The Universe Within (9 page)

Now comes the strangest part. You can make the light source so dim that the long interval between the flashes on the screen means there is never more than one photon in the apparatus at any one time. But then, set the camera to record each separate flash and add them all up into a picture. What you find is that the picture
still
consists of interference stripes. Each individual photon interfered with itself, and therefore must somehow have travelled through
both
slits on the way to the screen.

So we conclude that photons sometimes behave like
particles and sometimes behave like waves. When you detect them, they are always in a definite position, like a particle. When they travel, they do so as waves, exploring all the available routes; they spread out through space, diffract, and interfere, and so on.

In time, it was realized that quantum theory predicts that electrons, atoms, and every other kind of particle also behave in this way. When we detect an electron, it is always in a definite position, and we find all its electric charge there. But when it is in orbit around an atom, or travelling freely through space, it behaves like a wave, exhibiting the same properties of diffraction and interference.

In this way, quantum theory unified forces and particles by showing that each possessed aspects of the other. It replaced the world that Newton and Maxwell had developed, in which particles interacted through forces due to fields, with a world in which both the particles and the forces were represented by one kind of entity: quantized fields possessing both wave-like and particle-like characters.

NIELS BOHR DESCRIBED THE
coexistence of the wave and particle descriptions with what he called the “principle of complementarity.” He posited that some situations were best described by one classical picture — like a particle — while other situations were better described by another — like a wave. The key point was that there was no logical contradiction between the two. The words of the celebrated American author of the time, F. Scott Fitzgerald, come to mind: “The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.”
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Bohr had a background in philosophy as well as mathematics, and an exceptionally agile and open mind. His writings are a bit mystical and also somewhat impenetrable. His main role at the Solvay Conference seems to have been to calm everyone down and reassure them that despite all the craziness everything was going to work out fine. Somehow, Bohr had a very deep insight that quantum theory was consistent. It's clear he couldn't prove it. Nor could he convince Einstein.

Einstein was very quiet at the Fifth Solvay meeting, and there are few comments from him in the recorded proceedings. He was deeply bothered by the random, probabilistic nature of quantum theory, as well as the abstract nature of the mathematical formalism. He famously remarked (on a number of occasions), “God does not play dice!” To which at some point Bohr apparently replied, “Einstein, stop telling God how to run the world.”
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At this and subsequent Solvay meetings, Einstein tried again and again to come up with a paradox that would expose quantum theory as inconsistent or incomplete. Each time, after a day or two's thought, Bohr was able to resolve the paradox.

Einstein continued to be troubled by quantum
theory
, and in particular by the idea that a particle could be in one place when it was measured and yet spread out everywhere when it was not. In 1935, with Boris Podolsky and Nathan Rosen, he wrote a paper that was largely ignored by physicists at the time because it was considered too philosophical. Nearly three decades later, it would seed the next revolutionary insight into the nature of quantum reality.

Einstein, Podolsky, and Rosen's argument was ingenious. They considered a situation in which an unstable particle, like a radioactive nucleus, emits two smaller, identical particles, which fly apart at exactly the same speed but in opposite directions. At any time they should both be equidistant from the point where they were both emitted. Imagine you let the two particles get very far apart before you make any measurement — for the sake of argument, make it light years. Then, at the very last minute, as it were, you decide to measure either the position or the velocity of one of the particles. If you measure its position, you can infer the position of the other without measuring it at all. If instead you measure the velocity, you will know the velocity of the other particle, again without measuring it. The point was that you could decide whether to measure the position or the velocity of one particle when the other particle was so far away that it could not possibly be influenced by your decision. Then, when you made your measurement, you could infer the second particle's position or velocity. So, Einstein and his colleagues argued, the unmeasured particle must really have both a position and a velocity, even if quantum theory was unable to describe them both at the same time. Therefore, they concluded, quantum
theory
must be incomplete.

Other physicists balked at this argument. Wolfgang Pauli said, “One should no more rack one's brain about the problem of whether something one cannot know anything about exists all the same, than one should about the ancient question of how many angels are able to sit on the point of a needle.”
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But the Einstein–Podolsky–Rosen argument would not go away, and in the end someone saw how to make use of it.

· · ·

HAVE YOU EVER WONDERED
whether there is a giant conspiracy in the world and whether things really are as they appear? I'm thinking of something like the
The Truman Show
, starring Jim Carrey as Truman, whose life appears normal and happy but is in fact a grand charade conducted for the benefit of millions of TV viewers. Eventually, Truman sees through the sham and escapes to the outside world through an exit door in the painted sky at the edge of his arcological dome.

In a sense, we all live in a giant Truman show: we conceptualize the world as if everything within it has definite properties at each point in space and at every moment of time. In 1964, the Irish physicist John Bell discovered a way to show conclusively that any such classical picture could, with some caveats, be experimentally disproved.

Quantum theory had forced physicists to abandon the idea of a deterministic universe and to accept that the best they could do, even in principle, was to predict probabilities. It remained conceivable that nature could be pictured as a machine containing some hidden mechanisms that, as Einstein put it, threw dice from time to time. One example of such a theory was invented by the physicist David Bohm. He viewed Schrödinger's wavefunction as a “pilot wave” that guided particles forward in space and time. But the actual locations of particles in his theory are determined statistically, through a physical mechanism to which we have no direct access. Theories that employ this kind of mechanism are called “hidden variable” theories. Unfortunately, in Bohm's theory, the particles are influenced by phenomena arbitrarily far away from them. Faraday and Maxwell had argued strongly against such theories in the nineteenth century, and since that time, physicists had adopted locality — meaning that an object is influenced directly only by its immediate physical surroundings — as a basic principle of physics. For this reason, many physicists find Bohm's approach unappealing.

In 1964, inspired by Einstein, Podolsky, and Rosen's argument, John Bell, working at the European Organization for Nuclear Research (
CERN
), proposed an experiment to rule out any local, classical picture of the world in which influences travel no faster than the speed of light. Bell's proposal was, if you like, a way of “catching reality in the act” of behaving in a manner that would simply be impossible in any local, classical description.

The experiment Bell envisaged involved two elementary particles flying apart just as Einstein, Podolsky, and Rosen had imagined. Like them, Bell considered the two particles to be in a perfectly correlated state. However, instead of thinking of measuring their positions or velocities, Bell imagined measuring something even simpler: their spins.

Most of the elementary particles we know of have a spin — something Pauli and then Dirac had explained. You can think of particles, roughly speaking, as tiny little tops spinning at some fixed rate. The spin is quantized in units given by Planck's constant, but the details of that will not matter here. All that concerns us in this case is that the outcome is binary. Whenever you measure a particle's spin, there are only two possible outcomes: you will either find the particle spinning about the measurement axis either anticlockwise or clockwise at a fixed rate. If the particle spins anticlockwise, we say its spin is “up,” and if it is clockwise, we say its spin is “down.”

Bell hypothesized a situation in which the two Einstein–Podolsky–Rosen particles are produced in what is known as a “spin zero state.” In such a state, if you measure both particles with respect to the same axis, then if you find one of them to be “up,” the other will be “down,” and vice versa. We say that the particles are
“entangled,” meaning that measuring the state of one fixes the state of the other. According to quantum theory, the two particles can retain this connection no matter how far apart they fly. The strange aspect of it is that by measuring one, you instantly determine the state of the other, no matter how distant it is. This is an example of what Einstein called “spooky non-locality” in quantum physics.

Bell imagined an experiment in which the particles were allowed to fly far apart before their spins were measured. He discovered a subtle but crucial effect, which meant that no local, classical picture of the world could possibly explain the pattern of probabilities that quantum theory predicts.

To make things more familiar, let us pretend that instead of two particles, we have two boxes, each with a coin inside it. Instead of saying the particle's spin is “up,” we'll say the coin shows heads; and instead of saying the particle's spin is “down,” we'll say the coin shows tails.

Imagine you are given two identical boxes, each in the shape of a tetrahedron — a pyramid with four equilateral triangular sides. One side is a shiny metal base, and the other three are red, green, and blue. The coloured sides are actually small doors. Each of them can be opened to look inside the pyramid. Whenever you open a door, you see a coin lying inside on the base, showing either heads or tails.

Upon playing with the boxes, you notice that the bases are magnetic and stick together base to base. When the boxes are stuck together like this, the doors are held tightly shut, and there is a soft hum indicating the state of the boxes is being set.

Now you and a friend pull the two boxes apart. This is the analogue of the Einstein–Podolsky–Rosen experiment. You each take a box and open one of its doors. First, you both look through the red door of your box. You see heads and your friend sees tails. So you repeat the experiment. You put the boxes together, pull them apart, and each of you opens the red door. After doing this many times, you conclude that each result is entirely random — half the time your coin shows heads, and half the time it shows tails. But whatever you get, your friend gets
exactly
the opposite. You try taking the boxes very far apart before opening them, and the same thing happens. You cannot predict your own result, but whatever that result turns out to be, it allows you to predict your partner's finding with certainty. Somehow, even though each box gives an apparently random result, the two boxes always give opposite results.

It's strange, but so far there is no real contradiction with a local, classical picture of the world. You could imagine that there is a little machine that makes a random choice of how to program the two boxes when they are placed base to base. If it programs the first box to show heads when the red door is opened, it will program the second box to show tails. And vice versa. This programming trick will happily reproduce everything you have seen so far.

Now you go further with the experiment. You decide that you will both open only the green door. And you find the same thing as before — each of you gets heads or tails half the time, and each result is always the opposite of the other. The same happens with the blue door.

Still, there is no real contradiction with a classical picture of the world. All that is required to reproduce what you have seen is that when the two bases are held together, one box is programmed randomly and the other box is given exactly the opposite program. For example, if the first box is programmed to give heads/heads/tails when you open the red, green, or blue door, then the other is programmed tails/tails/heads when you open the red, green, or blue door. If the first box is programmed heads/heads/heads, the second is programmed tails/tails/tails. And so on. This arrangement would explain everything you have seen so far.

Now you try something different. Again, you put the two bases together and pull the boxes apart. But now, each of you chooses
at random
which door to open — either red, green, or blue — and records the result. Doing this again and again, many times, you find that half the time you agree and half the time you disagree. Initially, it seems like sanity has been restored: the boxes are each giving a random result. But wait! Comparing your results more carefully, you see that whenever you and your partner happen to open the same-coloured door, you always disagree. So there is still a strong connection between the two boxes, and their results are not really independent at all. The question is: could the boxes possibly have been programmed to always disagree when you open the same-coloured door but to disagree only half the time when you each open a door randomly?