Werner Heisenberg quantum mechanics |

## Uncertainty principle

- Werner Heisenberg declared a limit
- to what can be determined precisely.
- We don’t have this problem
- when talking about planets or billiard balls,
- only for elementary particles
- such as photons or protons.
- The more we know about one property of a particle,
- such as its position,
- the less we know about any related property,
- such as its momentum.

## Half ħ

- The standard deviations
- of position and momentum
- multiplied together
- is greater than or equal to
- half the reduced Planck constant.

## Unsure

- You’d think
- this’d be easy
- but I’m not sure.

Heisenberg’s uncertainty principle is a fundamental property of quantum systems, not merely a limit to how small a thing we can measure.

The illustration represents the work of Earle Hesse Kennard and Hermann Weyl. The standard deviation of position (sigma sub-x) multiplied by the standard deviation of momentum (sigma sub-p) is greater than or equal to half the reduced Planck constant.

See also in

The book of science:Planck constant—Max PlanckCompton scattering—Arthur Holly ComptonSchrödinger equation—Erwin SchrödingerDirac equation—Paul DiracZitterbewegung—Erwin SchrödingerReadings on wikipedia: