Read What a Wonderful World Online
Authors: Marcus Chown
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 = mc
2
.
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.
If a bird-watching physicist falls off a cliff, he doesn’t worry about his binoculars; they fall with him.
SIR HERMANN BONDI
One thing at least is certain, light has weight … Light rays, when near the Sun, do not go straight.
ARTHUR EDDINGTON
Einstein’s theory of relativity is a recipe for predicting what must happen to space and time in order for everyone to measure the same speed for a beam of light.
1
By ‘everyone’, Einstein meant people moving at constant speed relative to each other. A moment’s thought, however, reveals that this is a very special
circumstance
. Very few bodies move with uniform speed. A car in traffic slows down and speeds up before coming to a halt at traffic lights. A rocket rising on a column of orange flame and white smoke gets ever faster until it attains the 29,000 kilometres an hour necessary to stay in orbit above the Earth.
So all Einstein had figured out in 1905 was what the world looks like from the point of view of atypical, or ‘special’, observers, moving at constant speed with respect to each other. For his next trick, he needed to figure out what the world looks like to typical, or ‘general’, observers, who are varying their speed with time, or accelerating, with respect to each other. Somehow, he had to turn his special theory of relativity into a general theory of relativity. It was a monumental task that would take him a decade of mental struggle, but it would cement his place in history as the greatest physicist since Isaac Newton.
In attempting to generalise special relativity, Einstein faced a serious problem. Not only does special relativity describe a special situation, it is
completely incompatible
with one of the great cornerstones of science – Newton’s theory of gravity.
According to Newton, there is a force of attraction between any two bodies – for instance, the Sun and the Earth – that depends on their separation and on their masses. However, special relativity says that
all forms of energy
have an effective mass. If you heat a cup of coffee, for instance, its heat energy makes it marginally more massive than when it is cold.
Consequently
, all forms of energy must exert a gravitational force on each other, not just mass energy. It is
energy
not mass, as Newton believed, that is the source of gravity. Mass energy is simply the most familiar form.
And this is not the only incompatibility between special
relativity
and Newton’s law of gravity. According to Einstein, light sets the ultimate cosmic speed limit. His theory therefore predicts that, if the Sun were to vanish suddenly – an unlikely scenario but imagine that it did – the Earth would not realise right away. For the time it takes gravity, travelling at the speed of light, to go between the Sun and the Earth, the planet would continue blithely in its orbit. Only after 8½ minutes would it realise that the Sun had disappeared and fly off on a tangent towards the stars.
Contrast this with the prediction of Newton’s law of gravity. Two bodies feel an
instantaneous force
between them, which is synonymous with saying that the gravitational influence travels between them
infinitely fast
. Newton’s theory therefore predicts that, if the Sun were to vanish suddenly, the Earth would notice immediately, in violation of Einstein’s cosmic speed limit.
In concocting special relativity, Einstein had therefore
inadvertently
smashed one of the foundation stones of physics – Newton’s law of gravity. He must have felt like a vandal who topples a beautiful building without the slightest idea how to build a replacement. But, just when he was despairing of ever
finding a way, he had a brainwave. It concerned a simple observation that had been known about for centuries but whose significance no one before had recognised.
The seventeenth-century Italian scientist Galileo Galilei is supposed to have dropped a heavy mass and a light mass from the leaning Tower of Pisa and observed them hit the ground together. The same experiment, minus the complicating effect of air resistance, was later carried out on the Moon in 1972. Apollo 15 commander Dave Scott dropped a hammer and a feather together and, from the simultaneous puffs of moon dust,
demonstrated
that they hit the ground at the same instant.
Think for a moment how peculiar this is. If you were to take a small mass and a big mass and push both of them with exactly the same force, it is obvious that the small mass will gain the most speed. It is common experience that a big mass such as a fridge resists being moved more than a small mass such as a stool – it is the very basis of our
definition
of mass. But, when the force of gravity pulls a small mass and big mass groundwards, the two masses gain speed
at exactly the same rate
. In other words, the force of gravity goes up perfectly in step with the mass.
Somehow
, it
knows
to be bigger for a bigger mass. But how? It was Einstein’s genius to think of a circumstance in which such an adjustment would come about perfectly naturally.
Imagine an astronaut in a rocket far from the gravity of any planet or moon. The rocket is accelerating, at 9.8 metres per second per second.
2
Since this is precisely the rate at which a falling body accelerates towards the Earth – 1g, in the jargon – the astronaut’s feet are glued to the floor of his cabin just as if they were on the surface of the Earth. Now imagine that the astronaut holds a paperclip and a golf ball at the same height
above the floor and lets them go simultaneously. Unsurprisingly, perhaps, they hit the floor at the same time, just as on Earth.
Now zoom out. Imagine you are floating outside the rocket with X-ray eyes that reveal to you the interior of the rocket (this not a realistic story). What do you see from your godlike point of view? The astronaut lets go of the paperclip and the golf ball and they hang motionless in space. How could they not do? The rocket, after all, is far from the gravity of any planet. But, as the two objects hang there, unmoving, the floor of the cabin
accelerates
upwards to meet them.
Now, recall that on Earth it was a complete mystery how gravity achieves the trick of adjusting its strength so that it pulls a big mass down at exactly the same rate as a small mass. But, in the rocket scenario, there is no mystery at all. Since it is the floor of the cabin that accelerates upwards to meet the motionless paperclip and golf ball, how could they not meet the floor at the same time?
But, wait a minute, the rocket scenario can explain gravity only if gravity
is the same as acceleration
. Exactly! Einstein’s genius was to realise that the two things are completely
indistinguishable
. If the port holes of the rocket are blacked out and the
vibration
of the rocket is imperceptible, the astronaut experiences
exactly the same thing
as he would if he were in a blacked-out room on Earth. Gravity, Einstein realised,
is
acceleration.
Bizarrely, then, we are accelerating and we do not realise it. And, because we do not realise it, we have invented a force to explain what we experience: gravity.
It turns out that there is a point of view from which this fact is completely obvious, just as in the case of the rocket. But to appreciate it, it is first necessary to know a little background.
The rocket thought experiment showed Einstein that gravity and acceleration are the same. If he could therefore find a theory of what the world looks like from the point of view of an accelerated person, he would automatically have a theory of gravity as well.
Two theories for the price of one
. But how? At this point, Einstein, still working as a Swiss patent clerk, had what he later called his greatest thought. ‘The breakthrough came suddenly one day. I was sitting on a chair in my patent office in Bern. Suddenly, the thought struck me: If a man falls freely, he would not feel his own weight.’
Why was this a breakthrough? Well, since gravity and
acceleration
are the same thing, someone experiencing no weight – that is, no gravity – would not be accelerating. In other words, his situation would be described perfectly by special relativity, a theory that depicts what the world look likes to a non-
accelerating
observer. Not only had Einstein found that a theory of acceleration is one and the same thing as a theory of gravity, he had found the crucial bridge that connects it with special
relativity
, which he already had in his possession. A falling person feels no gravity and therefore his view of the world is described by special relativity.
A person accelerating with respect to him – that is, one
experiencing
gravity – could at each instant be assumed to be moving at constant speed. It was therefore possible to use special relativity to predict what his world looked like at one instant, then at the next instant, and so on.
Not surprisingly, since time appears to slow for someone
moving
with respect to you, time also appears to slow for someone accelerating with respect to you. But, since acceleration and
gravity are the same, this means time flows more slowly for
someone
experiencing stronger gravity.
In other words,
gravity slows time.
Take two people working on the ground floor and top floor of a building. The person on the ground floor is closer to the mass of the Earth, and so experiences marginally stronger gravity. Time therefore flows more slowly for them. If you want to survive a long time, live in a bungalow.
This slowing of time, or time dilation, is fantastically tiny, and you would need a super-precise atomic clock to show it. But,
incredibly
, in 2010, physicists at the National Institute of Standards Technology in the US were able to show that, if you were to stand one step lower than someone else on a staircase, time would flow marginally more slowly for you.
3
The slowing of time is appreciable, however, when gravity is strong. And the strongest source of gravity we know of is a black hole.
4
If you could hover near the edge, or horizon of a black hole, time would flow so slowly for you that you would be able to watch the entire future history of the Universe flash past your eyes like a movie in fast-forward.
Back to that question – so far unanswered – of why, if gravity is just acceleration, do we not realise we are accelerating?
Think of the rocket accelerating at 1g again. Imagine the astronaut shines a laser beam across the cabin, from one wall to the other, perfectly horizontally – at a height, say, of 1 metre above the floor. What does he see? The beam strikes the far wall of the cabin at a height of
less than 1 metre.
This may seem peculiar. However, it is not unexpected.
Although
light is the fastest thing in the Universe, it nevertheless takes time to cross the cabin. And, during its flight, the floor of the cabin accelerates up towards it. The astronaut therefore sees the light beam curve downwards towards the floor. (For an acceleration of as little as 1g, the effect would be
very tiny
but it would be measurable by precision instruments.)
Two things. First, one of the defining characteristics of light is that it always takes the shortest path between any two points. The astronaut would therefore have to conclude from the trajectory of the laser beam that the shortest path in an accelerating rocket is not a straight line but a
curve
. Secondly – and this is the big thing – since acceleration is indistinguishable from gravity, the astronaut would have to conclude that the path of a light beam in the
presence
of gravity is a curve. In other words,
gravity bends light.
Actually, Einstein had guessed, even before he came up with his general theory of relativity, that gravity bends the path of light. Special relativity, after all, predicts that all energy has an equivalent mass and therefore is affected by gravity (not to mention
exerts
gravity too). Since particles of light, or photons, possess energy, they have an effective mass and so should be bent by gravity. (‘Photons have mass?!?’ said Woody Allen. ‘I didn’t even know they were Catholic.’
5
)
Einstein’s theory of gravity, however, adds a new and subtle twist to this light bending. The claim is that gravity and
acceleration
are equivalent. But, in the case of the rocket, this is not completely true. From the point of view of the astronaut, the two objects they release ‘fall’ towards the floor along parallel trajectories. However, this is not what happens if the same two objects are dropped on Earth. The reason is that gravity is always
directed towards the
centre
of the Earth (in the extreme case of people living on opposite sides of the Earth, gravity pulls in
opposite directions
).
6
Because of this effect, the bending of a light beam by gravity is
twice as big
as naively expected.
Einstein’s prediction of the gravitational bending of light was triumphantly confirmed on 29 May 1919 during a total eclipse of the Sun. Since in a total eclipse the glare of the Sun is blotted out by the Moon, it is the only time stars can be seen very close to the disc of the Sun.
7
As their light passes the enormous mass of the Sun on its way to the Earth, it should be deflected from its path by the gravity of the Sun. Sure enough, an expedition led by English astronomer Arthur Eddington to Principe, an island off the west coast of Africa, confirmed that the light bending was exactly as predicted by Einstein’s general theory of relativity – twice the value expected from special relativity.