Uncertainty Principle

The uncertainty principle states that it is impossible to accurately measure both the position and velocity of particles at the same instant. In order to measure either position or velocity you shine light on the particle. Waves of light that are scattered will give the position of the particle, but disturb the velocity. This also works the other way, you cannot measure the velocity without disturbing the position.

Problem 1 - If the photon has a short wavelength, and therefore a large momentum, the position can be measured accurately. But the photon scatters in a random direction, transferring a large and uncertain amount of momentum to the electron. If the photon has a long wavelength and low momentum, the collision does not disturb the electron's momentum very much, but the scattering will reveal its position only vaguely.

Problem 2 - If a large aperture is used for the microscope, the electron's location can be well resolved (see Rayleigh criterion); but by the principle of conservation of momentum, the transverse momentum of the incoming photon and hence the new momentum of the electron resolves poorly. If a small aperture is used, the accuracy of both resolutions is the other way around.

The number of the uncertainty in the position of the particle times the uncertainty in the velocity times the mass of the particle can never be smaller than a certain fixed quantity. This means that if you halve the uncertainty in position, you must double the uncertainty in velocity. This also works the other way around. The fixed quantity in this equation is called Planck's constant.

(for information on Planck's constant) http://en.wikipedia.org/wiki/Planck_constant

The errors made in measuring position and velocity have little effect on our daily lives. Those errors though, prevent us from predicting any future events. In order to predict the future location of a particle, one must know the precise characteristics of the partice at any one moment. Since we cannot measure that, we cannot predict the future characteristics of the particle.

The uncertainty principle was created by Werner Heisenberg in 1927. Heisenberg was working on mathematical foundations in quantum mechanics when he formulated his principle. This principle was a huge discovery in the quantum theory.
Heisenberg once wrote: It can be expressed in its simplest form as follows: One can never know with perfect accuracy both of those two important factors which determine the movement of one of the smallest particles—its position and its velocity. It is impossible to determine accurately both the position and the direction and speed of a particle at the same instant.[8]

Website for diagrams
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Heisenberg's gamma-ray microscope for locating an electron (shown in blue). The incoming gamma ray (shown in green) is scattered by the electron up into the microscope's aperture angle θ. The scattered gamma-ray is shown in red. Classical [[/wiki/Optics|optics]] shows that the electron position can be resolved only up to an uncertainty Δx that depends on θ and the wavelength λ of the incoming light