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<   No. 2175   2009-01-09   >

Comic #2175

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Let's talk about black for a while.

Blackness is the absence of light. We perceive an object as black if it reflects very little of the light that falls on to it. An ideal, completely and utterly black object would reflect none of the light that hits it. No real object on Earth does this, but some materials can come pretty close.

There is, however, an object that indeed reflects absolutely none of the light that hits it. We call these things black holes.

A black hole is a region of space which contains enough matter, compressed into a small enough volume, to make the gravitational field of the matter strong enough that something would have to be moving faster than the speed of light to get away from it.

* Or any object, for that matter. Well, except a helium balloon. Or a live bird. Or a working model helicopter. Or a kite on a windy day. Or... On second thought, just imagine a ball, okay?
Stepping back a bit, imagine you throw a ball* into the air. What happens? It comes back down to the ground. It does so because the mass of the Earth exerts a force of attraction on the ball - the Earth pulls the ball back towards it. We're all familiar with this phenomenon in our everyday lives: if you drop something, it falls. It's such a normal, commonplace thing, that we take it completely for granted. But ask yourself: Why do things fall? You can often reach profound understandings of things by questioning what seems obvious.

** If you get nothing out of today's comic beyond this, learn this word. It's a good one.
Ancient peoples pondered this question too. Many came up with more or less teleological** reasons for why objects fall to the ground. Things fall to the ground because that's where they are meant to be. This works, after a fashion. If you assume a lump of rock "should" be on the ground, and you lift it up into the air and let it go, what's it going to do? In any reasonable universe it'll try to get to the ground as fast as it can. This may sound simple-minded to us today, but if you live by this assumption, it actually explains things reasonably well.

Except it's completely wrong. Inanimate objects have no sense of where they "should" be. There is no preferred location for anything, in any fundamental sense. Objects end up where they end up because of the accumulated effects of various forces that act on them. Where things go depends only on where they are now, what speed and direction they're currently moving in, and the changes to that speed and direction caused by other things acting on them.

This way of looking at the physical world emerged only slowly in the history of civilisation, with the scientific revolution in the latter part of the 17th century. It was first fully synthesised by Isaac Newton, when he formulated his three laws of motion, which can be summarised as:

*** i.e. If you push against something - anything - it pushes back. It doesn't always feel this way, because when we push against something we tend to brace ourselves, which transfers the force through our bodies to the ground (or whatever we're braced against). If you want to convince yourself that when you push against an inanimate object, it pushes back at you, try pushing something that is better braced than yourself: Stand with your toes touching a wall and, without moving your feet, push hard against the wall with your hands...
  1. An object either not moving, or moving in a straight line at a constant speed, will keep doing so unless an external force acts on it.
  2. The acceleration an object feels when a force is applied is equal to the force divided by the object's mass.
  3. If an object exerts a force on a second object, the second object exerts a force equal in strength but in the opposite direction on the first object.***

Okay, so why do things fall? Well, to cover that, Newton had to add the second big thing he's famous for: his law of gravity.

So what's gravity? Put simply, gravity is a force of attraction between any objects that have mass. Take any two objects. Gravity will pull those two objects towards one another. Everything attracts everything else! Really! So why doesn't everything around us all clump together like one big Katamari ball? Well actually, it does!

Everything on Earth is clumped together into one big ball. We call that ball "the Earth".

The slightly more enlightening answer to the question is that the force of gravity is extremely weak. It's so weak that you can hold a big mass (say, a brick) in one hand, and a big mass (say, a shopping bag full of tins of beans) in the other hand, and not even feel the force of gravity attracting them together. It's there, but it's so weak that you can easily hold the objects apart without noticing it.

This goes for everything else around us too. That truck on the street? Your house? Attracted to each other! Fortunately, the foundations of your house are strong enough to prevent it from flying off to crash into the truck and, also fortunately, the friction of the truck's tyres on the road is strong enough to prevent the truck from sliding over and crashing into your house. Phew!

**** But not too small to measure. There is a scientific measuring device called a torsion balance, which is designed to measure extremely small forces. One of these gadgets can measure the gravitational attraction between two objects the size of apples.
In fact, the forces holding those items in place are much greater than the gravitational attraction between the truck and your house. The force of gravity depends on the size of the masses involved. Even with things as massive as trucks and buildings, the gravity between them is too small to notice****. Even if you put the truck on ice, the friction would still be enough to stop it sliding into your house. (Those readers living in areas where the roads get icy sometimes can breathe another "phew" of relief.)

To get some serious gravity going, you need a really, really, really massive object. Fortunately we have one handy. It's called the Earth. The Earth is so much more massive than a building that we can feel the force of gravity it exerts on objects. Even so, it's still not so strong that we can't overcome it. The Earth is pulling everything down with all its might and all of its enormous mass. But we can still lift objects up, in defiance of 6 trillion, billion tonnes (6×1024 kg) of mass working against us. Yup, gravity is a wimp.

***** Astute readers will note that, according to Newton's third law, the ball also pulls the Earth up. What's more, it does it with the same amount of force! This is absolutely correct. However, according to Newton's second law, the acceleration of the ball is the force divided by the mass of the ball, while the acceleration of the Earth is the same force divided by the mass of the Earth. So while the ball plummets down, the Earth moves up approximately 1/1025 times as far - billions of times smaller than the size of an atom. Ain't no-one gonna notice that. Clever guy, that Newton.
All right, so let's get back to throwing a ball in the air. The reason it falls back down is that the gravity of the Earth pulls it down*****. The interesting thing is that you can make the ball go higher by throwing it up harder. The acceleration the ball feels from the Earth's gravity is the same (because the Earth's mass is the same - the acceleration doesn't depend on the ball's mass at all), but the higher initial speed means it takes longer for the ball to slow down and reverse direction, which means it can travel further upwards before it does so.

How high can you throw a ball? A few tens of metres maybe. To get it higher, you'd have to throw it faster, and there's a limit to how fast a human body can throw a ball. But we can build machines that can throw things a lot faster than we can throw them ourselves. Guns are machines for throwing things really fast. If you fire a bullet straight up, how high will it go?

The muzzle velocity of guns varies a lot, so the answer varies, but the real life MythBusters did the calculations for us for a couple of different guns. The answers are in the vicinity of 1 to 3 kilometres. Hmmm, interesting.

The atmosphere of the Earth gets thinner as you go up. There's no physical cutoff point where you can say that on one side you're definitely in the atmosphere and on the other you are in space. For most practical purposes, space is defined to begin at an altitude of 100 kilometres. What if you could throw an object so fast that it went over 100 km high? Would it drift off into space?

Not precisely. Gravity has no cutoff distance. It works no matter how far away you are from an object. It does, however, get progressively weaker with distance. But if you throw a ball 200 km high, it's still possible that the Earth's gravity will hold on to and bring it back down.

However, the mathematics works out (and I don't want to go into the gory detail) so that there is a certain speed at which objects thrown upwards will never be slowed down and turned around by the Earth's gravity. They don't escape the range of Earth's gravity (because that range is essentially infinite), but they do go fast enough that the acceleration from Earth's gravity drops off faster than it can slow the object down. The result is that the object flies away from Earth and never comes back.

The speed required to do this is called the Earth's escape velocity. It's about 11.2 kilometres per second. That's pretty darn fast. That's the speed you'd need to throw a ball from the surface of the Earth to throw it right out into space.

We build machines that can fly into space: rockets. If you fired a rocket from a big cannon at ground level (as done in Jules Verne's 1865 novel From the Earth to the Moon), you'd need to fire them at 11.2 km/s to get into space. But in reality we use a little trick to make the job a bit easier. Remember that the gravitational force of an object drops the further you get away from it. So the escape velocity also drops as you get further away. By the altitude of a few hundred kilometres, Earth's escape velocity has dropped to a bit under 11 km/s. So a rocket starts on the ground, fires its engines, and climbs up into the sky, picking up speed as it goes. By the time it gets to 11 km/s, it's already quite high up, so the rockets can turn off and the rocket can then coast into space, having exceeded the local escape velocity at that altitude.

So the escape velocity depends on two things: the amount of mass, and the distance you are from the mass. The more massive an object, and the closer you are to it, the higher the escape velocity. Now here's the question: what if you could cram so much mass into such a small space that you could get close enough so that the escape velocity was higher than the speed of light?

The answer is that any light trying to get away from the object wouldn't make it. Gravity would stop it getting away. This may seem a little surprising, since we don't think of light as having mass, and gravity is something that affects mass. At least that's how things work with Newton's physics. But even so, in the late 18th century, the geologist John Michell and mathematician Pierre-Simon Laplace wrote about the idea of an object so massive and compact that light could not escape from it.

This idea stagnated in the 19th century, but was revived early in the 20th century by the new theory of gravity proposed by Albert Einstein. While Newton's description of gravity worked for most cases, there were some peculiarities around the edges, in dealing with very large gravities such as those seen in astronomy. Einstein's theory of general relativity is essentially a replacement for Newton's gravity, and gives a more accurate description of how gravity works. In this theory, gravity is explained not as a force, but as a warping of the geometry of space in the vicinity of massive objects. We don't have time to go into further detail here, but the gist is that it works, and it explains a whole bunch of stuff that Newton's version of gravity couldn't.

One of the side effects of general relativity is that light, although having no mass, is affected by gravity. In short, since gravity is not a force, but a warping of space, light has to follow the same warped paths through space as an object with mass. The result of this is that it is possible to have an object so massive and small that light cannot escape from it.

****** Despite no light coming out of a black hole itself, there are two methods by which a black hole can produce light from regions near it. Firstly, with its high gravity, a black hole is good at sucking in lots of matter. As the matter gets close to the hole, it gets squished together. Squish it together hard enough and it starts to get hot and begins glowing (see further down in the main body of this annotation). Since this glow originates outside the black hole, it can escape and we can see it. The second method is Hawking radiation, which is a story for another day.
We call such objects "black holes". And now we're back at paragraph 3 of this annotation. The real point I want to make is that black holes are called "black" because no light whatsoever comes out of them - either reflected, or emitted******. They are, in a sense, the only truly black objects in the universe.

This is all an aside that is completely peripheral to my real point today, which is the concept of blackness. As we've seen, physicists call something "black" if it reflects and emits no light - which is basically the logical extreme of what we commonly refer to as "black". Physicists also apply this terminology to something called a black body, although with one important difference.

A "black body" is an idealised object that reflects no light - it completely absorbs any light that falls on to it. But, and this is important, a black body is allowed to emit light. A black body is "black" only in the sense that it does not reflect light. Why this distinction?

If you had a black body sitting on your desk, it would indeed look black. Imagine something really black, like a lump of charcoal. That's close enough to an ideal black body for our purposes here. Look at the lump of charcoal sitting on your desk. What colour is it? Black, of course. It's reflecting very little of the light falling on it, close enough to zero that it looks black to our eyes.

But where else do we see charcoal? In a barbecue, or cooking fire. What happens when we put a lump of charcoal into a fire? It gets hot, of course. But, after a while, you can see something different about the charcoal. It starts to glow.

It first becomes a dull, dark red colour. Then, as it gets hotter, the charcoal glows more brightly, and the colour changes from dull red to crimson, and then eventually becomes orange. When it's really hot, it's an orange-yellow colour, and really quite bright.

But the lump of charcoal is still a good approximation to an ideal black body. In fact, now that it's glowing red hot, it's an even better approximation of an ideal black body than it was when it was black. How can this be?

Remember that the definition of a black body is something that does not reflect light. The hot charcoal is reflecting no more light now than it did when it was black. The glow is actually the charcoal emitting light of its own accord. The fact that it's glowing does not disqualify it from being a black body. Because that's exactly what black bodies do - they emit light, depending on how hot they are.

This phenomenon is known as black body radiation, or thermal radiation. This is essentially the glow we see from hot objects. We know from experience that if things get hot enough, they start glowing. The appearance of the glow is described by Planck's law, which comes about because of certain interactions in quantum mechanics that I don't want to go into here. The basic result is that things glow when they're hot, and that the colour of the glow is directly related to the temperature.

Black body colours Most people will be familiar with the terms "red hot" and "white hot", and that "white hot" is hotter than "red hot". Charcoal glows red hot. An incandescent light bulb (which are vanishing these days as they are replaced by more energy efficient light sources) glows because it is hot - white hot. The filament of a light bulb is significantly hotter than a red hot piece of charcoal.

When things are at room temperature, they are also emitting light but, because the temperature is low, the amount and energy of the light emittied is very small. It actually appears mostly as infra-red radiation than as visible light. So when our lump of charcoal is cool and black, it is reflecting a little bit of light (because it's not an ideal black body), and emitting a very, very small amount of (mostly infra-red) light. So it's a decent approximation to a black body, but not a great one. When it's heated up and glowing red-hot, however, it's still reflecting the same little bit of light, but is now emitting lots of light - exactly as an ideal black body would at the same temperature. So when it's red-hot, it's actually a closer approximation to a black body than when it's cool and black.

In fact this is a general trend. Any object at all is a moderate approximation to a black body at room temperature. But when heated up until it glows, the light coming off the object resembles more and more that of an ideal black body. So, almost paradoxically, the closest things to ideal black bodies that we have are the things that are so hot that they glow - and the hotter and brighter they are, the more like ideal black bodies they are.

This is why scientists often refer to really bright things like light bulbs and stars as "black bodies". Stars, lordy, yes. Stars are almost perfect black bodies. They reflect very little of the light hitting them, but they generate enormous amounts of light themselves, because of their high temperatures.

******* Some light sources are green or purple, such as neon lights and some nebulae. The reason they can avoid the restrictions of being a black body colour is that they emit light by a different mechanism, not just by being hot. Also, some groups of stars can appear greenish if the light from them mixes together and you can't separate them with a telescope.
And here we come to the reason why some stars are reddish in colour, some yellow (like our sun), some white, and some blue-ish, but there are no green or purple stars*******. The light emitted by a black body follows Planck's law, which specifies how much light of different colours is generated. This starts off at the red end of the spectrum, with almost no yellow, green, blue, or violet light. Which is why as you heat something up, the first glow you see is a dull, dark red colour. As the object gets hotter, the colours adjacent to red get added to the mix: orange and yellow. So a red hot object brightens and gets more orange and then yellow as it does so.

By the time we get to green, however, there is lots of red and orange still in the mix, and the green gets drowned out without making an individual appearance, contributing only to making the light look whiter. The same with blue and violet. By the time we have the full range of colours being generated, the result is white light - the object is white hot. If you keep increasing the temperature, the amount of blue in the spectrum increases faster than the amount of colours at the red end, so the glow starts to get a faint blue tinge.

This sequence of colours, from red, through orange, yellow, white, and finally blue, is precisely the sequence of colours we see in the stars. What's more, the colours correspond precisely to specific temperatures, as shown in the diagram on the right (from Wikimedia Commons, released under the GNU Free Documentation Licence), with temperatures marked in Kelvins.

The really cool thing is that, using this, we can tell the temperature of any star just by looking at its colour. Our sun, for example, has a surface temperature very close to 6000K.

I could keep going here. I could tell you how knowing the temperature of the Sun, Planck's law tells us exactly how much energy it is emitting per unit of surface area. Newton's laws applied to the gravitational attraction between the Earth and Sun (or Einstein's - they're both good enough for this one), knowing how long it takes for Earth to travel around the Sun, tells us how far away the Sun is, and its mass. Knowing how far away it is, we can calculate its size in two completely different methods:

  1. Measure how big the Sun is on the sky, and calculate its size using geometry.
  2. Measure how much light from the Sun is received on Earth, and calculate its size based on knowing how big it would have to be to generate that much energy, given we know its temperature.
And the cool thing is that these two methods give exactly the same answer. I could tell you how knowing the mass of the Sun and how fast it is generating energy tells us how long the Sun will live before burning out. This, combined with the physics of hot gases and nuclear energy tells us how long ago the Sun was born. This physics also gives us another estimate of the mass of the Sun, based on how much energy it produces and how fast the nuclear reactions inside it need to go, which matches the one derived from gravity.

By cataloguing stars across the night sky we can measure all of their temperatures from their colours. By simple geometry we can measure the distances to nearby stars knowing the distance from the Earth to the Sun as a baseline. That distance, combined with how bright the stars appear from Earth tells us how bright they are close up, and how much energy they are producing. Combining that with the temperature and our models of nuclear physics we can measure the masses of those stars.

We discover that the temperatures and masses of stars follow a well-defined pattern - by measuring the temperature (from their colour) we can determine their mass. We learn that some stars pulsate, with periods that depend only on their masses. So we can measure the masses of stars a long way from us simply by measuring how fast they pulsate. And if we know the mass, we know the brightness, and if we know the brightness, and how bright they look from Earth, we can calculate how far away they are.

This is how science works. From understanding something as trivial as blackness, we can build an understanding of the world, and the universe around us. We can do things that previous generations could only dream of. We can measure the temperatures, masses, sizes, and distances to objects that are so far away that light itself takes millions of years to reach us from them. We understand how much of the universe works.

It took geniuses to figure this stuff out. People like Newton and Einstein and Planck, and the countless other scientists along the way who contributed to our understanding of the universe. But it doesn't take a genius to ponder some of it, and to understand the basic ideas behind how things work.

I hope you learnt something just now that you hadn't known or thought about before (even if was just the word "teleological"). If you already knew everything I've just said, I hope you've learnt something about the value of explaining science to people. (If you already knew that, I hope you're a science teacher!)

2021-05-30 Rerun commentary: Just reading back over all of what I originally wrote above, I don't think I can add much to it now. Except that that thing about the Katamari ball and We call that ball "the Earth". must be one of the cleverest things I've ever written.

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