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 absolute precision, for a given physical object. This is important in spectroscopy, whether medical imaging or astrophysics, satelite communications, laser design and many other technologies 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 principle deals with certain pairs of quantities called conjugate quantities. Position and momentum are conjugate quantities, as are energy and time. The principle then states:

Conjugate quantities of system cannot simultaneously be precisely measured.

The principle also provides an estimate of the maximum precision possible for a given system. In the case of position x and linear momentum in x-direction p_x, this is given by

$\Delta x\cdot \Delta p_{x}\geq {\frac {h}{4\pi }}$.

For energy and time:

$\Delta E\cdot \Delta t\geq {\frac {h}{4\pi }}$.

h denotes Planck's constant, which is very small. The uncertainties are here understood to be variances.

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.