Heisenberg's uncertainty principle

                                        Heisenberg's uncertainty principle

quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities^[1] 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.^[2] The formal inequality relating the standard deviation of position σ_x and the standard deviation of momentum σ_p was derived by Earle Hesse Kennard^[3] later that year and by Hermann Weyl^[4] in 1928:

${\displaystyle \sigma _{x}\sigma _{p}\geq {\frac {\hbar }{2}}~~}$

Ordinary experience provides no clue of this principle. It is easy to measure both the position and the velocity of, say, an automobile, because the uncertainties implied by this principle for ordinary objects are too small to be observed. The complete rule stipulates that the product of the uncertainties in position and velocity is equal to or greater than a tiny physical quantity, or constant (h/(4π), where h is Planck’s constant, or about 6.6 × 10⁻³⁴ joule-second). Only for the exceedingly small masses of atoms and subatomic particles does the product of the uncertainties become significant.