The Universe Within (10 page)

Imagine, for example, that the boxes were programmed to give, say, heads/heads/tails for your box and tails/tails/heads for your friend's. You pick one of three doors, at random, and your friend does the same. So there are nine possible ways for the two of you to make your choices: red–red, red–green, red–blue, green–red, green–green, green–blue, blue–red, blue–green, and blue–blue. In five of them you will get the opposite results, with one seeing heads and the other tails, but in four you will agree. What about if the boxes were programmed heads/heads/heads and tails/tails/tails? Well, then you would always disagree. Since every other program looks like one of these two cases, we can safely conclude that
however
the boxes are programmed, if you open the doors randomly there is always at least a five-ninths chance of your disagreeing on the result. But that isn't what you found in the experiment: you disagreed half the time.

As you may have already guessed, quantum theory predicts exactly what you found. You agree half the time and disagree half the time. The actual experiment is to take two widely separated Einstein–Podolsky–Rosen particles in a spin zero state and measure their spins along one of three axes, separated by 120 degrees. The axis you choose is just like the door you pick in the pyramidal box. Quantum theory predicts that when you pick the same measurement axis for the two particles, their spins always disagree. Whereas if you pick different axes, they agree three-quarters of the time and disagree one-­quarter of the time. And if you pick axes randomly, you agree half the time and disagree half the time. As we have just argued with the boxes, such a result is impossible in a local, classical theory.
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Before drawing this conclusion, you might worry that the particles might somehow communicate with each other, for example by sending a signal at the speed of light. So that, for example, if you chose different measurement axes, the particles would correlate their spins so that they agreed three-quarters of the time and disagreed one-quarter of the time, just as predicted by quantum mechanics. Experimentally, you can eliminate this possibility by ensuring that at the moment you choose the measurement axis, the particles are so far apart that no signal could have travelled between them, even at the speed of light, in time to influence the result.

In 1982, the French physicists Alain Aspect, Philippe Grangier, and Gérard Roger conducted experiments in which the setting for the measurement axis of Einstein–Podolsky–Rosen particles was chosen while the particles were in flight. This was done in such a way as to exclude any possible communication between the measured particles regarding this choice. Their results confirmed quantum theory's prediction, showing that the world works in ways we cannot possibly explain using classical notions. Some physicists were moved to call this physics' greatest-ever discovery.

Although the difference between five-ninths and one-half may sound like small change, it is a little like doing a very long sum and finding that you have proven that 1,000 equals 1,001 (I am sure this has happened to all of us many times, while doing our taxes!). Imagine you checked and checked again, and could not find any mistake. And then everyone checked, and the world's best computers checked, and everyone agreed with the result. Well, then by subtracting 1,000, you would have proven that 0 equals 1. And with that, you can prove any equation to be right and any equation to be wrong. So all of mathematics would disappear in a puff of smoke. Bell's argument, and its experimental verification, caused all possible classical, local descriptions of the world similarly to disappear.

These results were a wake-up call, emphasizing that the quantum world is qualitatively different from any classical world. It caused people to think carefully about how we might utilize these differences in the future. In Chapter Five, I will describe how the quantum world allows us to do things that would be impossible in a classical world. It is opening up a whole new world of opportunity ahead of us — of quantum computers, communication, and, perhaps, perception — whose capabilities will dwarf what we have now. As those new technologies come on stream, they may enable a more advanced form of life capable of comprehending and picturing the functioning of the universe in ways we cannot. Our quantum future is awesome, and we are fortunate to be living at the time of its inception.

· · ·

OVER THE COURSE OF
the twentieth century, in spite of Einstein's qualms, quantum theory went from one triumph to the next. Curie's radioactivity was understood to be due to quantum tunnelling: a particle trapped inside an atomic nucleus is occasionally allowed to jump out of it, thanks to the spreading out in space of its probability wave. As the field of nuclear physics was developed, it was understood how nuclear fusion powers the sun, and nuclear energy became accessible on Earth. Particle physics and the physics of solids, liquids, and gases were all built on the back of quantum theory. Quantum physics forms the foundation of chemistry, explaining how molecules are held together. It describes how real solids and materials behave and how electricity is conducted through them. It explains superconductivity, the condensation of new states of matter, and a host of other extraordinary phenomena. It enabled the development of transistors, integrated circuits, lasers,
LED
s, digital cameras, and all the modern gadgetry that surrounds us.

Quantum theory also led to rapid progress in fundamental physics. Paul Dirac combined Einstein's theory of relativity with quantum mechanics into a relativistic equation for the electron, in the process predicting the electron's antiparticle, the positron. Then he and others worked out how to describe electrons interacting with Maxwell's electromagnetic fields — a framework known as quantum electrodynamics, or
QED
. The U.S. physicists Richard Feynman and Julian Schwinger and the Japanese physicist Sin-Itiro Tomonaga used
QED
to calculate the basic properties and interactions of elementary particles, making predictions whose accuracy eventually exceeded one part in a trillion.

Following a suggestion from Paul Dirac, Feynman also developed a way of describing quantum theory that connected it directly to Hamilton's action formalism. What Feynman showed was that the evolution in time of Schrödinger's wavefunction could be written using only Euler's
e
, the imaginary number
i,
Planck's constant
h
, and Hamilton's action principle. According to Feynman's formulation of quantum theory, the world follows all possible histories at once, but some are more likely than others. Feynman's description gives a particularly nice account of the “double-slit” experiment: it says that the particle or photon follows
both
paths to the screen. You add up the effect of the two paths to get the Schrödinger wavefunction, and it is the interference between the two paths that creates the pattern of probability for the arrival of particles or photons at various points on the screen. Feynman's wonderful formulation of quantum theory is the language I shall use in Chapter Four to describe the unification of all known physics.

As strange as it is, quantum theory has become the most successful, powerful, and accurately tested scientific theory of all time. Although its rules would never have been discovered without many clues from experiment, quantum theory represents a triumph of abstract, mathematical reasoning. In this chapter, we have seen the magical power of such thinking to extend our intuition well beyond anything we can picture. I emphasized the role of the imaginary number
i,
the square root of minus one, which revolutionized algebra, connected it to geometry, and then enabled people to construct quantum theory. To a large extent, the entry of
i
is emblematic of the way in which quantum theory works. Before we observe it, the
world is in an abstract, nebulous, undecided state. It follows beautiful mathematical laws but cannot be described in everyday language. According to quantum theory, the very act of our 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.
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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.

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