## The Certainty of Uncertainty

A few weeks ago I was asked by some friends to explain the uncertainty principle, and in particular whether it could be violated. The reason for their inquiry was more interesting though – a group of experimentalists claimed that they had violated Heisenberg's Uncertainty Principle, but in their press release failed to give any explanation or details of where the law fails.

Let me begin by stating clearly that the Uncertainty Principle is not going to fail without a major revolution in physics – and that it will most likely come from theorists or involve a much bigger news item. I don't have a reference for a peer reviewed article from this group, but I am confident that they have made an error somewhere.

The reason being that the Uncertainty Principle is predicted to exist by the laws of quantum mechanics, and those laws have been tested in experiments to better than one part in a billion and are responsible for transistors and computer processors. It is simply not going to be violated without taking down all of modern science and technology.

Obviously a proper discussion of the uncertainty principle would require university level quantum mechanics and mathematics, and is a little more complicated than the usual popular physics explanations. However I am not going to allow a little mathematical imprecision get in the way of providing an simple overview, which is (hopefully) easier to understand (and will probably annoy many serious physicists :) )

Quite simply, Heisenberg's uncertainty principle states that there are certain properties of any system which cannot be known to perfect precision. The most common example given is with the momentum and position of a particle (or any object really). The uncertainty in the position of the particle, multiplied by the uncertainty in its momentum, must always be greater than a minimum value. If the position is measured more precisely, then the momentum will change in random ways and become less well known.

Consider the three diagrams given below:

Each represents the probability of finding a particle at some point along the horizontal axis, so that the first diagram has a moderate uncertainty in position, the second diagram has very little uncertainty in the position, and the third has a lot of uncertainty in the position of the particle. However according to the laws of quantum mechanics, the slope of the lines gives the momentum of the particle at each point along the horizontal axis, and the uncertainty in the momentum is related to the difference between the minimum slope and the maximum slope. And so the first diagram has moderate uncertainty in both momentum and position, the second diagram has very little uncertainty in position but the slopes are larger so there is a higher uncertainty in momentum, while the third diagram has a lot of uncertainty in position, but the much shallower slopes mean a very small uncertainty in momentum. (As an aside, it should also be noted that requiring the particle to be located somewhere means the area under each line is the same, specifically (max height)*(max width) = 2 in each case. )

When you drop a lot of the technical aspect of quantum mechanics, wave mechanics and Fourier transformations, that is the crux of the uncertainty principle. So to claim a violation of the uncertainty principle would be equivalent to producing a diagram like the ones above, but with a very narrow peak but no large slopes. It simply cannot be done.

And so that is the (perhaps overly?) simplified explanation for why Heisenberg's Uncertainty Principle is not going to be violated without destroying quantum mechanics. And since quantum mechanics is used successfully in all modern technology, that simply isn't going to happen.