Everything is Now

Revolutionary Ideas from String Theory

Bill Spence

• Publisher: CRC Press
• Year: 2020
• ISBN:
  9781000195842
• Edition: 1
• Topic: Mathematics
• Subtopic: Games in Mathematics
• Index: Mathematics

This engaging and beautifully written book gives an authoritative but accessible account of some of the most exciting and unexpected recent developments in theoretical physics.

– Professor Lionel J Mason, Mathematical Institute, University of Oxford

String theory is often paraded as a theory of everything, but there are a large number of untold stories in which string theory gives us insight into other areas of physics. Here, Bill Spence does an excellent job of explaining the deep connections between string theory, particle physics, and the novel way of viewing space and time.

– Professor David Tong, Department of Applied Mathematics and Theoretical Physics, University of Cambridge

Foremost amongst Nature's closest-guarded secrets is how to unite Einstein's theory of gravity with quantum theory – thereby creating a 'quantum space-time'. This problem has been unsolved now for more than a century, with the standard methods of physics making little headway.

It is clear that much more radical ideas are needed, and our front-line researchers are showing that string theory provides these. This book describes these extraordinary developments, which are helping us to think in entirely new ways about how physical reality may be structured at its deepest level.

Amongst these ideas are that

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• Everything can happen at the same time – it is all Now;

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• Hidden spaces, large and small, are everywhere amongst us;

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• The basic objects are 'membranes' that behave like soap bubbles and can explore the shape of spacetime in new ways;

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• We are holographic projections from higher dimensions;

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• You can take the 'square root' of gravity;

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• Ideas from the ancient Greeks are resurfacing in a beautiful new form;

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• And the very latest work shows that 'staying positive' is essential.

The book is aimed at a general audience, using analogies, diagrams, and simple examples throughout. It is intended as a brief tour, enabling the reader to become aware of the main ideas and recent work. A full list of further resources is supplied.

Bill Spence is the founding Director of the Centre for Research in String Theory at Queen Mary University of London. He has worked on string theory for over three decades.

Chapter 1

Introduction

This book describes the revolutionary ideas emerging from string theory. These ideas are new, intensely strange, but utterly beguiling. Indeed, the entire history of physics can be seen as revealing strange properties of nature in radical ways that seem to contradict everyday experience. An early example of this was the discovery that the earth is not at the centre of the solar system. And around a hundred years ago, two profoundly radical and counter-intuitive theories totally revolutionized physics – relativity and quantum mechanics. Perhaps we are entering the time when string theory will similarly overturn our current understanding of the universe.

Whilst Einstein's special relativity showed that space and time were inextricably linked, it was his general theory that revealed the almost unimaginable idea that space and time, rather than being ‘where and when things happen’ could in themselves be tangible physics – that the actual force of gravity is a manifestation of the curvature of space-time. A little later the mysterious world of quantum mechanics was revealed – matter is neither a wave nor a particle, but somehow something intermediate which could shape-shift into either, depending on how you looked at it.

The last hundred years has seen intense work trying to take Einstein's work further, on two fronts. The first has been trying to prove that the other forces of nature, nuclear and electromagnetic, are manifestations of some property of space-time in the same way gravity is. The second has been trying to understand how the ideas of quantum mechanics could be applied to gravity, to space-time itself. There has been wonderful progress in understanding the physical world in this period. Special relativity has been successfully combined with quantum mechanics to create quantum field theory, and then this was used to formulate the so-called Standard Model, which describes all the non-gravitational forces that have been discovered. This theory has now been successfully tested to tremendously high accuracy and precision.

The entire history of physics has been a great process of unification, whereby previously apparently different or complex phenomena have been shown to be described much more simply as different manifestations of a more fundamental underlying theory. For example, the existence of all the chemical elements like hydrogen, iron, uranium, etc., can be understood as the different ways that just three types of particle (protons, neutrons, and electrons) can combine under nuclear and electromagnetic forces. The Standard Model in turn understands how these three types of particle, together with many others that have been discovered and which are related to them, can be understood in terms of a combined theory of just three forces.

How the curved space-time description of gravity fits with the other forces has been the outstanding question in fundamental physics for more than a century. But attempts to unify gravity and quantum theory have so far been epic failures. Many of us in theoretical physics feel that this is simply because we haven't been sufficiently radical in our ideas, and that string theory, whatever its eventual fate, will liberate our imaginations enough to light a path to future unification. The ideas emerging from string theory now may just be sufficiently crazy to achieve this liberation.

First, a few notes on the book. There is a wide gulf between the abstruse mathematical language of theoretical physics and the everyday written word; in attempting to bridge this I have inevitably taken much license. I have covered the ideas via a roughly historical route, but have not reviewed all the major areas of research in string theory. The subject has become tremendously broad and deep and this short book is intended to be simply a taster of the subject. There are other popular and more detailed works listed at the end of the book where further material can be found, although the subject moves extremely fast and the very latest material may not be covered.

You will find very few formulae here, as the book is intended for readers without formal mathematical training. But just to be clear, the properties of the theories described in this book can all be derived from the mathematics used to set them up. It is not the case that you can just say anything. In physics, once you have written down the theory, the consequences flow from the mathematical formalism and basic physical principles. This is what is so extraordinary about string theory; it is full of astonishing possibilities. This doesn't mean it is right, as the final judge is reality itself, accessed by repeatable experimental tests.

In summary, there are no qualifications needed for reading this book, no degrees or special scientific knowledge. You only need curiosity about the world and a readiness to stretch your imaginations past the limits of experience.

Chapter 2

Everything Is Now – Then

The United Kingdom is fortunate to be the home of one of the world's most extraordinarily creative mathematicians – Roger Penrose in Oxford, who started producing seminal ideas in his youth and, currently past the age of 88, continues to do so. He has written some blockbuster (literally, some might double as house-bricks) books which attempt to describe his theories and more speculative proposals.

One of his early mathematical inventions led to a radical transformation of how we view space and time. This is his theory of twistors, originating in the 1960s. Prior to this, physicists described the world purely in terms of events happening at some place in space at some time, in other words at a ‘point in space-time’.^* This is hardly remarkable, but it is so obvious an assumption that it is, first, very hard to even recognize it as such and, second, even harder to imagine a different way to think.

Whilst quantum mechanics has been very successfully combined with special relativity to form quantum field theory, this has the rather unsettling feature that most of the calculations in the theory yield the same answer – infinity! (Or sometimes minus infinity, which is not much consolation.) This ‘infinity’ is not a number in itself, but a formal mathematical object that is bigger than any number you can think of, like what you would get if you kept adding 1 + 1 + 1 + …forever.

It is a bit much to ask our experimental colleagues to test this, as you always get some particular, finite number when you do any measurement. Fortunately, there is a long-standing procedure which is applied here, which puts another set of infinities with opposite signs into the mathematics at the beginning. These are used to cancel off the rest of the infinities coming from the original calculations. This has the reassuringly innocuous name of ‘renormalization’. It is not the sort of thing any scientist feels comfortable with, and would never have been countenanced, except that it has two utterly convincing features. First, it is in fact a well-defined procedure, and second, it gives definite, finite answers that can be tested, in some cases agreeing with experiments with a precision of one part in a hundred million.

Some of the infinities that arise when you combine quantum mechanics and special relativity are due to events such as the interaction of particles with each other at very precise points in space-time. Forcing quantum particles to be at precise locations is known to cause various issues, as quantum objects like to be ‘uncertain’, so this is not surprising perhaps. One idea to deal with the infinities of quantum field theory is that if one could formulate it in a language that is not ‘point-like’, then one might resolve this problem. But this means finding a radically different conceptual approach, and the necessary mathematics to represent it.

This is indeed what happens in string theory, as we will see later, but first let us also think about what seems like a totally different question at first sight, the question of what ‘mass' is. Some of the fundamental particles that make up all matter have mass, like the proton or electron, whilst others are massless, like the photons that light is made from. This is really a bit odd – what is this thing called ‘mass' and why do some particles have it and some do not? Contrary to what common sense might tell you, there are reasons to think that ‘mass' is not a fundamental property, but that it emerges as particles move. Intuitively, mass is a sort of resistance to being moved, and there is an analogue of this for massive quantum particles. This is that their mass might be due to being immersed in a sea of other quantum particles that drag upon them and slow them down.

How does this work? The basic reason is because in quantum theory there is really no such thing as ‘nothing’. You might think simply of creating nothing, so to speak, by having a box, and taking everything out of it, so that what is left inside is ‘nothing’. But what about the air that's still there? In physics, the inside of an empty box without any air or other matter inside is called a ‘vacuum’. The space between the stars is pretty close to a vacuum – there are about a million molecules in each cubic centimetre (sugar cube sized region). It is actually extremely hard to take everything out of a box – laboratory vacuum chambers still contain ten billion molecules in that volume. Most of these molecules are hydrogen and helium. Compare this to the air we breathe, which has more like ten billion, billion molecules per cubic centimetre. Still, you might imagine that somehow you could catch all the molecules in a box and take them out, leaving nothing inside.

But this turns out to be impossible, as in quantum theory there is the counter-intuitive result that particles can be created out of nothing, as long as they disappear again quickly enough, roughly speaking. This can be understood as being due to an Uncertainty Principle. The commonly known Uncertainty Principle states that you can't know, at the same time, the exact position and momentum (mass times speed) of a quantum particle, and that there is an inverse relationship between these. The more accurately you know one, the less precision you can have with measurements of the other.

There is another Uncertainty Principle that relates energy and time in the same way, stating that the more you pin some event down in terms of when it happened, the less you know about the energy involved, and vice versa. Then the thing about the vacuum, due to this Uncertainty Principle, is that you can have some energy appearing in the form of particles, as long as this doesn't last long. Thus, the ‘vacuum’ of quantum theory, where all the real particles are taken out, is not then nothing, but is a sea of virtual particles which pop out of not...