Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle is a fundamental states that for any two quantum observables which do not commute, the product of the standard deviations of the measurements of those observables must be greater than or equal to a positive constant, related to Planck's constant (<math>\hbar</math>).

The most common example is of a particle's momentum <math>p</math> and its position <math>x</math>. Mathematically it is represented with this equation:

<math>\left(\Delta x \Delta p\geq\frac{\hbar}{2}\right)</math>.

In English, this means that we can never measure both the position and momentum of a particle simultaneously with arbitrary precision. The more precisely we wish to measure one observable, the less precisely we can measure the other at that time.

Contrary to popular belief, this is not merely a measurement issue. While it is often stated that it is not possible to know the precise position and momentum of a particle at the same time, this is misleading; it implies that the particle has precisely defined position and momentum, but that information is unavailable to us. In fact, the Uncertainty Principle tells us that a particle cannot have precisely defined position and momentum simultaneously.