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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In my last post, I mentioned that in my alternative interpretation of quantum mechanics, I rejected the Born interpretation as being fundamental, and instead I argued that because the wave must keep up with the particle it had to transmit energy. That means the square of the amplitude of the wave should equal that energy, as it does in general wave physics. There is a further difference of definition. I use a term, the wave displacement, to reflect at a coordinate the value of ψ.ψ*, whereupon the amplitude becomes the maximum value of that displacement. This does not mean that Born is wrong because if we think of energy density at a point, that should be roughly proportional to probability, but there are differences. The wave has nodes, and there is a lot of arm-waving in answer to the question, in a stationary state such as an orbital, how does an electron cross a nodal surface, because as soon as it is on it, the probability of it being there is non-zero, but you cannot go from plus to minus, i.e. crest to trough, without going through zero. The problem goes away if the square of the amplitude reflects an energy rather than probability.

There is one further difference. The phase of the wave is given by exp(2πiS/h). That is generally agreed in all textbooks, although it is usually written differently, using %u0127 instead. Now, what is action? Basically, it is the time integral of the Lagrange function, which in turn is an energy (usually the difference between the kinetic and potential energy).  What is important here is that it is something that increases with time, which is why the phase proceeds as an oscillation. The stationary wave, as in the particle in a box, is actually really two running waves proceeding in equal and opposite directions. The reason that is relevant is that from Euler, who developed the mathematics of complex numbers,  exp(iπ) = -1. Thus when S = nh  the value of the phase is 1; when S = nh/2, n odd, the value of the phase is -1.  All other values of S lie somewhere between. In the textbooks, you will see that ψ is always complex.  That is not exactly true and at the antinodes, it becomes real, with A, A the amplitude.
So, what does that mean? Let us assume, for the moment, that the wave only means something physically when real. You may well say, that is just another assumption, but I argue it is not an additional one to what we already have because if so, then it is easy to derive the Uncertainty Principle, which, as an aside, now becomes a physical principle and has nothing to do with the observer. Physicists would generally accept that. As for what it means for general quantum mechanics, apart from requiring the Uncertainty Principle, which was already required, not much because you cannot know the phase of a quantal matter running wave.

However, for a stationary wave, such as the particle in a box, or the wave for a stationary state, as in a free atom or molecule, the antinode defines the amplitude of the wave, and the square of the amplitude of the wave is proportional to the energy of the system. If so, the problem for the chemical bond reduces itself to finding the location of the antinode, and applying the electric field coupling at that point. That is relatively easy because when the nature of the motion is independent of time, the action can be represented as ∫pdq, p the momentum, q the generalized coordinate, and from our discussion on Euler, the action must be quantized over a period, which gives the de Broglie relation pλ = h. So, it is comforting to know that, coming from a somewhat different route that is not conventional, we arrive at a totally conventional relationship. The important point here is the quantization of action gives the covalent radius and that radius gives the bond energy through calculating the potential energy at that point. This means that a good approximation to the bond length and energy of the hydrogen molecule is essentially no more complicated than mental arithmetic, or with a hand held calculator, solely from thinking of the electric field. Errors are about 0.3%.  Better agreement can be found by including some of the more minor contributions.

For molecules in general, there is a little more to it than that because the nature of the waves between the nuclei change for atoms other than hydrogen but the need for computation is still within the hand-held calculator's ability. There are still deviations from observed values, but the results should be close enough to be useful, and as an example, the dissociation of the Sb2 molecule is calculated to be 298.1 kJ/mol (obs 299.2).  In fairness, that is one of the better results, and bismuth, boron and sodium are relatively poorly behaved, but that is in part because their atomic ionization potentials do not behave well either. If interested, details can be obtained in an ebook: https://www.amazon.com/dp/B07GCDYDRR
 
Posted by Ian Miller on Oct 7, 2018 10:02 PM BST
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
A long time ago I gave a computer game to my son, and it had characters that aged. If you aged too far, all you were good for was sitting around the campfire telling stories. Maybe I have got to that age, but the 50th anniversary of the Czech invasion by the Russian military has me looking backwards. As some may have realized, especially after my post on an alternative interpretation of quantum mechanics, I sometimes do not fit in with what everyone expects. So it was then. I was doing a post-doc at The University, Southampton under professor Cookson, and while most people took holidays doing popular touristy things, I did a road trip behind the Iron Curtain. I am putting together a series of posts on that, the first one being at https://wordpress.com/post/ianmillerblog.wordpress.com/867
There will be at least two more, each Thursday. For those who are at post-doc level, or who can recall what they were like, you might want to check them out and see what you might have done. Not a lot of chemistry there; the nearest was comparing Czech and Polish beer, and a search for hydraulic oil. Nevertheless, it was a different summer vacation to anything you will have had.
 
Posted by Ian Miller on Aug 27, 2018 3:58 AM BST
My last post her related to the use of quantum mechanics in chemistry, and it was intended as a prelude to a post about the ebook I had written and was editing. As you may see from looking at the dates, this has taken somewhat longer than I expected. This book outlines a methodology by which, ignoring minor effects, the chemical bond length and energy for covalent bonds involving only s and p electrons can be calculated often within less that 1% error solely by means of wave properties, the quantization of action, and the electric field coupling at the wave antinode. The only inputs are quantum numbers, the Exclusion Principle, and the number of electrons, hence simple analytical functions are obtained. The procedure uses atomic orbitals that do not correspond to the excited states of hydrogen, and this leads to a previously unrecognised quantum effect, and then counts the number of interactions, and for bonds between different sized atoms, especially hydrides, a wave reflection procedure is proposed that has the consequence that the less the sharing, the shorter the bond. The effects of lone pair interactions and delocalization are presented. A new hybridisation effect is proposed that, in the absence of lone pair back donation, leads to bond lengthening and weakening when n = 3 and 5.
The basis of this is what I call a guidance wave. The concept of this is very similar to the de Broglie/Bohm pilot wave, but it has some significant differences. The wave function ψ is, in all quantum mechanic interpretations of which I am aware, given by ψ = A exp (2πiS/h), where S is the action, and an important point is that action evolves. That means that from Euler, the wave function becomes real at the antinode. I then make the assumption that the wave front has to travel at the same velocity as the particle, the reason being that in the two slit experiment, the diffraction does not depend on the distance to the slits and the particle should get there at the same time. That means the square of the amplitude is proportional to the particle energy and that is why you can calculate the bond properties from any position of the antinode (because the particle can only have one energy). It remains to be seen whether anyone has any interest in this, and the results are not totally accurate, nevertheless a molecule like Sb2 has a bond energy within a few kJ/mol of the calculated value. At the risk of self promotion, "The Covalent Bond from Guidance Waves" is at https://www.amazon.com/dp/B07GCDYDRR
Posted by Ian Miller on Aug 12, 2018 3:53 AM BST
The February edition of Chemistry World had an article on the prospects for life throughout our solar system, and this was of interest because I intend to give a paper at an International Conference on Astrobiology in Rotorua in June. In my opinion, many of the statements in this article were overly optimistic, which raises the question, when would chemical signatures indicate the possibility, even, of life. The problem is, a chemical signal only indicates one thing when the set of possible causes leading to the signal has one element.
The article stated that there were three essential needs for life: an abundance of chemical building blocks (although these were unspecified), liquid water, and an energy source. The article seems to think that heat is adequate for an energy source, but I disagree. I think photons are critical. The reason comes from the thought that one key requirement for life is that it can reproduce. To do that, it needs a functional group that can link the information-carrying mers into a polymer, and that requires two bonds. Such links also need to be able to be hydrolysed, but not too readily. The reason for this is that initially we are going to get random polymerization, and if the consequences are effectively locked away for ever, we run out of raw materials before something sensible appears. Finally the link needs a variable solubilizing ability because to reproduce, there has to be a way to pull the strands apart so they can act as scaffold for new duplexes. (Without a duplex you have no means of transferring information to the new entity.) The only trifunctional linking group that I see as satisfactory is phosphate, which links through ester formation. Further, it is only marginally satisfactory, because divalent cations usually precipitate phosphate. Our modern life forms might be able to use very dilute phosphate solutions, but the initial life forms would not.
The only way I know of that has been shown to lead to adenosine monophosphate (as well as ATP) was powered by light. Accordingly, anything under permanent ice will not get such light. The issue here is not whether life could live there; it is whether it could evolve there. That alone, in my opinion, rules out the ice moons. Equally, if they do have liquid seas, we would expect some weathering of the dust, and the extraction of calcium and magnesium into the waters. That would remove most phosphate from the waters.
A further issue with reproduction is the necessity of having prodigious amounts of reduced nitrogen material. The Saturnian moons avoid this difficulty, as they seem to have or seem likely to have, ammonia in their oceans, if they have oceans. Enceladus has had ammonia detected in its geyser effluent. Europa has an extremely tenuous atmosphere. The most common species are oxygen and hydrogen, which are products from the photolysis of water. Also present are oxygen atoms, hydroxyl radicals, sodium, and at up to five orders of magnitude less common than oxygen, carbon dioxide and sulphur dioxide.  These species are believed to be formed by photolysis of surface ice, or ice fragments ejected by sputtering due to high-energy particle impacts. Despite measurements over five orders of magnitude in concentration in barely detectable pressures, there are no nitrogen species detected. This, at least, is in accord with what is outlined in my ebook "Planetary Formation and Biogenesis": Saturnian moons potentially have nitrogen because they were formed by the coalescence of dust/ice, where the ice had methanol and ammonia within it. By the time the dust got to the Jovian system, the ammonia and methanol had boiled away in the higher disk temperatures.
Accordingly, in my opinion, there will be no life in the outer solar system. So what about Mars? That is a more complicated story.
Posted by Ian Miller on Mar 4, 2018 8:44 PM GMT