The Humpty Dumpty Tendency

How the fact that teacups break but never unbreak is telling us that the Universe must have expanded from a big bang

‘Humpty Dumpty sat on a wall.

Humpty Dumpty had a great fall.

All the king’s horses and all the king’s men

Couldn’t put Humpty together again.’

Nursery rhyme (unknown origin)

‘Lettin’ the cat outta the bag is a whole lot easier ’n puttin’ it back in.’

Will Rogers

A teacup slips from your grasp. It hits the floor and shatters into a dozen pieces. Such an everyday accident may seem of little consequence, but it is telling us something profound about our Universe. It is telling us that the Universe must have begun in a highly unusual, ordered state, one which is possible if it expanded from a Big Bang explosion.

How can the birth of the Universe in the Big Bang have anything to do with something so prosaic as a teacup shattering? The answer is subtle. And it explains not only why teacups break rather than unbreak but why tea left in a cup grows cold rather than hot and even why you grow older rather than younger with every passing year.

Think of that disintegrating teacup. It illustrates perfectly a paradox at the heart of the world, one which for a long time baffled physicists. The paradox arises because of a striking feature of the fundamental laws of physics which orchestrate the Universe and decree what can and cannot happen. If those laws permit a particular process to happen, they always permit its opposite too.

Take Newton’s laws of motion, which describe the movement of bodies under the influence of forces. A manoeuvre often used by the American space agency NASA to boost a space probe so it can reach the outer Solar System is a so-called sling-shot. A space probe, moving under the influence of the Earth’s gravitational force, approaches the Earth, swings around the planet and boomerangs back out into the depths of space. Imagine you were shown a movie of this flyby and a movie of the fly-by running backwards. In the latter case, the space probe approaches the Earth from the direction in which it formerly receded and recedes along the direction it approached. The question is: could you tell simply by looking which depicted the manoeuvre actually used by NASA?

The answer is no. If a certain trajectory for a spacecraft is permitted by Newton’s laws of motion, so too is its opposite. The laws are ‘time-symmetric’, which means you can never tell whether the movie is running forwards, as normal, or backwards. Both situations are equally permissible.1

What has this got to do with a shattering teacup? Well, each fragment flying through the air is as much under the influence of Newton’s laws of motion as a space probe swinging around the Earth. Say you were shown a movie of a single shard tumbling through the air and the same movie running backwards. Assuming the camera had focused only on the shard and nothing else tell-tale in the surroundings, could you pick the movie which depicted reality and the one which showed reality running backwards? As with the space probe, the answer is no.

But now zoom out from the fragment to the teacup shattering on the floor. If you were to see a movie of this event and a movie of the event running backwards, could you tell which was reality and which was reality in reverse? The answer is, of course, yes. In the real world, teacups shatter. They never unshatter. But how can a teacup whose component fragments are governed by fundamental laws that are time-reversible behave in a way that is so emphatically not time-reversible? This is the paradox that for so long baffled the world’s best physicists.2

And it is not just teacups that behave like this. If you were to watch a movie in reverse of any event in the everyday world, you would know instantly which was reality and which was not. People run after buses, they do not run away from buses; dogs chase cats, they do not un-chase cats; people grow old, they do not grow young. So how is it that we can live in a world orchestrated by fundamental laws that permit things to happen equally well backwards or forwards in time and yet be surrounded by events which happen only forwards? The man who provided the language to discuss the paradox in a precise way was the Austrian physicist Ludwig Boltzmann.

It would be nice to relate a quirky or amusing anecdote about Boltzmann. Unfortunately, he had a pretty tragic life. It was a shame because, by all accounts, the short, stout, bespectacled Boltzmann, known to his fiancée as ‘my sweet fat darling’, was kindly and well liked. He could never refuse a request for a favour and cared so much for his students, especially those of poorer means, that towards the end of his life no student was ever permitted to fail one of his examinations. But Boltzmann was dealt a number of personal blows. His father died when he was 15, a time in the life of a child that is well known to be the worst to lose a parent, and his first son, Ludwig, died of a burst appendix. Boltzmann blamed himself for not recognising early enough the seriousness of his 11-year-old’s condition, though it is hard to imagine that, in an age before antibiotics, anything would have made a difference. These events probably played a role in triggering, at the age of 44, Boltzmann’s manic depression, although they probably just exacerbated an existing, though not so obvious, condition. For the rest of his life Boltzmann oscillated between periods of euphoria when he felt himself the master of the world – or at least of the world of physics – and often worked feverishly until 5 a.m., and episodes of terrible black despondency when all his triumphs seemed but worthless dust and ashes. It was in 1906, during one of these episodes of depression, which coincided with a family holiday in Duino, a village on the Adriatic coast near Trieste, that his 15-year-old daughter Elsa – the sunshine of his life – returned from swimming to find him hanging in his room. Boltzmann was 62.

Undoubtedly, a contributory factor in Boltzmann’s suicide was the hostility directed at him by an army of scientific zealots who considered that atoms, which nobody had ever seen or touched and on which Boltzmann’s ideas were founded, were a dangerous idea that must be ruthlessly rooted out of science, lest they bring the whole edifice tumbling down. The irony is that only the previous year Einstein had shown how the mysterious jittery motion of pollen grains suspended in water could be explained if they were coming under constant machine-gun bombardment from atoms in the water, and, in 1908, Jean Baptiste Perrin would even use this Brownian motion and Einstein’s theoretical framework to measure the size of atoms. Atoms were no fiction, as Boltzmann’s enemies claimed. They were real. The final tragedy of Boltzmann’s life was that he did not experience the glorious victory of his ideas, nor was he around to see his elevation to the pantheon of the greatest physicists who ever lived.

It was one of Boltzmann’s greatest triumphs to show how time-symmetric laws of physics could lead to an everyday world with a very definite direction of time. The key, he realised, was probability.

Think of the teacup again. Specifically, think of how many ways it could shatter. It could shatter, for instance, into ten fragments, or 19, or 48. It could shatter into a small number of big fragments and a large number of small fragments. It could shatter exclusively into small fragments. And so on. It does not take much imagination to realise that the number of possible ways a teacup can break is monumentally huge. Now, among all these possibilities, is the possibility that the teacup does not shatter at all but remains intact. But there is only one way this can happen. Consequently, if all outcomes for the teacup are equally likely – and this was Boltzmann’s reasonable assumption – then it is overwhelmingly probable that the teacup will shatter.

Now imagine the event in which a teacup unbreaks. Say you drop a collection of cup fragments, they hit the floor and come together miraculously to make an unbroken teacup. In how many ways could this happen? Well, as pointed out before, there is only one way the cup can be intact. Contrast this with the astronomically huge number of ways that the cup can remain broken: it can stay in the same number of pieces, or all of its pieces can shatter into even smaller pieces, or some of its pieces can stay intact and others crumble to dust, and so on. The point is that there are hugely more ways the cup can remain broken than reassemble into an unbroken cup. Once again, if all possibilities are equally likely, it is overwhelmingly probable that we will not see the shards of the teacup leap back together again to make a pristine vessel. It is not totally impossible; however, it is an event so mind-bogglingly improbable that you would have to keep dropping teacup shards over and over, for far longer than the current age of the Universe, before you were lucky enough to witness such an extraordinary event.

Such improbable events turn out to have huge philosophical implications if the Universe is infinite in extent, either in space or in time. After all, in such a universe anything, no matter how mad and unlikely, is certain to happen. The trouble is, we appear to live in such a universe. In 1998, physicists and astronomers in the US and Australia discovered that the expansion of the Universe is speeding up, driven by ‘dark energy’, invisible stuff with the repulsive gravity that fills all of space. It appears that the dark energy may cause the Universe to grow without limit. Nobody knows what the dark energy is. However, like all things quantum, it will inevitably undergo quantum fluctuations, conjuring particles of matter out of nothing. Such quantum fluctuations could create a man in a space suit floating in space. Or a computer. Or a brain with a single giant eye. These possibilities are, of course, mind-bogglingly unlikely. However – and this is the crucial point – in a universe with an infinite amount of space and an infinite amount of time, they are certain to happen; in fact, they are certain to happen an infinite number of times over. The problem is that eventually such ‘Boltzmann brains’, as they are known, will outnumber ordinary observers like you and me who have evolved over billions of years by the hand of natural selection. This is a problem because our models of the Universe – the Big Bang models – are founded on the idea that we are typical observers and that what we see as we look outwards at the Universe is typical of what all cosmic observers see. If most observers are Boltzmann brains, staring out at unending tracts of utterly empty space, then they are the typical observers. The foundation stone of our cosmology would crumble, and with it everything we thought we understood about the Universe.

But back to teacups. What characterises the state of the intact teacup is ‘order’, while the state of the shattered teacup is characterised by ‘disorder’. Physicists have a technical name for disorder: ‘entropy’.3

Boltzmann’s key insight was that when a body has a large number of subcomponents, the disordered possibilities open to it vastly outnumber the ordered possibilities. If all possibilities are equally likely, there is therefore an overwhelming tendency for the body to become more disordered with time – for it to increase its entropy. Since we associate the direction in which order becomes disorder with the direction of time – a teenager’s bedroom tends to get more untidy with each passing day, not more tidy – this neatly explains why in the everyday world there is a direction, or ‘arrow’, of time. It shows how, despite the fact the underlying laws of physics permit the subcomponents of a body to do things equally well forwards or backwards in time, the body itself always behaves like a forward-running movie.

Everything around us is made of subcomponents – atoms. You are made of about 1,000 billion billion billion, and it would take 10 million, laid end to end, to span the full stop at the end of this sentence. Since the number of atomic subcomponents is so enormous, it is not simply teacups shattering into a thousand pieces that are characterised by a change from order to disorder. So too are all everyday processes.

Changes from order to disorder in your surroundings may not appear obvious. Someone claps their hands. How does this increase disorder? Or, to take a more esoteric example, someone fires a bullet into a steel wall. How does this boost entropy? The answer is that such processes add to the disorder of the Universe in a subtle way – by producing ‘heat’.

Heat is actually random microscopic motion. For instance, it is the jiggling of atoms about their average locations in a ‘solid’. It is the frenzied motion of atoms like a swarm of angry bees in a ‘gas’ such as air (such atoms fly about according to Newton’s laws of motion just as surely as a space probe flying through space). It is the random machine-gun sputter of particles of light, or photons, emitted by the atoms of a hot body.4 Heat is the very epitome of disorder.

In the case of a person clapping their hands, the concussion of flesh jiggles the air molecules in the immediate vicinity, which jiggle their neighbours, exporting disorder into the surrounding air. It heats up a little. In the case of the bullet burying itself in the steel wall, friction jiggles the atoms in not only the wall but the bullet itself. They heat up a lot.

When any form of energy is turned into heat energy, it is as unlikely for that heat energy to be turned back into the original form as it is for a teacup to unbreak. And for the same reason. In the case of the person clapping their hands, it would require the zillions of jiggling air atoms in the thin layer between the person’s hands suddenly to find themselves jiggling outwards in perfect unison so as to push the hands apart again. Though not totally impossible, this is a fantastically unlikely thing to happen. And in the case of the bullet embedded in the steel, the jiggling atoms of the bullet would all have to find themselves jiggling in the same direction – away from the steel wall – so that the bullet leapt back out towards the gun. How likely is that? The answer, of course, is overwhelmingly unlikely.

All this leads to a fundamental asymmetry in the law of conservation of energy when it involves heat energy. Although it is possible to convert 100 per cent of any form of energy into heat energy, it is not possible to turn 100 per cent of any heat energy into another type of energy. The reason is that heat represents energy dispersed among many, many things – for instance, among the many molecules in a hot gas. To convert this energy into useful ‘work’ involves concentrating energy into a few things – for instance, the motion of a single bullet. The reason heat cannot be changed into work with 100 per cent efficiency is simply that it is extremely unlikely for the energy in a hot substance, which is spread among many, many states, to pass into a few states, such as the motion of a bullet.

It is not at all obvious in the case of the bullet and the steel wall – or in the case of the clapping hands – that disorder has increased. In fact, it would appear that in both instances the opposite has happened. After all, two hands glued together seems a more ordered state than two hands held apart. A bullet and a steel wall welded into one entity is more ordered than a bullet and a wall as two entities. What is not obvious to us – because it is invisible to the naked eye – is that these local increases in order have been more than paid for by an increase in global disorder – by the export to the environment of microscopic disorder, or heat.

The fact that order can increase locally at the expense of disorder being boosted elsewhere hints at how humans and all other living things on Earth have bucked the trend of ever-increasing entropy. A baby feeds on its mother’s milk and the energy this provides enables a proliferation of neuronal connections in its brain, creating the most ordered entity in the known Universe. But in metabolising that milk, heat is produced – we all know we get warm when we eat – and the environment pays. Overall, the disorder of the Universe increases.

The fact that disorder can never decrease is known as the ‘second law of thermodynamics’. Although it is an inviolable law – any law in physics that is found to contradict it is instantly discarded – it is actually on a different par to other fundamental laws of physics. Whereas they determine what happens with 100 per cent certainty, the second law is statistical. It ordains only what is overwhelmingly likely to happen, rather than what is certain to occur.

One of the consequences of the transformation of order into disorder in the Universe – of the remorseless increase of entropy – is a running down of things. A constant degeneration. A degradation. Ultimately, it explains why we grow older – how the function of our cells becomes ever more compromised by disorder. It is the hand of entropy at work as surely as in the shattering of a teacup.

But if all processes in the Universe increase its net disorder, then a logical conclusion that can be drawn is that one day the Universe will reach a state of maximum disorder. In such a universe, it will be impossible for anything at all to happen since, as pointed out, no everyday process can happen without an increase in the Universe’s disorder. Even worse, the past and the future will lose all meaning since we identify the direction from past to future – the arrow of time – with the direction in which things become increasingly disordered.

That there exists a hypothetical state of maximum disorder for the Universe was first recognised by physicists in the nineteenth century. They christened it ‘heat death’, and it is the nightmare scenario when all activity grinds to a halt. The Universe, in the words of T. S. Eliot, ends ‘not with a bang but a whimper’.

The way to understand precisely why nothing can happen in a state of heat death is to realise that not all disorder is equal. There is usable disorder and unusable disorder. It all depends on a particular property of heat: its temperature, or degree of hotness.

Most people recognise the difference between heat and temperature. A lighted match has a high temperature but contains little heat – try using it to heat a saucepan of water – while a household radiator contains a lot of heat but has a low temperature – if you touch it you will not burn yourself. And it turns out that if you have two sources of heat at different temperatures, it is possible to do useful ‘work’ – for instance, to drive a piston in a steam engine. It is exactly like having a difference in water level, such as in two ponds at different heights. If water flows from the higher pond to the lower one, it can turn a water wheel. But the inevitable result of this is that all the water ends up at the same level in the lower pond and, with no difference in water level, the water wheel can no longer be turned.

The same thing happens in a steam engine. Steam at high temperature drives a piston and then is condensed, or turned to water, and discharged into the atmosphere at a lower temperature. Since the discharged heat is at the same temperature as the atmosphere, it is spent and can do no more work. And this is what physicists of the nineteenth century realised would happen to the Universe when it reached heat death.

The key temperature difference that drives everything in the Universe is the one between the stars, which are hot, and empty space, which is cold. All processes on Earth ultimately derive their energy from sunlight, which is radiated into space because there is a temperature difference of about 6,000 degrees between the solar surface and the surrounding space. For instance, sunlight drives the circulation of the ocean and atmosphere. It drives photosynthesis in plants. Ancient microorganisms and trees soaked it up and, after being squeezed beneath the ground for millions of years, became fossil fuels such as oil and coal.

But as the stars pump heat into space, they inevitably get cooler and space gets warmer.5 Eventually, the temperature difference between them will be ironed out. The Universe will be filled not only with disorder but unusable disorder. Disorder at the same temperature. This is the dreaded state of heat death.

So how close is the Universe to such a state? Well, space is criss-crossed by photons pumped out randomly by stars. It turns out that their contribution to the disorder of the Universe far outweighs that of all the jiggling particles of matter put together. And even the photons from stars account for a mere 0.1 per cent of the photons currently abroad in the Universe. An enormous 99.9 per cent are tied up in the leftover heat of the Big Bang fireball – the afterglow of creation. In fact, there are 10 billion of these photons for every particle of matter. Hold up your hand. Every second a million billion photons from the Big Bang are bouncing off your skin.

The leftover heat of the Big Bang is telling us that the Universe today is essentially in a state of heat death. Orbiting a star, we exist in a rare cosmic location where activity can still go on. Shockingly, it seems that most of the Universe succumbed to heat death well within the first second of its existence. It happened when an orgy of particle–antiparticle annihilations, each of which created a pair of photons, destroyed most of the Universe’s matter and antimatter. Because some as-yet-not-understood asymmetry in the laws of physics had ensured that for every 10 billion particles of antimatter there were 10 billion and 1 particles of matter, when the dust finally settled there were about 10 billion photons for every surviving particle of matter. It is these photons we see today as the afterglow of the Big Bang – cosmic background radiation.6

The fact that the Universe is currently so close to heat death means that there is actually very little scope for disorder to increase in our Universe, so it is not possible to explain why time flows the way it does – why teacups shatter and people grow old – by the Universe being far away from a state of heat death. What, then, is the explanation for the arrow of time? Well, it is a statement of the blindingly obvious, but a teacup can become more disordered in the future only if it was more ordered in the past. Consequently, the fact that time flows the way it does is telling us that in the Big Bang the Universe must have been in a highly ordered, highly improbable, special state.7

Physicists have an abhorrence for accepting that there is anything special or unlikely about our Universe. It smacks of religion. It goes back to Nicolaus Copernicus’s discovery that there is nothing special about our position in the Universe – the Earth orbits the Sun along with the other planets and is not the centre of things – and Charles Darwin’s discovery that there is nothing special about our place in the natural world – human beings are just one among myriad other animal species on our planet. However, to make sense of the arrow of time we experience, physicists have been forced to accept that the Universe must have started in an unlikely, highly ordered state. Most harbour the hope that such a state will one day be shown to be an inevitable consequence of a ‘theory of everything’ that explains all of creation in one neat set of equations.

However, one physicist thinks that it is not necessary to look to the super-physics of an elusive theory of everything to explain how the Universe started out in an unlikely, ordered state. According to Lawrence Schulman, of Clarkson University in New York, there is a relatively mundane explanation. Regardless of how the Universe started out, he believes, it naturally made a transition to an unlikely, low-entropy state when it was about 380,000 years old. The key was gravity, which, for the first time, gained control of the Universe.

The era 380,000 years after the moment of creation was of crucial importance in the history of the Universe. At this time, the expanding fireball of the Big Bang had cooled to about 4,000 degrees, a sufficiently low temperature for atomic nuclei and electrons to combine to make the first atoms.8 Before this time, photons – of which there were about 10 billion for every particle of matter – had a powerfully disruptive effect on matter. They ricocheted, or ‘scattered’, off free electrons, blasting them apart and so preventing gravity from gathering together any clumps of matter. After that time, electrons were bound up inside atoms and so relatively shielded from the disruptive effect of photons. For the first time, gravity could begin to cause matter to clump. It was the start of a long process that would lead ultimately to galaxies, stars, planets and you and me.9

It was the ‘switch-on’ of gravity at this ‘epoch of last scattering’, 380,000 years after the birth of time, that Schulman believes explains why the arrow of time points in the direction we know and love. Before this epoch, the glowing matter of the Big Bang fireball was smeared uniformly throughout space. In fact, present-day observations of the cosmic background radiation – the expansion-cooled photons of the Big Bang fireball – tell us that matter at that time was smooth to a level of about one part in 100,000. A state as smooth as this turns out to be the most likely high-entropy state when there are no long-range forces. Think of a gas in a box. The atoms of the gas, flying about freely, spread themselves evenly throughout the box.

However, once a long-range force – gravity – switched on in the Universe, things changed radically. The most likely state for matter in the presence of gravity is not a smooth state but a clumpy one. Just look around at today’s Universe, filled as it is with galaxies and stars and planets. When gravity switched on at the epoch of last scattering, therefore, the smoothed-out state of the Universe suddenly switched from being highly likely to highly improbable.

It is subtle. The distribution of matter was exactly the same before and after the transition. However, what had been a high-entropy, typical state when gravity was playing no part in events suddenly became a low-entropy, special state when gravity entered the game.

Schulman freely admits that his argument says nothing about the direction of time before the Universe was 380,000 years old. It is possible that there was no arrow of time. Or maybe there was an arrow of time set by some earlier physical processes. Figuring out what the arrow of time was doing at such impossibly remote times may indeed require a theory of everything.

However, by showing how the Universe could have made a transition to a special, low-entropy state early on, Schulman appears to have finally explained why we experience the direction of time we do.10 And it is all because of an event caused by the expansion-driven cooling of the Universe, for it was this that led to the formation of atoms and the ‘switching on’ of gravity. It was the latter event that put the Universe in the special, low-entropy state so essential for explaining the observed arrow of time. The fact you grow old, not young, that your coffee gets cold, not hot, that eggs break rather than unbreak is therefore telling you that the Universe must have expanded from the Big Bang. There can be few better examples of how the cosmic is connected to the everyday.11

Notes - CHAPTER 9

1. Incidentally, it follows from the fact that a fly-by and its opposite are indistinguishable that the manoeuvre can never boost the velocity of a space probe relative to the Earth. After all, if it did, you would know which movie was the correct one – the one in which the space probe gained speed. Why, then, does NASA bother? Because while it is perfectly true that a space probe cannot be boosted relative to the Earth, the Earth is moving around the Sun. Consequently, it is possible to choose an ingoing trajectory so that the planet’s speed relative to the Sun either adds to or subtracts from the space probe’s speed relative to the Earth. Such fly-bys can therefore be used to boost a space probe’s speed to reach the planets of the outer Solar System, reduce its speed to reach the planets inside the Earth’s orbit, or merely to change its direction. Having said all this, the six spacecraft that have flown past the Earth since 1980 have shown velocity changes relative to the planet. The origin of these ‘fly-by anomalies’ is currently a mystery. See ‘Anomalous Orbital-Energy Changes Observed During Spacecraft Flybys of Earth’ by John Anderson et al. (Physical Review Letters, Vol. 100, 091102, 2008).

2. Even if you insisted that the laws holding the teacup together are quantum rather than Newtonian, the quantum laws are also time-symmetric. Actually, there is an intrinsic time asymmetry in the law governing nature’s weak nuclear force. However, the effect, known as CP violation, is extremely tiny. Also, it seems to have no bearing on processes like the shattering of teacups.

3. Boltzmann’s working definition of entropy – synonymous with disorder and randomness – is the ‘number of microscopic states possible for a given macroscopic state’. In other words, it is the number of possible ways that the components of an object can be arranged and still yield the object.

4. The light given out by warm bodies, including human bodies, is in the form not of visible photons but invisible ‘infrared’ photons. Some animals such as pit vipers have organs to ‘see’ heat, or infrared, enabling them to spot their warm-blooded prey even in the dead of night.

5. Actually, although in the long term the nuclear fuels that replace lost stellar heat become depleted and stars become cold, in the short term they get hotter. In fact, the Sun is about 30 per cent hotter than when it was born. This is because a star is a giant ball of gas. When the gas loses heat, it is no longer able to push outwards as hard against the gravity trying to crush it. The ball shrinks and, in shrinking, is squeezed and heats up. Lewis Carroll knew this. In Alice in Wonderland, Tweedledum and Tweedledee pose the riddle: ‘What gets hotter as it loses heat?’ Answer: a star. (Though I am sure I read this long ago, frustratingly I have not been able to find exactly where and confirm it.)

6. See Chapter 7.

7. Boltzmann, who had also come to the conclusion that the Universe must have been in a special state in the past, speculated that there had been some huge entropy-lowering statistical fluctuation and that our present arrow of time is a consequence of that. Recall that entropy is only overwhelmingly likely to increase. It is not ordained. In highly unlikely circumstances it can decrease. Boltzmann, however, was probably wrong about there being an entropy-lowering event in the past.

8. The nuclei were about 90 per cent hydrogen and about 10 per cent helium, with a tiny sprinkling of other light nuclei such as lithium. All were cooked in the era of ‘nucleosynthesis’, which took place between about one and ten minutes after the start of the Universe.

9. The Universe also contains invisible, ‘dark’ matter, which outweighs ordinary matter by a factor of six or seven. It does not interact with photons of light (which is why it is dark) and so is not thought to have been disrupted by their presence. Consequently, it is believed to have started clumping before ordinary matter.

10. A similar argument has recently been proposed by the Oxford mathematician Roger Penrose. It seems that Schulman’s idea is ‘in the air’.

11. A purist might dispute the connection between cups breaking and what the large-scale Universe is up to. After all, the Earth could have started out in a highly ordered state – the prerequisite for disorder to increase – simply by chance. Boltzmann’s explanation of why entropy increases is a statistical thing. It is not ordained that entropy will increase, only overwhelmingly probable. Consequently, an ordered Earth could have arisen as a highly unlikely local ‘statistical fluctuation’. But although this might be a plausible explanation for our local arrow of time, it fails to explain why the stars – a more cosmic phenomenon than teacups – are pumping starlight into space and thus continually boosting the entropy of the Universe. They can be doing this only if every one of them started off in a more ordered state, which implies the Universe started off in an ordered state. So here the local is explicitly connected to the cosmic.