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Classical physics was on loose footing with problems of wave/particle duality, but was caught completely off-guard with the discovery of the uncertainty principle.

The uncertainty principle also called the Heisenberg Uncertainty Principle, or Indeterminacy Principle, articulated (1927) by the German physicist Werner Heisenberg, that the position and the velocity of an object cannot both be measured exactly, at the same time, even in theory. The very concepts of exact position and exact velocity together, in fact, have no meaning in nature.

Any attempt to measure precisely the velocity of a subatomic particle, such as an electron, will knock it about in an unpredictable way, so that a simultaneous measurement of its position has no validity. This result has nothing to do with inadequacies in the measuring instruments, the technique, or the observer; it arises out of the intimate connection in nature between particles and waves in the realm of subatomic dimensions.

Ordinary experience provides no clue of this principle. It is easy to measure both the position and the velocity of, say, an automobile, because the uncertainties implied by this principle for ordinary objects are too small to be observed. The complete rule stipulates that the product of the uncertainties in position and velocity is equal to or greater than a tiny physical quantity, or constant (about 10-34 joule-second, the value of the quantity h (where h is Planck's constant). Only for the exceedingly small masses of atoms and subatomic particles does the product of the uncertainties become significant.
According to Heisenberg's uncertainty principle, it is not possible to determine precisely both the position and the momentum (or velocity) of a moving microscopic particle, simultaneously with accuracy.
Mathematically this principle is expressed as:

Where Î”x is uncertainty with regard to the position and Î”p is uncertainty with regard to the momentum of the particle. If Î”x is very small Î”p would be large, ie, uncertainty with regard to momentum will be large. On the other side if we attempt to find out the momentum exactly the uncertainty with regard to position will be large.

Explanation: To determine the position of a small body like electron, it has to be illuminated with
electromagnetic radiation. Low energy radiations like ordinary light waves cannot be used to illuminate a small body like electron, since the size of the electron is very small when compared with the wavelength of ordinary light. Therefore to irradiate electrons, radiations with shorter wave length are used. When such a high energy radiation is allowed to fall on an electron its velocity changes by a large value. Consequently if we find the position of an electron precisely, there is always an uncertainty in finding the velocity of an electron simultaneously. Thus the determination of position and momentum of a moving electron precisely and simultaneously is impossible.

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