How many universes are there?

Maths and the multiverse

An ebook by Plus, the online maths magazine (http://plus.maths.org).

This ebook is © University of Cambridge 2013.  Copyright of the individual articles is held by the authors and they are reproduced here with permission.

Table of contents

How many universes are there?

What happened before the Big Bang?

by John D. Barrow

Are there parallel universes?

by Marianne Freiberger

Playing games in many worlds

by Marianne Freiberger

A celebratory snapshot from 2012

From planets to universes

by Martin Rees

Bang, crunch, freeze and the multiverse

by Marianne Freiberger

Further reading

How many universes are there?

Well, no one really knows the answer to that question. But it’s quite possible that there might be more than one, in fact there may be infinitely many, popping in and out of existence like bubbles in the bath.  From the Big Bang, the evolution of our Universe to the tantalising possibility of alternate lives in parallel universes, we will see how mathematics has allowed us to ask and answer some of the most surprising questions.

Plus (http://plus.maths.org) is an award-winning free online maths magazine that aims to open a door onto the world of mathematics for the general public.  Our articles, interviews and podcasts feature some of the best writers, mathematicians and scientists, including Marcus du Sautoy, Ian Stewart, Stephen Hawking and John Conway.  And we are also a starting point for many budding science writers and researchers speaking to the public for the first time.  Covering topics including medicine, politics, science, philosophy and music – we try to reveal how mathematics is the language of our Universe.

This is one of our first ebooks: collections of Plus articles on particular themes that have intrigued, challenged and entertained our online readers.  You can tell us what you think about this ebook and find many others at http://plus.maths.org/ebooks.  We’d love to hear your feedback and we hope you enjoy the read!

What happened before the Big Bang?

by John D. Barrow

The term Big Bang has several layers of meaning. What most astronomers mean when they refer to a Big Bang theory of the Universe is the idea that the Universe is expanding, as Edwin Hubble first discovered in the 1920s — distant galaxy clusters are moving away from one another with ever increasing speed. This implies that in the past things in the Universe were closer together, the Universe was more compressed, hotter and denser, and that in the future it will become even less hot and dense.

But within this picture there are all sorts of options. One is that as you go back into the past, following the Universe to earlier and earlier times when it was hotter and denser, you reach some special time when, if you believe your equations, density and temperature were infinite. Einstein's theory of gravity gives you a way of calculating when this infinite state occurred: only 13.7 billion years ago. This is very striking, because you can walk around places in Scandinavia and Scotland and pick up rocks that are 3 billion years old. We believe that the whole solar system is only about 4.6 billion years old. So we're apparently very close to what seems to be the beginning of everything.

And this is where scientists start to worry. A prediction of something infinite is often a sign that the theory you are using to make that prediction has reached the limits of its applicability. For example, imagine you are an aerodynamicist wanting to predict the speed of an air flow. If your model is very simple, for example if it ignores the friction of the air, then it might predict that something changes infinitely quickly in a finite time. But no aerodynamicist would believe that this is what really happens. They would take that prediction as an indication that you have to go back to square one and make your model a little bit better, for example by introducing the friction of air. When you then solve the equations you will find that things change very, very quickly, but not infinitely quickly.

So what cosmologists are working very keenly on today is a possible extension of Einstein's theory of gravity, one which includes quantum theory, which can give a more accurate description of the apparent beginning of the Universe. Nobody agrees on exactly how to do this: it's right on the edge of current research. Some theories predict that the Universe doesn't have a beginning at all, but that if you follow it backward in time, it eventually bounces, almost like a ball, into a previous state in which it was contracting. The Universe may behave cyclically — contracting, expanding and contracting again — or it may be that it bounced into expansion only once and will keep on expanding forever. Another possibility is that the Universe began in some rather uninteresting stationary state, and then started to expand due to the effect of quantum fluctuations. In that scenario, the expansion has a beginning, but the Universe itself doesn't necessarily have one.

The inflationary universe

There are also many more exotic possibilities which have come to light in the last ten years, and they are usually associated with the idea of a multiverse. Our Universe might be one of many possible universes. Or, more specifically, our part of the Universe might be behaving differently to other parts of the Universe. Imagine a Universe which is expanding in different ways in different places. In some places it's rather cool, like the part that we live in, but elsewhere it may be much hotter. In some parts it may be collapsing, rather than expanding. If the Universe is infinite, there is no end to the amount of variation possible.

This type of scenario has emerged from a theory called the inflationary universe, which explains rather well many of the properties that we observe our visible part of the Universe to have. The theory requires that in the past, the very, very distant past, there was a short period of time when the expansion of the Universe accelerated. This results in a rate of expansion very close to the one we see today, and it also makes rather definite predictions about the little fluctuations and differences in density and temperature we should observe today, some of which turned into galaxies and stars. We can test this theory using satellite observations and it has survived all the tests that we have set it so far: there is very good agreement between observation and theory.

But there is an extension to the inflation theory that is much more controversial. It says that the early burst of accelerated expansion should have affected different parts of the Universe in different ways. If we could see far enough into the Universe, we would eventually see regions of different density, with different structure to what we see in our own neighbourhood (and our neighbourhood is around 14 billion light years in size), that resulted from the accelerated expansion of our part of the early Universe.

The bubble multiverse

The next aspect of the inflation theory, which was discovered by cosmologists, is that the early surge of expansion can become self-perpetuating in each piece of the Universe. So a region will surge, and within it there will be another little piece that suddenly surges again. It is like a foam of bubbles where each bubble creates more bubbles that expand too. You should think of each bubble in the foam as being rather like the whole of our visible part of our Universe today. If we could see outside of our bubble, we would see into another bubble in the foam where conditions are different.

An inflating bubble multiverse

One rather shocking thing about this bubble making is that the whole process need not have a beginning or an end. In fact, the equations that describe it predict that it doesn't have an end, and almost certainly doesn't have a beginning. But each individual bubble, like the one we're in, does have a beginning, and it may also have an end. Suddenly the question of whether the Universe has a beginning has a slightly more complicated answer. It is a bit like the lifetime of the human race: each individual has a particular finite life time, but the age of the race as a whole is much greater. So the new possibility that has emerged is that the Universe may become very different if we look at it on a large enough scale, and that its history is very complicated. Before the apparent beginning of our part of the Universe, there would have been a quantum "foam" which was missing our bubble, but had many others that may have been very different in structure.

I believe that the inflationary universe is a theory that contains a large part of the truth, because its predictions fit our observations extremely well. So we have some confidence that our bit of the Universe underwent this surge in expansion.

Our bubble

The theory of the bubble Universe predicts that inflated bubbles may be very different from each other, and there are only some bubbles that we could possibly exist in. For example, those that only last for a second are no good: we can only be in a rather long-lived bubble, which lasts for at least ten billion years and so gets really big. This is because there needs to be time for stars to form, and for stars to provide elements like carbon, nitrogen and oxygen in order to enable such a complex thing as life to evolve. We have to be in a big, rather old, and cold bubble.

There is an interesting unsolved problem, which is to try and work out the probability that you get bubbles with particular characteristics. What's the likelihood that you get a big, old bubble of the sort you need for life? Is it fantastically improbable, is it really fairly probable, or just in between? This is one of these problems that we hope will soon be solved. It's really a mathematical problem to formulate probability in this cosmological situation.

Other bubbles

Another interesting question is how we could ever test whether all the other bubbles exist. We can't see them because they're beyond the visible horizon of the Universe 14 billion light years away. This is a philosophical question, almost like a science-fiction scenario. Since we can't see the other bubbles, should we allow them to be part of our picture of the Universe at all? In the 1930s there was a great debate about whether the philosophy of science should be based upon verification: you make a prediction and then you test by experiment if you can verify it and the theory. This approach soon went out of favour: if your theory predicts that all apples are green, and you only find green apples, then this doesn't prove that your theory is correct. There may be some other explanation, rather different from your theory, for why apples all seem to be green, or you may not have run into red apples yet. Philosophers like Karl Popper instead focused on falsification. You falsify your theory, if you find a red apple; then you can definitely rule it out, and maybe you can rule out lots of other theories too.

We can't verify the existence of other bubbles, but it may still be possible to falsify the theory. If there are other bubbles, then there might be a particular observable feature, which is the same in each. Then, if you didn't observe this feature in our bubble, the theory would be falsified. So although we can't see the other bubbles, it's still conceivable that we could test our theory, because it might say things about all bubbles. That may be the best that we can hope for.

What do we mean by an expanding universe?

Many people think of the expansion of the Universe like an explosion, so it must have a centre and there must be an edge. If we see everything expanding around us in the Universe, doesn't this mean that we're at its centre? But there is no centre of the Universe and there is no edge of expansion. The easy case to visualise is that of an infinite Universe. Let's think of a two-dimensional Universe, a rubber sheet that goes on infinitely in each direction. If this infinite sheet was being stretched, then no matter where you stood on it, you'd see everything expanding away from you. You could draw a circle around yourself which describes the edge of your observable universe — the radius of that circle would be the distance that light has been able to travel since the sheet started expanding. We call that our horizon. It's not that there is no sheet beyond the boundary of that circle, it's just that we can't see it yet.

But what if the Universe is finite? If you pick up a flat piece of paper, it seems obvious that there has to be a centre and an edge. But the Universe is all there is. It's not an explosion and it's not expanding into something. So a two-dimensional Universe can't be flat like a piece of paper. But it can be like the surface of a sphere. It's finite — if you wanted to paint that surface you'd need only a finite amount of paint — but if you were an ant walking around on it, you'd never run into an edge. So a curved surface can be finite but have no edge.

This is how we should think of a finite expanding Universe. If we inflate a balloon marked with crosses, all the crosses move away from each other as the balloon expands. If you were sitting on the balloon, you'd see all the crosses moving away from you. The centre of the expansion does not lie on the balloon.

About the author

John D. Barrow is a cosmologist working on the early history and large scale structure of the Universe at the University of Cambridge. He has also written a large number of popular science books and is Director of the Millennium Mathematics Project of which Plus is a part.

Are there parallel universes?

by Marianne Freiberger

Are there parallel universes? Universes in which, rather than reading this article, you are still asleep; in which you are happier, unhappier, richer, poorer, or even dead? The answer is "possibly". It's a controversial claim but one that has won more and more followers over the last few decades.

Fuzzy reality

The origin of this parallelism lies in the physics of the very small. At the beginning of the twentieth century physicists developed quantum mechanics to understand the world at the smallest scales. The theory suggests that in this tiny world reality is fuzzy. Little particles, for example electrons, don't need to be either here or there, they can be in several places at once. And they can also simultaneously possess other properties we would normally deem mutually exclusive. When this happens physicists say that the particles are in a superposition of several different states. Experiments have confirmed that superposition is real. Even molecules as large as buckyballs, which consist of 60 carbon atoms, can indeed be in several places at once.

It may well take you a few deep breaths to take this in and you'll immediately ask the obvious question. Why, when I look for a particle, do I only ever find it in one place? This is the famous measurement problem of quantum mechanics. More dramatically, since we are all made up of particles, why are we ourselves (apparently) only ever in one place?

Quantum mechanics itself does not give an answer to this question. One possibility is that the theory doesn't give you the full picture. Perhaps there is another mechanism in nature, one we don't yet understand, which forces reality to snap to exactly one of all the superposed states when we make a measurement. Reality might be fuzzy at the tiniest scales, but as soon as something larger interferes, an experimenter or a measurement device, it is forced down one route only. "If you think there is something extra, then you have the problem of describing what that extra thing could be," says Adrian Kent, a quantum physicist at the University of Cambridge. "How do we describe it mathematically, how can we test it empirically? That's a great big ongoing research programme."

Taking the maths literally

The other possibility is one that requires another deep breath. Perhaps all the possible outcomes of a measurement are equally real: when you make the measurement, to see where a particle is for example, the world splits into different branches. In each branch a copy of you sees the particle in one of the possible locations.

This many-worlds idea was first proposed by the physicist Hugh Everett in his PhD thesis published in 1957. It might seem crazy, but it is rooted in the maths that underlies quantum mechanics. The equations of quantum mechanics don't indicate that something special should happen at the point of measurement, so why not let them run their course and see what happens? "What the mathematics then tells us is that if a particle is [in superposition of two states A and B], the person doing the measurement goes into a superposition of seeing the particle in [state A] and seeing it in [state B]," explains David Wallace, a philosopher of physics at the University of Oxford. So microscopic superposition turns into macroscopic superposition.

But while the maths does not decide between A or B, neither does it blend the two beyond recognition. The mathematical expression describing the situation can be split into two parts each describing a world in which the experimenter sees exactly one of the two possibilities. If you take this literally, then you have to admit that reality has split.

The branching universe

But is a physicist making a measurement the only thing that can cause reality to split? The answer is no. A measurement of a system in superposition is an interaction with that system and there are other physical processes that can interact with it too. For example, cosmic rays can be in a superposition of going in lots of different directions at once. If one of these directions is homing in on a crystal on Earth, then the impact of the ray will leave a track on the crystal. The crystal is effectively measuring where the ray is. And since the ray is in superposition of homing in on the crystal and not homing in on it, the crystal goes into superposition of having a track and not having a track. And thus, so goes the Everett interpretation, reality splits.

The physicist Erwin Schrödinger devised a famous thought experiment in which a cat in a box is in superposition of two states: dead and alive. According to the Everett interpretation, when you open the box and observe the cat the world splits into two branches: in one of them the cat is dead and in the other alive. Image: Dc987.

With the need for an observer eliminated you can imagine the branching game as having gone on since the beginning of time. "[According to the many-worlds view] this has been going on right from the Big Bang," says Kent. "The Universe started out perhaps in a simple quantum state, but it very quickly became a superposition of lots of different descriptions of the Universe, lots of configurations of galaxies. In some of these branches the Earth would have formed and in some of them it wouldn't. And in some of those where the Earth formed we would have evolved and in some we wouldn't."

Pleased to meet me?

But why are we never aware of those other versions of ourselves? Why do we never see big objects like fridges or people in more than one place at once? Intriguingly, Everett's original formulation couldn't rule that out. In principle reality could split in the wrong way so that an experimenter would see an electron, say, in some weird indeterminate location. But Everett hadn't reckoned with the outside world. As soon as the electron interacts with the outside world, with photons or cosmic rays whizzing past, any perceptible interference between the states "the electron is in location A" and "the electron is in location B" essentially leaks out into the wider world and dissipates. Just as the ripples caused by a stone thrown into a lake peter out as they spread, so the interference becomes so small as to be imperceptible — and the observer sees only one definite outcome when looking at the electron. This process, called decoherence, happens incredibly fast, within a fraction of a second, so we're never aware of it.

Since people and fridges interact with zillions of particles all the time, decoherence grounds them firmly in a one-track world: they are either here or there. If you're dealing with something microscopic, like an electron, then you may be able to isolate it from the outside world sufficiently well to observe superposition. Not by looking at it directly, but by leaving it well alone and then looking for tell tale signs that superposition must have taken place — that's exactly how scientists have been able to confirm that it exists. "But the bigger a system gets the harder it is to isolate it from the external environment," explains Wallace. "So then it becomes harder and harder to detect that what we have is two interacting goings-on rather than just one goings-on."

Which me is real?

What does all of this mean for us? "In Everett's view [all the different branches] are there in reality," says Kent. "There are many copies of you and it makes no sense to ask which ones are real. There is a democracy among those copies, they are all equally valid. You would have the same memories [as all the other copies of you] until the point that you split. After that there could be very slight differences between the copies of you, or [after some time] there could be huge ones."

Kent, who is not a proponent of the many-worlds view, also points out that it should have profound consequences for your attitude to life. "It could make you very nihilistic, because after all what's the point of making a big effort, in some branches whatever you try to achieve will work out anyway. You could also be overwhelmed with grief: every time you're driving down the motorway little branches of you will peel off as they crash and die. Or you could devote your life to being as risk averse as possible in order to look after future copies of yourself as much as you can. People who take an altruistic view of society, leaning to socialism or egalitarianism, ought to take the same kind of view of their successors. Even more so because they are all you, so you have an even stronger moral responsibility [to look after them]."

The many-worlds view may not appeal to common sense but proponents praise its scientific elegance: it relies on the existing maths of quantum mechanics. You don't have to introduce that mysterious "extra something" that makes reality snap from a state of superposition to a definite, single state. "There isn't a new postulate or a new physical principle," says Wallace. "It's just what emerges from taking the theory we have and taking it seriously."

Not everyone is a believer — and this isn't down to the apparent craziness of the theory. After all, many theories seemed crazy when they were first conceived and today no physicist worth their salt would be deterred by that. It's down mostly to two problems. Some people, including Kent, don't quite believe that decoherence is enough to explain the neat splitting of the world into branches in which the world looks like it does. They worry that, after all, some extra assumptions are necessary to make decoherence work.

The other problem is that the maths equips different branches of the world with what looks like probabilities. But if all branches are equally real, how can it make sense to say that one is more likely than another? In the 1990s the physicist David Deutsch came up with an intriguing way to make sense of this: imagine that you're betting on your future selves.

About this article

Marianne Freiberger is Editor of Plus. She interviewed Adrian Kent and David Wallace in December 2012. Kent and Wallace are co-editors of the book, Many Worlds?: Everett, Quantum Theory & Reality.

Playing games in many worlds

by Marianne Freiberger

Would you stake your fortune on a 100 to 1 outsider? Probably not. But what if, somewhere in a parallel universe, the straggling nag does come in first? Would the pleasure you feel in that universe outweigh the pain you feel in the one in which you've lost?

Questions not dissimilar to this one occupy physicists and for entirely respectable reasons. Quantum mechanics suggests that reality is fuzzy, at least at very small scales. Particles can be in a state of superposition, simultaneously possessing properties we would normally deem mutually exclusive. For example, they can be in several places at once.

The big question is why we never see superposition in everyday life. Traditional interpretations of quantum mechanics say that when we make a measurement (such as looking where a particle is) the superposition somehow collapses and only one of the superposed states remains real. We don't know which one that will be but quantum mechanics provides us with probabilities. The method which extracts those probabilities from the maths of quantum mechanics is known as the Born rule.

The many-worlds interpretation takes a different approach. It suggests that when the measurement is made the world splits into separate branches. In each of the branches you see one of the possible outcomes.

But then, what of the Born rule? If every possible outcome happens, it makes no sense to talk about the chance of it happening — that chance is 1. If the many-worlds interpretation is to be taken seriously, then the Born rule needs a new explanation. What do the numbers it attaches to different outcomes, to different branches of the world, mean?

Looking after yourself

Probability is a slippery concept even in the ordinary one-world view of reality. Yet we all use some notion of it, albeit perhaps a hazy one, whenever we ponder a decision. Whether it's buying a house or deciding whether to go on a date, we come up with some sort of assessment of how likely it is that things turn out well. Combining this with some assessment of how much we care how things turn out, we make a decision. And a lot of the time what we are trying to look after when making the decision is the well-being of our future self.

This still applies if you're an inhabitant of a many-worlds world. "If I believe that I live in branching reality and I know that there will be various versions of me after branching, I have the same reasons to care about those various versions of me as I have to care about the one version of me if there wasn't any branching," says David Wallace. "So I can ask: what are my preferences between various actions I can choose?" This intriguing idea lies at the heart of an attempt to make sense of the Born rule in the many-worlds context that was pioneered in by the physicist David Deutsch in the 1990s.

How to bet wisely in one world...

It makes sense to phrase all of this in the language of betting. Suppose you're just about to perform a measurement of a quantum system. For example, electrons have an electromagnetic property called spin and when you measure spin it can come out to be pointing up or down. Now someone offers you a bet: if the spin points up you win £10, if it points down you lose £10.

There is a rational way of approaching this problem in the ordinary one-world view in which there is no branching and you get either spin-up or spin-down but not both. First you should rate how much you like or dislike each possible outcome of the bet (in the technical language, you attach a utility to each outcome). You might simply rate each outcome by its monetary value, so that’s +10 for spin-up and -10 for spin-down. But maybe you resent losing £10 more than you enjoy winning it, so in that case you might rate spin-up as only, say, 5 and spin-down as -10. You also rate the value of not taking the bet. Write u(up) and u(down) or the utilities you attach to spin-up and spin-down, and u(no bet) for the utility you attach to not taking the bet.

Now suppose you believe that the probability of spin-up is p. The probability of spin-down is therefore 1-p. The expected utility of taking the bet is

.

This quantity measures the average amount of utility, or satisfaction, you’d expect to get if you repeated the bet many times. The expected utility of not taking the bet is simply u(no bet).

There is a mathematical result which says that a rational person (someone adhering to certain principles of rationality) should aim to maximise their expected utility. That is, if your expected utility of taking the bet is bigger than the expected utility of not taking it

),

then you should take it, otherwise you shouldn’t.

...and how to bet wisely in many worlds

Now let’s go back to the many-worlds situation. You know that the moment you measure the electron spin the world splits into two branches. In one of them you observe spin-up and in the other you observe spin-down. So if you accept the bet, then in one branch you win £10 and in the other you lose £10.

What should you do now? You might calculate how much the bet would gain you on average over the two branches,

.

and see how that compares to the utility of not taking the bet. This is the same calculation as a person in a non-branching universe would make, in which the probabilities of spin-up and spin-down are both 1/2.

But perhaps you feel sorry for the you in the loosing branch. In that case you might base your decision on the quantity

.

in which spin-down counts for more than spin-up. You’d be behaving like a person in a non-branching universe, where the probability of spin-up is 1/4 and the probability of spin-down is 3/4.

The question of which weight to attach to each outcome, whether it’s 1/2 to both or 1/4 to one and 3/4 to the other, could of course be very tricky — until you realise that quantum mechanics comes with an inbuilt suggestion for the weights. The Born rule attaches a number to each outcome, say p to spin-up and 1-p to spin down, which the traditional view point interpreted as a probability. So why not use those numbers for the weights? Then, like a person in a non-branching universe, you’d base your decision on the quantity

.

You’d accept the bet if Ep  is bigger than the expected utility of not accepting it.

In an intriguing result Wallace, building on work by Deutsch, has shown that this is indeed the only rational way to go. "[If you know that you live in a branching universe] and you think that the underlying laws of physics are [those given by] quantum mechanics, then not only is it rationally required to bet according to some probabilities, it's rationally required to bet as if the probabilities were the [numbers given by the Born rule]," explains Wallace. Anything else will contravene one of several principles of rationality.

The result does not just apply to this simple toy example of spin measurement, it works in a more general setting too. Suppose the universe is just about to split into a number of branches to each of which the Born rule attributes a number. Then if you are faced with a number of possible action (to bet or not to bet) you're rationally compelled to choose the one that maximises your expected utility, calculated using the numbers given by the Born rule.  But why does this "explain" the Born rule in the many-worlds context?

Proponents of the many-worlds view argue that the Deutsch/Wallace result makes sense of the Born rule in the many-worlds context. The numbers it attaches to each outcome of a measurement, or more generally to each branch of the universe, are no longer redundant or mystifying. They are the numbers that any rational person must use in their decision making.

The idea that human behaviour can explain quantities that have popped out of theoretical physics might seem weird at first. In the traditional interpretation of quantum mechanics the numbers given by the Born rule are interpreted as probabilities. Probability is something solid and objective, so we are happy to let that stand. But human behaviour? Solid and objective?

Rationality and probability

There is a two-part answer to this qualm. In their arguments Deutsch and Wallace assume that people's preferences stick to certain basic principles of rationality. For example, when faced with a variety of actions, a person should be able to order them according to preference. The result says that as long as these rationality principles are adhered to, there is only one possible course of action when you are faced with a set of decisions in a branching universe. This course of action involves the numbers given by the Born rule. Viewed in this way, the Born rule begins to acquire the flavour of inevitability we expect from a physical law.

The second answer is that even in an ordinary, non-branching, world probability, as a concept, is far from solid and objective. We say that the probability of heads coming up when you toss a perfectly symmetric coin is 1/2. But how can you justify this statement? You can toss that coin many, many times and note that it comes up heads in roughly half of the tosses. But it's hardly ever going to be exactly half of the tosses. So how can we insist that probability is something fixed and absolute? "Probability seems to be something perfectly objective, it's not just a matter of opinion," says Wallace. "But equally it's not clear what that something objective is."

People have looked to decision theory as a way of making sense of probability long before Deutsch and Wallace adapted the idea for branching universes. "One way of seeing what somebody's own assessments of the probabilities are is to ask them what bet they would take in a given circumstance," says Wallace. "Even if you don't understand probability, you can still understand action, preferences, choices and decisions. This kind of strategy as a way of understanding why probability calculus has the form it does has been very influential."

If you are happy to think of probability in terms of the role it plays in rational decision making, then there is not much difference between the interpretation of the Born rule in the many-worlds view and its interpretation in the one-world view. "The question of whether [the Born rule numbers] are really probabilities, or just [pretend] probabilities, starts to collapse into a question of language," says Wallace. And, crucially, there is no reason to reject this interpretation in the many-worlds view if you accept it in the one-world view.

And there is something else. Traditional decision theory, applied in a one-world situation where a coin comes up heads or tails, but not both, tells you how to make rational decisions, like accepting a bet on a coin toss, based on what you believe the probabilities are. If you happen to falsely believe that the probability of heads is 0.99, then that's your problem. It doesn't contravene any of the rationality axioms.

But the Deutsch/Wallace result goes further. Not only does it tell you how to make optimal decisions using some probabilities (if we call them that), it tells you that those probabilities must be the ones given by the Born rule. So what started out as a weakness of the many-worlds view, not knowing what the Born rule meant, lead to a result that is stronger than its counterpart in ordinary decision theory.

But really?

Not everybody is convinced however. The Born rule is something we observe experimentally. If it says that the probabilities of observing spin-up and spin-down are both 1/2, and you repeat the experiment of measuring spin many times, then roughly half of the times you will measure spin-up and the other half spin-down. Any decent scientific theory should explain these experimental observations directly. "[The Deutsch/Wallace result] doesn't tell you why you see experimental outcomes that follow [the Born rule]," argues Adrian Kent, who opposes the many-worlds view. "What we need is some story about probabilities, or some other concept that replaces probabilities, that has direct scientific use. The whole thing about decision theory is answering the wrong question."

Another sticking point are the principles of rationality that underlie the Deutsch/Wallace result. "[What if] I don't believe the [principles] of rationality?" asks Kent. "Why are they right? In the end no-one can prove that they are. I think there are perfectly well-defined strategies for which you can make a rational case and which don't satisfy those axioms."

As an example, one of those principles says that there should be no conflict of interest between yourself and one of your future selves. If one of your future selves prefers being rich to being poor, then your present self should also prefer that future self to be rich rather than poor.

But suppose you can ensure that your future selves are either filthy rich or poor but decent. You may prefer being filthy rich, but for moral reasons you may still decide to make sure that half of your future selves are poor. This violates the principle: your present self wants some of your future selves to be poor but the poor future selves might themselves want to be rich. But can this strategy really be deemed irrational?

Kent also points out that mathematically it is not entirely clear exactly how the world splits into branches and which numbers the Born rule attaches to each branch. How can a person possibly make decisions about whether or not to accept a bet without that information?

The debates surrounding these issues are subtle and technical. For proponents of the many-worlds view, the Deutsch/Wallace result is a triumph. By suggesting a meaning for a major component of the mathematics of quantum mechanics it has removed a major obstacle to taking the many-worlds view seriously. And there is no doubt that the result is intriguing at the very least.

Other evidence for many worlds?

Ultimately though hardline opponents of the many-words view will only be swayed by more direct experimental evidence. Is there any on the horizon? The many-worlds theory hinges on the idea that superposition exists not only in very small systems, involving small particles or molecules, but all the way up to the scale of the universe. So whenever an instance of superposition in a larger system is confirmed in the lab, that can be counted as evidence for the many-worlds view.

But the tell tale signs of superposition are very delicate: you can only observe them in systems that are extremely well isolated from their surroundings. For larger systems this level of isolation is currently beyond reach. But experimentalists are hard at work, not least because we need such methods to build superfast quantum computers, which exploit superposition. It's a long way away, but perhaps one day the shadowy signatures of our other selves will be revealed.

A celebratory snapshot from 2012

Many of the greatest thinkers in cosmology and theoretical physics came together to celebrate Stephen Hawking’s 70th birthday in January 2012.  The scientific programme discussed the cutting edge of research, including our understanding of the early universe, the state of the multiverse and progress towards the elusive “theory of everything”.  Meanwhile, the speakers at the public symposium provided more accessible accounts of this elusive territory with an overview of progress in the last 70 years, as well as a glimpse into the future of the field.  Here are just a few articles from our coverage of the conference, including two based on the talks by the Astronomer Royal, Martin Rees, and Stephen Hawking himself.

From planets to universes

by Martin Rees

This article is based on Martin Rees’ lecture at Stephen Hawking's 70th birthday symposium in January 2012.

It's a privilege to have this platform to congratulate Stephen Hawking. His insights will live on in the annals of science. He's enlightened millions through his books and lectures — and inspired still more by his personal example. We first met as graduate students. Astronomers are used to large numbers, but few are as large as the odds I'd then have given against this celebration today.

Back then, Stephen and I shared two bits of good luck. First we were both in the research group at the Department of Applied Mathematics and Theoretical Physics in Cambridge led by Dennis Sciama — a charismatic and enthusiastic man. Stephen was two years ahead of me. George Ellis had just finished his PhD, and Brandon Carter was an exact contemporary.

We all had a second piece of good luck: the mid-1960s saw the birth of relativistic astrophysics. Astronomers discovered the first compelling evidence that our Universe had expanded from the Big Bang. And they had discovered objects like neutron stars and quasars, where Einstein's theory was crucial, not just a tiny correction to Newton's. There were also mathematical insights, especially from Roger Penrose whose work with Stephen and with George Ellis deepened our understanding of black holes and the Big Bang.

The research community was then quite small — indeed most relativists were associated with one of three "schools": Dennis Sciama's, and those centred on John Wheeler in Princeton and Yakov Zeldovich in Moscow.

That's enough history. The good news is that today is an equally good time for young researchers — the pace of advance has crescendoed rather than slackened. We've discovered a whole menagerie of exotic objects, and surveyed millions of galaxies. The age of the Universe, and its ingredients, are pinned down to a precision of a few percent, its temperature is measured more precisely still.

But the advances bring into focus some deeper mysteries — the main questions that challenge us today couldn't even have been formulated back in the 1960s.

We study the Universe on four levels. First, we must explore what's out there. Astronomy is the grandest environmental science. We want to interpret the phenomena — realising that they manifest conditions far more extreme than can be simulated in the lab. We want, moreover, to understand not just the way things are now, but how the cosmic panorama, of which we're part, emerged from our Universe's hot dense beginning. And what its long-term future is too.

Hunting for distant planets

Stephen Hawking was asked on the BBC Today Programme what new discovery would excite him most. He said it would be finding intelligent life in space. I agree with him — I'm not holding my breath. But this gives a pretext to mention the hottest current topic in astronomy, even though it's not something Stephen has himself worked on.

This is the realisation that many other stars — perhaps even most of them — are orbited by retinues of planets, like the Sun is. These planets are not detected directly but inferred. The prime technique is shown in figure 1. If a star is orbited by a planet, then both planet and star move around their centre of mass — the barycentre. The star, being more massive, moves slower. But the tiny periodic changes in the star's Doppler effect can be detected by very precise spectroscopy.  Already more than 500 extra-solar planets outside our solar system have been inferred in this way.

Figure 1: Image courtesy NASA.

The evidence pertains mainly to giant planets — objects the size of Jupiter or Saturn. Detecting Earth-like planets — hundreds of times less massive — is a real challenge. They induce motions of merely centimetres per second in their parent star.

But there's another technique that works better for these smaller planets: looking for their shadow. A star dims slightly when a planet is in transit in front of it. An Earth-like planet transiting a Sun-like star causes a fractional dimming, recurring once per orbit, of one part in 10,000. The Kepler spacecraft has been monitoring the brightness of over 100,000 stars, at least twice every hour, with this precision. It's already found more than 2,000 planets, many no bigger than the Earth.

We're specially interested in possible "twins" of our Earth — planets the same size, on orbits with temperatures such that water neither boils or stays frozen. And the real goal, of course, is to see them directly. But this is hard. To realise how hard, suppose an alien astronomer with a powerful telescope was viewing the Earth from 30 light years away — the distance of a nearby star. Our planet would seem, in Carl Sagan's phrase, a "pale blue dot", very close to a star (our Sun) that outshines it by many billions: a firefly next to a search light. The shade of blue would be slightly different, depending on whether the Pacific ocean or the Eurasian landmass was facing the alien astronomer. They could infer the length of our day, the seasons, the gross topography, and the climate. By analysing the faint light, they could infer that the Earth has a biosphere.

Within 20 years, a huge telescope planned to be built by the European Southern Observatory — with a mirror 39 metres across — will be drawing inferences like this about planets the size of the Earth, orbiting other Sun-like stars.

Would there be any life on them — even intelligent life? Perhaps life so intelligent that it would find string theory a doddle? Here we're still in the realm of science fiction. (But it's better to read first-rate science fiction than second-rate science, which is far less stimulating and may also be wrong.)

Star births and deaths

What has surprised people about these planetary systems is their great variety. But their existence wasn't surprising because of what we've learnt about how stars form and how they die. They form in places like the Eagle Nebula in figure 2 via the contraction of clouds of dusty gas.

Figure 2: The Eagle Nebula. Image courtesy NASA/ESA.

If the cloud has any angular momentum, it will spin faster as it contracts and spin off a dusty disc around the so-called protostar, as shown in figure 3. In such a disc dust agglomerates into rocks and planets — this should be a generic process in all protostars.

Figure 3: Artist's conception of the dust and gas disk surrounding the star Beta Pictoris. A giant planet may have already formed and terrestrial planets may be forming. The inset panels show two possible outcomes for mature terrestrial planets around Beta Pic. The top one is a water-rich planet similar to the Earth; the bottom one is a carbon-rich planet, with a smoggy, methane-rich atmosphere similar to that of Titan, a moon of Saturn. Image: NASA/FUSE/Lynette Cook

We do not only see stars forming, but we see them dying. The figure 4 below shows the Eskimo Nebula, whose gas composed the outer layers of a sun-like star only 10,000 years ago. This is how our Sun will look like in 6 billion years.

Figure 4: The Eskimo Nebula. Image courtesy NASA/ESA.

Our galaxy is a huge ecological system where gas is being recycled through successive generation of stars. And it will continue for billions of years. So let me expand a little on our future.

The future

The stupendous time spans of the evolutionary past — the four billion years of Darwinian evolution — are now part of common culture (though maybe not in Kentucky and parts of the Muslim world). But most people somehow still think that we humans are the culmination of the evolutionary tree. That hardly seems credible to an astronomer. The Sun's got 6 billion more years before its fuel runs out. It then flares up, engulfing the inner planets.

Any creatures witnessing the Sun's demise won't be human. They'll be as different from us as we are from a bug. Posthuman evolution — here on Earth and far beyond — could be as prolonged as the Darwinian evolution that has led to us — and even more wonderful.

Moreover, the death of the Sun won't be the end of the Universe. Indeed, our Universe may expand forever, becoming ever darker, ever emptier. To quote Woody Allen, eternity is very long, especially towards the end.

Distant galaxies

Let's now enlarge our spatial horizons to the extragalactic realm. If you could get two million light years away from Earth and look back at our galaxy, it would look like this.

Figure 5: The Andromeda Galaxy. Image courtesy NASA.

That is of course Andromeda — the nearest big galaxy to us. A spinning disc, viewed obliquely, with a hundred billion stars spinning around a central hub.

Figure 6 shows the Whirlpool Galaxy, estimated to be 23 million light years away from our galaxy, seen face on.

Figure 6: The Whirlpool Galaxy. Image courtesy NASA/ESA.

We have huge samples of galaxies like these to study. But how much can we actually understand? Physicists who study particles can probe them and crash them together in accelerators. Astronomers can't crash real galaxies together. And galaxies change so slowly that we only see a snapshot of each. But we can do experiments in a "virtual Universe".

Here is a virtual collision — 10^15 faster that it would actually happen. Everything in each galaxy exerts a gravitational pull on the other — causing distortion, tidal plumes and so forth. This could happen to our galaxy and Andromeda in 4 billion years.

When we look in the real sky we find very similar looking systems like the one shown in figure 7.

Figure 7. Image courtesy NASA Marshall Space Flight Center.

Having done such simulations, we'd infer that these two galaxies have got dangerously close — they're in the process of merging.

We can do such simulations making different assumptions about the mass of stars and gas in each galaxy, and so forth and see which matches the data best. Importantly, we find, by this method and others, that all galaxies are held together by the gravity not just of what we see.  They are also bound together by a mysterious substance known as dark matter. That's an inference that has been firmed up since the 1980s.

But more recently we've had a big surprise. On the cosmic scale gravitational attraction is overwhelmed by a mysterious new force latent in empty space which pushes clusters away from each other. The cosmic expansion is speeding up. The number that describes this cosmic repulsion is called Lambda, and we will return to Lambda later on in this lecture.

Just after the Big Bang

Let's now look backwards to an era before the first galaxies formed. One second after the Big Bang everything was at about 10 billion degrees — a mixture of radiation (mainly photons), some protons and neutrons, and also some other particles that now make up the dark matter. This is as well established as anything geologists tell you about the early history of the Earth.

Our present complex cosmos manifests a huge range of temperature and density — from blazingly hot stars to the dark night sky. People sometimes worry about how this intricate complexity emerged from an amorphous fireball. It might seem to violate a hallowed physical principle — the second law of thermodynamics — which describes an inexorable tendency for patterns and structure to decay and disperse.

The answer to this seeming paradox lies in the force of gravity. Gravity enhances density contrasts rather than wiping them out. In an expanding Universe any patch that starts off slightly denser than average would decelerate more, because it feels extra gravity; its expansion would lag further and further behind, until it eventually stops expanding and separates out.

This movie below shows a simulation of a "virtual Universe" — it models a domain large enough to make thousands of galaxies. The expansion is scaled out, so the picture stays the same size. You can clearly see incipient structures unfolding and evolving. In these galaxy-scale clumps, gravity enhances the contrasts still further, gas is pulled in, and compressed into stars.

And there's another important point. The initial fluctuations fed into the computer model weren't arbitrary — they're derived from the observed fluctuations in the temperature of the microwave background, radiation which has travelled to us from a time just after the Big Bang, by a number we call Q. The temperature fluctuates by only one part in 100,000. The fluctuations trace tiny variations in the density of matter which, computing forward, are amplified by gravity into the conspicuous structures in the present Universe.

Do we live in a multiverse?

We can trace the development of our Universe back to one second after the Big Bang. Indeed we can probably be confident back to a nanosecond after the Big Bang. That's when all the particles had as much energy as can be achieved in the Large Hadron Collider and the entire Universe was squeezed to the size of our solar system.

But questions like "where did the fluctuations come from?" and "why did the early Universe contain the actual mix we observe of protons, photons and dark matter?" take us back to the even briefer instants when our Universe was hugely more compressed still — when energies and densities were so extreme that experiments offer no direct guide to the relevant physics.

Warning! These are speculative theories.

So let us mention some speculative issues. According to the popular inflation theory the entire volume of the Universe we can see today with our telescopes "inflated" from a hyper-dense blob no bigger than a few centimetres across. And the gross properties of the Universe depend on the physics at these ultra-extreme conditions.

So what are these properties? For instance, do we know how big the Universe is? We can only see a finite volume, a finite number of galaxies. That's because there is a horizon — a shell around us delineating the distance light can have travelled since the Big Bang. But that shell has no more physical significance than the circle that delineates your horizon if you're in the middle of the ocean. We'd expect far more galaxies beyond the horizon. There is no perceptible gradient in temperature or density across the Universe — that suggests it stretches thousands of times further. And that's just a minimum.

If it is stretched far enough, then all combinatorial possibilities will be repeated. There will, far beyond the horizon, be replicas of you, replicas of the entire region we can see today.

Be that as it may, even conservative astronomers are confident that the volume of spacetime within range of our telescopes is only a tiny fraction of the aftermath of the Big Bang, most being in principle never directly observable.

But that's not all. "Our" Big Bang may not be the only one. The most popular idea, developed over the last 30 years, is that of eternal inflation. Our island could be just one island of spacetime in a vast archipelago. There are many variants of this idea — but they are still speculative because they depend on still unknown physics.

A challenge for 21st century physics is to see which of the following possibilities is correct. Are there many Big Bangs rather than just one? If there are many, are they all governed by the same laws of physics? If they are not, some of what we call "laws of nature" may in this grander perspective be local bylaws governing our cosmic path.

There are several features our Universe must possess in order to evolve from an amorphous dense beginning into its present complexity. For example there must be gravity and there must be some fluctuations for gravity to feed on. These conditions might not be fulfilled throughout a multiverse. Many universes could be still-born or sterile — the laws prevailing in them would not allow any kind of complexity. We therefore couldn't expect to find ourselves in a typical Universe. Rather, we'd be in a typical member of the subset where an observer could evolve. This is what's called anthropic selection.

It's interesting to explore what range or parameters would allow complexity to emerge. (Those who are allergic to multiverses can regard this just as an exercise in counterfactual history.) We will illustrate this with the two parameters I mentioned earlier. One is Lambda, which measures the rate of cosmic expansion . String theorists suggest that there could be an immense range of possibilities for its value. The other is the fluctuation amplitude Q, which measures how "rough" the early Universe was. The bigger it is, the earlier structure forms and the bigger the structures get. There is no firm theoretical argument for its values and it is still uncertain.

The figure below shows the allowable region for values of Lambda and Q in which an observer can possibly evolve. If Q is smaller, then there may be no second-generation stars containing heavy elements, and so no planetary systems at all. For really small values of Q gas would be unable to cool. Larger values of Q would lead to a Universe of massive black holes and no galaxies. And for Lambda above the line bound systems won't form because the cosmic repulsion starts to overwhelm gravity before they have started to collapse. We're far from knowing what determines Lambda and Q — even further from putting a measure on the relative likelihood of each combination of constants. But if we could, we'd know whether we are in a typical habitable Universe.

The allowable region is of Lambda and Q.

A planetary flashback

I started this talk by describing newly-discovered planets orbiting their stars. I'd like to end with a flashback to planetary science 400 years ago. At that time Johannes Kepler thought that the Earth was unique, and that its orbit was a circle, related to the other planets by beautiful mathematical ratios. We now realise that there are zillions of stars, each with planetary systems. The Earth's orbit is special only insofar as it's in the range of radii and eccentricities compatible with life.

Maybe we're due for an analogous conceptual shift on a far grander scale. Our Big Bang may not be unique, any more than planetary systems are. Its parameters may be "environmental accidents", like the details of the Earth's orbit. The hope for neat explanations in cosmology may be as vain as Kepler's numerological quest.

If there is a multiverse, it will take our Copernican demotion one stage further — our solar system is one of billions of planetary systems in our Galaxy, which is one of billions of galaxies accessible to our telescopes. But this entire panorama may be a tiny part of the aftermath of "our" Big Bang, which itself may be one among millions.

It may disappoint physicists if some of the key numbers they are trying to explain turn out to be mere environmental contingencies. But in compensation, we'd realise that space and time were richly textured — on scales so vast that astronomers aren't directly aware of it — any more than a plankton whose "universe" was a litre of water would be aware of the world's topography and biosphere.

Stephen Hawking famously enjoys betting on scientific issues. So do others.  At a conference in Stanford there was a panel discussion where the panelists were asked how strongly they'd bet on the multiverse concept. I said that, on the scale "would you bet your goldfish, your dog or yourself" I was on the dog level. Andrei Linde said he was far more confident — after all he had devoted 25 years of his life to the eternal inflation idea. And the great theorist Steven Weinberg later said he'd be happily bet Martin Rees' dog and Andrei Linde's life.

I wonder what Stephen Hawking would offer. He certainly takes the multiverse seriously. His newest book is called The Grand Design. Nothing could be grander than this concept — and none a greater challenge to younger scientists.

About the author

Martin Rees is Astronomer Royal and Professor of Cosmology and Astrophysics at the University of Cambridge.  This article is based on his lecture at Stephen Hawking's 70th birthday symposium in January 2012.

Bang, crunch, freeze and the multiverse

by Marianne Freiberger

Some of the things I overheard at Stephen Hawking's 70th birthday conference did make me wonder whether I hadn't got the wrong building and stumbled in on a sci-fi convention. "The state of the multiverse". "The Universe is simple but strange". "The future for intelligent life is potentially infinite". And — excuse me — "the Big Bang was just the decay of our parent vacuum"?!

So to make some sense of these utterances I cornered two of the speakers during a busy tea break. First up was David Spergel, a theoretical astrophysicist at Princeton. His talk had attracted me because of its intelligible title: "380,000 years after the Big Bang". So what, I asked him, happened 380,000 years after the Big Bang?

David Spergel

The past

"The Universe got cold enough so electrons and protons could combine to form hydrogen," he says. "So the Universe went from being a dense plasma of electrons to a neutral gas of hydrogen. Radiation can flow freely in that neutral gas, so radiation was able to travel from then to now."

The radiation Spergel talks about is the afterglow of the Big Bang: light whose wavelength has stretched to the microwave part of the spectrum. This makes it invisible to the naked eye, but the glow can be detected using sensitive radio telescopes. The first glimpse of this cosmic microwave background (CMB), as it's called, was captured in the 1960s. It earned its discoverers the 1978 Nobel Prize in Physics and counts as strong evidence that our Universe did indeed originate in a Big Bang. "When we look out at the microwave sky we look back in time by 13.7 billion years," says Spergel. "The image we see in our microwave data is an image of what the Universe looked like back then."

The cosmic microwave background temperature fluctuations from the Wilkinson Microwave Anisotropy Probe data. Image courtesy NASA.

This baby picture of the Universe, which has since become more detailed, shows up the tiniest fluctuations in temperature throughout space, fluctuations at the level of a few millionths of a degree. "We think these fluctuations in temperature were actually generated during the very first moments of the Universe, during the first 10-30 seconds. So we can see things that go back to near the Universe's emergence," says Spergel.

Scientists also believe that the tiny temperature fluctuations trace small variations in the density of matter in the early Universe. Over time the force of gravity amplified these slight irregularities in the distribution of matter into the structures — stars, galaxies, planets, ourselves — we see today. So our complex adult Universe emerged from a nearly uniform beginning.

This idea is part of a theory called the standard cosmological model, which describes how the Universe formed. Astonishingly, the model depends on just five numbers. "The five parameters are the Universe's age, the density of atoms, the density of matter, how lumpy the Universe is (how much density of matter varies from place to place), and how that lumpiness varies with scale — are the fluctuations larger on small scales or on large scales," explains Spergel.

Once you know what these numbers are, the theory will tell you what the Universe should look like — and it does so with an amazing degree of accuracy. "Once you specify those five parameters the theory is completely predictive. It predicts the statistical properties of the microwave sky and it's completely predictive about the statistics of matter today. To me what is really incredible is that such a simple model fits so many observables." In this sense the Universe is indeed very simple.

The future

Given its success it's tempting to ask what the standard cosmological model says about the future of our Universe. "In Big Bang cosmology the Universe has two possible fates. One is that it keeps expanding forever, the other is that it collapses in a Big Crunch. I like to think of it in terms of Robert Frost's poem, that the Universe will either end in fire, or end in ice," says Spergel.

"Our current data suggests that it will end in ice. The Universe will become ever less dense, the stars will eventually burn out and things will expand forever. To be an optimist about freezing, as Freeman Dyson has pointed out, if our ability to have intellectual thoughts becomes more efficient with time, faster than the Universe expands, we can stay ahead of the game. The Universe will get colder, but if we can do more with less, something we have to do anyway, then the future for intelligent life could be infinite."

Incidentally, the standard cosmological model also hints at an interesting new piece in the puzzle of particle physics. It fits observations even better if you assume that there's an extra type of subatomic particle, a special type of neutrino, that we haven't detected yet. This is reminiscent of the recently revealed evidence for the Higgs boson: no one caught sight of it directly, but if you build the implications of its existence into your theory, it fits observations quite a lot better.  "I don't think we have a convincing case yet [that the extra neutrino exists], but the data is suggestive. What's exciting is that over the next year the data will get better. Data from the Planck mission should give us a definite answer on that. And we're hoping that ground-based experiments might do that even quicker."

But despite the standard cosmological model's success, we're still very far away from truly understanding the Universe. "As I mentioned in my talk, the Universe is both simple and strange. Atoms, the stuff we're made off, make up only 4.5% of the Universe," says Spergel. "The rest is in the form of dark matter and what we call dark energy."

The multiverse and our parent vacuum

And this brings us to the multiverse and the second of my interviewees from that day, Raphael Bousso, a theoretical physicist at the University of California, Berkeley. In the 1990s it was discovered that the Universe isn't only expanding, but that it's doing so at an accelerating rate. Things are being driven apart by a mysterious repulsive force that comes with empty space — that's what we call dark energy. The cosmic repulsion is described by a single number, known as the cosmological constant.

The cosmological constant can be thought of the "weight", or the energy, of empty space. "If I take everything away from this room, the chairs, the tables, the air, you might think that there is nothing left," explains Bousso. "But actually the room is still seething with activity." Quantum theory tells us that, surprisingly, empty space is a mass of virtual particles popping in and out of existence.

The behaviour of such tiny particles is described to an amazing degree of accuracy by another theory: the standard model of particle physics. But the model runs into problems when it comes to the cosmological constant. "The problem is that [according to the standard model of particle physics] empty space should weigh a lot more than we know it weighs, by about 120 orders of magnitude. So that's a terribly bad prediction of an otherwise wonderful theory," says Bousso.

What is more, the standard model of particle physics does not take account of the force of gravity. All attempts to fit in gravity have led to mathematical results that make no physical sense. Physicists have been working hard to find a bigger "theory of everything" that can accommodate both particle physics and gravity. One candidate theory (to be precise it's a whole collection of theories) is called string theory. And string theory suggests that our Universe isn't all there is — that we live in a multiverse.

"The multiverse isn't as dramatic as it sounds like," says Bousso. "What people mean, or at least what I mean when I talk about the multiverse, is that the Universe can have regions in which the laws of physics are effectively different from each other. Not because they are fundamentally different, but because the world is put together a little bit differently [in different regions]. For example, if you're a fish and you live in the water, you may not know that there's another place called air. The laws of physics are effectively different in water and air: the sound speed is different, the speed of light is different, the conductivity is different, and so on. Water is just one way of putting electrons and protons together and there are other ways of doing it, so you can make other materials like air, and iron and wood."

"There are theories we have good reason to consider seriously, which tell us that the world that we live in should have widely separated and very large regions — so we really are like fish in a very large tank — which have different laws of physics. The reasons we haven't discovered these other laws is that we have not been able to take the electrons and protons and neutrons apart and put them together in a different way. The energies we'd need for doing this are just too high."

In a multiverse the puzzle of our cosmological constant being so small becomes less puzzling. Nothing forces it to be so small in principle, indeed in other parts in the multiverse it could be much larger. Only we can never experience such parts. "String theory suggests a very large Universe with these different regions and different physics," says Bousso. "If the cosmological constant is too large [in a particular region] then there is no room for complexity, there is no room for observers to develop, so it's not surprising that we find ourselves in a region [with a small cosmological constant] where there is room for us."

But what about the Big Bang being the "decay of our parent vacuum"? This is where things get truly mind-boggling. In quantum physics a vacuum state is a state with the lowest possible energy. (In accordance with our usual understanding of a vacuum, this usually contains no particles.) Being in a vacuum state is akin to sitting at the bottom of the lowest valley in the energy landscape. However, it's also possible to be in a false vacuum state: this means you're sitting at the bottom of one of the valleys, but not the lowest one.

The idea of the inflationary Universe, which is part of the standard cosmological model, is that the Universe (or some patch of it) started out in a false vacuum state. This false vacuum comes with a negative pressure, which turns gravity into a repulsive force, causing the Universe to "inflate" at break-neck speed, doubling its size in just 10-37 seconds.

However, the false vacuum isn't stable. Just as radioactive atoms decay into other elements after some time, the false vacuum will decay into a true vacuum. The rapid inflation slows down and the excess energy is converted into a hot soup of particles. This soup then explodes in the traditional Big Bang as we know it.

But there's another twist to the story. The decay of the false vacuum doesn't have to happen everywhere at the same time, stopping the whole Universe from expanding. Rather, it can happen in small regions in space, creating pockets which then experience a Big Bang event. The idea is that we live in one of these pockets, so we're back to the multiverse. Surrounding these pockets, like a cake surrounding its raisins, the Universe keeps inflating much faster than it can decay, and it will keep doing so forever. This idea (which is compatible with string theory) is called eternal inflation. Science really is stranger than fiction.

About the author

Marianne Freiberger is co-editor of Plus.

Further reading

For more information on...

1. superposition, see our introduction to Schrödinger's equation

2. the measurement problem and other difficulties in interpreting quantum physics, read Schrödinger's equation – what does it mean?

3. detecting extra-solar planets, read Hunting for life in alien worlds

4. dark matter, read What is dark matter?

5. dark energy, read What is dark energy

6. cosmic repulsion and the cosmological constant, read Lambda marks the spot

7. string theory and M-theory, read Tying it all up

8. supersymmetry and the Higgs boson, read Particle hunting at the LHC and Hooray for Higgs

You can also find lots more on these and other topics online at Plus.

We hope you’ve enjoyed this ebook. You can tell us what you think and find many more ebooks at http://plus.maths.org/ebooks.  We’d love to hear your feedback!