The Universe Within by Neil Turok Page B

observing the world forces it into terms we can relate to, describable with ordinary numbers.
    In fact, the power of i runs deeper, and it is profoundly related to the notion of time. In the next chapter, I will describe how Einstein’s theory of special relativity unified time with space into a whole called “spacetime.” The German mathematician Hermann Minkowski clarified this picture, and also noticed that if he started with four dimensions of space, instead of three, and treated one of the four space coordinates as an imaginary number — an ordinary number times i — then this imaginary space dimension could be reinterpreted as time. Minkowski found that in this way, he could recover all the results of Einstein’s special relativity, but much more simply. 51
    It is a remarkable fact that this very same mathematical trick, of starting with four space dimensions and treating one of them as imaginary, not only explains all of special relativity, it also, in a very precise sense, explains all of quantum physics! Imagine a classical world with four space dimensions and no time. Imagine that this world is in thermal equilibrium, with its temperature given by Planck’s constant. It turns out that if we calculate all the properties of this world, how all quantities correlate with each other, and then we perform Minkowski’s trick, we reproduce all of quantum theory’s predictions. This technique, of representing time as another dimension of space, is extremely useful. For example, it is the method used to calculate the mass of nuclear particles — like the proton and the neutron — on a computer, in theoretical studies of the strong nuclear force.
    Similar ideas, of treating time as an imaginary dimension of space, are also our best clue as to how the universe behaves in black holes or near the big bang singularity. They underlie our understanding of the quantum vacuum, and how it is filled with quantum fluctuations in every field. The vacuum energy is already taking over the cosmos and will control its far future. So, the imaginary number i lies at the centre of our current best efforts to face up to the greatest puzzles in cosmology. Perhaps, just as i played a key role in the founding of quantum physics, it may once again guide us to a new physical picture of the universe in the twenty-first century.
    Mathematics is our “third eye,” allowing us to see and understand how things work in realms so remote from our experience that they cannot be visualized. Mathematicians are often viewed as unworldly, working in a dreamed-up, artificial setting. But quantum physics teaches us that, in a very real sense, we all live in an imaginary reality.

THREE
    WHAT BANGED?
    â€œThe known is finite, the unknown infinite; intellectually we stand on an islet
in the midst of an illimitable ocean of inexplicability. Our business in
every generation is to reclaim a little more land.”
— T. H. Huxley, 1887 52
    â€œBehind it all is surely an idea so simple, so beautiful,
that when we grasp it — in a decade, a century, or a millennium — we will all
say to each other, how could it have been otherwise?”
— John Archibald Wheeler, 1986 53
    SOMETIMES I THINK I’M the luckiest person alive. Because I get to spend my time wondering about the universe. Where did it come from? Where is it going? How does it really work?
    In 1996, I took up the Chair of Mathematical Physics at the University of Cambridge. It was an opportunity for me to meet and to work with Stephen Hawking, holder of the Lucasian Chair — the chair Isaac Newton held. It was Hawking who, three decades earlier, had proved that Einstein’s equations implied a singularity at the big bang — meaning that all the laws of physics fail irretrievably at the beginning of the universe. In the eighties, along with U.S. physicist James Hartle, Hawking had also proposed a way to avoid the singularity so