The Science of Extraterrestrials - Eric Julien-pages

Page 41 of 400

Page 41 of 400
The Science of Extraterrestrials - Eric Julien-pages

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Erwin Schrédinger proposed the quantum version of a particle’s wave function @ (r,t), where every moving particle is associated with a bundle of concentrated waves in space, of which the propagation equa- cou a where i is the imaginary number, v-1,ris the position of the particle, t is time, and A is the Laplacian” operator. To the right of the = we find kinetic energy (where h=h/2n, h is Planck’s constant) and potential energy. However, what is the meaning of @? The physicist Max Born affirmed that the square of the wave function at a given point constitutes the probability to find the particle at this point at the moment in question. The wave functions then become probability waves. The wave function G(r, t) is also called amplitude of probabil- c ' ity of presence! A simpler formalism, which considers only a single displacement axis (x), allows us to write the wave function with two variables: t and x, ie., a time and a position on the disruptive sine curve. This is writ- ten as y(t, x), or yet f(x-ct) where c is the propagation speed, t is the moment of measurement and x is the wave displacement. The wave function depends only on t and to x via the quantity t- |x| /c. The posi- tion of x therefore depends on the propagation speed and the moment c Having said that, one of the great principles of quantum mechan- ics is the Heisenberg uncertainty principle, in which a limitation on accuracy of simultaneous measurement of observables, such as the position and the momentum of a particle, is expressed. It is important to understand that the Heisenberg uncertainty principle in quantum mechanics is based on the assumption that it is impossible to know x if tis not defined. This is like asking two questions at the same time, where the answer to one depends on the answer to the other. How- ever, the definition itself of t or x influences the answer! The propaga- tion rate is an uncertainty in itself, because it will be influenced by the measurement instrument. Furthermore, c depends on a number of iterations in the doubling theory. As a result, the trajectory concept is of no use in quantum mechanics, just as it is impossible to construct a device that determines the position of a particle without changing it. In fact, the underlying principle is the wave-corpuscle duality, but this duality is explained nowhere. In reality, quantum mechanics talks tion is as follows’: ih(d/odt)o(r,t) = — (h?/2m)Ag(r,t) + V (r)A(r,t) of measurement.