No people who have the same word for yesterday and tomorrow can be said to have a firm grip on time.
Salman Rushdie, Midnight’s Children
It’s 8:50 … roughly … or so my wristwatch tells me. The weak February sun is trying to climb above the rooftops of the houses opposite. The radio is on, the coffee is brewed. The beginning of another day. But the pulse of Prokofiev’s Cinderella vibrating the speakers in my radio alarmingly reminds me that time is pressing on. The chimes for twelve o’clock are telling Cinderella that her time at the ball is up. And here I am procrastinating on the Internet. I’ve just put my birthday into Wolfram Alpha and it’s telling me that I’ve been alive for 18,075 days. But when I ask it how many more I have left, it says it doesn’t understand my query. Probably just as well. I’m not sure I want to know how many more times the hands on my watch will go round before the pulse beneath stops.
When I was younger I thought that it might be possible to know everything. I just needed enough time. As the years tick by, I’m beginning to realize that time is running out. The youthful sense of infinity is becoming the middle-aged acknowledgement of finitude. I may not be able to know everything. But that’s my own personal limitation, which I shall return to in the next Edge. But is there still hope that humanity can know it all? Or is time going to run out for us collectively too? Will time run out full stop? Whether space is infinite may well be something we can never know. But what about time? I think we all have the feeling that time will probably go on forever. Keep putting batteries in my watch and it will carry on ticking. But when it comes to the question of what happened at the other end, people are less sure: did time have a beginning, or has it been there forever?
I may not be able to look into the future and make predictions, but the past has happened. So can’t I look back and see whether time stretches endlessly into the past or if it had a beginning? Our current model of the universe involves a beginning. Tracing the expansion of the universe backwards has led us to a moment we call the Big Bang, when space was infinitely dense, a singularity that occurred 13.8 billion years ago. But what about before the Big Bang? Is that simply a no-go area for scientific investigation? Or are there telltale signs in the current state of the universe that might show me what was going on before it all began?
The nature of time has troubled philosophers and scientists for generations, because tied up in the attempt to understand this slippery concept is the challenge of understanding why there is something rather than nothing. To talk about a moment of creation is to talk about a moment in time.
The Big Bang certainly represents the beginning for most people. Even those with a religious bent are prone to admit a Big Bang as the moment of the creation of the universe. Either way, we are inevitably pushed to ask: what happened before the Big Bang?
I must admit I rather liked the stock answer that I’d picked up from speaking to mathematical cosmologist friends over the years. To talk about a ‘before’ presupposes the existence of time as a concept before the Big Bang. Given the revelations of Einstein’s theory of relativity – that time and space are inseparably linked – perhaps time exists only once you’ve created space. But if time as well as space came into being only at the Big Bang, the concept of time ‘before’ the Big Bang has no meaning.
But there are rumblings in the cosmological corridors. Perhaps time can’t be mathematically packaged up so easily. Perhaps the question of what happened before the Big Bang is not so easily dismissed. But to try and unravel time means diving into some pretty mind-bending ideas.
As I stare at my watch I can’t actually see the hands moving, but if I look away and then look back again after some time has passed, the hands have moved on. It’s saying 9:15 now … or thereabouts. Tiny cogs inside the watch are driven by a tiny electric motor that in turn is driven by 1-second pulses that have their origin in the oscillations of a tiny quartz crystal. The battery that sits inside the watch sets up a voltage across the crystal that makes it vibrate like a bell with a frequency tuned to 32,768 vibrations a second. This number is chosen for its mathematical properties. It is 2 to the power 15. Digital technology likes powers of 2 because computer circuitry can quickly convert this into a mechanical pulse to drive the cogs every second. Importantly, this frequency is not greatly affected by the surrounding temperature, air pressure or altitude (factors which affect a pendulum, for example). And it is this vibrating, the repetition of motion, that is key to marking the passage of time. But is this sufficient to describe the idea of time?
With my watch ticking away on my wrist, there are no further excuses for procrastinating. So …
Most attempts to define time very quickly run into difficulties that become quite circular. It’s something my watch keeps track of … It’s what stops everything from happening at once … The fourth-century theologian St Augustine summed up the difficulty in his Confessions: ‘What then is time? If no one asks me, I know: if I wish to explain it to one that asketh, I know not.’
Measuring time is at heart a very mathematical process. It depends on spotting things that repeat, things with patterns in them, such as the movement of the planets or the passing of the seasons or the swinging of a pendulum or the pulsing of an atom. As the nineteenth-century Austrian physicist Ernst Mach had it: ‘Time is an abstraction at which we arrive through the changes of things.’
The Lascaux caves in France are believed to contain evidence of one of the first attempts by humans to keep track of time. Dating back 15,000 years, the caves were discovered in 1940 by four French boys after their dog Robot came across a hole leading down into the caves. The caves are famous for the extraordinary Palaeolithic paintings of animals running across the walls: bison, horses, deer and aurochs.
I’ve had the chance to visit the caves, but because of the delicate nature of the 15,000-year-old drawings, I got to see only the replica cave that has been built alongside the original. They are still impressively atmospheric, and there is a dramatic sense of energy captured by the ancient images. But it isn’t only animals that the artist depicts. There are also strange arrangements of dots that punctuate the paintings, which some archaeologists believe are evidence of ancient humans keeping track of the passage of time.
One collection of dots is generally believed to be a depiction of the constellation of the Pleiades. The reappearance of this constellation in the night sky was regarded by many ancient cultures as marking the beginning of the year. As I moved around the cave I came to a sequence of thirteen dots with a rectangle drawn at the end. Above the rectangle is a huge image of a rutting stag. Further along the wall there is a sequence of what could be counted as 26 dots with a huge pregnant cow at the end.
The dots have been interpreted by some archaeologists as marking quarters of the Moon’s cycle, what would become the seven days of the week. These quarter phases of the Moon were easily identifiable in the night sky. So 13 quarters of the Moon represents a quarter of a year, or a season. Counting on a quarter of a year from the reappearance of the Pleiades gets you to the season of rutting stags, when they are more easily hunted. Then the 26 dots can be interpreted as two lots of 13 dots, representing two seasons, or half a year. This gets us to the point in the year when the bison are pregnant and again vulnerable and easily hunted.
The paintings on the wall might represent a training manual for new hunters: a calendar telling them what to hunt at what point in the annual cycle. This early evidence of time-keeping relies on spotting patterns that repeat themselves. Identifying repeating patterns would always be key to understanding the nature of time.
The cycle of the Sun, Moon and stars would inform the way we measured time until 1967. There is nothing in the natural cycle that dictated how we partition our day. Rather, it was the mathematical sensibilities of the Babylonians and Egyptians that gave us a day divided into 24 units of time and an hour subsequently divided up into units of 60. The choice of these numbers was based on the high divisibility of the numbers 60 and 24. Napoleon did attempt to make time decimal by introducing a day with ten hours, but it was about the only unit of measurement that he failed to get the world to count with their ten fingers.
Until 1967, the second, the basic unit for measuring time, was defined variously in terms of the time it takes the Earth to rotate on its axis or the Earth to rotate around the Sun, neither particularly constant when measured against our modern concept of time. For example, 600 million years ago the Earth rotated once on its axis every 22 hours and took 400 days to orbit the Sun. But the tides of the seas have the strange effect of transferring energy from the rotation of the Earth to the Moon, which results in the Earth’s rotation slowing down and the Moon gradually moving away from us. Similar effects are causing the Earth and Sun to drift apart, changing the time it takes to complete an orbit.
Given the vagaries of the motions of the planets, from 1967, instead of measuring the passage of time by looking outwards to the universe, metrologists looked to the atom to define the second, which is now understood as:
the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at rest at a temperature of 0 K.
Quite a mouthful. And you should see the clock that does the measuring. I visited the National Physical Laboratory in southwest London to see the atomic clock that tells Big Ben and the pips on the radio when to sound the hour. It’s enormous. Definitely not something that you could wear on your wrist. It includes six lasers that trap the atoms of caesium before launching them upward into a microwave chamber. As they fall back down under the effect of gravity in what’s called a caesium fountain, the atoms are zapped with microwaves, causing them to emit the radiation whose frequencies are used to define the second.
The atomic clocks that sit at the national laboratories across the world are some of the most extraordinary measuring devices created by humans. The regularity and universality of the atom means that two atomic clocks put next to each other would after 138 million years differ by at most a second. These clocks produce some of the most precise measurements ever made by humans. So perhaps we can say we know time. The trouble is that time isn’t as constant as we had hoped. If two atomic clocks are moving relative to each other, then, as Einstein famously revealed at the beginning of the twentieth century, they will soon be telling very different stories of time.
Newton believed that time and space were absolutes against which we could measure how we move. In the Principia he laid out his stall: ‘Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external.’
For Newton, space and time were like a backdrop upon which nature played out its story. Space was the stage on which the story of the universe was performed and time marked the passage through this story. He believed that you could place clocks across the universe, and once they had all been synched they would continue to show the same time at whatever point you were in the universe. Others were not so convinced. Newton’s arch-rival Gottfried Leibniz believed that time existed only as a relative concept.
A discovery made in 1887 by American scientists Albert Michelson and Edward Morley ultimately led to Leibniz’s view winning out over Newton’s. The American scientists found that if we measure the speed of light in a vacuum, then, regardless of whether we are moving towards or away from the source of the light, the measurement remains the same. This revelation was the seed for Einstein’s discovery that time was not quite as absolute as Newton had envisioned.
At first sight, the fact that the speed of light is the same however I am moving relative to the light source seems counterintuitive. Consider the Earth orbiting the Sun. If I measure the speed of the light coming from a distant star, I would expect it to be faster when I am heading towards the star than when I am heading away from the light source.
Newtonian physics implies that if I am running 10 miles an hour down a train travelling at 90 miles an hour then relative to someone on the platform I am travelling at a combined speed of 100 miles an hour. So why isn’t the same true of light shining from a torch on the train? Why isn’t the speed of light 90 miles an hour faster for the person measuring it on the platform? It transpires that Newton was wrong about both the speed of light and the speed of the runner on the train relative to the person on the platform. You can’t simply add their speeds to the speed of the train. The calculation turns out to be more subtle.
It was by trying to understand why the speed of light is invariant that Einstein, in 1905, made the breakthrough that changed our perspective on the universe. He discovered that time and space are not absolute but vary according to the relative motion of the observer. Einstein was famously employed at the time as a clerk in the Swiss patent office evaluating applications for a range of new inventions from gravel sorters to electrical typewriters. But he also had to assess attempts to create devices to electrically synchronize time, an important task for a world that was becoming increasingly interconnected. It was such apparently mundane work that fired the thought experiments that led to Einstein’s special theory of relativity.
To calculate the apparent speed s of a passenger running at u miles an hour down the length of a train travelling at v miles an hour Einstein discovered that you need to use the following equation:
where c is the speed of light. When the speeds u and v are small compared to c, the term uv/c2 is very small. This means that the speed s can be approximated by adding the speeds u + v. But when the speeds u and v get close to the speed of light, the approximation breaks down and the formula gives a different answer. The formula is such that it never outputs a combined speed that is faster than the speed of light.
To explain Einstein’s new ideas about time, I need a clock. A clock requires something that repeats itself at regular intervals. I could use one of the atomic clocks at the National Physical Laboratory or my wristwatch, but in fact light is the best clock to use to reveal the strange effect relative motion has on time. I am going to exploit the discovery by Michelson and Morley that the speed of light does not seem to depend on how you are moving when you measure it.
So let me consider time measured by a device in which each tick corresponds to the light bouncing between two mirrors.
I am going to take one such clock onto a spaceship and the other clock I will leave with you on the surface of the Earth. Because it will turn out that distance in space is contracted in the direction of movement, I need to place the clock so that the light travels perpendicular to the direction of the spaceship. This will ensure that the distance between the two mirrors is the same in both locations. To show that – from your perspective on Earth – my spaceship’s clock ticks at a slower rate relative to the clock on the Earth requires nothing more sophisticated than Pythagoras’ theorem.
Einstein’s revelation depends on the fact that the person on the Earth must record the light going at the same speed on the spaceship as it does on the Earth. This is the important discovery made by Michelson and Morley: the speed of light is the same everywhere. Just because the spaceship is moving, that movement can’t add speed to the light. To record speed, you need to measure distance travelled divided by the time it takes to travel that distance (with respect to the measuring devices on Earth). So let us look at how far the light travels when it is emitted from one mirror and hits the opposite mirror in my clock on board the spaceship.
Suppose the mirrors are 4 metres apart. Let me suppose also that in the time it takes for the light to travel between the mirrors on the spaceship, the ship has moved 3 metres as measured by you on Earth. Pythagoras’ theorem implies that actually the light has travelled across the hypotenuse of the triangle and has therefore covered 5 metres. That’s all the maths you need to understand Einstein’s theory of special relativity.
From this we can calculate that the spaceship is travelling at ⅗ the speed of light relative to the Earth – the spaceship covers 3 metres in the time that it takes light to travel 5 metres.
The spaceship’s clock moves 3 metres in the time it takes the light to travel between the mirrors set at 4 metres apart. By Pythagoras’ theorem, this means the light has actually travelled 5 metres.
The key point is that light on the Earth will have travelled the same distance, since the speed of light must be the same everywhere. Your clock on the Earth has the same dimensions, so the light there must be covering the same distance, i.e. 5 metres. But the mirrors are 4 metres apart. This means it must have hit the top mirror, and be on its way back down again, one quarter of the way through a second tick. So time is running faster according to the person on the Earth because one tick of the clock on the spaceship takes the same time as 1¼ ticks of the clock on Earth. According to you, my clock in space is going 4⁄5 slower!
To get a sense of why this is happening, take a look at the beam of light as it travels on the spaceship and on the Earth. The beam of light is going at the same speed in the clocks on the Earth and the spaceship. The freeze-frames on the next page show where the light will be at various points in time. Because the light on the spaceship has to travel through space in the direction of the movement of the spaceship, it can’t travel as far in the direction of the opposite mirror in the clock on the spaceship. So from your perspective on the Earth, the light in your clock reaches the mirror before the light on my clock on the spaceship does. This means that your clock on the Earth is ‘ticking’ faster.
Dotted line represents where each beam of light will be at each freeze-frame taken from the Earth.
In some ways, fair enough … and yet when I compare the clocks from my perspective on the spaceship things get very counterintuitive. To understand why things get so weird I need to apply what is known as the ‘principle of relativity’. This says that if you are in uniform motion (i.e. not accelerating and not changing direction) then it is impossible to tell that you are moving. This principle of relativity was not due to Einstein but is already in Newton’s Principia, though it is probably Galileo who should be credited with the realization. It captures that strange experience you may have had when you’re in a train alongside another train at a station and then your train starts moving relative to the train alongside. Until the platform is revealed, it’s impossible to tell which train is moving (this requires the acceleration to be so gradual that you can’t detect it).
When this is applied to our clocks on the spaceship and on Earth, it leads to a rather strange outcome, because as far as I am concerned in my spaceship, it is the Earth that is whizzing by me at ⅗ the speed of light. The same analysis that I performed above implies that I will calculate that it is your clock on Earth that is going slower, not my clock. Time, it turns out, is far less obvious a concept than we experience in everyday life.
The whole thing seems so bizarre as to be unbelievable. How can the spaceship clock be ticking slower than the Earth clock and at the same time the Earth clock be ticking slower than the spaceship clock? But as soon as I have the indisputable observation that the speed of light is constant regardless of how I measure it, the mathematics leads me to this conclusion. It’s one of the reasons I love mathematics. It is like a rabbit hole of logic dropping you into unexpected wonderlands.
It’s not just the ticking clock on the spaceship that appears to be slowing down from the perspective of Earth. Anything that keeps track of time must also slow down. If I am sitting on the spaceship I cannot tell that my clock is doing anything strange. So it means that anything that measures time will be similarly affected, including the quartz pulsating in my wristwatch, the Prokofiev on the spaceship’s radio, the ageing of my body, my brain’s neural activity. On board the spaceship I will not be aware that anything strange is happening because everything on board the spaceship will be ticking at the same rate.
But from your perspective on the Earth, it appears that my watch is losing time, the Prokofiev has turned into a deep-sounding dirge, I am ageing slower, and my neurons aren’t firing quite as fast as they usually do. Time and the sensation of its passing are relative. It depends on comparing things. If everything is slowing down or speeding up at the same rate, I can’t tell any difference. Everything seems normal on board my spaceship. The curious thing is that when I look down at you, I see everything around you slowing to a snail’s pace.
A rather striking example of this relative difference in the passage of time is the strange case of muon decay that I encountered in the Second Edge. When cosmic rays hit the upper atmosphere the collisions create a shower of fundamental particles, including the muon, a heavy version of the electron. These muons are not stable and very quickly decay into more stable forms of matter.
Scientists talk about something called half-life. This is the amount of time it takes for the population of muons to be reduced by half because of decay. (Knowing when the decay will happen for a particular particle is still something of a mystery, and, as I discussed in the Third Edge, I have only the mechanism of the throw of my casino dice to give me any predictive power.) In the case of muons, after 2.2 microseconds, on average half of these particles will have decayed away.
The speed at which they decay should mean that, given the distance they must travel to the surface of the Earth, not many of them will survive the journey. However, scientists detected far more muons than they expected. The explanation is that a clock on board a muon is going slower because these particles are travelling at close to the speed of light. So the half-life of the muon is actually longer than we’d expect when measured by a clock on Earth. The muon’s internal clock is going slower than the clock on Earth, and hence, since not so much time has passed in the frame of reference of the muon, the 2.2 microseconds that it takes for half the muons to decay takes much longer than 2.2 microseconds measured by a clock on the Earth’s surface.
But how does this work from the perspective of the muon? The clock on board the muon is running normally, and it’s the clock on Earth that is running slow. So, from their perspective, what causes more muons to reach the surface of the Earth than expected? The point is that it isn’t only time but also space which is affected by things travelling at speed relative to each other. The space between the planet and the muons is also affected. Distances shrink when they are moving, so the distance from the outer atmosphere to the surface of the Earth from the muons’ perspective is much shorter than it is from our own perspective. So the muon doesn’t think it has as far to go, meaning more reach their destination.
Is this a strategy I can use to steal some more days out of my finite life? Can I cheat my own half-life? The trouble is that, as I explained, everything slows down on my speeding spaceship. I’m not going to squeeze any more time out of the universe to solve the mathematical problems I’m working on by speeding along near the speed of light, because while my body may age more slowly, my neurons will fire more slowly too. The principle of relativity means that, as far as I am concerned, I appear to be at rest and it’s everything else that is speeding by.
The ideas that Einstein came up with in 1905 reveal that the time I see on my watch is much more fluid than I first thought. The absolute nature of time in the universe is challenged even further when you try to understand what it means for two events to happen at the same time. This was the problem Einstein had confronted when working on patents to synchronize time. It turns out that this doesn’t make sense as a question. Or at least the answer will depend on your frame of reference.
Let’s start with a scene from a fictional movie called Relativity Dogs in homage to Tarantino. It takes place on a train (as many things do in relativity). Two people with identical guns are standing at either end of the train. Exactly halfway between them is a third member of the gang. The train is racing through a station. A police officer is watching the scene. Let me first consider the situation on the train. As far as the gang members are concerned, the train can be considered at rest. The guns go off. The bullets hit the man in the middle at the same time. The speed of the bullets and the distance they have to cover is the same, and as far as everyone on the train is concerned the gunmen both shot at the same moment. Indeed, the victim saw light flash from the guns at the same moment, just before being hit by the bullets.
But what about the perspective of the police officer? Let’s suppose the victim passes the police officer at precisely the moment both flashes of light reach the victim, so that the police officer witnesses the flashes at the same time too. But then he begins to wonder: how far has the light travelled? Although they are the same distance away from him now, when they went off, the gun at the front of the train was actually nearer to him. So the light had a shorter distance to travel than the light at the back of the train. In which case, since the speed of light is constant, if the light arrived at the same time it must have left the gun at the back of the train earlier than it left the gun at the front. So to the police officer it seems that the gunman at the back of the train shot first. But if I put another officer on a train going in the opposite direction, then everything is reversed and the second police officer will conclude that the gun at the front of the train must have gone off first.
So who shot first? The gunman at the back shot first from the perspective of the policeman on the platform; but the gunman at the front shot first from the perspective of the policeman on the train speeding in the opposite direction. To talk about which gun was fired first is therefore meaningless in an absolute sense. Time takes on different meanings for different frames of reference. It turns out that there is something which is absolute for all of the observers, but it requires combining time and space.
The trouble is that I have been trying to measure the distance between two objects, and this changes according to how I move relative to the two points. Similarly, the time between two events also changes. But if I now define a new distance that measures the distance in time and space, I can get something invariant, i.e. not dependent on who is doing the measuring. This was the great idea of mathematician Hermann Minkowski, Einstein’s former teacher at the Polytechnic in Zürich. On hearing about Einstein’s ideas, he immediately understood that the high-dimensional geometries discovered by German mathematician Bernhard Riemann 50 years earlier were the perfect stage for Einstein’s theory.
For those happy to contemplate a formula, the distance between an event happening at location (x1, y1, z1) at time t1 and an event happening at location (x2, y2, z2) at time t2 is defined by
The first three bits of the equation
make up the usual distance measured in space (using Pythagoras’ theorem). The last bit is the usual measurement of the difference in time. Your first intuition might be to add these two distances together. The clever thing that Minkowski did was to take the second away from the first. This creates a very different sort of measure, leading to a geometry which doesn’t satisfy the usual laws of geometry as developed by the Greeks. It views the universe not as three-dimensional space animated in time but rather as a four-dimensional block of something called space-time, whose points are located by four coordinates (x, y, z, t), three for space and one for time. Minkowski introduced this new geometrical way of looking at the universe two years after Einstein’s announcement of his special theory of relativity in 1905.
If the formula leaves you none the wiser, don’t despair. Einstein too was rather suspicious of what he regarded as something of a mathematical trick. But Minkowski’s four-dimensional geometry would provide a new map of the universe. As Minkowski declared: ‘Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.’
This was Einstein’s response to the mathematization of his ideas: ‘Since the mathematicians pounced on the relativity theory I no longer understand it myself.’ But he soon realized that it was the best language for navigating this strange new universe called space-time.
The power of measuring distance in space-time is that if I take a different observer moving relative to these events, although the time and distance will both have different values, this new distance between events in space-time is actually the same. So Newton was right that there should be some background which is absolute. His mistake was to consider time and space separately. Post-Einstein, we must consider the two simultaneously. And it’s this mixing of the nature of time and space that makes the question of what happened before the Big Bang really interesting.
For a start, it forces us to consider time in a very different light. We should regard the universe as a block of space and time in which the ideas of ‘before’ and ‘after’ are as questionable as saying what point of space is in front of another: it depends on your perspective. This is very disconcerting. For both policemen in my fictional movie scene, there is a moment when one of the gunmen still hasn’t squeezed the trigger. Perhaps there is time for them to stop and consider their actions, to decide not to shoot and let the other person be responsible. But hold on! For the policeman on the platform that decision is in the hands of the man at the front of the train. But for the policeman on the train going in the opposite direction, it’s the gunman at the back. Does that actually mean the future is not really in our hands at all?
Usually when I draw a graph of distance against time, the time axis runs along the horizontal and the distance, travelled by a ball, say, is represented on the vertical. But space-time doesn’t allow me divide time and space up so neatly. When I think of space-time as a block, I must be careful not to think of one privileged direction in this block representing time and three other independent directions keeping track of space. Two different directions in this space-time can represent the time dimension. It just depends on how you are moving through space. Time and space are mixed in this new view.
On your timeline, events A and B happen simultaneously and C happens later. However, for me, B and C are simultaneous events, while A happened earlier. If A and C are causally linked then for everyone’s timeline A will always happen before C. But B is not causally connected to either A or C, so there are timelines that place event B before A, or alternatively after C.
This is a real challenge to my intuition about the universe. Suppose I am speeding away from you on a spaceship. If I draw a line connecting all simultaneous events from my perspective in this space-time geometry, they will be a very different set of lines from yours.
In Hindi and Urdu the word kal is used to mean both yesterday and tomorrow. In the quote from Midnight’s Children at the head of this chapter, Salman Rushdie joked that people who have the same word for yesterday and tomorrow cannot be said to have a firm grip on time. But could they in fact be on to something? The idea of ‘before’ or ‘after’ is not as clear as some languages imply.
And yet, even with this mixing of space and time, time does have a different quality from space. Information cannot travel faster than the speed of light. Causality means that we can’t place ourselves at a point in space-time where the bullet hits the victim before it was fired. There are constraints on how these timelines can be drawn in space-time. My intuition about space and time is not going to help me. Instead, as Einstein reluctantly conceded, I have to rely on the mathematics to lead me to the limits of the universe and knowledge.
Just as I can talk about space having a shape, I can also talk about space-time having a shape. My initial instinct is to think of time as a line, which makes it very difficult for me to think of anything other than a line that is finite and therefore has a beginning, or a line that is infinite. But there are other possibilities. Since time and space make up four dimensions, I’ve got to consider shapes that I can’t see. I need mathematics to describe them. But I can picture shapes representing parts of space-time which enable me to understand what I mean by the question: what happened before the Big Bang? For example, imagine there was only one spatial dimension, so that space-time is two-dimensional. This creates a surface that I can see, like a rubber sheet that I can play with and wrap up in interesting ways.
I think most people’s model of two-dimensional space-time would be an infinite flat sheet with time extending infinitely backwards and forwards and space also one-dimensional and infinite. But, as I explored in the last Edge, space could be finite. I could wrap space up to make a circle and then time would extend this circle to make space-time look like a cylinder. I could of course join the cylinder up to make a bagel- or torus-shaped space-time. That would make time finite too. In this model of space-time I could loop round and return to a previous moment in history. Logician Kurt Gödel proposed solutions to Einstein’s equations of general relativity that have this feature. Gödel, as I shall explain in my final Edge, greatly enjoyed messing with people’s logical expectations. But Gödel’s circles of space-time are generally regarded as curiosities, because going back in time causes too many problems when it comes to causality.
Possible shapes for a two-dimensional space-time.
To get a more realistic picture of space-time, I need to create a geometry that takes into account our current model of the history of the universe, which includes a beginning: the Big Bang. To see this point in my two-dimensional space-time universe, I could wrap up the surface so that it looks like a cone. The universe, which is just a circle, shrinks in size as I go back in time until I hit the point at the end of the cone. This is where time begins. There is nothing before that. No space. No time. Just a point of infinite density. This is a good model for something rather like the Big Bang.
Or, rather than pinching space-time at a point, perhaps it could look like a sphere, like the surface of the Earth. This has its own implications for how I answer the question: what happened before the Big Bang? If I head south along a line of longitude, then when I hit the South Pole there is a sudden flip and I find myself on another line of longitude on the other side. But these are just numbers that we give to these points on the Earth’s surface. It doesn’t actually represent a discontinuous flip in the shape, just a jump in the way that we measure it.
So by changing the coordinates, what appears to be a singular point can look quite smooth. This is one of Hawking’s ideas for time. Perhaps I should try to embed space-time in a shape such that this point which seems to show time stopping is actually just the south pole of the shape. After all, how do you answer the question: what’s south of the South Pole? The question doesn’t really make sense.
It is striking that often when a question arises to which it seems we cannot know the answer, it turns out that I need to acknowledge that the question is not well posed. Heisenberg’s uncertainty principle is not really an expression of the fact that we cannot simultaneously know both the momentum and position of a particle, more that these two things don’t actually exist concurrently. Similarly, attempts have been made to show that the question ‘What happened before the Big Bang?’ isn’t one whose answer we cannot know. Rather, the question does not really make sense. To talk about ‘before’ is to suppose the existence of time, but what if time existed only after the Big Bang?
By picturing the shape of space-time I begin to get a sense of why many scientists have dismissed the question of understanding time before the Big Bang as meaningless. But there are other shapes which allow time to have a history before the Big Bang. What if the cone, instead of coming to a point and ending, actually bounced out of a contracting universe before the Big Bang? To truly get a sense of time’s history as I head back towards the Big Bang, I need to understand what happens to time as it approaches a point with increased gravity. This was Einstein’s second great discovery: that gravity also has an effect on the ticking clock of time.
Einstein’s second assault on the nature of time came when he threw gravity into the mix. His general theory of relativity, developed between 1907 and 1915, describes the very geometric nature of gravity. Gravity is not really a force but a property of the way this four-dimensional sheet of space-time is curved. The Moon orbits the Earth because the mass of the Earth distorts the shape of space-time in such a way that the Moon simply rolls around the curved shape of space-time in this region. The force of gravity is an illusion. There is no force. Objects are just free-falling through the geometry of space-time, and what we observe is the curvature of this space. But if massive bodies can distort the shape of space, they can also have an effect on time.
This was yet another of Einstein’s great revelations, and it is based once again on a principle of equivalence. The strange consequences of special relativity are teased out of the principle of relativity, which states that it is impossible to tell whether it is me who is moving or my environment that is moving past me. Einstein applied a similar principle of equivalence to gravity and acceleration.
If you are floating out in space in a spaceship with no windows and I place a large massive planet underneath the spaceship, you will be pulled towards the floor. This is the force of gravity. But if instead I accelerate the ship upwards, you will experience exactly the same sensation of being pulled towards the floor. Einstein hypothesized that there is no way to distinguish between the two: gravity and acceleration produce the same effects.
This is particularly striking if I apply this to the photon clock inside our spaceship. Let’s suppose that our spaceship is as tall as the Shard in London. I’m going to place a photon clock at the bottom of the spaceship and another at the top of the spaceship. Next to each clock I’m going to station an astronaut who will help me compare the running of these two clocks.
The astronaut at the bottom of the spaceship is going to send a pulse of light to the astronaut at the top each time his clock ticks. The astronaut at the top can then compare the arrival of these pulses with the ticking of her clock. Without acceleration or gravity, the arrival of the pulses and the ticking of the clocks will be in synch. However, let me now accelerate the spaceship in the direction of the top of the spaceship. A pulse is emitted at the bottom of the spaceship, and, as the spaceship accelerates away, the light has further to travel each time, so that it takes longer and longer for each pulse to reach the top of the spaceship, and the astronaut at the top will receive the pulses at a slower rate. This is similar to the Doppler effect we experience with sound, where moving away from the source causes the frequency to decrease, resulting in a lower pitch. But in this case it is important to note that the spaceship is accelerating rather than just flying along at a constant speed.
The interpretation, though, of the drop in frequency is that the clock at the bottom of the spaceship is going slower than the clock at the top. What if I reverse the experiment and get the astronaut at the top of the spaceship to send pulses down to the bottom of the spaceship? Because the astronaut at the bottom is accelerating towards the pulses, he is going to receive them at a faster rate than the pulses of light he is sending. So he will confirm that his clock is running slower than the clock at the top of the spaceship. This is in contrast to two clocks that are travelling at constant speeds relative to each other, in which case both astronauts think their clock is going faster.
Acceleration and gravity have the same effect: slowing the clock at the bottom of the Shard spaceship.
The interesting conclusion of the experiment comes when I replace acceleration with gravity. According to Einstein’s principle of equivalence, whatever effect acceleration had on the clocks in the spaceship, the effect of gravity must be the same. So when I place a large planet at the foot of our Shard-sized spaceship, the impact is the same as if the spaceship was accelerating through space: clocks run slower at the foot of the Shard than they do at the top.
Since the ageing body is a clock, this means that you age slower the closer you are to the centre of the Earth – people working at the top of the Shard in London are ageing faster than those on the ground floor. Of course, the difference in the speed of the clocks is extremely small at this scale, but it makes a significant difference if we compare the ticking of atomic clocks on the surface of the Earth with those in orbit on satellites. The difference in gravity experienced by the two clocks results in them ticking at different rates. Since these atomic clocks are integral to the functioning of GPS, it is essential that the effects of gravity on time are taken into account if these systems are to be accurate.
There is a classic story that reveals the strange nature of time in Einstein’s new world. It involves sending twins, or actually one twin, on a space journey. It is particularly close to my heart because I have identical twin girls, Magaly and Ina. If I send Ina off on a spaceship travelling at close to the speed of light and then bring her back to Earth, the physics of relativity implies that, although she will think that she’s been away for only ten years, her twin sister’s clock on Earth has raced ahead, so that Magaly is now in her eighties.
To truly understand the asymmetric nature of the story, I need to take into account Einstein’s revelation about the effect of gravity and acceleration on time. Once Ina is travelling at a constant speed close to the speed of light, Einstein’s first revelation declares that neither twin can tell who is moving and who is still. Ina will think Magaly’s clock is running slower, and Magaly will think Ina’s is slower. So why does Ina return younger? Why aren’t they the same age?
Ina returns younger because she has to accelerate to get to her constant speed. Similarly, when she turns around she needs to decelerate and then accelerate in the opposite direction. This causes her clock to slow down relative to that of her twin on Earth, who doesn’t accelerate. This asymmetry results in Ina heading into Magaly’s future. If I sent both twins off in spaceships in opposite directions and brought them back together then they’d be the same age – and everyone on Earth would have aged quicker.
Einstein’s general theory of relativity revealed that time as well as space gets pulled about by things with mass. Gravity is actually the distortion of this space-time surface. If something has mass, it curves the surface. The classic way to imagine this is to consider space-time as a two-dimensional surface, and the effect of mass as that of placing a ball on this surface. The ball pulls the surface down, creating a well. Gravity can be thought of as the way things get pulled down into this well.
This distortion of space-time has an interesting effect on light. Light follows the shortest path between two points – the definition of a ‘straight’ line. But I am now talking about lines in space-time, where distance is measured using Minkowski’s formula that includes the coordinates of space and time. Weirdly, using Minkowski’s formula, it turns out that the distance between two points in space-time is reduced if the light takes longer to get there.
So in order to find the shortest space-time path, light will follow a trajectory that tries to balance a minimizing of distance travelled against a maximizing of time taken. By following a trajectory such that the light particle is essentially free-falling, the clocks on board the particle will go faster. Pull against gravity and you are accelerating and thus slowing your clock down. So Einstein’s theory predicted that light would be bent by the presence of a large mass. It was a highly unexpected prediction of the theory, but one that could be tested: a perfect scenario for a scientific theory.
Convincing evidence for this picture of a curved space-time was provided by the British astronomer Arthur Eddington’s observations of light from distant stars recorded during the solar eclipse of 1919. The theory predicted that the light from distant stars would be bent by the gravitational effect of the Sun. Eddington needed the eclipse to block out the glare of the Sun so that he could see the stars in the sky. The fact that the light did indeed seem to bend round objects of large mass confirmed that the shortest paths weren’t Euclidean straight lines but curved.
We experience the same effect on the surface of the Earth. An aeroplane flying from London to New York takes a curved path passing over Greenland rather than the straight line we’d expect by looking at a map of the Earth. This curved line is the shortest path between the two points on the Earth. Light too found the shortest path from the star to Eddington’s telescope on Earth.
Eddington announced his experimental evidence confirming Einstein’s ideas on 6 November 1919. Within days, newspaper headlines across the world trumpeted the great achievement: ‘EINSTEIN THEORY TRIUMPHS: Stars Not Where They Seemed To Be, but Nobody Need Worry’ announced the New York Times; ‘Revolution in Science’ declared the London Times. Although we’re quite used to Higgs bosons or gravitational waves hitting the headlines, this was probably the first time in history that a scientific achievement was given such public exposure. Heralded by journalists as the new Newton, the obscure 40-year-old Einstein shot to international fame.
If you are finding all this warping of space and time bending your brain, don’t despair. You are in good company. After Eddington announced his discovery that light bends, a colleague came up to congratulate him: ‘You must be one of only three people in the world to understand Einstein’s theory.’ When Eddington failed to respond, the colleague prompted: ‘Come, come, there is no need to be modest.’ ‘On the contrary,’ replied Eddington, ‘I was trying to think who was the third.’
But trying to say what happens to time as we head back towards the Big Bang would test even Eddington’s understanding of Einstein’s theory.
