‘What day is it?’ asked Winnie the Pooh.
‘It’s today,’ squeaked Piglet.
‘My favourite day,’ said Pooh.
A. A. MILNE, Winnie the Pooh
I can’t talk to you in terms of time – your time and my time are different.
GRAHAM GREENE, The End of the Affair
Imagine you look out of your window and see Normans, and, behind them, Romans, and, behind them, Egyptians. Crazy? No crazier than it is for astronomers looking out across the Universe with their telescopes. The further away a celestial object the further back in time it is.
Light travels at about 300,000 kilometres a second in a vacuum. But if, instead, it travelled at a mere 100 metres a century, about a kilometre away you would indeed see William the Conqueror still invading England; about 2.2 kilometres away, Publius Scipio still battling Hannibal and his elephants; and not far from the horizon, about 4.5 kilometres away, the Pharaoh Khufu still making his weekly inspection of the building site of the Great Pyramid of Giza.
The reason all these events would still be visible is because, at 100 metres a century, the light bringing you news of them would crawl snail-like across the intervening distance. The point? Douglas Adams memorably observed, ‘Space is big. Really big. You just won’t believe how vastly hugely mind-bogglingly big it is.’1 What this means is that light, despite travelling 10 million billion times faster than 100 metres a century, nevertheless crawls snail-like across the enormous expanses of the Universe.
Standing outside on a crystal-clear night, you see the Moon as it was 1¼ seconds in the past; the nearest star system, Alpha Centauri – and you need to live in the southern hemisphere to see this – as it was 4.3 years ago; and the Andromeda Galaxy – the most distant object visible to the naked eye – as it was when our Homo erectus ancestors were first venturing out onto the African savannah 2.5 million years ago.
With the aid of powerful telescopes, astronomers can drill back yet farther through cosmic time, revealing galaxies that lived and died long before the Sun and Earth were born. And, out at the very edge of the observable Universe, they can see the shimmering veil of the ‘surface of last scattering’,2 13.8 billion years back in time and the furthest it is possible to see with light.
What all this demonstrates is that time is not what we think it is. Because of the finite speed of light, time is inextricably bound up with distance. Or, as Einstein said, ‘There is an inseparable connection between time and the signal velocity.’ As we look outwards from the Earth, we might think we see the Universe as it is ‘now’. But, actually, what we see are ‘shells’ of space at successively earlier times.
Telescopes drill through the onion-skin layers of cosmic time just as archaeologists dig through the dirt layers of terrestrial time. Astronomers, however, have the great advantage that they can actually see the past. Although they cannot know what the Universe looks like ‘now’, their compensation is that they can see the entire history of the Universe played out before their telescopic eyes.3
In our Universe, then, the concept of ‘now’ is meaningless. It is impossible know what it is like on Alpha Centauri at this moment since the light, carrying news of the star system, permits us to know only what it was like a minimum of 4.3 years ago.
The connection between time, space and the speed of light is as true on Earth as it is in the Universe. The crucial difference, however, is that terrestrial distances are far shorter. The light carrying an impression of the face of a friend you are talking with reaches your eyes in less than a billionth of a second. This is about 10 million times shorter than the briefest interval of time that can be perceived by your brain. Consequently, you notice no delay. The concept of ‘now’, which does not exist at all in the large-scale Universe, is on Earth in most circumstances a very good approximation. We can all safely assume that we are living in the same present.
Or can we?
According to Einstein, the finite speed of light does more than simply delay news of events. Light is the cosmic speed limit and everyone, no matter what their speed relative to a source of light, measures exactly the same speed for a beam of light.4 This can happen, as Einstein realised in 1905, only if the space of someone moving relative to you shrinks in the direction of their motion while their time slows down.
Einstein later generalised special relativity. According to his general theory of relativity of 1915, if someone is accelerating with respect to you – which is equivalent to experiencing stronger gravity – their time appears to slow down.5 For instance, when astronomers look out across the Universe to a shell of space at an earlier epoch, the matter of the Universe at that time occupied a smaller volume than today – simply because space has been expanding since the big bang. With matter more concentrated, the Universe ’s overall gravity was stronger, and time flowed more slowly.
With time flowing at different rates for people moving relative to each other or who are experiencing different gravity, it is impossible for people to agree on what is past, present and future. In fact, the concept of a common past, present and future simply does not appear in Einstein’s theory of relativity, our fundamental description of reality. The question then is: why do we have such a strong impression that it exists?
The answer is that the effects of relativity on time are appreciable only if two people are experiencing markedly different gravity or are moving relative to each other at an appreciable fraction of the speed of light. And, on Earth, all 7 billion of us are experiencing pretty much the same gravity and, even when flying in jet planes, moving relative to each other at less than a millionth the speed of light.
This is not true, by the way, for the Global Positioning Satellites, with respect to which electronic devices such as mobile phones calculate our location on the planet. In their elongated orbits, they swoop down towards the Earth before swinging back out into deep space. This means that not only do they speed up and slow down during each orbit but they also experience strong gravity close to the Earth and weaker gravity further away. As a consequence, the satellites do not experience a common past, present and future. And this must be taken into account by the program that computes our position relative to the GPS satellites. Relativity, it turns out, is not such an esoteric theory. It is an essential part of our everyday lives in the twenty-first century.
Still, we ourselves live our lives in the ultra-slow lane and in ultra-weak gravity where relativity would appear to have few consequences. Appearances, however, can be deceptive. Relativity, it turns out, still has a trick up its sleeve. And it has devastating consequences for our concept of time.
Einstein showed not only that one person’s interval of time is different from another person’s interval of time. He showed that one person’s interval of time is another person’s interval of time and space. And that one person’s interval of space is another person’s interval of space and time. ‘From now on, space of itself and time of itself will sink into mere shadows and only a kind of union between them will survive,’ said Hermann Minkowski, Einstein’s one-time mathematics professor.
Minkowski’s union is space–time. ‘The most important single lesson of relativity theory’, says British physicist Roger Penrose, ‘is that space and time are not concepts that can be considered independently of one another; they must be combined together to give a 4-dimensional picture of phenomena: the description in terms of space–time.’6
As lowly 3D creatures, we are incapable of experiencing 4D space–time in its full glory. All we can experience are shadows of 4D space–time, as Minkowski put it. And those shadows – space and time – change their magnitude depending on how fast we are moving relative to someone else. We might think we live in a universe with three dimensions of space and one of time but, actually, we live in a universe with four dimensions of space–time.
And herein lies the devastating problem for our concept of time.
Each of the four space–time dimensions has the character of space. Which means that space–time has the character of a map – a 4D map, granted, but a map none the less. And, just as New York, Los Angeles and the Grand Canyon are locations on a terrestrial map, the big bang, the birth of the Earth and the end of the Universe are locations on the 4D map of space–time. Along with all the events of your life. What this means, according to Einstein, is that the past, present and future all exist simultaneously.
Disconcerting as this is to most people, it gave comfort to Einstein when, in 1955, his long-time friend, Michele Besso, died. In a letter to Besso’s bereaved family (which they might not have entirely appreciated), Einstein wrote, ‘Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.’
But, if the past, present and future are only a stubborn illusion and in no sense do we actually move through time, why do we have such a strong sense that we do? In fact, why do we have such a strong sense that we are not only moving through time but moving through it in a particular direction? Why do we experience the past as L. P. Hartley’s ‘foreign country’?
For a long while – even before the advent of Einstein, who threw things into sharp focus – this was a complete mystery to physicists. The fundamental laws of physics do not prefer any direction of time. The law of gravity, for instance, could equally well allow the Earth to orbit the Sun in a backward direction. Despite this time reversibility, we emphatically cannot live our lives backwards, going from grave to cradle, growing younger with each passing year. Yet, incredibly, there is no explanation of why we feel we are moving through time – and in a particular direction – in fundamental physics. But there is such an explanation somewhere else – in thermodynamics.7
If you were to show a picture of a castle and the same castle as a crumbled, vine-covered ruin, you would know that the derelict castle came later. Castles crumble. They do not uncrumble. The direction in which things decay, or become disordered, is the direction we associate with the direction of time. And it is the second law of thermodynamics that provides this ‘arrow of time’.
There is a simple way of seeing this. Throw the fragments of a broken cup into the air. It is possible that the pieces come down to reassemble into an intact cup. However there is only one way this can happen, only one way a cup can be intact. Contrast this with the countless ways that the cup can come down in even more broken pieces. It is because there are overwhelmingly more ways that the cup can come down broken than intact – overwhelmingly more disordered states than ordered states – that cups break and do not unbreak. This is why time flows forwards but not backwards. It is why castles crumble but do not uncrumble, why coffee left in a cup grows cold rather than hot, and why people grow old rather than young.
And this is the way that the nineteenth-century Austrian physicist Ludwig Boltzmann formulated the second law of thermodynamics8 – in terms of the number of possible ways in which the components of a body can be arranged and still be the body.9 There is only one way for an intact cup. But trillions upon trillions for a broken cup. If all outcomes are equally likely, therefore, it is overwhemingly likely that a cup will stay broken, not leap back together as an intact cup. It is not utterly impossible – the second law of thermodynamics is different from fundamental laws of physics in not being cast iron but statistical – but the likelihood is you would have to wait many times the current age of the Universe to see such a bizarre thing happen.
So, even though our basic picture of reality – relativity – predicts that all of space–time is laid out like a map, and nothing actually moves through time, the thermodynamic arrow of time explains why we experience time flowing remorselessly in one direction only.
So, what is the ultimate origin of the arrow of time? Well, clearly, the Universe can get more disordered only if in the past it was more ordered. If it was already maximally disordered, it would have nowhere to go. So, the ultimate reason there is an arrow of time is that the Universe in big bang was in a highly ordered state.10
So maybe at last we are getting somewhere in understanding time. Although the concept of a common past, present and future appears nowhere in our fundamental description of reality – relativity – we nevertheless experience them because we live out our lives in the cosmic slow lane and in weak gravity. And, although relativity sets no direction for time, we grow old rather than young because the big bang was an unusual, highly ordered state.
But, actually, none of this really explains why we experience a present – why we focus our attention on the information most recently gathered by our senses. Why do we not have a delayed present, for instance, and focus on information that was collected, say, 10 seconds ago? Why do we not have two presents, and focus on data collected, say, 10 minutes apart? According to physicist Jim Hartle of the University of California at Santa Barbara, we are looking in entirely the wrong place when we look for an explanation in physics. Instead, we should be looking in biology.
Hartle thinks that, when life arose on Earth, organisms might have experienced time in a multitude of different ways. For instance, there might have been creatures with a delayed present, or two presents, or three presents, and so on. But imagine life for a tree frog with a delayed present, says Hartle. It sees a fly. It flicks out its tongue. But, because it is using out-of-date information, by the time its tongue is fully extended, the fly has long gone. Handicapped in this way, sadly, the frog eventually starves to death.
And this, says Hartle, is why we focus on most recently acquired information – why we have a ‘now’.11 Because it ensures our survival. Because all other ways of experiencing reality would have led to our extinction. Hartle therefore believes that, if there are other creatures in the Universe, they will experience time just like us.
Mysteries remain. For instance, our belief that time flows cannot possibly be true. After all, if something flows – such as a river – it changes with respect to something – like a river bank. If time really flows, then it must flow with respect to something else. There must be a second type of time, which is nonsense.
‘Aside from Velcro,’ says American humorist Dave Barry, ‘time is the most mysterious substance in the Universe. You can’t see it or touch it, yet a plumber can charge you upwards of seventy-five dollars per hour for it, without necessarily fixing anything.’ Einstein’s genius was not to get bogged down in what time is but to stick to what we can usefully say about it. ‘Time’, he said, ‘is what a clock measures.’ The great American physicist John Wheeler managed to encapsulate both Einstein’s pragmatism and Barry’s bafflement. ‘Time’, he said, ‘is what stops everything happening at once.’
1 Richard Feynman, The Feynman Lectures on Physics, vol. 1.
2 The idea that the world is, at its root, simple is a powerful one. It is the unspoken act of faith that has driven physics since Newton. No one knows why it is true. However, it has undoubtedly been successful in guiding us to uncover ever deeper and simpler laws of nature.
3 Individual atoms were first seen directly only in 1980. Gerd Binnig and Heinrich Rohrer of IBM in Zurich, Switzerland, invented the Scanning Tunnelling Microscope. The STM senses the up-and-down motion of a super-fine needle as it is dragged across the surface of a material. Think of a blind person building up a picture of someone by dragging their finger across their face. Using their STM, Binnig and Rohrer were able to ‘see ’ the atomic landscape. Atoms looked like tiny footballs, like oranges stacked in boxes, just as Democritus had imagined them more than 2,000 years before. For their invention of the STM, Binnig and Rohrer won the 1986 Nobel Prize for Physics.
4 See Chapter 14, ‘We are all steam engines: Thermodynamics’.
5 James Clerk Maxwell, ‘On the Motions and Collisions of Perfectly Elastic Spheres’, Philosophical Magazine, January and July 1860.
6 Tom Stoppard, Hapgood.
7 Although a single neutrino is hardly ever stopped by an atom, these elusive particles can be detected by putting in their path a lot of atoms. The SuperKamiokande detector, deep in a mountain in Japan, is a 14-storey ‘baked-bean can’ filled with 50,000 tonnes of ultrapure water. Occasionally, a neutrino interacts with a proton in a water molecule. The subatomic shrapnel flies outwards through the water and creates the light equivalent of a sonic boom. This blue, Cherenkov, light – characteristic of ponds holding spent nuclear fuel – is picked up by light detectors, which cover the interior of the baked-bean can. SuperKamiokande has produced one of the most amazing images in the history of science. It is a picture of the Sun, taken at night, not looking up at the sky but down through 12,760 kilometres of rock to the other side of the Earth, not with light but with neutrinos. http://tinyurl.com/ao4wdny.
8 While neutrinos take just 2 seconds to emerge from the Sun and a further 8½ minutes to travel across space to the Earth, sunlight takes about 30,000 years to get out of the Sun. Consequently, today’s sunlight is about 30,000 years old. It was made at the height of the last ice age.
9 See Chapter 16, ‘The discovery of slowness: Special relativity’.
10 See Chapter 15, ‘Magic without magic: Quantum theory’.
11 Technically, the Pauli Exclusion Principle is a consequence of the fact that particles such as electrons are (1) indistinguishable, (2) behave like waves, and (3) behave like fermions, which technically means they have half-integer spin. See Chapter 15, ‘Magic without magic: Quantum theory’.
12 It is possible to have more neutrinos if they are of a type known as sterile. The normal neutrinos, although antisocial, do interact with normal matter very occasionally via nature ’s weak nuclear force. Sterile neutrinos would not even do this. Their sole interaction with normal matter would be via the gravitational force.
13 See Chapter 16, ‘The discovery of slowness: Special relativity’.
14 See Chapter 17, ‘The sound of gravity: General relativity’.
15 Technically, fermions have half-integer quantum spin and bosons have integer spin. This leads to fermions obeying the Pauli Exclusion Principle – which means they are very antisocial – and bosons ignoring the Pauli Principle – which makes them very gregarious (see ‘No More than Two Peas in a Pod at a Time’, Chapter 3 of my book We Need to Talk About Kelvin).
16 See Chapter 21, ‘The day without a yesterday: Cosmology’.
17 Murray Gill-Mann, ‘What Is Complexity?, Complexity, vol. 1 no. 1, 1995.
18 See ‘Random Reality’, Chapter 10 of my book We Need to Talk About Kelvin.
19 Forest Ray Moulton (ed.), The Cell and the Protoplasm, p. 18.