Exact uncertainty sounds like a contradiction in terms, but that is what governs the quantum world, according to a theoretical physicist who has created an improved version of the famous Heisenberg uncertainty principle.
Heisenberg worked out that there is a degree of inherent fuzziness to the world. You cannot measure both the position and the momentum of any particle with perfect accuracy. The better the accuracy of your momentum measurement, the more uncertain your position measurement must be, and vice versa.
Heisenberg quantified this in the uncertainty relation, which says that the product of the two uncertainties must always be greater than a certain fixed amount. This does not say how big the uncertainty might actually be, however.
Michael Hall, who is a visiting fellow at the Australian National University's Institute of Advanced Studies in Canberra, wondered whether this could be quantified more exactly. He supposes that quantum systems can be broken down into two parts: there is a classical part that can in principle be measured exactly, and a quantum part that has only probabilities of having different values. In other words, it is fuzzy and cannot be measured precisely.
To quantify this quantum uncertainty, Hall borrowed a mathematical tool developed in 1925 by British statistician Ronald Fisher. Fisher worked out how to quantify differences between human populations by sampling a few members of each. This kind of method gives you an uncertainty in your results, and Hall saw that making measurements on quantum particles was a mathematically similar process.
The result is an expression that looks like Heisenberg's original relation, but gives the exact uncertainty in the measurements of position and momentum. Hall says it is an equation rather than an inequality, which is "a far stronger relation".
So strong, in fact, that in a paper published this month in Journal of Physics A , Hall and Marcel Reginatto of the Physical-Technical Institute in Braunschweig, Germany, have managed to derive the basics of quantum mechanics from it, including the Schrodinger equation that describes the behaviour of quantum-mechanical wave functions.
"I find it remarkable that the Schrodinger equation no longer has to be god-given," says Wolfgang Schleich, who studies the foundations of quantum mechanics at the University of Ulm. You still have to make the assumption that there is some quantum uncertainty, but this is much simpler than assuming Schrodinger's equation.
Unusually for work in such fundamental physics, the new formulation might even have practical applications. Hall says it implies a tight relationship between uncertainty and energy that makes it easier to understand why, in quantum mechanics, systems have a minimum kinetic energy even if there aren't any forces acting. "There's a kind of quantum kinetic energy that comes from the uncertainty," he says.
What's more, the new uncertainty equation makes it possible to estimate the minimum energy that a given quantum system should have. This is useful in cases when it's not possible to calculate the lowest energy levels precisely, particularly in complicated systems such as atoms with many orbiting electrons.
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