The velocity of light in our theory plays the part, physically, of an infinitely great speed.
ALBERT EINSTEIN
When does Zurich stop at this train?
ALBERT EINSTEIN
Infinity is a number bigger than any other. If a body could travel at infinite speed, you would never be able to catch it up. Not only that but, no matter how fast you moved, the body would always appear to you to be infinitely fast, since your speed would always be negligible by comparison.
In our Universe, the role of infinite speed, for some reason, is played by the speed of light – 300,000 kilometres per second. No material body can ever catch it up. And no matter how fast you move relative to a source of light, or a source of light moves relative to you, the light will always appear to be travelling at 300,000 kilometres per second.
The remarkable fact that the speed of light – christened c by physicists – is doggedly unchanging was revealed by American physicists Albert Michelson and Edward Morley. In 1888, they measured the speed of light when the Earth, in its orbit around the Sun, was flying in the same direction as their light beam; and, six months later, when the Earth was moving in the opposite direction. To their consternation, they found that the speed of their light was the same in both cases. In fact, even had the Earth been orbiting the Sun at the truly enormous speed of half the speed of light, Michelson and Morley would still have measured the speed of light as c – not (c +½c) = 1½c; or (c -½c) =½c. What does the peculiar constancy of the speed of light mean? That question was answered by Einstein in his miraculous year of 1905.
The speed of anything is simply the distance it travels in a given time – for example, a car may travel 50 kilometres in an hour. So, for everyone to measure the same speed for a beam of light – no matter how fast they are moving or how fast the source of light is moving – something weird must have to happen to each person’s measurement of distance and time.
We think of one person’s interval of space – say, a metre – as being the same as someone else’s, and one person’s interval of time – say, a minute – as the same as another’s. But this cannot be true if everyone is to measure the same speed for light. If the speed of light is the rock on which the Universe is built, space and time must be like shifting sand.
In fact, as Einstein realised, space shrinks and time slows down from the point of view of a moving observer. Or, to be more precise, if someone is moving relative to you, you see them shrink in their direction of motion and slow down as if they are moving through treacle.1 ‘Moving rulers shrink,’ goes the saying, ‘and moving clocks slow.’
Einstein had a more tongue-in-cheek – and, by today’s standards, less PC – way of saying it: ‘When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute – it’s longer than any hour. That’s relativity!’
But what is it like from the point of view of the person flying past you? Well, they see you shrink in the direction of your motion; they see you slow down as if wading through treacle. This is because what you each see depends only on your relative motion – and both of you have the same relative motion.
This fact reveals the second foundation stone of Einstein’s theory – in addition to the constancy of the speed of light – and explains why the theory is called relativity. Galileo, four centuries ago, was the first to realise that all people travelling at constant speed relative to each other see the same thing. Take, for instance, someone who throws a ball, which loops through the air to a friend who catches it. The ball will follow the same trajectory whether the thrower and catcher are on a beach or on a ship ploughing through the sea.
When Galileo maintained that all people travelling at constant speed relative to each other see the same thing, he specifically meant that they see the same laws of motion. Two and a half centuries later, Einstein simply extended Galileo’s idea. It is not just the laws of motion that are the same, he claimed, it is all the laws of physics, including the laws of optics, which dictate that the speed of light is unvarying.
Think of the person moving past you at constant speed, and their space shrinking and their time slowing. From their point of view, you are moving with respect to them at the same relative speed – you are just moving backwards. So both of you see the same thing. That is the magic of relativity.
An obvious question is: why do we never see the weird effects of relativity – technically, time dilation and Lorentz contraction? Specifically, when someone runs past us on the street, why do we not see them shrink in the direction of their motion and slow down? The answer is that such effects are noticeable only for bodies flying past each other at speeds approaching that of light. But the speed of light is tremendously fast – about a million times faster than a passenger airliner. We do not see the effects of relativity because we live our lives in the cosmic slow lane. Relativity, in a sense, is the discovery of our slowness.
But, if we do not see the effects of relativity, how do we know that time really slows as we approach the speed of light? How do we know that space really contracts? The evidence is actually coursing through your body at this very instant.
Muons are subatomic particles, created about 12.5 kilometres up in the atmosphere when cosmic rays, high-energy atomic nuclei from supernovae, slam into atoms of the air. Like subatomic rain, muons shower down through the atmosphere. But there ’s the rub. A muon disintegrates after a characteristic interval of time.2 The interval is very short – a mere 1.5 millionths of a second. By rights, therefore, none should travel more than about 500 metres down through the atmosphere before disintegrating. Certainly, none should reach the ground, 12.5 kilometres below.
But they do.
The reason is that muons are travelling at 99.92 per cent of the speed of light. From your point of view, they live their lives in slow motion. In fact, time passes 25 times slower for them than for you, which means they take 25 times as long as usual to realise it is time to disintegrate. When they do, they have already reached the Earth’s surface.
But, of course, there is another point of view – that of the muon. From its angle, time is passing at its normal rate – after all, a muon is stationary with respect to itself, as are you. Instead, it sees you shrink in the direction of its motion – or, rather, your motion, since, from the point of view of a muon, it is the ground that is approaching at 99.92 per cent of the speed of light. But not only do you shrink, so too does the atmosphere. It shrinks to a mere 1/25th of its normal thickness. Which means the muons have time to get to the surface before they disintegrate.
Whatever way you look at it – from your point of view, where the muon’s time slows down; or from the muon’s point of view, where the atmosphere shrinks – the muon gets to the ground. It is one more example of the magic of relativity.
But what would it be like if you, like a muon, could travel at close to the speed of light? For one thing, you would learn some profound truths about the world. You might think that relativity tells us that one person’s interval of time is not the same as another’s. It does. But, more specifically, it tells us that one person’s interval of time is another person’s interval of time and space. In other words, what one person sees as two separate events at the same location – say, two explosions – might appear to someone else as two events at different locations.
You might also think that relativity tells us that one person’s interval of space is not the same as another’s. But, actually, it tells us that one person’s interval of space is another person’s interval of space and time. In other words, what one person sees as two events happening simultaneously another person might see as two events happening at different times.3
But, if at speeds close to that of light, intervals of space morph into intervals of time and vice versa, then surely space and time cannot be fundamental things? Exactly. The fundamental entity, which becomes apparent only close to the speed of light, is space–time. It turns out that, in a low-speed world, we only ever see shadows of this seamless entity – a space shadow or a time shadow.
Here is an analogy. Imagine a walking stick suspended from its midpoint like a giant compass needle. It is in a square room with windows on two adjacent sides. Oh, and it is gloomy in the room so you cannot tell you are looking at a walking stick, just an object. You look through one window and you call what you see ‘length’. Then you look through the adjacent window and you call what you see ‘width’. Makes perfect sense. So far, so good.
Now imagine the walls of the room are on a turntable (this is not a simple analogy!). It turns. And you look through the windows again. To your surprise, you see that the length has changed. And so too has the width. It dawns on you that your labels of length and width were not sensible at all. The fundamental thing is the object – the suspended walking stick. But you have mistaken mere projections – shadows – of the object for the fundamental thing.
This is the way it is for space and time. The fundamental object is space–time. But we have mistaken mere projections of it – shadows – for the fundamental thing. It is not our fault. Our mistake becomes glaringly obvious only at speeds approaching that of light when space morphs into time, and time into space. Actually, in a deep sense, travelling close to the speed of light is like rotating our viewpoint – just as with the room on a turntable – so that we see different space and time projections of space–time.
It was not Einstein who had this insight but his former mathematics professor, Herman Minkowski, who famously called his pupil a ‘lazy dog’. On later realising his mistake, Minkowski also recognised the key importance of space–time. ‘From now on,’ he said, ‘space of itself and time of itself will sink into mere shadows and only a kind of union between them will survive.’
The speed of light is uncatchable by any material body. This is pretty amazing. After all, if we were really talking about infinite speed, it would be obvious that, no matter how hard and how long we pushed a body, it would never attain infinite speed. But the speed of light, though huge by human standards, seems so much smaller than infinity.
Well, since the speed of light is unattainable – the cosmic speed limit – something must happen as you push a body faster and faster. There must be some kind of resistance to your pushing, and the resistance must become infinite close to the speed of light so that no amount of pushing will ever get you there.
One property of a body provides resistance – its mass. In fact, that is how we define mass. A body that resists being pushed a lot, such as a loaded fridge, is said to have a big mass, while a body that resists very little, such as a feather, is said to have a small mass. See where this is going? If, as a body approaches the speed of light, its resistance grows, it must mean that it gets more massive.
But where is the extra mass coming from? There is a fundamental law of physics called the law of conservation of energy that says energy can be changed only from one form into another, and never created nor destroyed. For instance, electrical energy can be changed into heat energy in an electric fire; the chemical energy of your food can be changed into energy of motion in your muscles. But, if you are pushing and pushing the body and the energy you are putting in is not going into energy of motion, it must be going somewhere. Well, the only thing that is changing is the mass of the body. The energy you are putting in must be increasing its mass. But remember, energy can be transferred only from one type into another. Mass must therefore be a form of energy.
And, in fact, this is true. Not only did Einstein discover that space and time are mere facets of the same thing, he discovered that energy – energy of motion, sound energy, any energy you imagine – has an equivalent mass.
If you think all this is esoteric, with nothing much to do with you, think again. The quarks that contribute most of your mass are very insubstantial indeed.4 In fact, they account for only about 1 per cent of your mass. This is explained by something called the Higgs mechanism. You may have heard of the Higgs particle, whose discovery was announced with a huge fanfare at the Large Hadron Collider near Geneva on 4 July 2012.5 So where does the lion’s share of your mass – the other 99 per cent – come from? The answer is relativity.
The quarks within the protons and neutrons of atoms are whirling around at close to the speed of light. This means they have enormous energy of motion. And this energy of motion, according to Einstein, has mass. It accounts for most of the mass of protons and neutrons – and, therefore, you. Without the effects of relativity, you would weigh less than 1 kilogram.
You may ask: why are the quarks whirling around at speeds approaching that of light? The answer is that they are in the grip of the enormously powerful strong nuclear force. A force field contains energy, which, according to Einstein, has mass. Ultimately, then, it is this gluon field that accounts for most of your mass. It does not matter how you look at it. Ultimately, something as mundane and everyday as your mass is inexplicable without the effects of relativity.
But Einstein showed that not only does energy have a mass but that mass has an energy associated with it. In fact, mass is the most concentrated form of energy known, and its energy is given by the most famous formula in all of physics, E = mc2.
The formula applies both ways. Take subatomic particles circulating in opposite directions around the giant buried racetrack of the Large Hadron Collider. When the particles collide head on, their energy of motion can be converted into the mass energy of new particles, which appear out of the vacuum like rabbits out of a hat. But also – and this is the most shocking thing – mass energy can be converted into other forms of energy such as heat energy. This happens in a nuclear bomb, when a small amount of mass is converted into the tremendous amount of heat of a nuclear fireball.
You might think that relativity strips away our certainties about the world. But, in fact, it lifts the veil and reveals a deeper layer of reality beneath.
The world is complex, bewildering, ever changing. When we try to make sense of it, we are like shipwrecked mariners clinging to rocks in a turbulent sea. Physicists grab desperately for anything that seems solid and permanent. Specifically, things that are the same for everyone – that do not depend on a particular point of view.
Once upon a time, physicists believed space and time were the rocks of the Universe – that everyone would measure the same length of a given object; that everyone would measure the same interval of time between events. Einstein showed they were mistaken. What people measure depends on their point of view – specifically, how fast they are moving relative to each other.
Once upon a time, physicists believed mass was a rock of the Universe – that a body with a mass of 1 kilogram today would have a mass of 1 kilogram tomorrow and for all eternity. Einstein showed that they were mistaken. In an H-bomb, almost 1 per cent of the mass disappears, converted into other forms of energy, principally heat energy.
But what nature takes from us with one hand, it gives back with the other. Mass might not be the solid rock we thought it was – but energy is, with mass being merely one form of energy. Space and time might not be the rocks we thought they were – but space–time is.6 Physics, it turns out, is the search for truths about the world that are independent of our point of view. Einstein, in lifting the veil of reality, showed us what is truly rock-like, truly invariant.
1 See Chapter 18, ‘The roar of things extremely small: Atoms’.
2 Werner Heisenberg, Physics and Philosophy.
3 Werner Heisenberg, Quantum Theory.
4 There is an interesting parallel here with space–time. Space–time, being 4-dimensional, is ungraspable by 3-dimensional creatures such as us. Instead, we experience merely facets of space–time – space and time (see Chapter 16, ‘The discovery of slowness: Special relativity’). In the same way, we see only the particle-like and wave-like facets of light.
5 If the Universe were not fundamentally unpredictable, there would not be a Universe – or at least a Universe of the complexity necessary for us to be here. The reason is that, according to the standard picture of cosmology, known as inflation, the Universe started out so ultra-tiny that it contained hardly any information. Today, it contains a truly vast amount – just imagine how much would be needed to describe the type and location of every atom in the Universe. The puzzle of where all the information came from is explained by quantum theory since randomness is synonymous with information. Every quantum event since the big bang, such as the decay of a radio active atom, has happened randomly, injecting information/complexity into the Universe. When Einstein said, ‘God does not play dice with the Universe ’, he could not have been more wrong. If God had not played dice, there would be no Universe – certainly no Universe with anything interesting going on in it. See ‘Random Reality’, Chapter 10 of my book We Need to Talk about Kelvin.
6 Technically, the probability of finding the atom at a particular location is the square of the amplitude of the quantum wave, or wave function, at that location.
7 ‘I bet that was fun for the rest of the Thomson family at get-togethers. “It is. It isn't! It is …!”’ said @Katharine_T29m, one of my Twitter followers.
8 The incredible thing is that, even if Davisson, Germer and Thomson had fired their electrons at their crystal one at a time, with an hour gap between each one, over time they would have observed exactly the same pattern: there would have been directions in which electrons are seen alternating with directions in which they are never seen. So it is not interference between the quantum waves of different electrons that creates the pattern. It is interference between quantum waves of a single electron. Each electron is in a superposition corresponding to it going in all directions at once and it is the individual waves of this superposition that interfere with each other. Quantum theory is truly mind-bending.
9 Technically, spin ½ means that an electron has a spin of ½ × (h/2*π), where h is Planck’s constant.
10 If history had run itself differently, not only would the particle with the smallest spin have been assigned a spin of 1 unit, the particles with the smallest electric charge would have been assigned a charge of 1 unit. Instead, the electron has ended up with a spin of ½, and the quarks charges of magnitude 1/3 and 2/3.
11 See Chapter 8, ‘Thank goodness opposites attract: Electricity’.
12 See Chapter 16, ‘The discovery of slowness: ‘Special relativity’.
13 See Chapter 8, ‘Thank goodness opposites attract: Electricity’.
14 The wavelength of a particle, as Louis de Broglie guessed in 1923, is inversely proportional to its momentum. To be specific, it is (h/2*π)/p, where p is the momentum.
15 The resistance of an electron wave to being squashed gives rise to a force known as electron degeneracy pressure. In 5 billlion years’ time, when the Sun has exhausted its heat supply, gravity will gain the upper hand and shrink it down to the size of the Earth. The force that will prevent it shrinking any more than this will be electron degeneracy pressure – the resistance of electron waves to being squeezed. From the particle point of view – which is more complicated than the wave point of view – the force is said to be due to the Heisenberg Uncertainty Principle. This merely says that the smaller the volume in which a particle is confined, the greater its momentum. Think of a bee that buzzes about more angrily the smaller the box in which it is confined.
16 See Chapter 18, ‘The roar of things extremely small: Atoms’.
17 ‘I’m more of a glass is 0.00000000000001% full kinda person myself,’ said @MrDFJBaileyEsq, one of my Twitter followers.
18 A planet cannot quite orbit anywhere in the Solar System. The space between the orbits of Mars and the giant planet Jupiter, for instance, is populated only by chunks of rocky rubble, or asteroids. A fully fledged planet was prevented from forming here by the disruptive effect of Jupiter’s powerful gravity.
19 The details of how electron spin, waviness and indistinguishability spawn the Pauli Exclusion Principle are described in ‘No More than Two Peas in a Pod at a Time’, Chapter 3 of my book We Need to Talk About Kelvin.