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imagination. Science is the investigation of the real, and if the real seems surreal then so be it. There is no better demonstration of the power of the scientific method than quantum theory. Nobody could have come up with it without the most meticulous and detailed experiments, and the theoretical physicists who built it were able to suspend and jettison their deeply held and comforting beliefs in order to explain the evidence before them. Perhaps the conundrum of the vacuum energy signals a new quantum journey, perhaps the LHC will provide new and inexplicable data, and perhaps everything in this book will turn out to be an approximation to a much deeper picture – the exciting journey to understand our Quantum Universe continues.

When we began thinking about writing this book, we spent some time debating how to end it. We wanted to find a demonstration of the intellectual and practical power of quantum theory that would convince even the most sceptical reader that science really does describe, in exquisite detail, the workings of the world. We both agreed that there is such a demonstration, although it does involve some algebra – we have done our best to make it possible to follow the reasoning without scrutinizing the equations, but it does come with that warning. So, our book ends here, unless you want a little bit more: the most spectacular demonstration, we think, of the power of quantum theory. Good luck, and enjoy the ride.

Epilogue: the Death of Stars

When stars die, many end up as super-dense balls of nuclear matter intermingled with a sea of electrons, known as ‘white dwarves’. This will be the fate of our Sun when it runs out of nuclear fuel in around 5 billion years time. It will also be the fate of over 95% of the stars in our galaxy. Using nothing more than a pen, paper and a little thought, we can calculate the largest possible mass of these stars. The calculation, first performed by Subrahmanyan Chandrasekhar in 1930, uses quantum theory and relativity to make two very clear predictions. Firstly, that there should even be such a thing as a white dwarf star – a ball of matter held up against the crushing force of its own gravity by the Pauli Exclusion Principle. Secondly, that if we turn our attention from the piece of paper with our theoretical scribbles on it and gaze into the night sky then we should never see a white dwarf with a mass greater than 1.4 times the mass of our Sun. These are spectacularly audacious predictions.

Today, astronomers have catalogued around 10,000 white dwarf stars. The majority have masses around 0.6 solar masses, but the largest recorded mass is just under 1.4 solar masses. This single number, ‘1.4’, is a triumph of the scientific method. It relies on an understanding of nuclear physics, of quantum physics and of Einstein’s Theory of Special Relativity – an interlocking swathe of twentieth-century physics. Calculating it also requires the fundamental constants of Nature we’ve met in this book. By the end of this chapter, we will learn that the maximum mass is determined by the ratio

Look carefully at what we just wrote down: it depends on Planck’s constant, the speed of light, Newton’s gravitational constant and the mass of a proton. How wonderful it is that we should be able to predict the uppermost mass of a dying star using this combination of fundamental constants. The three-way combination of gravity, relativity and the quantum of action appearing in the ratio (hc/G)1/2 is called the Planck mass, and when we put the numbers in it works out at approximately 55 micrograms; roughly the mass of a grain of sand. So the Chandrasekhar mass is, rather astonishingly, obtained by contemplating two masses, one the size of a grain of sand and the other the mass of a single proton. From such tiny numbers emerges a new fundamental mass scale in Nature: the mass of a dying star.

We could present a very broad overview of how the Chandrasekhar mass comes about, but instead we’d like to do a little bit more: we’d like to describe the actual calculation because that is what