The Saga of Light, Part 2: The Hardest Fall in the Universe and How Hot Pockets can Fell Telescopes… And Some Stuff on the EM Spectrum

Binning Light: Visible

Alright let’s go deeper, but now we’re getting to much smaller sizes. So it’s a good idea to give a bit of a new “meter stick”, which is, ya know, smaller than a meter. So not a meter stick… Don’t you love how clear I’m being right now? A micron, or micrometer, is about a hundredth the width of a human hair (i.e. the width of a human hair is ~100 microns). So let’s stop talking about meters and start talking in microns.

Our next line in the sand for light occurs when the wavelength is shorter than 0.1 cm (10,000 microns) and goes to about 0.7 microns. Light here is called infrared. We’ll have a lot to say about this range later. For one, in Part 1 when we talked about black-body radiation and I said you and everyone you’ve ever known is glowing, and you rightly thought I was full-of-it because they’re clearly not… Well, as we’ll find out in a later post, you’re actually glowing in the infrared. But for our first exposure, we’re just learning the names, so let’s just push on.

You’ll notice that the definition of infrared ends at a very precise point: 0.7 microns. You know, radio ended at some nice power-of-ten round value of 1 meter, microwave at some nice round value of 0.1 centimeters, but infrared ends at 0.7. Why? Well, it’s because the next range of light has a very precisely defined range of wavelengths, specifically from 0.7 micron to 0.39 microns. This precision reflects the fact that this range of light means a lot to us humans. In human experience, we make such a huge difference between, say, light that is 0.7 microns, which we call the color “red”, and light that is only 0.2 microns different – 0.5 microns – which we call “green”. That’s because the little fleshy eyeballs we’ve evolved can only detect EM waves with wavelengths of 0.7 microns to 0.39 microns. We’re oblivious to EM waves that have shorter or longer wavelengths.

By the end of these posts, you’ll understand exactly why we evolved to see in this range, and how some animals, like the Predator (totally exists!), benefit from expanding this range. But again, for now, let’s push on.

As we get past violet (0.39), we move into another loosy-goosily defined range that goes from 0.39 microns to about 0.01 microns. This is called the ultraviolet, which again we’ll have a lot more to say about (wear your sunscreen!) later, once we understand more about light, but we’ll just keep going to our next case.

Binning Light: X-Rays

Once wavelengths are less than 0.01 microns, we’ve given them the name “X-rays”, and the X-ray range goes from 0.01 microns to about 0.0001 microns (some say 0.00001 microns). Our micron scale is getting a little unwieldy now, so at the level of X-rays it’s worthwhile to consider a new “meter stick”: the nanometer (or simply “nm”), which is 0.001 microns, or a billionth of a meter. Using this new “meter-that’s-not-a-meter stick” the color red is about 700 nm, violet is about 390 nanometers.

In a normal solid material, the space between atoms is typically on the order of about 0.0001 microns, or 0.1 nanometers. Thus, we see that the wavelength of X-rays is about the same as the spacing between atoms. This is why we have techniques like X-ray crystallography (or X-ray diffraction, also called simply XRD) that allow us to use X-rays to image the positions and arrangement of atoms in materials and molecules. But also, we see that at the scale of nanometers (or, more accurately, tenths of nanometers) we’re now talking about the scale of inter-atomic distances.

The Worst Fall in the Universe (Bremsstrahlung and X-rays)

While we’re on the topic of X-rays, let’s take a bit of an interesting aside and bring in some of our knowledge. In the previous part, we became acquainted with two important ways in which the acceleration of electrical charges could result in the emission of light. The first of these was Bremsstrahlung, or “braking radiation”, which occurs when a charged particle is brought to a stop (or simply has its direction scattered), and we looked at the classic example of the X-ray tubes at the heart of airport luggage and medical CT scanners. In these devices, electrons were accelerated to very, very fast speeds near-ish that of the speed of light (~10%-40% of the speed of light) and shot at a metal slab, called a “target”, which abruptly brings them to a stop – i.e. an abrupt deceleration which results in X-ray emission through this Bremsstrahlung.

Another important type of emission we talked about was when a charged particle, like an electron, orbits something else. In circular motion, the direction of motion is constantly changing which means that the object is under constant acceleration (like the Earth in its orbit around the Sun), and thus light must be emitted. We then talked about why this type of emission helped spell the end of classical physics as it implied that pre-quantum ideas of the atom could not be correct. However, here we’ll talk about a very different scenario where this same type of emission really does happen, but at a much grander scale.

Barring black holes, neutron stars are the densest objects in the universe. They are in a sense, black hole wannabes who went through all the same motions of black holes (made a star, did some fusion, blew up in a super nova, ya know, classic life milestones) but just didn’t quite make it to “singularity” status. What’s special about both black holes and neutron stars is their density, cramming many times the mass of our Sun into a very, very tiny volume (or potentially infinitely small volume in the case of black holes). However, neutron stars aren’t quite as odd as black holes, as they have a clear extent and a real surface.

It is not uncommon for neutron stars to form in the vicinity of another large body of mass, like a second star. When this happens, the second object, which can sometimes be called a “donor” and other times simply “dinner”, will find that much of its mass (i.e. gas and particulate) will be cannibalized by the neutron star as it is pulled into its gravitational influence. Initially such mass will have some net rotation about the neutron star, it will essentially orbit it. However, as the particulate will have a random spread of masses and speeds, this orbiting is far from perfect, and you will have a great deal of random “friction” and collisions between the particles that acts to rob some of them of their net rotational speed and cause them to gradually spiral inwards.

Neutron_Star2

As we’ve discussed, this orbiting is associated with a constant emission of light. As the matter begins to spiral inwards, it picks up speed – like a figure skater drawing their arms in while spinning – which is an acceleration. If that sounds confusing, another way of thinking about it is that the matter is in a kind of free-fall towards the neutron star.

Imagine the speed you would have if you free fell towards Earth from orbit the moment before you hit the ground. Now if you know a little about such things, you know that on Earth you will actually only accelerate in free-fall to a certain maximum speed, called terminal velocity. Terminal velocity is the result of the fact that Earth has an atmosphere, and as you fall you’re pushing air out of the way and the faster you’re going the hard this is to do. In a nutshell, atmospheric drag increases with your speed until you reach a speed where this upward drag force is equal to the downward gravitational force you’re feeling and you stop picking up speed. On a neutron star, this doesn’t happen, you continually accelerate.

You continually accelerate until… you hit the surface. Now big tip for intergalactic thrill-seekers, if you want to achieve the absolute highest possible speed while free-falling towards celestial objects (everyone needs a hobby) you want an object that is both heavy but also has that mass concentrated to as small a volume as possible. That’s really the key point, but if you’d like a more clear idea why I’ve added an optional note below:

Optional Excessive Detail

Now the greater the mass of an object, the greater the gravitational force you feel towards it and thus the greater the free-fall acceleration you experience. In other words, all other things being equal, the amount of speed you pick up each second you fall is greater the more massive the object is. If a planet or neutron star was not a solid object, but magically some weird incorporeal thing, this acceleration would continue, with you picking up more and more speed, until you reached the center where your acceleration and speed would achieve its maximum possible value. However, since neutron stars and planets ARE solid objects, you will be brought short of achieving this maximal speed when you hit the surface. Thus, all other things being equal, the longer you can fall before hitting the surface, the faster your final speed would be. In other words, for the same mass, if the object is more dense and thus packed into a smaller space so you get closer to the center, picking up speed as you go, the faster your final speed will be.

Another way of thinking about this is simply in terms of gravitational potential energy, if you’re familiar with the concept. The amount of gravitational potential energy you have on the surface of a planet/neutron star is proportional to the mass of the planet divided by the radius of the planet. If you do a perfect free-fall starting from a point with no initial speed, the amount of kinetic energy you have before hitting the ground will simply be the gravitational potential energy. Thus, to maximize your final kinetic energy you want mass big and radius small.

Anyways, don’t worry if that’s a bit… dense (puns!), or if you just skipped it, the point simply is that surface collision speed is maximized by having large mass and high density. So if you have a neutron star whose mass may be 10-30 times that of our own Sun and which has been compressed under its own weight to the size of a large city (a mass of a couple dozen Suns shrunk to the size of a few dozen kilometers)… Well, that’s going to be arguably the biggest Wile E. Coyote >THUD< in the entirety of the cosmos.

And remember our Bremsstrahlung? When this mass finally smashes into the surface, the outrageously high deceleration associated with going from 0.99999% the speed of light to 0 releases X-rays. In fact, such X-rays were the *first* astronomical X-rays we ever detected. In 1962 when we launched our first X-ray telescope, we came face-to-face with Scorpius X-1, which – besides having the bitching-est name for a star ever – is the brightest source of X-rays in our sky, other than our own Sun. Of course it's emitting waaaaayyyy more X-rays than our Sun, but it is 9,000 light years away and, as we discussed in Part 1, intensity of light – like X-rays – decreases with distance (but not nearly as much as the intensity of static electric and magnetic fields, which was also a big point of Part 1). In fact, Scorpius X-1 puts out 23,000 billion, billion, BILLION (2.3 x 1031) Watts worth of X-rays. It puts out 60,000 times more X-ray light than our Sun puts out over all ranges of light (i.e. radio + microwave + visible, etc.).

Neutron_Bremsstrahlung2

That light is coming from a neutron star, which is being supplied with a constant stream of new matter by its “donor” star, and as that matter falls inwards it releases some light and as it falls more and more and its acceleration increases that light emission increases until finally it impacts the surface. When the particulate impacts the surface, you then get a *huge* Bremsstrahlung release and the emission spikes in the X-ray range. The worst fall in the universe.

Binning Light: The End of the Line

Okay, enough about X-rays time for our final wavelength range. If an EM wave has a wavelength shorter than 0.0001 microns or 0.1 or 0.01 nm (the end of X-rays), then it’s just called a cosmic gamma ray. Doesn’t matter if it’s just a bit shorter or outrageously shorter, gamma rays are the end of the line when it comes to binning light.

This whole range of classifications of EM waves based on their wavelength (or frequency) constitutes what is called the ”electromagnetic spectrum”

EM_Spectrum
[Source: https://commons.wikimedia.org/wiki/File:BW_EM_spectrum.png]

Reviewing it, I’m sure you got the sense that these distinctions are fairly arbitrary. They were definitely man-made definitions figured out in some committee and it shows. For example, in a certain community or field of engineering that commonly works in X-rays you had, over time, this community generally agree on what the wavelength of an X-ray was. Let’s call these people “X-ray workers”. However, say technology in that community changed and suddenly the typical wavelength used in their technology got shorter. Do they throw up their hands and change all their desk placards to say “Gamma ray workers”? No, they’ll just fudge or broaden the definition of X-rays. They’ll make up the terms “soft X-rays” and “hard X-rays” and so on.

This is why we have terms like “UV”, “Deep UV”, “Extreme UV” and so on. People got used to their job title and didn’t want to change it when the wavelengths they typically dealt with shifted. So other than the visible spectrum, which is rigidly defined from 0.39 to 0.7 microns, based on capabilities of the human eye, all the other boundaries between these classification are fairly arbitrary. A 0.09 centimeter wavelength EM wave (which is technically in the microwave) is really no different than a 0.11 centimeter EM wave (technically infrared). You just have to draw your lines in the sand somewhere.

We now have an idea of some common situations where light is produced and some idea of the way humanity has categorized light by wavelength/frequency. In the next two posts, we’re going to look more at how light behaves when it interacts with something, like materials. We’re going to learn about where color comes from, and how white is different than a mirror, and we’ll even talk about how you can see through objects.

After that we’ll be continuing our greater journey with discussions of photons and predator-vision and medical tricorders and neon signs and the ozone layer and much, much more.

See ya there.

QUICK SUMMARY

Light is divided up into bins based on wavelength, with the longest wavelength of light being radio, followed by microwave then infrared then the visible spectrum (which is the only range humans can detect), followed by ultraviolet, X-rays and gamma rays. These bins comprise the so-called electromagnetic spectrum. Life sucks for matter trapped near a neutron star, and radio telescopes and microwave ovens don’t always get along.

10 thoughts on “The Saga of Light, Part 2: The Hardest Fall in the Universe and How Hot Pockets can Fell Telescopes… And Some Stuff on the EM Spectrum

    1. Wow, great question! There’s actually a lot to unpack in your question and some of the specifics actually take things to the fringes of physics, specifically by talking about absolute zero. In fact, talking about temperature and accelerating reference frames is an extremely difficult (and often ill-defined) topic. I’ll maybe talk a little bit about why saying absolute zero in this scenario is actually opening up a Pandora’s Box, but first let’s just talk about the finite-temperature case.

      In the finite-temperature case if I have a “Box O’ Charge” sitting on the surface of a neutral rotating sphere we can kind of simplify our thinking to really just a charge confined to make loops around a circular track. In this case, as it is accelerating, it will emit light in the forward-ish direction and as a result of what’s call a “recoil reaction” it will slow down as it does this until it eventually comes to a stop. If we bring the planet into this then the box – through the frictional interaction between the bottom of the box and the surface of the planet – would act to essentially slow down the rotation of the planet. So in principle, if we assume that the planet is rigidly attached to the box, then this deceleration of the box will also bring the planet’s spin to a halt.

      Now, I haven’t said anything about the thermal system and that’s because generally we conceptually separate the, so-called, “center-of-mass” motion of an object from the random thermal motion. Thus, the temperature of the box doesn’t come into it as it is its center-of-mass acceleration that is driving EM emission and that emission is in turn stealing energy resulting in a reduction of center-of-mass velocity. So the entire story rises and falls on the behaviour of the center-of-mass motion.

      Now for just a little bit about the “can of worms”. Temperature is a somewhat nebulous concept when we start talking about both non-accelerating or accelerating frames of reference. It’s generally the case that even if different observers measure an object as having a different CONSTANT (i.e. no accelerating) speed they still agree on the temperature of the object, which relates back to what we’ve talked about (center-of-mass motion and random thermal motion being distinct). For reference frames that aren’t accelerating, temperature is not frame dependent. However, I’ll get back to that in a second because let’s consider a simpler question: “can an object, through black-body emissions, reduce its temperature to absolute zero”. The answer here is “no” because a thermal system is always in thermal contact with another system, even in a vacuum of space it must trade heat with the vacuum of space through our thermal radiation/black-body emission. Thus, you can’t get colder than the thermal “reservoir” you’re in contact with. From this you might say “but space has no temperature”. It actually does, there’s a couple ways of defining it, either in terms of the temperature of particles (there’s still about 1 hydrogen atom per cubic centimeter in interstellar space) or – more commonly – in terms of the Cosmic Microwave Background Radiation (CMB) that permeates the universe. This CMB sets a hard floor throughout the universe of about 3 degrees above absolute zero for any object cooling itself through thermal radiation. However, let’s say there was no CMB, then what? Well, here’s where we reach the fringe of physics and what is called the “Unruh effect” (google it if you’re curious). This Unruh effect is an unverified and somewhat controversial prediction of general relativity which basically says: “an accelerating observer will observe blackbody radiation where an inertial observer would observe none”. Put another way, it predicts that an accelerating observer sees the universe as HOTTER than a non-accelerating one. So by the way you’ve set up the problem, our “Box O’ Charge”, if the Unruh effect is true, would see the vacuum of the universe as being hotter than absolute zero, even ignoring dilute hydrogen atoms and the CMB and thus could not be at absolute zero.
      Anyways, that was maybe a bigger trek to the frontier of physics than you were looking for but hopefully that helps clarify things, or at least made things very confusing, but in an interesting way.

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      1. That’s quite interesting to read, but it’s actually not what I was intending to get at. If I understand general relativity correctly, there’s no difference between an accelerating frame of reference and a non-accelerating frame of reference that’s in a gravitational field. If that’s correct, wouldn’t it imply that a charged particle on the surface of a non-rotating planet would also emit Bremsstrahlung radiation, since it’s undergoing proper acceleration?

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      2. Ah, I see. That’s actually a well known paradox of GR/E&M and one that took quite a while to pick apart, you can see a wikipedia about it here:

        https://en.wikipedia.org/wiki/Paradox_of_radiation_of_charged_particles_in_a_gravitational_field

        The key point is that radiation is defined as energy transfer, via the EM field, at infinity and the “supported observer” (i.e. someone sitting beside the box on the planet) and an “unsupported observer” (someone watching in space far from a gravitational field) have frames that don’t have the same “at infinities”. Thus, the unsupported observer observes radiation but the supported does not, which is fine because the infinity of the unsupported observer is outside the observable horizon.

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      3. Ok, so an observer in the same non-inertial frame as the particle doesn’t observe the radiation. But what about the inertial observer? If they observe radiation, that would appear to be energy coming from nowhere. What’s losing energy in order to balance it out?

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      4. Ok, so an observer in the same non-inertial frame as the particle doesn’t observe the radiation. But what about the inertial observer? If they observe radiation, that would appear to be energy coming from nowhere. What’s losing energy in order to balance it out?

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      5. Ok, so an observer in the same non-inertial frame as the particle doesn’t observe the radiation. But what about the inertial observer? If they observe radiation, that would appear to be energy coming from nowhere. What’s losing energy in order to balance it out?

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  1. Ok, so an observer in the same non-inertial frame as the particle doesn’t observe the radiation. But what about the inertial observer? If they observe radiation, that would appear to be energy coming from nowhere. What’s losing energy in order to balance it out?

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