Kepler 7.0

Prof. Dr. Peter Bauer Institut fLir Experimentalphysik Johannes Kepler Universitat 4040 Linz Austria... 

J. Kepler. The Six-Cornered Snowflake, translated by C. Hardie. Oxford Clarendon Press, 1966. Originally published as Sen de Nive Sexangida. Frankfurt am Main Godfrey, Tampach, 1611). 

In the realm of natural product synthesis, Kepler and Rehder utilized the K-R reaction to synthesize ( )-calanolide A (56), a potent non-nucleosidal human irmnunodeficiency virus (HIV-1) specific reverse transcriptase inhibitor. Propiophenone 57 was allowed to react with acetic anhydride in the presence of sodium acetate to afford benzopyranone 58 in 56% yield subsequent deacetylation of 58 gave 59. Flavone 59 was then transformed to ( ) calanolide A (56) over several steps. 

Christian Doppler Laboratory for Plastic Solar Cells Physical Chemistry Johannes Kepler University Linz AltenbergerstraBe 69 A-4040 Linz Austria... 

The capacity to solve novel problems by constructing analogies to already-used visualisations. (Gilbert, 2008). For example, using Kepler s model of the Solar System to explain the electronic structure of an atom, in the manner of Bohr, and hence being able to predict, very approximately, the absorption spectram that it will produce. 

Historical prelude Kepler s laws Historical prelude Maxwell Theory Axiomatic teaching of Quantum Mechanics Problem lack of reference points Problem imprecise boundaries Problem inaccurate formulation Solution reference points from a journey Solution precise boundaries Solution accurate formulation Intuitive teaching of Quantum Mechanics Conclusion... 

In any course of NM, one of the first applications is the derivation of Kepler s laws of planetary motion. Historically this is one of the great triumphs of NM. Kepler s laws state that the orbits of the planets around the sun are ellipses with the sun in one of the focal points and that the speed of the planets is such that equal areas inside of the ellipse are swept in equal times. 

Now consider the hypothetical problem of trying to teach the physics of space flight during the period in time between the formulation of Kepler s laws and the publication of Newton s laws. Such a course would introduce Kepler s laws to explain why all spacecraft proceed on elliptical orbits around a nearby heavenly body with the center of mass of that heavenly body in one of the focal points. It would further introduce a second principle to describe course corrections, and define the orbital jump to go from one ellipse to another. It would present a table for each type of known spacecraft with the bum time for its rockets to go from one tabulated course to another reachable tabulated course. Students completing this course could run mission control, but they would be confused about what is going on during the orbital jump and how it follows from Kepler s laws. 

The principles of Kepler s laws and orbital jumps in isolation would leave students confused. Alternatively suppose students were taught that only free-falling space flight can be understood from Kepler s laws, and that the tables for course corrections had been constructed from careful experimentations and observations. In this case, students would not be confused either. The confusion comes from stating that everything will be explained theoretically and then only explaining half. 

However, in Maxwell s days everyone assumed that there had to be a mechanical underpinning for the theory of EM. Many researchers worked on very detailed hidden variable theories for the EM field, in an attempt to prove that the laws of EM were in fact a theorem in NM, just like Kepler s laws are a theorem in NM. No one noticed that it was impossible to do this, since Maxwell s equations are not Galilei invariant and Newton s laws are. That includes Lorentz who discovered around 1900 that the Maxwell equations are invariant under another transformation that now bears his name. 

This separation will allow the students to properly assess the measurement process, which plays a special and complex role in QM that is different from its role in any classical theory. Just as Kepler s laws only cover the free-falling part of the trajectories and the course corrections, essential as they may be, require tabulated data, so too in QM, it should be made clear that the Schrbdinger equation governs the dynamics of QM systems only and measurements, for now, must be treated by separate mles. Thus the problem of inaccurate boundaries of applicability can be addressed by clearly separating the two incompatible principles governing the change of the wave function the Schrbdinger equation for smooth evolution as one, and the measurement process with the collapse of the wave function as the other. 

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