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The '''Heisenberg Uncertainty Principle''' states that it is impossible to measure [[precision|precisely]] at the same time both the position and momentum of a particle. The more precisely we wish to measure one observable, the less precisely we can measure the other at that time.

The '''Heisenberg Uncertainty Principle''' states that it is impossible to measure [[precision|precisely]] at the same time both the position and momentum of a particle. The more precisely we wish to measure one observable, the less precisely we can measure the other at that time.  This is fundamental to [[quantum mechanics]].

In mathematical terms, the principle is stated as follows:  for any two [[quantum]] observables which do not commute, the product of the [[standard deviation]]s of the measurements of those observables must be greater than or equal to a positive constant, related to [[Planck's constant]] (<math>\hbar</math>).  

In mathematical terms, the principle is stated as follows:  for any two [[quantum]] observables which do not commute, the product of the [[standard deviation]]s of the measurements of those observables must be greater than or equal to a positive constant, related to [[Planck's constant]] (<math>\hbar</math>).