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The '''Heisenberg Uncertainty Principle''' states that 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>).  

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.

 

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>).  

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:   

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>.   

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

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; this statement 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 or momentum.

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; this statement 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 or momentum.