Another Werner Heisenberg Essay

Rather than the classical idea of the position and

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Rather than the classical idea of the position and the motion, or momentum, of the electron at each instant in time, Heisenberg introduced his square arrays or matrices, which depict the electron as existing simultaneously in all possible Bohr orbits. After Heisenberg's discovery, the classical concept of the electron as a particle was no longer justifiable. Heisenberg was led to these revolutionary ideas by his insistence on utilizing only those quantities in a theory that are directly observable. Since the orbit of an electron is not observable, it can have no place in a theory. Only the spectral lines are observed, and, since these involve pairs of orbits, all quantities that are used to describe the electron inside the atom should be associated with such pairs. Such thinking led to Heisenberg's matrices. One of the important features of matrices is that it is not commutative. If the array representing the position of an electron is q and an array representing its momentum is p, then the product pq is not the same as the product qp. This showed Heisenberg that the uncertainty relationship is purely an algebraic consequence of his matrix theory. If you picture the product pq as representing a measurement of the position of the electron followed by a measurement of its momentum; qp, on the other hand, represents the measurement of the momentum of a particle followed by at the measurement of its position. That these two sets of measurements give different results simply means that the measurement of the momentum of a particle destroys our knowledge of its position, and vice versa. It follows that it is impossible to obtain or to have precise knowledge of the position and the momentum of a particle simultaneously; this is the essence of the uncertainty principle. Its significance for the structure of the atom is that we have no way of
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determining the orbit of an electron inside the atom observationally. As Heisenberg pointed out in his analysis of the Copenhagen interpretation of quantum theory, an electron can be observed inside an atom only with a gamma-ray microscope which, because of the short wavelength of gamma rays, has a high resolving power. This microscope shows us where the electron is at any moment, but at least one gamma-ray photon must be reflected from the electron.
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