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 September, 2018
In my last post, I announced that I had self-published an ebook that used my alternative interpretation of quantum mechanics to calculate properties of the chemical bond, and obvious questions include why do it that way, and why not use standard quantum mechanics? The answers are, of course, linked, and go way back to when I was an undergraduate.

The first question I felt required answering was why did the two-slit experiment give a diffraction pattern. In standard quantum mechanics the answer to that is the equations give the probability pattern, so shut up and calculate. Do not ask why they give a diffraction pattern, even when the particles go through the slit one at a time (provided you send enough through.) The equations certainly seem to predict what happens nicely; while there is a rather limited set of situations where you can actually solve the equations, even without solving them they give a good account of what we see. Nevertheless, they do not answer why whatever happens. In logic, there seem to be three possibilities: there is a particle; there is a wave; there is a particle and a wave, and the wave guides the particle. This third option is the concept used by de Broglie and Bohm with their pilot wave interpretation. I agree with that concept, so why do I think I am different still?

I am defining "particle" as an entity with mass that is constrained to a limited volume of space. My view was that only a particle going through one slit would give the pattern that you got when you closed a slit, while the idea of a particle going through both slits would mean the electron was not a particle within the given definition. Therefore there should be a wave and a particle. As to why you cannot detect this guidance wave, there are two reasons. The first is it is mainly complex, although, from Euler it is real at the antinode, however there is a more interesting reason.

If you do a little mathematics, you can find that the phase velocity of the wave is E/p, E the energy, p the momentum. The momentum is easily defined, but what is the energy? Heisenberg put the energy as the kinetic energy, which gives the somewhat odd result that the wave proceeds at half the velocity as the particle. Somehow, that does not look right. To get around that, others put E = mc^2. That means the wave is superluminal, and moves at infinite speed when the particle is stationary. That, of course, raises the frame of reference issue: stationary with respect to what? There is a huge difference between infinite and finite. The phase velocity of the wave should not be infinite for some observers, but not others. Added to which, I do not think something that is fundamental should ever have an infinite value.

My opinion is that the simplest answer to that is to ask the wave to be at the slits at the same time as the particle, so it can guide the particle. It cannot do that if it is long gone, or yet to arrive. But if that is the case, then E is twice the kinetic energy of the particle. If so, then the wave does what every other wave does: it transmits energy, and the energy within the wave equals the energy of the particle (assuming the particle actually contains the kinetic energy and that is not also in the wave; either way, the square of the amplitude of the wave is proportional to the energy of the particle). Accordingly, you cannot detect the wave because to detect something you have to interact with it, and that usually involves changing its energy. If you change the energy of the wave, you also change that of the particle, which means you have also interacted with the particle. That is the reason why it is so difficult to detect the wave, at least in this interpretation.

So, why is this interesting? It means the square of the amplitude of the wave gives the energy of the wave, and the amplitude is located at the wave antinode. For many cases, this makes no real difference, but for molecules it is important. So why I am arguing for this different interpretation is in principle it should greatly simplifies chemical theory, if it is valid. Can you see how, before next post? Test your ability at generating theory by assuming that wave description above is correct. Of course you still have to test it later, but you find it difficult to get anywhere without a provisional assumption.
Posted by Ian Miller on Sep 17, 2018 3:24 AM BST