The Heisenberg uncertainty principle is a principle of nuclear physics, first described by theoretical physicist Werner Heisenberg. It states that one cannot accurately and precisely measure the momentum and position of a given sub-atomic particle simultaneously. The principle also states that the accuracy of the two measurements is inversely related — the accuracy of one measurement is correspondingly reduced as measurement of the other approaches the limit of its accuracy. Heisenberg clarified the principle, by stating that it had nothing to do with experimental techniques or measurement apparatus. Even under theoretically ideal and perfect conditions, it would remain valid.

In Heisenberg's paper on uncertainty with respect to sub-atomic particles, the Heisenberg uncertainty principle states that "The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa." This statement seems simple but had important implications for the very new sciences of quantum mechanics and quantum physics. It revolutionized the way scientists understood physics, the universe, the nature of matter, and reality. Prior to the development of this idea, physics was based on the supposition that, theoretically, there was an exact and precise value for every aspect of every particle in the universe, even if the means for measuring those properties did not exist.

The Heisenberg uncertainty principle says that not only is this not the case but that it can never be the case and that this fact is a result of the fundamental structure of matter and the way in which the particles that make it up behave. Rather than exact values for the various properties of sub-atomic particles, quantum mechanics instead deals with the probabilities of such values and of how the particles will behave. It is also related to the ability of light to act as both a wave and a particle and the finite speed at which it travels.

As part of his work in developing the principle, Heisenberg worked out what are called uncertainty relations. As the basis for this work, he used a hypothetical single electron moving through a vacuum. Observations of the electron are described in terms of its momentum, which is defined as its velocity — speed and direction — multiplied times its mass, its charge, and the time involved in the observation. He used a thought experiment, using an imaginary gamma ray microscope, to show that his principle indicates that it is impossible to know the exact value of all the variables of such a particle's properties.