Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle, named for Werner Heisenberg, , states that certain pairs of properties (called conjugate quantities) cannot simultaneously be measured with perfect precision, for a given physical object. This is important in spectroscopy, whether medical imaging or astrophysics, satelite communications, laser design and many other devices used daily.

For particle physics, this was the problem of determining the state of a fundamental particle (electron, etc.) at any given moment. The problem arises experimentally as, in order to determine the state of any particle, we (the observers) must look at it. In order to see it, we must bombard it with photons. The interaction of photons with the sub-atomic particles changes the state of the particle leading us to the ironic conclusion that it is impossible for an observer to determine experimentally the state of any particle, because there is always an error margin equal to the wavelength of the photon. Though the wavelebngth can be made shorter in order to reduce the error margin, this also disturbs the motion of the measured particle. Thus, for Heisenberg, physicists can only predict the probabilities of where or what the given state of a particle would be.

Fundamental particles thus exist in a fog of probabilities. It was this theorem that led to Einstein's famous quip that "God does not play dice."

The Principle

The uncertainly principle does not limit the precision with which either the particle's momentum or its position may be measured, but only the precision which with both may be measured simultaneously. This uncertainty is expressed mathematically as

$(\Delta X)(\Delta p_{x})\geq {\frac {h}{4\pi }}$

where

$\Delta X$ indicates uncertainty (that is, variance) in the measurement of position. $\Delta p_{x}$ is the uncertainty in the momentum measurement. $h$ is Planck's constant.

An alternative and equally valid way of expressing this uncertainty, in terms of energy and time, is

$(\Delta E)(\Delta t)\geq {\frac {h}{4\pi }}$

where

$\Delta E$ indicates uncertainty in the measurement of the energy $\Delta t$ is the uncertainty of the time at which the energy was measured.

Quantities such as these, who cannot simultaneously be measured precisely, are called conjugate quantities. As such, energy and time are conjugate quantities, as are instantaneous momentum and position in a given direction.

Applications

In string theory, another constant (C) related to the Planck scale is introduced into the equation. This constant poses a minimal value on the uncertainty with which particles can be located.

In other fields, such as the behavioral sciences, this principle also applies. For anthropologists studying the interactions of social groups, interactions may change as a result of the researcher's presence. For psychologists studying individual behavior, reasons and actions may change because the individual knows he is being observed.