What is Quantum Mechanics – Reality or Magic?

Non-fiction article about the unreality of some real science

Ordinary Mechanics

Somehow, the phrase Quantum Mechanics crept into a conversation I was having with a mate down the pub the other day. "I’ve no idea what it is," he said. I said that it was the most important, most successful, most far-reaching scientific theory ever devised by the human race, and that it affects everything around us.

"But what exactly is it?" he asked.

That is a hard one. Never one to resist a challenge – unless I’ve got something better to do – I shall try to explain the underlying principles on which the entire Universe works, in as few words as possible. To save time, I’ll chuck in a few diagrams. And no maths.

First of all, we need to back-track. What’s classical mechanics? A little bit to do with cars, it’s just how ordinary matter interacts – what happens when you push something, what happens when things collide. By "ordinary" I mean everyday-sized objects. A pool table gives loads of examples of mechanics in action.

Figure 1. The moving red ball collides with the stationary blue ball.

When the moving red ball has a sidelong collision with the blue ball, the blue ball moves off, forwards, in the opposite direction from the collision. The red ball moves the other way (bouncing off the side cushion, giving a very tiny amount of movement to the table and the Earth on which it rests.

There are all sorts of rules you can work out about these collisions. One obvious one is that the blue ball can never move backwards. Lots of tests would show that the balls always come to a halt eventually – what would happen if the table was frictionless? Other rules can be worked out about speed and direction, especially what happens when balls of different sizes are used.

So what’s Quantum Mechanics? It’s the mechanics of the very, very small. Is it different from classical mechanics? Very, very much so.

Enter the Atom

How small are we talking here? We’re looking into the world of the atom. The idea of the atom comes originally from ancient Greek philosophers, some of whom believed that there was a lower limit to how much you could grind up a piece of matter (others thought you could grind it up endlessly.) Those who thought there was a limit called the smallest pieces atoms, which means ‘can’t be split.’ There were more nearly right than the other lot, but not spot on. A typical pool ball is about four centimetres across. If you expanded the ball so that an atom was a few centimetres across, the whole ball would stretch about one tenth of the way across the entire Universe! So, you must remember, we’re talking about really small things here. This will be important later on.

It took a long time for modern day scientists (that is, going back just a hundred years) to discover that atoms really did exist, and it was less than a hundred years ago to learn that, despite their tiny-ness, they had an internal structure – they are not the same all the way through. You may well have been taught this sort of structure at school in basic chemistry.

Figure 2. Model of the Atom - a bit too simplified.

Looking a bit like the Solar System with a central sun and orbiting planets, even this model took some time to come up with. The core is known as the nucleus and is itself made up of still smaller particles, called protons and neutrons, while other, very light particles, called electrons whiz round the outside. For many explanations this model works quite well, like a model aeroplane. But it is only a model and a very simplified one at that. (Incidentally it’s not to scale – the nucleus takes up only 100,000th the diameter of the atom – it is mostly completely empty space – whatever that is.)

The first problem is that the protons in the nucleus are electrically charged and, like magnets of the same pole, repel each other with enormous force, so something has to glue them together. We won’t be going into how this glue works, but we will need to consider how we can get things unstuck at some point.

The second is the electrons are negatively charged and should be strongly attracted by the nucleus. Just whizzing about isn’t enough to stop them spiralling into the nucleus, giving off energy, and all the matter in the Universe should just collapse in an instant and a loud bang. But it doesn’t, so something must be stopping it.

Light – Particle or Wave?

But let’s talk about something else here. Light is energy that flies across space from any glowing object. Some folk speculated that it must travel instantly from place to place, but that wouldn’t explain why my hand casts a shadow on the wall when I shine a light at it – the light must hit my hand before the wall so light’s speed must be finite (though still very fast.) Sir Isaac Newton thought light, too, might be little particles, though he doesn’t seem to have tested this; perhaps he was too busy working out how gravity works. Other people did experiments later that proved light was a wave. How do you do this? Imagine waves on a pond striking a barrier that has two narrow gaps in it. Waves pass through the gaps in an orderly fashion spreading out till they hit the shore of our pond.

Figure 3. Two lots of waves interfere with each other.

Where two crests, from the two lots of waves, hit the shore together, we get an even higher crest. Similarly, where two troughs meet, we get a deeper trough. We can show the places on the shore with the biggest waves as white bars. Where a wave and a trough meet, they cancel each other out and we get little wave activity, which we show as dark bars. Overall we get an alternating pattern of great activity and quietness which is called an interference pattern. It is a characteristic of anything than travels in waves.

Experiments carried out projecting light though a blind with slits, then on to a screen, reveal interference patterns. This simply cannot happen with particles so light must be a wave. In fact light waves, radio waves, microwaves, x-rays and gamma rays are the same sort of thing, just with different wave lengths. But they are definitely waves, not particles. (You try dropping blobs of putty – particles – through two different holes in the floor and you will not get an interference pattern, just two piles of putty.)

There was just one problem with this. Some experiments with light only work if you assume light is made of particles. When talking about light as particles it is usual to call them photons. One example is the way things glow; classical physics expects hot things to glow with as much energy as possible in one go – this means every hot thing should look violet. But we all know things glow red, then yellow as they get hotter. (This is known as black-body radiation, and the classical, wrong answer as the ultraviolet catastrophe.) Another example is that you can knock electrons – particles – out of atoms. This is why some metals give off electricity when light is shone on them. It’s called the photoelectric effect and is used in light meters in photography, amongst other uses. You simply cannot explain the photoelectric effect (or any of the other experiments) if light is a wave. So it must be a particle. But it also must be a wave to explain interference patterns. What the devil is going on?

It gets worse. Once you can get electrons – particles – flying through space you can project them through slits and on to screens. And you get interference patterns.

This turns out to be true for other particles – whole atoms even – that can behave like waves when we perform experiments to find waves but perform like particles we look for particles. The only way round this is to talk about wave-particle duality and say that tiny bits of matter and energy behave like wave-particles. But, I stress, this happens only at the scale of the ultra-small. Nothing we have on a pool table or on a pool for paddling in – the ordinary scale of things – behaves like this. In fact, we cannot even make an ordinary everyday-sized object that has wave-particle duality – we can’t even imagine what it looks like. But it’s how the ultra-small world works. And it has to work like this, otherwise the Universe wouldn’t work at all. Things get even weirder, as we shall see.

Quantum Leaps

Just before we do this, I need to explain just a little more of the photoelectric effect. Photons can have any amount of energy, from the absolutely feeble to enough to crack a nucleus. It was noticed though, that only a photon of a certain energy, or size, would dislodge an electron from any given type of atom. Too little and it didn’t work. Too much and it didn’t work either. In a similar way, and electron can be moved from a lower orbit to a higher orbit – that is, not knocked off altogether, just shifted, by supplying a photon with exactly the right energy. If waves had been able to do this, there wouldn’t have been a need for this preciseness. A chap called Max Planck suggested that it was a certain-sized packet of energy that did the trick. Only he didn’t like the word ‘packet’ so he coined the word ‘quantum’ – meaning a precise quantity, instead ("So that’s where the word comes from!")

As a footnote to this, the electron in the higher orbit has absorbed this quantum of energy, and is in what is called an excited state. After a while, the electron prefers to go to the lower energy state (a bit like things cooling off) into what is called its ground state. When it does so, it gives off a photon of light energy. (Emission spectra are explained in the article, Somewhere Seen Through The Rainbow, elsewhere.) This photon has exactly the same amount or packet of energy as the photon that excited the electron in the first place. No more, no less.

We’re are close to an explanation (admittedly not a full one) of why electrons cannot spiral down into the nucleus, or, indeed, give off (or absorb) other amounts of energy. Each atom’s electron orbits correspond to whole quanta (the plural of quantum.) you could think of two orbits being like railway tracks – your carriage can be on one track or the other, but not half way in between.

Figure 4. Quantum orbital tracks: an electron can leap from one track to another, but it can't run along in the gap in between.

Half a quantum (or, indeed, any fraction) is not allowed. So electrons can only be in certain orbits and can’t go up or down just as they feel like it. A quantum leap is the smallest leap an electron can make, and no smaller. People who talk about "quantum leaps" as if they are giant leaps (usually of progress) are therefore making a big mistake and look rather silly (to those of us who know what a quantum leap really is. Chuckle.)

By the way, the movement of large numbers of excited electrons is what makes lasers possible, from laser-guided missiles to laser bar-code readers in shops.

But can’t a quantum be of any size? I hear you ask. Well, yes. So there must be something about which orbits are ‘allowable’ and which aren’t. Yes. One explanation is that the electron particles have a wavelength as they go round the orbit. When an electron sets off it is some point in its wave. If it is to be in the same part of the wave when it completes an orbit, then the length of the orbit must be a whole number of electron wavelengths. If the orbital length was not a whole number of wavelengths, then the electron wave would interfere with itself and wipe itself out. Therefore only certain orbits are possible.

Figure 5. If the length of the orbit is not exactly a whole number of electron wavelengths, the electron interferes with itself and wipes itself out.

This might not be easy to visualise (and my diagrams, drawn free-hand, aren’t as good as they might be) but it shows again that, at the size of the ultra-small, things are both particles and waves.

Quantum Mechanics has a lot more to say about how electrons populate orbits – henceforth known as orbitals – in what are known as shells and sub-shells. This is too complicated to go into here, but in a nutshell, only so many electrons can fit in a shell and once it is full, no more are permitted (this is an example of something known as the exclusion principle.) This is why every chemical element has a different arrangement of electrons and these determine its chemical properties, what chemical compounds they can form and also why matter is solid (even if atoms aren’t.)

Another question you might ask is, "Where is the electron as it moves between orbits, making its quantum jump?" That’s a good question (which means I don’t know the answer.) But things are going to get so much weirder it doesn’t really matter. It turns out, in the quantum world, we can’t really tell where anything is.

Uncertainty

Obviously, finding out anything about things so small must be difficult – where they are, how fast they are going, for example. It turns out, however, that it is not difficult, it is absolutely impossible. In the normal, pool-table world, we might be able to say exactly where a ball is; we might also be able to say how fast it is moving. With quantum objects, these properties simply do not exist. Many physics books describe this problem incorrectly; they suggest something like this: if you have a glass of hot water that you want to measure the temperature of and you put a cold thermometer into it, then the result you get (after waiting a while) is the temperature of the water after the thermometer has cooled it down and that therefore the measurement is inaccurate. But we could allow for this – either by estimating what effect the thermometer’s glass has on the water or by using such a tiny thermometer it would make very little difference. This implies that, if only we could develop measuring instruments delicate and sensitive enough, we could measure and electron’s position, or speed. This is absolutely not so, because these things do not exist. Not even the electron ‘knows’ where it is or how fast it is going.

If this sounds bizarre, then that’s because it is. An electron doesn’t have a position we can measure any more than a field has an area you can get just by measuring the length of one side. Length is measured in metres, area in square-metres – two similar sounding, but completely different units. You may as well try to weigh something in degrees Celsius.

What the electron ‘knows’ – and then only approximately – is it’s position-momentum. Momentum is just speed times weight; if you want twice the momentum, you either go twice as fast, or get twice as heavy. This is one of the few examples where ordinary mechanics is exactly like quantum mechanics. However, to simplify things: if we are talking about electrons, they all weigh the same so we can just think about the speed. Even so, an electron has position-speed and you can only measure the two things together as if they were one. And, even then, you can’t know what this is, exactly.

Imagine, for a moment, taking a photograph of a rapidly moving racing car. When you look at the picture, all you see is a long, streaky blur. If you know the length of the exposure at which you took the photo, you could estimate, from the length of the blur, how fast the car was moving. But you can’t say exactly where the car is because it isn’t at any one fixed point in the photo. So you try again, this time with a much shorter exposure. Now, you may get a much sharper picture – one with only a tiny amount of blur, and with the car at apparently, more or less, one position.

But you can no longer say how fast the car is moving.

The more you pin down position, the less you know about speed. The more you know about speed, the less you know about position. But this is still not the end of it. In the quantum world, no matter which way you do it, you cannot get an exact measure of position-momentum. This is not because of the limits of your instruments but because there is a limit to how exact this double property is. It’s like an exactness speed limit. The man who discovered this, Werner Heisenberg, called it Unbestimmtheit. This is always translated into English as Uncertainty, but an alternative might be Inexactitude. Don’t ask why the Universe is like this in the ultra small, it just is. If you imagine the Universe to be like a map with grid lines, then there is just a bottom limit to how close the grid lines are drawn together. (It sounds a bit like the Greeks who thought there was a limit below which it is impossible to split matter.)

I said position-momentum is a double-barrelled property. This means that you are entitled to try to measure the position of something as accurately as you like. But, like car in the photo, you will know less about its speed. Measure its speed with great accuracy, and you lose the position. The position and the momentum multiplied together can never be more accurate than the quantum limit. This limit is a number that even has a name – it is known as Planck’s Constant (remember him?) It’s an exceedingly small number which is why it only is noticeable with ultra tiny things. Pool balls and cars don’t count, so we don’t notice what a crazy, fuzzy place the Universe is.

So who cares? If it’s only a problem with the ultra-tiny, how can it affect us? Well, it does, when we start using quantum mechanics to work out how the world works, chemicals, light-bulbs, people and so on. As we shall see.

There is another double-barrelled property that involves the Uncertainly Principle. This is energy-time. In a system, as scientists like to call it, there can be a certain amount of energy and the rules state that energy cannot be created or destroyed, so this amount is fixed. But what the Uncertainty Principle says is that a system can have more energy, providing it is only for a very short time, because of the limit on certainty. The more extra energy you want, the shorter the time. Again, the ‘system’ doesn’t ‘know’ how much energy its got for a very brief interval. Or it can have just a tiny bit more energy for a longer interval and still not know.

This is a bit like having an account at a bank which checks your balance at the end of the day. If you withdraw more money than you have actually got in the morning, so long as you get it back by afternoon, the bank never knows. For argument’s sake, imagine the bank is a little more cautious with large withdrawals. If you take out a very large sum, then the bank double checks your account, at the end of the day and also at lunchtime. But if you get the money back before then, the bank is none the wiser.

Does the Universe really act in this balmy, irresponsible way? Oh, yes! Can we tell? Sure we can. The Sun wouldn’t burn and atom bombs wouldn’t explode without it.

However, this is still not the end of the weirdness. Because, it turns out, that, in a sense, nothing really exists at all! That is, nothing exists, until we decide to take a look at it. Then, depending on what we are looking for, things spring into existence. For more surprises, read on.

Quantum Unreality

Remember when I said we find waves when we look for waves and particles when we look for particles? What happens if we cheat?

The double slit experiment is looking for waves (that form interference patterns) and, hey presto – we get ‘em. What happens if we put some sort of particle detector at one of the slits?

Figure 6. Looking for waves and particles. What happens?

The answer is more incredible than you can possible imagine.

Remember, a wave can spread out and go through both slits. But a particle can go through only one slit – what’s more it can’t make an interference pattern. Suppose we do this experiment with a source of electrons (an electron microscope would do fine.) It’s very easy to sneak an electron particle detector up to one slit, sit back, then just switch it on. And detect particles.

And the interference pattern vanishes.

You have to think hard about this. We had an experiment that was looking for wave evidence and we got waves. But the moment we switch to looking for particles, we find particles and the wave evidence disappears. We see a particle go through one slit. And, as a particle can’t go through two slits simultaneously, nothing, goes through the other slit. The really weird thing is a particle can go through the other slit, but, because we’re looking for particles at the first slit, it’s like the ‘particle’ knows we’re looking and so it behaves like a particle. How does it know, at one slit, what is going on at the other? We don’t know. But we’re sure it happens. Experiments prove it.

To get a feeling for this, see how it might look if the every day world behaved like this: imagine I am in Manhattan, standing on the corner of 34th Street and 5th Avenue – not far from the Empire State Building – and an event has just occurred at the junction on the opposite corner of the city block, at 33rd and 4th. I don’t know what it is yet, but I do know it can be one of only two possible events, and I will find out in a few moments which it was.
The event at 33rd and 4th is one of the following: either a fire hydrant has burst and sent a torrent of water (it’s a really big fire hydrant, you must understand) in all directions; or a taxi has just set off on its way to 34th and 5th. It can go along 33rd Street from 4th to 5th Avenue then from 33rd to 34th Street, or it can go up 4th Avenue to 34th Street, then along to 5th Avenue. In other words, it can take one of two routes to me, but – because taxis can’t split in two, not both routes. Just one or the other. A torrent of water can of course split in two and go two routes at once.
Now here is a funny thing on this day in Manhattan. Somehow, if I shut my eyes and don’t look to see what is coming towards me, I will be soaked! But, if I look up, then a taxi will arrive and no water will appear. Think very carefully about this. If I have my eyes shut and the fire hydrant bursts, water will set off down the streets. But if I open my eyes, the water will disappear on both streets and be replaced by a taxi, on just one street. Magic!

It gets stranger still. Suppose I have closed-circuit television cameras on both routes. If I switch them on, or even just one of the cameras on, all I will see is a taxi, or an empty street (which will mean there is a taxi going by the alternate route. But if I leave them switched off, then a wave of water will inundate me from both directions. Even if water had set off originally, switching even one camera on makes the water disappear as if it never existed and the taxi (which until now had effectively never existed) suddenly appears as if it existed all the time.

This one-slit-affects-the-other is known as non-locality. Einstein called it "spooky action at a distance." I think this sums it up nicely, not least because the distance between the slits makes no difference – switch on the particle detector at one and the other one knows, instantly.

We can try another experiment; get rid of the particle detector at the slit and send one ‘particle’ at a time at the two slits, one after another, like someone throwing balls randomly at two holes in a wall. At first, it seems that each particle goes through one slit or another, but without the detector, we can’t be sure. What happens at the screen? At first, no obvious pattern is recognisable. Amazingly however, after we’ve sent thousands of particles through the whole experiment, we get an interference pattern once more. It’s like the experiment knows we’re no longer looking for particles; what’s more, each wave-particle also knows where on the screen to land – it’s even like it knows the past and the future of the experiment – in order to give a wave result.

What happens if we have the particle detector switched on? You’ve guessed it – we get particles – the interference pattern disappears.

A good question to ask now is – what happens in other areas of the experiment? The short answer is simple – we don’t know! Until we look, we can’t be sure, and when we look, we find what we are looking for. Again, it is like the experiment knows what we are doing. Our observation becomes part of the experiment! Our decision affects the result! Science isn’t supposed to work like that! Meanwhile, the whole of empty space is boiling with virtual bits of matter that come into existence then disappear again before they are detected by virtue of the Uncertainty Principle not knowing they ever existed.

The first work on the theory of Quantum Mechanics started at the beginning of the 20th Century. By 1930, scientists had done enough experiments to want to sit down and summarise what was going on. The result of this is known as The Copenhagen Interpretation. It’s not the only one but it works as well as any of the others. It was concluded that, in the gaps in the experiment where we are not looking, the electrons or photons or whatever are not really in existence at all! More accurately, they are in a superposition of possible states, each having its own probability, like odds in a race. When the wave-particles reach the screen, they have to decide, depending on these odds, where they are going to appear. Some places are more likely than others which is why you get the fringes of the interference pattern. But until they hit the screen they could be anywhere.

This is a bit like tuning into the radio at tea-time to get the horse racing results. The horses have different odds of winning, but once the winner has past the post, its ‘odds’ of winning become certainty and all the other ‘odds’ become zero. You would like to think that, even before you’ve switched on the radio, the results of the races already exist. But, in the Quantum World, the results don’t exist until you listen to them! What’s more, once you stop listening, the uncertainty starts creeping back in as if the race was still being run.

This is described like this in The Copenhagen Interpretation. The object travelling through space might set off as a particle but it travels as a wave of probability. When it encounters a detector at some point, this collapses the wave function so that one result becomes definite and all the others impossible – a particle at one place. To give a different example to get the feel of this, imagine a crowd coming out of a theatre. Some people may drive home, some may get a bus and some a taxi, while some may just walk. We can work out the relative odds of each outcome, saying, for instance, 30% will get a taxi. But, take any one individual, and we have no idea what he or she will do, just that the odds are 30 in a hundred they will get a taxi. Until he gets a taxi we don’t know what he is going to do. This doesn’t sound like the sort of physics Newton would have liked. Einstein didn’t like it either – he was prompted to say, "I cannot believe God plays dice with the Universe!"

No-one seems to have told God this.

We are all made up of matter that could exist in a superposition of states. And yet, we seem real enough. In which case, who has collapsed our wave functions. Who is looking at us? What makes us exist in reality? Tricky.

Is Quantum Mechanics Real?
One scientist once said, "It’s like our everyday-scale Universe is real, but the things it is made up of are not." Whatever happened to reality? Is everything all magic? Those are questions for another day (and another article.) Does all this peculiar goings-on – wave-particle duality, collapsing probabilities, and uncertainty about position-momentum and energy-time – have anything to do with us in the ‘real’ world? Well, yes, fortunately.

For one thing, it accounts for how anything glows (this includes radio transmitters, microwave ovens and x-ray machines too.) It also accounts for how the eye works, how photographic film works and enabled us to make TV cameras and digital cameras too, and makes astronomy possible, as well as movies and why we don’t have to grope around in darkness.

It also explains why we could grope around in darkness if we had to because it explains why you can’t put your hand through solid matter, or just melt into it.

It explains how all chemical elements bond together, so it accounts for all chemical compounds. This was particularly important in understanding the structure and shape of deoxyribonucleic acid, or DNA, because without knowing its structure we wouldn’t know how it works. This applies to the rest of molecular biology as well.

It also accounts for how, in stars nuclear burning of elements like hydrogen and helium and so on can take place to create, ultimately, all chemical elements. And how stars work generally up to where some of them collapse to become Black Holes (though it doesn’t seem to be able to say what happens next.)

Again, Quantum Mechanics explains radioactivity. Remember when I said the nucleus is held together by very strong glue. It is, but it works over a very short distance – the size of a nucleus. Because the exact position of the parts of the nucleus is not determined, occasionally bits can be outside the nucleus – where they take the opportunity to fly off. In reverse, inside stars, the inexact position of nuclear particles allows these particles to sneak into the nucleus, making nuclear fusion possible and for stars to burn. Alternatively, you can think of the radioactive particle gaining extra energy by the Uncertainty Principle; either way, it’s known as quantum tunnelling and it explains the fission and fusion of nuclei.

It explains how electricity flows through conductors such as wire and not through insulators such as plastic (imagine where we would be otherwise in the modern world.) It explains what happens to super-cold materials that make super-fluids and super-conductors possible. These might seem a little exotic – take, for example, a super conductor – something that allows an electric current to flow with no resistance. If you put such a current in a ring it will flow forever and I mean forever. This makes superconducting magnets possible – really high powered magnets that are used in magnetic resonance imaging which is used in medicine to investigate the inside of the body and to detect tumours, for example.

It also explains how to use materials called semiconductors to make transistors – one of the most universal practical applications in the world. Transistors were originally seen as a replacement for vacuum tubes, also known as valves, in early radios and amplifiers. But they can also be used as switches and as such made ultra powerful computers that were also very much smaller and cheaper (not to mention more reliable.) Again, computers were invented first, but it was the application of Quantum Mechanics to materials science that made the microchips we have today.

Quantum Mechanics also accounts for lasers, both how to make them, and how they are used. When you look at the colours reflected off a Compact Disk, that is a quantum mechanical effect. In fact, when you think of the disks, the amplifier, the computer control circuitry and the laser in a CD player, you have a superb example of a device that relies on the application of Quantum Mechanics to make it possible.

But, then again, that goes for just about everything, if you look at it close enough. However you look at it, Quantum Mechanics is the most successful scientific theory ever and it’s here to stay.

The End.

Somewhere seen through the Rainbow

Summary

Non-fiction, popular science article about light

After a heavy downpour of rain, the clouds roll away. A young couple walk with their backs to the dazzling sunlight. The air, still mist-sparked and sodden after the storm, holds the last traces of the shower. The couple look up and, in the distance, a huge arching band of every colour – a rainbow – glows before them. The beauty of the sight makes their hearts leap (as Wordsworth would say.) Their fingers touch, and they fall in love…

Figure 1. A rainbow.

Or something like that.

To some, this would be the end of the story, at least as far as the rainbow is concerned (what the couple get up to afterwards is largely their business though it may require finding a spot of dry ground or a promising weather forecast; we’ll get back to them later.) But the real beauty lies far beyond this. It is in what we can see through the rainbow. I don’t mean the hollow bit in the middle, but actually through the band of colours. Never mind "where does the rainbow end?" Where did it come from?

After all, our couple were walking in white sunlight, and now they are seeing colours, floating in the air. Something very strange is going on here. And very, very important.
It turns out that what is floating in the air is, as hinted, remaining droplets of rain. Each drop of water is taking the white light and reflecting it back. It is also breaking the white light up into different colours. In order to understand how it does this, we have to understand what colour is and what light is.

(As for finding the end of the rainbow – well, you can’t. Firstly, the rainbow doesn’t have an end, it is part of a circle. You can’t normally see this because the ground gets in the way, but you can see a rainbow as a whole circle if you happen to catch sight of one from up in an aircraft. Secondly, the image of the rainbow is formed in the eye from the light reflected by thousands of raindrops and it doesn’t actually have a location – as you move, it moves, so you would never reach a point at which the rainbow hits the ground.)

Firstly, light. In order to understand light, we have to take another step back and look at magnets. Hopefully you’ve seen a magnet and know that they can attract pieces of iron and other magnets. Also, hopefully, you have seen a magnetic rod, left floating or suspended on a bit of thread and been fascinated by the way it always to swing round to point north. This is, of course, known as the North end of the magnet, while the opposite end is the South. There are lines of magnetic force that point out from the North and curve round to the South. This can be demonstrated by putting a sheet of paper over the magnetic rod and sprinkling iron filings on top. The little fragments of iron line up along the lines of force, in what is called a magnetic field. Nothing actually moves from North to South – this was just a convention to show which way the lines are pointing.

Figure 2. A magnet’s field of force.

A similar force seems present when you rub a piece of plastic on a piece of cloth – something woollen is quite good. A plastic comb run through the hair works the same way. The piece of plastic can now attract little pieces of paper and fluff. This is because the plastic has become charged with electricity. (When experiments like this were first done, they used amber, and the Greek word for amber is elektron.) Like magnets, there are two types of electric charge, but instead of being called North and South, they were called Positive and Negative. An electric field was said to point from a positive charge to a negative charge, in an electric field. Again this was just a convention adopted at the time – nothing actually moves.

Figure 3. Two charges’ field of force.

After a while, it was realised that if you moved something that could conduct electricity, such as a wire, through a magnetic field, electricity would start to flow down it. In this case, electric charge does move.

It took no more than a twinkle to realise an electric force could be used to make a magnetic field.
In fact, it was soon realised that an electric field always has a magnetic field at right-angles to it and vice versa, that is, a magnetic field has an electric field at right-angles to it.

Figure 4. Electric current from a wire moving in a magnetic field.

Using this, it is possible to make moving magnets make an electric current (moving electricity) and electric currents to make magnets move, in things now called dynamos and electric motors respectively.

This seems a long way from rainbows, or light generally. But it’s not.
Clearly a magnet has a magnetic field that reaches a long way from the magnet itself (consider the Earth’s magnetic field.) But suppose you move the magnet – does the magnetic field a distance way change instantly? What if the magnetic was rotating, spinning even, what happens to the magnetic field?

Figure 5. A rotating magnet.

The answer is that the field changes, but it takes a little time for the change to arrive. If you set the magnet spinning the field would change and the change would move in a wave out into the distance.

Figure 6. The magnetic field of a rotating magnet.

It would move very, very rapidly and it would be hard (impossible, in fact) to see this with a bit of paper and some iron filings, but it’s happening all the same. And, at the same time – and at right-angles, the electric field would be changing too. So we would have an electromagnetic wave moving through space.

That’s what light is – a wave of electromagnetism.

Figure 7. An electromagnetic wave.

Two things. This wave moves, as I said, moves very, very quickly. At the speed of light, in fact (Duh!) This is 300,000 kilometres per second. (That’s one reason why you wouldn’t see it moving across a small sheet of paper.)

The other thing is that the waves are very, very small. The average length of a wave of light that you can see is 500 billionths of a metre. (Again, you’d be hard pressed to spot that on your bit of paper.)

The reason why I’ve gone into all this detail explaining that light is an electromagnetic wave is because you need to know what happens if you take wave lengths that are longer and shorter than average.

First of all, light at average wavelength looks green. If you increase the wavelength to about 600 billionths, the light looks yellow. Longer still, and it looks orange, then red, with a wavelength of 740 billionths. If you shorten the wavelength to 450, it looks blue.

So the colour of a beam of light depends on its wavelength. Put another way, our eyes recognise different wavelengths of light by interpreting them to the brain as different colours.

But where does the rainbow get all the different wavelengths from? And what is white light?

Well, it’s again something to do with how the eye works when it is given a mixture of different wavelengths. This is the same as mixing two or more colours together. Anyone who has ever tried painting knows you can get a new colour by mixing different coloured paints together. Much the same is true if you mix different lights together, through the results are slightly different. For instance, a mixture of red and green light is seen by the eye as yellow. Inside the eye, tiny cells at the back of the eye in an area called the retina that detect red or green light both fire and the brain interprets this as yellow. Light that actually is yellow, with a wavelength of 580 billionths, causes both types of cell to fire, so the brain gets the yellow message.

Figure 8. Addition of coloured light, as seen by the eye.

In fact, the retina actually has cells that can detect just one of three colours – red, green or blue. But different colours in between cause the some or all the cells to fire off messages so we see all the other colours as well. If all the cells are firing at the same time with just the right mix of red green and blue, we see the light as white! (Ah!)

This still doesn’t explain how the rainbow is made from white light. The reason is because the raindrops can split up the white light with all its wavelengths of different colours.

How does this happen?

Well, first of all, when light hits the surface of a rain drop, its direction is changed. This also happens when light enters water in a pool or a piece of glass. Indeed, you can use a triangular block of glass, known as a prism, and white light to make your own rainbow. This is actually known as a spectrum.

Figure 9. A prism creating a spectrum from white light.

Why does the light bend? In effect, this is because the light slows down as it hits the more solid water (or glass.) This is like putting on the brakes on one side of a moving car, causing it to twist to that side (similar to, but not exactly the same as, a handbrake turn!) The important thing is, how much does the light bend? This depends on the wavelength. The shorter the wavelength and more blue the light, the more it bends. The more red it is. The less it bends. This causes the single beam of white light to split up, by bending at different amounts, into all the colours that make it up. This is where all the rainbow’s colours come from.

The next thing that happens is that all the different coloured beams reflect off the back of the raindrop and shine back almost the same way the came in.

Figure 10. A raindrop creating a spectrum.

The collective effect of seeing all these is as a band of colours. The reason why this is curved or bowed is that each raindrop at a slightly different place in the air has to reflect light in a slightly different direction for it to come to you, which, if you work it backwards, means that the collection of raindrops making your rainbow have to be lying in a curve, in much the same way as having a collection of mirrors in a clothes shop are in a curve to allow you to see how you look in your new clothes. (It also means that someone stood at a different position from you is not, technically, seeing exactly the same rainbow as you – but don’t worry – you can’t ever see anything exactly the same as somebody else unless you are stood in exactly the same position, which is of course impossible, because the other person is in the way!)

Figure 11. Why a rainbow is (a) bowed and (b) slightly different for everyone who sees it.

There is another way of making a spectrum from white light instead of using a prism, which exploits the fact that light is a wave. However, before we look at this, and its uses, there is something to add about the wavelengths of visible light. Are these the only wavelengths there are?

Of course not. We could have wavelengths longer than red, at 740, or shorter than even violet (a very deep blue), at 380. It just that our eyes cannot see them! Beyond red lies infra-red, then microwave, then all the different wavelengths used by radio – radio waves can be thousands of metres long! Meanwhile, going in the other direction is ultra-violet, used – unwisely – to get a sun-tan and beyond that are x-rays, at ten-billionths of a metre that will go through flesh and are used in hospitals (more about these later.) Beyond that are gamma rays, that occur in radioactivity, with wavelengths as short as a hundred-trillionth of a metre. These are highly dangerous.

The important thing is that the visible spectrum, like you see in a rainbow, is just one very tiny part of the electromagnetic spectrum as a whole. In effect, realising that there were so many colours we can see, we came to realise there were an awful lot more that we can’t.

Figure 12. The whole electromagnetic spectrum.

We also cottoned on to the idea that there were ways in which we could use this "light we can’t see." One of these was radio, with all the applications that has enabled, from transmitting messages and music and television, to a whole new way of looking at the Universe with radio telescopes. At the other end, for example, as already mentioned, x-rays are used to see through living bodies to find out any damage inside, as well as a way of treating tumours. There is also a form of astronomy known as x-ray astronomy (which, ironically can only be done from spacecraft as x-rays will not pass through the atmosphere.) And there’s another use we’ll look at in a moment.

But back to light, and how to split up light into different colours. An alternative to using a spectrum (or a raindrop) is a device called a diffraction grating. This is just a grating – a glass slide covered with something opaque such as black paint – with very finely scored lines in covering to let the light through. If the lines are on the same scale as the wavelength of the light, they make it split up into a rainbow of colours as before.

Figure 13. A diffraction grating creating a spectrum from white light.

(This is proof also that light must be made up of waves – a diffraction grating wouldn’t work otherwise. If light were made up of little particles, for example which had been an alternative theory. Unfortunately, there is also irrefutable proof that light is made up of particles, not waves, which is very weird – but another story altogether. See the article Quantum Mechanics Magic.)

An example of a kind of diffraction grating is a compact disk. Here you don’t have a slide you can see through but a mirrored surface that is covered in tiny lines. This is why you see colours coming off a compact disk that’s reflecting white light. For a really good look at this, sit in a dark room and put a CD under a desk lamp – you should see rainbows on the ceiling!

When we split up light like this – how many colours do we get? Some people, especially English-speakers, talk of seven, while in other countries sometimes five are mentioned. I’ve shown seven in my diagrams. But in fact there are as many colours as you can think of names for, in a continuous smoothly changing collection. So what happens if we ever do have gaps?

Yet again, we have to take a step backwards. This time, we need to think about what happens when certain things are heated up until they glow, possibly, for example, by having an electric current put through them. While it is possible, deliberately, to make something that glows at a number of wavelengths to give white light – in an electric light bulb, for example – most things glow with a characteristic colour. One of the most familiar examples of this is street lighting that uses glowing sodium to make the light, which has a very noticeable orangey-yellow colour. This is what happens with most things are made to glow – mercury vapour lights, also used for street lighting, have a bluish light. Fluorescent strip lights actually have a coating inside the tube which absorbs the light originally created in them and gives off a number of different colours so that they look white. And so on.

Technically, the colour or collection of colours something gives off like this is known as an emission spectrum, for hopefully obvious reasons. What is useful is that everything has a different emission spectrum, like a finger-print. But we can turn things around. What happens when we shine white light through a gas, such as mercury vapour or vaporised sodium? This time, we find that the spectrum we get from the light coming out of the other side has gaps. The colours that a given substance emits when it is made to glow are the very same as the colours that are absorbed when white light is shone through them. This is known, again for obvious reasons, as an absorption spectrum.

The exact reason for this is a little complicated and I won’t go into it here. Let it be enough to say that the very colours that something most likes to emit are also the colours that it most likes to absorb.

This means that, if we shine a light through a gas, make a spectrum from the light (using a prism or a diffraction grating) and spot a pattern of gaps (known as absorption lines) we can tell what the gas is made of. Like a finger-print, the absorption spectrum is a dead give-away and we’ve caught whoever was in the spotlight!

Figure 14. Absorption lines in a spectrum. (Note that the pattern is not regularly spaced nor are the lines all the same thickness. However the pattern is unique for any given chemical.)

This is very useful for working out what stars are made of, without having to go to the tedious bother of flying in a spacecraft to one to find out. Indeed, one chemical element, Helium, was first detected in the Sun by examining its spectrum closely, before the gas was later found on Earth. Its very name comes from a Greek word for ‘Sun.’

Using some similar tricks of the trade, we can quite easily tell how hot and therefore how bright stars actually are. We then compare their true brightness with their apparent brightness – the effect of being so far away makes the star look dimmer – and so work out how far away they are. Along with a few other clues, we can start to work out how the whole Universe is constructed, how big it is and what it is made of. The full story would fill a book, but we’re going to leave it there and look at one other final thing.

I said earlier that a diffraction grating could scatter white, visible light into a spectrum. But what about other electromagnetic radiation? Yes, that can be scattered too. It would be very hard to make a diffraction grating to work for x-rays, because x-rays have such a short wavelength. But we don’t have to – Nature makes its own diffraction gratings in the form of crystals.

A crystal is just a collection of atoms arranged in a very regular pattern – known as a lattice – very close together. However, there are lots of patterns possible and – as you may well have guessed, these depend on what the crystal is made of. Light has too long a wavelength to work out these patterns, but x-rays work a treat. Once we know the structure of a crystal, we can say other things about it, such as what that crystal might be able to do, given the chance. This way of examining crystals is known as x-ray crystallography.

Figure 15. Molecules in a crystal lattice.

Once again, we have for a moment to take a detour into another part of Nature. For generations (a very important word, that) humans have bred plants, animals and themselves. They couldn’t help noticing that characteristics of the parents were often passed on to the children. The question was: "how?" What sort of substance could both pass on the information – known as genetic information, or, simply, a gene – for making offspring as well as make the copies of the information in the first place? It would take a very clever chemical that could first of all make copies of itself from simpler chemicals.

Research suggested several candidates. One group, that is found in the nucleus of the cells of living things, were acids that, because of their location, were known as nucleic acids. One in particular attracted attention. It is made up of surprisingly simple components. Most notable is a sugar called deoxyribose. This may seem like a slightly odd name, but a little explanation might help. There is another sugar, called ribose, which is not unlike another, more familiar sugar, glucose, and is not in itself particularly special. Deoxyribose, is its poorer brother, having one fewer oxygen atoms in it. That’s why its called deoxy-ribose.

This too, is nothing special on its own. However, deoxyribose’s atoms can link together using a another bunch of atoms called a phosphate group, to form a chain. This chain can be any length and, just to jazz things up a bit, it can also grab on to another chemical group called a base. (There are two types of base, known as either a purine or a pyrimidine, but you don’t really need to know that. Again, these are not particularly special. An example of a common purine is caffeine, which you get in coffee.)

It’s when you put all this together that you get something interesting. It is a substance (which you’ve probably guessed if you’ve been paying attention) that’s called deoxyribonucleic acid, or DNA for short.

But nobody knew whether DNA was special or not. At least, not without knowing its structure. DNA could be turned into a crystal by drying it out – all that was needed was a way to find out its structure. That’s where x-ray crystallography came in.

This makes it sound a lot simpler than it actually is to do – it’s like trying to shine a light through a forest and work out where the trees are from the shadows. However, one thing that helps is, as I said earlier, crystals have very regular patterns, so you get patterns in the shadows. Once you know how to interpret the shadows you get the structure of the crystal.

Which is what duly happened. And when people saw the shape of the crystal, they realised it was very special indeed. Because it turns out that you don’t get one chain in a DNA molecule, but two chains twisted around each other. What’s more, in certain ways, in this double chain, the second chain was like a reflection of the first. If you were then to split the two chains apart, each could create another ‘reflection’ chain to team up with. The two new double chains would be exactly the same as the original.

Figure 16. A double chain of DNA. The ‘backbones’ are sugar-phosphate, the ‘links’ are pairs of bases. These can occur in any order and either way round, but each half of the pair can only match with one other half.
(The way these chains are held together is in another article, Magic Water.)

This was rightly recognised as a way of both encoding genetic information and, most importantly, of making copies of it to pass on to children. The way in which the information is encoded, and how it is used, is, sadly, too complicated to go into here. But it was finding out the structure using that part of the rainbow known as x-rays that helped us find out.

So, at last, we can leave our loving couple, their passion raised by the beauty of the rainbow, to go and do what comes naturally and make babies (in, of course, a duly responsible fashion within an enduring, loving relationship.) And the reason we know how they can is because we found more secrets in a rainbow than just the colours, by looking through it and beyond.

That’s the true beauty of a rainbow, if you ask me.

Figure 17. A picture of a real rainbow, in Missouri © Dan Bush (further pictures at http://www.missouriskies.org/rainbow/february_rainbow_2006.html)

THE END