Is science sometimes in danger of getting tunnel vision? Recently published ebook author, Ian Miller, looks at other possible theories arising from data that we think we understand. Can looking problems in a different light give scientists a different perspective?

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Archive for November, 2018
In my last post, I started by explaining why I had embarked on finding a new quantum mechanical interpretation. The actual answer to why I got started was of course personal and not that important, but there was a better reason why I kept going: currently, theoretical chemistry depends on some hideously difficult computations that arise when one considers it in terms of particle-particle interactions. That means you have to compute the probability locations of all the electrons, the position of each thus depending on what the others are doing. The fundamental underlying equation cannot be solved, so various procedures are used to approach the solutions, and as Pople noted in his Nobel lecture, certain constants are "validated" by comparison with observation. This is not quite as ab initioas some may think. 

My current Guidance Wave solution to this problem approaches the issue from a different direction: it states that certain properties can be defined solelyby considering waves. This has three consequences: as a consequence of linearity it is far simpler, it automatically leads to localised bonds in defined circumstances through wave interference properties and hence predicts the functional group, and finally it requires a previously unrecognized quantum effect. That last point is critical; if correct, it means that many current computations cannot get the correct answer for the right reason. 
So, is my approach correct? That is for you to think about. Which raises its own interesting question: most readers of this blog will either have PhDs or will be intent on getting one. So, how often do you think philosophically? Only too many adopt "Shut up and calculate something", or their thoughts relate to how to do something, or how to make something. This is the artisan or gild way of thinking; you become an expert at doing something, but you are not concerned with why it works. But, you argue, if the mathematics give the right answer, you must have the right theory. Not so. Consider planetary motion. It is not that difficult if you can manage something like Fourier Transforms to end up with the epicycle theory of Claudius Ptolemy. You get the right answers to your calculations, but I would argue your physics would be wrong.

The major differences between this guidance wave approach and the standard approach are:
  1. Like the pilot wave, I assume a wave causes diffraction in the two-slit experiment.
  2. To do that, it has to arrive at the slits at the same time as the particle.
  3. If so, the wave transmits energy proportional to the particle energy. This is similar to the quantum potential of Bohm, except now it has a precise value.
  4. Since the phase of the wave is given by exp(2πiS/h), Sthe action, from Euler the wave becomes real at the antinode.
  5. The square of the amplitude is proportional to the energy transmitted by the wave. (That is what waves do generally.)
  6. Therefore, for the stationary state, the energy at the antinode is equal to the energy of the particle.
  7. The nodal structure of the wave is that given by . I. J. Miller 198 Aust. J. Phys. 40: 329 -346. That represents the energy of the atomic orbitals solely in terms of quantum numbers.
  8. The charge distribution of each atomic orbital is represented in terms of Cartesian components that are separable.
  9. The waves interfere linearly, which is what waves usually do.
  10.  New interactions are introduced, which means new wave components. The bond energy comes from these new interactions (because of linearity).
  11. The position of the antinode is determined by the constancy of action (because it is quantized) which is whythere is a covalent radius.
  12. The orbital of hydrogen is different, therefore there is partial wave reflection at the antinode and "overlap" is less complete. Therefore the intensity of the new interactions are less than simply additive in charge, so to maintain constant action, the bond has to shorten.
  13. The zone between the nuclei has a wave component similar to the particle in the box. That means that the nodal structure determined for the atomic orbitals (7 above) has to change. Again, it is dependent only on quantum numbers.
  14. Zero point energies are not calculated. Either observed zero point energies or estimated zero point energies were used.
Anyone can say that. The question then is, performance. In the following, a selection of calculated data (pm for bond lengths, kJ/mol for bond energies) with the best observational data I could get in brackets are:
Bond lengths: H237.4  (37.1); Li2134.6 (133.6);  Cs2234.5 (230); Si-Si 232.8 (232 – 236); C–H sp3108.9 (109.1); C-C sp3151.4 (151 – 154); P2188.6 (189.3) C-C sp 121.4 (120.3); N2109.9 (109.76)
Covalent radii  P 111.1 (110 – 111); Sb 140.0, (138 – 143); S 103.1 (104 – 105); Te 139.0 (138 – 141); Cl 95.7 (99); I 135.4 (133.6); spSi  111.9 (111)
Bond Energies: H2: 435.6 – 438.1, depending on zero point energies from two different sources (436); D2445.6(443.5); Li2105.4 (102.3) 41.6 (44.8); P-H 141.9 (142); Sb-H 247.1 (257); S-H 366.8 (365); Te-H 267.0 (265); Cl-H 432.4 (432); I-H 310 (298);  C-C sp3361.6 (358.3 – 360.5); C-H sp3411.4 (411); Sn-H 224.7 (219); O-H sp3462.7 (463); F-H sp3570.6 (570.4); P2491.8 (489.5); Sb298.1 (299.2); C-C sp 831.9 (835); N2945 (945.3)
The bond energies for hybridized elements follow the analysis of Dewar and Schmeising. As can be seen, given their simplicity, I argue the calculations show something useful. 

So, as can be seen, this is somewhat different from the standard approach, but the calculations are sufficiently straightforward that a hand-held calculator should be all you need. The bond energies so calculated are not in exact agreement with observation, in part because the atomic orbital energies are not exactly given by the quantum number relationship, and since there are further small regularities in these differences, there is seemingly something further that is yet to be understood. However, most of these differences cancel out in the bond energy calculation, although there are three atoms, boron, sodium and bismuth where this does not happen. A further reason the agreement may not be as good as required could be that there are errors in the observational data. It is usually wrong to criticise that, however, the single bond energy agreement for antimony is poor, yet when that is used in one of the bonds for Sb2, with two πbonds added in, the triple bond strength is in very good agreement.

So, does this interest you? I guess I shall see in due course.
Posted by Ian Miller on Nov 4, 2018 8:36 PM GMT