Heisenbergs uncertainty principle. n quantum mechanics, the uncertainty principle is any mathematical inequality asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously where ħ as the reduced Planck constant . In 1927 Werner Heisenberg stated that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. The reason there is uncertainty is because of the resolution of our optical equipment and the laws of physics NOT quantum mechanics itself. I want to show you a different mathematical way to illustrate the uncertainty principle. Heisenbergs uncertainty principle states that there is no way to determine the velocity (v) and the position (x) of a sub-atomic particle with arbitrary precision simultaneously. This can be described with a mathematical relationship... Er(x)·Er(v)≈c which basically states that for an electron, if a scientist measures the error on the position in centimeters (cm) and the error of the velocity in centimeters per second (cm/s) then the scientist will have approximately c≈1 cm^2/s. Now to see a macroscopic object you must strike it with light rays which are then defected to your eye or the detecting instrument. You must also remembers that light rays are a electromagnetic wave. The wavelength used to see an object sets a limit to the precision with which it is possible to locate an object in space. The resolving power of an optical instrument cannot be greater than the wavelength of the radiation being used. The resolving power of a microscope or any detection instrument is limited by the proportional wavelength λ and limited inverse proportional to the angular aperture of the lens which is α. This can be described by this equation Er(x) ≈ λ/sin α when a wave interacts with a sub-atomic particle it transfers some of its momentum expressed by the equation P=h/λ and to determine how much momentum has been transferred to a sub-atomic particle you must be able to determine the scattering angle. But the precision with which a scientist can determine the scattering angle is limited by the angular aperture of the lens. Er(v) ≈ sin α·h/m·λ is the equation representing the error of determination of the velocity. Er(x) ≈λ/sin α is the equation representing the minimum error in the determination of the position Er(x) · Er(v) ≈ h/m is basically Heisenbergs Uncertainty Principle.
Posted on: Tue, 15 Jul 2014 07:34:55 +0000
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