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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.
Uncertainty or incertitude refers to situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. [1]
In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties ... In component notation, the equation ...
This last equation is in a very high dimension, [2] so the solutions are not easy to visualize. ... Equation Heisenberg's uncertainty principles: n = number of photons;
Uncertainty propagation is the quantification of uncertainties in system output(s) propagated from uncertain inputs. It focuses on the influence on the outputs from the parametric variability listed in the sources of uncertainty. The targets of uncertainty propagation analysis can be:
In this equation, and denote the uncertainties in position and momentum, respectively. The term ℏ {\displaystyle \hbar } represents the reduced Planck constant, while β {\displaystyle \beta } is a parameter that embodies the minimal length scale predicted by the GUP.
For example, an experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum can estimate the value of the local gravitational acceleration constant g. The relevant equation [ 1 ] for an idealized simple pendulum is, approximately,
In quantum mechanics, information theory, and Fourier analysis, the entropic uncertainty or Hirschman uncertainty is defined as the sum of the temporal and spectral Shannon entropies. It turns out that Heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies.