Werner Heisenberg And The Heisenberg Uncertainty P — страница 4

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onrelationships between quantities which in principle, are observable. Itdealt with observed frequencies and intensities of emitted and absorbedlight, and in doing it enabled a momentous breakthrough in physics,ensuring Heisenberg s place in modern physics. Heisenberg then laid the groundwork for the new theoretical “matrixmechanics”. The next semester, Heisenberg wrote a paper on the topicbut was not sure if he should publish it. He gave it to Born to read,and while he was away at Cambridge, England Born sent the paper to the”Zeitschrift f r Physik”, a leading German physics journal. Theprinciple of matrix mechanics utilized the same principle of themultiplication of matrices. On March 22, 1927, Heisenberg submitted a paper to the “Zeitschrift f rPhysik” entitled

“On the perceptual content of quantum theoreticalkinematics and mechanics” This twenty-seven page paper forwarded fromCopenhagen contained Heisenberg s most famous and far-rangingachievement in physics, his formulation of the uncertainty orindeterminacy principle in quantum mechanics. This uncertaintyprinciple formed a fundamental component of the Copenhageninterpretation of quantum mechanics. The other two portions were Bohr scomplementary principle and Born s statistical interpretation ofSchr dinger s wave function. The Copenhagen Interpretation was anexplanation of the uses and limitations of the mathematical apparatus ofquantum mechanics the fundamentally altered our understanding of natureand our relationship to it. This was the most controversial andprofound

transformation in physics that has not been equaled since. Heisenberg compared this to how Newtonian mechanics had to be replacedby a new relativistic mechanics such as how the effects of Einstein stheory of relativity transformed our notions of space and time undercertain conditions, which are high speeds, and enormous expanses ofspace and time. Heisenberg continued how a similar transformation isrequired in the realm of small masses and short distances such as theorder of atoms and electrons. It was impossible to observe theindividual workings of atoms, only the external workings of largenumbers of atoms. Prior to the Heisenberg Uncertainty Principle it wascommon belief that it was able to describe the electron s motion bynoting its position and velocity at any given moment. In

his essay,Heisenberg argued this belief and stated that this concept would notwork; the previous belief would only be accurate if the object weremacroscopic and in the viewable world. When objects are sill viewableand measurable, Newtonian physics still applies, but when objects becomeso minute they are not able to be measured with an accurateness. It isimpossible for the physicists to know any more than it is possible forthem to measure. This is his explanation for this concept, “If oneseeks to measure the exact position of an electron, one could use amicroscope of very high resolving power, which would require theillumination of the electron with the light of very short wavelengths. But the shorter the wavelength, the grater the energy of the lightquantum (or the greater the

pressure of the light wave) hitting theelectron – thus the greater the recoil velocity of the electron.” Henoted that there seemed to be a reciprocal relationship between theuncertainties with which it is possible to simultaneously measurevelocity and the position of the electron in any given instant. “Themore precisely we determine the position, the more imprecise thedetermination is the determination of velocity in this instant, and viceversa” This statement had profound implications on the way physicistswould look at the quantum world. In the essay, Heisenberg also statedthat with the new boundary of precision, the causalty theory becameinvalid. The causalty theory stated that with every action or effect,there is a cause for that action or effect. In Heisenberg

expressed,”In the strict formulation of the causal law – if we know the present,we can calculate the future – it is not the conclusion that is wrong butthe premise.” This basically states that without knowing the preciselocation and velocity of the electron, it is only possible to calculatea range of possibilities for the location and velocity of the electronat any point in the future. The uncertainty relations that Heisenbergused to mathematically explain are: DpDq | h/2p DEDt | h/2p This first equation expresses the relationship when the position q, andthe velocity p are measured simultaneously. The error in the precisionof p and q are expressed as Dp and Dq at a given instant. The productof these uncertainties have to be at least equal to h/2p. This numberis very