Dec 2, 2015 10:10 AM
http://fqxi.org/community/articles/display/207
EXCERPT: Is the concept of an omniscient God compatible with the laws of physics? In the 1960s, Swiss mathematician Ernst Specker set out to find the answer. His investigation led him, along with American mathematician Simon Kochen, to codify one of the strangest rules of quantum reality: contextuality. To understand the oddness of contextuality, imagine that choosing to step on the scale and measure your weight could change your eye color. That’s the everyday equivalent of what seems to happen when we decide how to measure the quantum properties of a particle.
[...] Quantum theory often feels like a piling-on of the bizarre. We’re told, for instance, that the simple act of making a measurement can change a particle’s state in an unpredictable manner. But contextuality is a fresh violation of our intuition about how the world is supposed to work. To illustrate just how counterintuitive it is, Larsson offers the example of a coin flip. Imagine taking three coins from your pocket—a penny, a nickel, and a dime, for example—and flipping any two of them. Say that you choose to flip the penny and the dime. The outcome of the dime flip shouldn’t depend on whether you flipped it along with the penny or along with the nickel—and, of course, in the everyday world, it does not.
Now transpose this scenario to the quantum world. Instead of pulling two of three coins from your pocket, imagine that you have a particle on which you can make two of three possible measurements. The measurements are all of the same property, a quantity called the magnetic quadrupole moment (which is equivalent to the value of the particle’s spin, squared). The quadrupole moment is three-dimensional, and you can choose two of three axes along which to measure it: the x-axis, the y-axis, and a third which is 45 degrees away from the y-axis but still perpendicular to the x-axis. Just like the coin toss, you don’t expect that your choice to measure along the second or third axes should affect the result you get for the measurement along x-axis. Yet, in the quantum world, it does. This strange link between the choice of one measurement and the result of a second is called contextuality.
[...] contextuality [...] wasn’t formally described until 1967, when Kochen and Specker devised a mathematically elegant proof. The duo wanted to see if a more intuitive deterministic picture of reality—such as the one preferred by Einstein—could explain the outcome of particle experiments. In this view, particles do not pick their properties in an instant, at the point of measurement, apparently on a whim, as standard quantum theory asserts. Instead, the particles contain "hidden variables" that determine the outcome of any future measurements in a predictable manner. These hidden variables provide a complicated set of instructions, even pre-programming particles to return different responses to the same measurement, depending on the order in which measurements are carried out—thus mimicking contextuality. But crucially, since experimenters have no access to these hidden variables, to them, the results appear to be mysterious and are impossible to predict before the experiment is performed.
With their theorem, Kochen and Specker showed that such "non-contextual" theories that invoke hidden variables cannot explain the outcome of quantum measurements without hitting a paradox. The mathematicians achieved this by considering how such information might be stored within a single particle, and proved that there’s simply no way to encode these instructions so that you cover every possible different result that could be seen in an experiment. These theories are fundamentally at odds with quantum mechanics.
[...] Cabello believes that contextuality does not force physicists to give up a belief that there is real world out there. But perhaps it is not as concrete as some might wish. "We do believe in a reality," says Cabello. "An electron has an electric charge, for instance." But other properties of the quantum system have no deeper reality; they are created by the act of measurement, he says....
EXCERPT: Is the concept of an omniscient God compatible with the laws of physics? In the 1960s, Swiss mathematician Ernst Specker set out to find the answer. His investigation led him, along with American mathematician Simon Kochen, to codify one of the strangest rules of quantum reality: contextuality. To understand the oddness of contextuality, imagine that choosing to step on the scale and measure your weight could change your eye color. That’s the everyday equivalent of what seems to happen when we decide how to measure the quantum properties of a particle.
[...] Quantum theory often feels like a piling-on of the bizarre. We’re told, for instance, that the simple act of making a measurement can change a particle’s state in an unpredictable manner. But contextuality is a fresh violation of our intuition about how the world is supposed to work. To illustrate just how counterintuitive it is, Larsson offers the example of a coin flip. Imagine taking three coins from your pocket—a penny, a nickel, and a dime, for example—and flipping any two of them. Say that you choose to flip the penny and the dime. The outcome of the dime flip shouldn’t depend on whether you flipped it along with the penny or along with the nickel—and, of course, in the everyday world, it does not.
Now transpose this scenario to the quantum world. Instead of pulling two of three coins from your pocket, imagine that you have a particle on which you can make two of three possible measurements. The measurements are all of the same property, a quantity called the magnetic quadrupole moment (which is equivalent to the value of the particle’s spin, squared). The quadrupole moment is three-dimensional, and you can choose two of three axes along which to measure it: the x-axis, the y-axis, and a third which is 45 degrees away from the y-axis but still perpendicular to the x-axis. Just like the coin toss, you don’t expect that your choice to measure along the second or third axes should affect the result you get for the measurement along x-axis. Yet, in the quantum world, it does. This strange link between the choice of one measurement and the result of a second is called contextuality.
[...] contextuality [...] wasn’t formally described until 1967, when Kochen and Specker devised a mathematically elegant proof. The duo wanted to see if a more intuitive deterministic picture of reality—such as the one preferred by Einstein—could explain the outcome of particle experiments. In this view, particles do not pick their properties in an instant, at the point of measurement, apparently on a whim, as standard quantum theory asserts. Instead, the particles contain "hidden variables" that determine the outcome of any future measurements in a predictable manner. These hidden variables provide a complicated set of instructions, even pre-programming particles to return different responses to the same measurement, depending on the order in which measurements are carried out—thus mimicking contextuality. But crucially, since experimenters have no access to these hidden variables, to them, the results appear to be mysterious and are impossible to predict before the experiment is performed.
With their theorem, Kochen and Specker showed that such "non-contextual" theories that invoke hidden variables cannot explain the outcome of quantum measurements without hitting a paradox. The mathematicians achieved this by considering how such information might be stored within a single particle, and proved that there’s simply no way to encode these instructions so that you cover every possible different result that could be seen in an experiment. These theories are fundamentally at odds with quantum mechanics.
[...] Cabello believes that contextuality does not force physicists to give up a belief that there is real world out there. But perhaps it is not as concrete as some might wish. "We do believe in a reality," says Cabello. "An electron has an electric charge, for instance." But other properties of the quantum system have no deeper reality; they are created by the act of measurement, he says....