation of radius 1 AU every 365 days and thus if we assume a perfectly circular orbit the velocity is v= 2\pi (1\textrm{ AU})/(365\textrm{ days}) \rightarrow a =v^2/(1\textrm{ AU}) = 0.006\textrm{ m/s}^2 . The ratio of those is 1.5 \times 10^{25} . So the Larmor emission could potentially be something else for such a neutral object, but even if it wasn’t, the ratio is negligibly tiny. I estimate ~10-58 Watts of energy loss per electron. For comparison, the orbital kinetic energy of that same electron is ~10-22 Joules. So it would take it ~1028 years to decay due to Larmor emission, which is 19 orders of magnitude longer than the age of the universe. So even if this derivation over estimates things it’s still absurdly negligible.

What’s to Come

Alright, let’s finally bring this post to a close. We discussed a number of ways where light can be produced. However, we certainly didn’t discuss all of them. We will meet many more, such as neon-signs, phosphorescence, sodium-vapor lamps and more in future posts. We’ll also talk about things like predator-vision and tricorders and concerns over the ozone layer and laser thermometers and seeing through walls and much, much more. However, the topic of the immediate next post is on the ways of classifying and describing light and the electromagnetic spectrum

See ya then

QUICK SUMMARY

Electric charges are surrounded by electric fields and the strength of those fields reduce the farther away you are from the charge such that at great distances you cannot detect the existence of this field at all. Moving charges produce magnetic fields. If the charge is moving with a constant speed, the resulting magnetic field is much like the electric field in that its strength decreases with distance such that it is undetectable from afar. However, when a moving charge is accelerating or decelerating the electric and magnetic, or “electromagnetic” field it produces is that of a radiating wave that can be detected even at great distances. This electromagnetic wave is what light is.

Common scenarios where light results are: 1) when particles collide with one another, which is called Bremsstrahlung or, if part of a macroscopic thermodynamic system in thermal equilibrium, black-body radiation, 2) when charged particles undergo circular motion either due to a magnetic field or by “orbiting”. When emission of light happens due to an accelerating charge, the charge is slowed down since light itself carries energy and thus, since energy is conserved, this emission robs the particle of motional/kinetic energy.

4 thoughts on “The Saga of Light, Part 1: Electromagnetic… RADIATION!!!

  1. Great blog post. Thanks for creating it. I have a somewhat related question. Why does changing magnetic field give rise to electrical current? I know it has to be so, it has been proven experimentally, and Maxwell’s equations describe it. However, what is happing in the conductor at the atomic level to make the electrons move in response to the conductor’s relative motion to the magnet? I have scoured the internet for a while but haven’t found a satisfactory answer, except that it is just so. I will appreciate any help in understanding this phenomenon. I am not studying this for an exam; I am just curious. I have been enjoying your YouTubes videos too. Thanks.

    Like

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