Sunday, May 29, 2011

Heisenberg Uncertainty Principle

In quantum mechanics, the Heisenberg uncertainty principle states precise inequalities that constrain certain pairs of physical properties, such as measuring the present position while determining future momentum; both cannot be simultaneously done to arbitrarily high precision. That is, the more precisely one property is measured, the less precisely the other can be controlled or determined. On the other hand, it is possible to imagine a hypothetical apparatus that measures the history of a particular particle's successive positions and momentums while also measuring times and energies to arbitrary accuracies.

The Uncertainty Principle is often misstated so as to imply that simultaneous measurements of both the position and momentum cannot be made. There is a simple Gedanken experiment that illustrates what physics does allow. Imagine a hollow evacuated sphere where the internal surface is covered by microscopic detectors that measure the position and time of contact of a He atom. Inside the sphere is one single He atom that bounces randomly from one point to another. Each time it contacts the wall, its position is measured to arbitrary accuracy, therefore its future momentum is uncertain. The time of the contact can be measured with arbitrary accuracy, therefore the future energy is uncertain. However, at the next contact with the inner surface of the sphere another accurate measurement of position and time can be made. Knowledge of those accurate times and positions allows us to compute a history of arbitrarily accurate simultaneous positions and momentums along with times and energies.

Published by Werner Heisenberg in 1927, the principle correctly implies that it is impossible to simultaneously both measure the present position while "determining" the future momentum of an electron or any other particle with an arbitrary degree of accuracy and certainty. This is not a statement about researchers' ability to measure one quantity while determining the other quantity. Rather, it is a statement about the laws of physics. That is, a system cannot be defined to simultaneously measure one value while determining the future value of these pairs of quantities. The principle states that a minimum exists for the product of the uncertainties in these properties that is equal to or greater than one half of ħ the reduced Planck constant (ħ = h/2π).

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