Uncertainty principle

In quantum mechanics, the uncertainty principle, also known as Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position x and momentum p, can be known.

Introduced first in 1927, by the German physicist Werner Heisenberg, it states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.

 The formal inequality relating the standard deviation of position σx and the standard deviation of momentum σp was derived by Earle Hesse Kennard later that year and by Hermann Weyl  in 1928:

(ħ is the reduced Planck constant, h / 2π).


The evolution of an initially very localized gaussian wave function of a free particle in two-dimensional space, with colour and intensity indicating phase and amplitude. 

The spreading of the wave function in all directions shows that the initial momentum has a spread of values, unmodified in time; 

while the spread in position increases in time: as a result, the uncertainty Δx Δp increases in time. image: wikimedia

A nice demo and explanation of this animation in the real world is using lasers:

Source adapted from: Uncertainty principle. (2016, December 20). In Wikipedia, The Free Encyclopedia. Retrieved 07:16, December 20, 2016, from https://en.wikipedia.org/w/index.php?title=Uncertainty_principle&oldid=755798907