# Quantum Uncertainty Principle

A Quantum Uncertainty Principle is a physics principle that asserts 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 simultaneously.

**See:**Wave-Particle Property, Momentum, Planck Constant, Observer Effect (Physics), Quantum Fluctuation.

## References

### 2024

- (Wikipedia, 2024) ⇒ https://en.wikipedia.org/wiki/Uncertainty_principle Retrieved:2024-4-27.
- The
**uncertainty principle**, also known as**Heisenberg's indeterminacy principle**, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the more accurately one property is measured, the less accurately the other property can be known.More formally, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the product of the accuracy of certain related pairs of measurements on a quantum system, such as position,

*x*, and momentum,*p*. Such paired-variables are known as complementary variables or canonically conjugate variables.First introduced in 1927 by German physicist Werner Heisenberg,

^{[1]}^{[2]}the formal inequality relating the standard deviation of position*σ*and the standard deviation of momentum_{x}*σ*was derived by Earle Hesse Kennard later that year and by Hermann Weyl in 1928:_{p}where [math]\displaystyle{ \hbar = \frac{h}{2\pi} }[/math] is the reduced Planck constant.

The quintessentially quantum mechanical uncertainty principle comes in many forms other than position–momentum. The energy–time relationship is widely used to relate quantum state lifetime to measured energy widths but its formal derivation is fraught with confusing issues about the nature of time. The basic principle has been extended in numerous directions; it must be considered in many kinds of fundamental physical measurements.

- The

### 2014

- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/uncertainty_principle Retrieved:2014-12-26.
- In quantum mechanics, the
**uncertainty principle**is any of a variety of mathematical inequalities 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 simultaneously. For instance, in 1927, Werner Heisenberg stated that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.^{[3]}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 later that year and by Hermann Weyl ...

- In quantum mechanics, the

- ↑ Werner Heisenberg (1989),
*Encounters with Einstein and Other Essays on People, Places and Particles*, Princeton University Press, p. 53. - ↑ Kumar, Manjit.
*Quantum: Einstein, Bohr, and the great debate about the nature of reality.*1st American ed., 2008. Chap. 10, Note 37. - ↑ .
Annotated pre-publication proof sheet of Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik, March 23, 1927.