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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Before Christmas, I raised the question, how could the ancients have proven the Earth goes around the sun? I guess it is about time to get started on answering it. The first task was to review the literature. It then becomes obvious that you have to overturn Aristotle. There are various places where one can start, but one is to decide why we have day and night. Let us use Aristotle’s own methodology, which is to break the issue down into discrete issues. Thus we say, either the Earth is fixed and everything rotates around it, or everything is more or less fixed, and the Earth rotates. Aristotle had reached that step, and had “proven” that the Earth did not rotate. Therefore the day/night must occur through the sun orbiting the Earth. The heliocentric theory, despite its advantages, is falsified.
 
At this point, we should examine the methodology of the experiment. It is important to recognize that Aristotle was very clear on one point, and he has been badly misrepresented on this ever since. Aristotle clearly asserted that logic must be applied to experimental observations, and that observation alone was critical. So, what was his experiment? Aristotle argued that if you threw a stone vertically into the air, it always came back to the same place. Had the earth been rotating, the path length of a rotation increased with height, in which case the stone should drag back westwards. It did not, so the earth did not rotate. Note that at this point, Aristotle was effectively arguing for the conservation of angular momentum, or even better, the principle of least action. I wonder how many of my readers would recognize that, and know why it is so significant? Before reading any further, what do you think about Aristotle’s experiment? What is wrong, and how would you correct it, bearing in mind you have only ancient technology?
 
In my ebook, Athene’s Prophecy, my protagonist dismisses the experiment by arguing that vertical is defined as the point where the stone falls back to the same place. By defining the point thus, if the stone does not come back to the same place, it was not thrown vertically. He then criticizes Aristotle by arguing that the correct way to do the experiment is to simply drop the stone from a high tower. The reason is that while Aristotle would be correct in that there should be a drag to the west going up, exactly the opposite should occur on the way back down. What should happen if dropped from a tower is that the stone would strike the ground slightly to the east of the vertical position, and in Rhodes, where this was being discussed, also slightly to the south. Can you see why?
 
What happened next is that my protagonist refused to carry out the experiment. This is a somewhat difficult experiment to carry out, but in my opinion, it might be of considerable interest to senior school students, and it introduces them to many of the issues of science that still apply. They need a high tower (or some equivalent), and the first problem is to define the exact vertical spot below it. This is difficult enough to do today with modern surveying equipment, but in those days, the error range is likely to exceed the effect. The school could set this up, with the help of external surveyors, or even physicists if they can find any. The students have to select the right material (a small lead cone, dropped point down without tumbling would probably be optimal) and correct for wind speed. This experiment, more than any other I can think of that is suitable for schools, introduces the concept of experimental error, and they can get illustrations of this because the experiment, in theory, besides proving the Earth rotates, with a little mathematics permits two measurements of the size of the Earth. The answers are likely to be hilarious, unfortunately, once the student confronts the issue of required accuracy. The problem is the difference between the height and the earth's radius, but it may give a new appreciation to the extreme requirements of the large hadron collider, where protons (look up their size) circle a 26 km loop and collide.
Posted by Ian Miller on Mar 2, 2014 8:20 PM GMT
In my last post of 2013, I gave a problem that provides part of the plot of my ebook novel Athene's Prophecy: how could a Roman prove the heliocentric theory? The short answer is, it was not possible for a Roman to do this directly from then current knowledge. This is a fine example of how you cannot get from A to B directly, but have to through some other places first. That would have been possible, but it did not happen. Why not? The question is of interest because it goes to the heart of what science is about, and that is a more difficult question to answer than you might think, because most scientists do not really have the time to consider it.
 
As an example, during my early working time in an institution, only too much was wasted writing proposals, trying to get funding, trying to keep funding, trying to get or get access to equipment, in other words, doing just about anything except science. Then when I was doing science, the most important thing was to get the material for another paper, because failure to produce enough papers meant failure with the funding, etc. What happened to me was exactly what Kuhn argued would happen: I always started a project that I thought had a very good chance of success.
 
So, back to the question of the title. The first problem would be, why bother? Aristotle was generally believed to be correct, and even if he were wrong in something, who cared? The important point was that the then current theory was splendidly capable of predicting everything of general interest, and, more to the point, it "proved" that the heliocentric theory was wrong. The Ptolemaic model was perfectly adequate for calculating and predicting the timing of things of astronomical, agricultural and religious interest. There was no apparent need to change it. This is where I disagree, because the problem lay in an incorrect understanding of dynamics. As a consequence, their wrong dynamics arguably inhibited progress. I believe that if you understand what is correct, you are more likely to make advances.
 
Aristarchus challenged the "fixed earth" model, but he was hardly rewarded well for what he did, and even now, how many people realize he made more progress than Copernicus? The real problem lay in the proof of the fixed earth model, which relied on experimental proof, in which the observations were interpreted in terms of Aristotle's dynamics, and these were just plain wrong, oddly enough because in getting to them, Aristotle abandoned his own methodology and relied on "the obvious".
 
What Galileo did was to show the "proof" was wrong, he undermined Aristotle's dynamics, and further, he showed the satellites of Jupiter did not fit at all well with the model of Claudius Ptolemy. However, telescopes were not available to my Roman, so he had some work to do. In my next post I shall look at the actual problem in more detail, but in the meantime, how many scientists even now ask themselves whether the conclusions they reach from their experiments could be wrong because the theory they assumed in reaching it could be wrong? Obviously much of our theory is very well tested, but is all of it? Our understanding of electromagnetism is almost certainly correct, so our instruments should give us the correct results, but if we go deeper into our chemical interpretations, how much is actually dependent on a hypothesis that is difficult to test?
Posted by Ian Miller on Feb 16, 2014 10:29 PM GMT
This update covers two months and focuses on some compositional issues. Why is composition important? In my theory, initial accretion is driven by chemical interactions, hence material that accretes at different temperatures may have different compositions. The mechanism of initial accretion in standard theory is undefined, but is usually considered to be due to gravitational interactions, in which case there should be no compositional differences, apart from outer bodies being icy. Unfortunately, the following does not show much light on this issue.

One paper involved the formation of the Moon (Nature 504: 27 - 29) The problems here are reasonably simple. Collisional dynamics suggest that which is flung off Earth comprises mainly material from the impactor, and this should have different isotope compositions from Earth, since it appears that certain isotopes varied in relative concentration by some radial function of their location in the accretion disk. However, isotope evidence indicates both bodies came from the same source. Thus the oxygen, chromium, titanium, tungsten and silicon isotope compositions of the two bodies are indistinguishable, which suggests common origin. The answers to this usually invoke extra processes, such as extensive mixing or a later gravitational resonance with the sun, but the feasibility of any of these as explanations is unclear. There are differences in composition between the Earth and the Moon. The Moon has less than 10% iron, and is poorer in volatile elements. The collision theory explains the former in terms of the iron core of the impactor merging with the earth's core, while the lack of volatile elements is consistent with these being lost from a hot disk.  It appears that refractory elements have similar abundance in both bodies. Seemingly, either the Moon formed from material from Earth's mantle, or that the Moon and the silicate portion of Earth each formed from an identical mix. My explanation is that both formed at the same radial distance and hence formed the same way from the same material, the Moon having come from either one or two bodies that grew at the Lagrange positions L4 or L5, and were dislodged when they became too big to remain in those positions. That concept is not original, but my theory makes accretion of solid bodies much more probable at our solar distance. Further, a late-forming body at L4 or L5 would have less iron, because the body, and the outer part of Earth, would form from material that started further from the sun (because it is the last part of material moving inwards).

The second major set of publications was the collection of papers in vol 343 of Science relating to results from Curiosity in Gale Crater, Mars. These results have already been announced, and as far as theories of planetary formation are concerned, these were not very interesting. One point that was of interest was the evidence of water flow and of aqueous leaching. The rover found sedimentary rock, smectites (clays, both Fe and Al rich being present) and calcium sulphate that had been precipitated from water. The evidence is in excellent agreement with the theory put forward some years ago that when an impactor struck Mars and formed a crater, it would also heat the ground beneath it and liquefy any ice. Calculations indicated this could remain in the liquid state for perhaps thousands of years. The water at Gale Crater was estimated to have been liquid for a minimum time of hundreds to tens of thousands of years. Such a short time is consistent with this impact theory, but of course since the measurements were taken inside an impact crater, it may not be relevant to Mars in general.

Finally localized sources of water vapour were detected by far infrared spectroscopy on the Herschel Space Observatory on the dwarf planet (1) Ceres (Nature 505: 525 – 527). This water vapour appeared to have been emitted from localized mid-latitude sources. The cause of the water evaporation could not be determined, but it could be due to either comet-like sublimation or to cryo-volcanism. The amount of water on Ceres is of interest because it might indicate that Ceres did not originate in the asteroid belt. More will be known about Ceres when the Dawn space craft reaches it.
Posted by Ian Miller on Feb 3, 2014 1:59 AM GMT
In my last post of 2013, I gave a problem that provides part of the plot of my ebook novel Athene's Prophecy: how could a Roman prove the heliocentric theory? Before doing that, however, I have to go on a diversion to discuss how you actually prove a theory. Yes, I know, you usually see people write, you can never prove a scientific theory; all you can do is falsify it. That is actually wrong. Let us suppose you have a theory A that predicts the set of observations P if experiment E is carried out. Equally, we could have theory B that predicts the set of observations Q if experiment E is carried out. We carry out E and observe O. There are several possibilities: O can be an element of either P or Q, or of both, or of neither. If both, the experiment is irrelevant in terms of being definitive, if neither both theories are wrong, and if one but not the other, the other is wrong. Under this circumstance, no theory is proven. To prove a theory, it must be of the form, if and only if theory A is correct, then we shall see the set of observations P if experiment E is carried out. The problem, of course, is to justify the "only if" part, so that is what has to be done by my Roman to prove the heliocentric theory.
 
In practice, there is more to it. The first step to overturning a theory, which is what had to be done here, is to review the literature. Personally, I find classical science to be quite interesting because it shows some very interesting issues that apply today just as then, and further, if you look carefully, what we read today about the ancients is really not fair to them, and in the next series of posts, I hope to illustrate that point.
 
Now, there are two ways of reviewing the literature. The first is to read what is there, accept it, and try to work out how to develop what from it. I believe that is the common practice today and most scientists are quite happy to accept the literature explanations and use them to solve more puzzles, in the spirit of Kuhn's "normal science". The second way is to deeply question certain issues, to be sure the theory is on sound ground. In my opinion, this is done only too infrequently. How many current scientists have ever really questioned something of fundamental nature given by authority? Throughout history, everybody seems to think "they are on the right track". We know classical science was not, but how many think we are currently more or less correct? Quantum electrodynamics is regarded by many as the most accurate theory ever in science, but it can be regarded as a subset of quantum field theory. The vacuum energy predicted by quantum field theory appears to be wrong by a factor of at least 10^107. That is an enormous difference, in fact one could say it is well outside any experimental error! But how many scientists actually think quantum field theory might be wrong in some way? More importantly for you, how many theories or explanations in chemistry have you ever thought could be wrong? If the answer is more than zero, what did you do about it? Why not?
 
That last question gets to the heart of the matter: the reviewer has to have an urge to overturn something. The "official" line is, that urge is provided by observations that do not fit the theory, however I think that is wrong. The vacuum energy error mentioned above is an example. The fit with theory is appalling but there is no attempt to overthrow the theory because quantum electrodynamics makes some absolutely remarkably accurate predictions elsewhere. When the theory works much of the time, as Kuhn noted, awkward results tend to be placed in the drawer and forgotten. The average scientist does not wish to overturn the apple cart. The reason for not wishing to do this are clear: most of the time he believes he will not get anywhere, and spend a lot of time not getting there. Einstein spent over fifteen years trying to get relativity in order, and how many scientists have his ability? With promotions, funding and general standing in the scientific community at stake, who wants to spend years not getting anywhere, getting publications rejected, or being regarded as a curiosity? In classical times, the problem would have been worse because if you succeeded, who would care? People work for reward, and for most scientists, reward means, acknowledgement by your peers. You do not get that by trying to show they are wrong. In classical times, most of the time you had no peers. Archimedes made his discovery not to unravel nature, but to solve a problem given to him. There would be no reward for a Roman to prove the heliocentric theory, because current theory did everything that was required of it.
 
Finally, I promise I shall get to the issue, but not next post, because it is time for a review of planetary formation theory.
Posted by Ian Miller on Jan 27, 2014 1:20 AM GMT
A Happy New Year to you all. In my last post of 2013, I gave a problem that provides part of the plot of my ebook novel Athene's Prophecy: how could a Roman prove the heliocentric theory? I shall give the answer in due course, but in the interim I commented on another post that I would start a discussion on how to get an idea so here goes. I should mention that I intend to follow the procedure of my first ebook, Elements of Theory 1, and the example I am going to use, that of the 2-norbornyl cation, had a chapter in that devoted to it, and I suggested an answer. The example has gone on through my chemical career: the non-classical carbenium ion.
 
What is the first step in having an idea? In my view, identifying a reason to have one. If you are satisfied that all is well, your brain will not devote time to the problem of what if it is not well. So, let me start on this non-classical ion. In Chemistry World (August, p 20, and January 2014, p 26) we see that a German group had isolated the ion and found that it was symmetrical. As Chemistry World put it, "Case closed!" Or is it? Recall that in "The Hitch-hiker's Guide to the Galaxy" the final answer was given, but what was the question? My first point is, if you accept the "Case Closed" situation, you will never have a contrary idea because you are not looking for one. The first step is to recognize you need it. This must be closely followed by the asking of questions of what you know.
 
The original question regarding the non-classical 2-norbornyl ion was clear: why did the exo 2-norbornyl derivatives solvolyse much more rapidly than the endo derivatives? Accordingly, the first question is, is this symmetrical ion pertinent to the original question? It is reasonably obvious that Chemistry World thinks so, but let us ask a further question:  if the activated state is the fully developed carbenium ion, then how does exo and endo give dramatically different rates of solvolysis, because the substituent is now lost? If the activated states for exo and endo derivatives are different (which they must be to get different reaction rates, unless our concept of reaction rates is entirely wrong), then in what way, and why? The why would appear easiest: in the activated state the anion has yet to fully leave. Another question: how can a species on an energy maximum be isolated and live long enough to have its nmr spectrum measured? The answer to that question, surely, is that the carbenium ion must be in an energy well, not at an energy maximum. If so, under standard activation theory, the energy maximum is before the fully developed ion forms, in accord with the previous conclusion that the anion is still present.
 
Thye next question is, was there any pertinent evidence to question whether the activated state was a partially developed symmetric ion? The answer is, yes there is. In the symmetric ion, C1 has an equal exposure to the positive charge, but Brown had shown by substitution that in the activated state there was no particular positive charge at that site, and that was his biggest point against the "non-classical ion". Now, back to the question, how to have an idea? The activated state is now defined as having the leaving group to have partially left. What does that mean? Surely there is a significant dipole between C2 and the leaving group, along the bond axis. The partial positive charge is located at C2, not at C1 (by substitution data) with C6 unclear at this point. The next question is, what mechanism can conceivably stabilize this system and not be available to the endo substituent? That requires you to think about all the possibilities available, and list them. There are not that many. The answer to that, in my view answers, the question, and the case is not closed by the existence of a symmetric ion, as previously claimed. That does not mean the determination of the symmetric ion is wrong, but rather that while it exists, it does not actually answer the original question.
Posted by Ian Miller on Jan 20, 2014 1:39 AM GMT
At the end of the year it is traditional to survey the major events as seen by the surveyor, but I must confess that this year struck me as one in which, for chemistry at least, a massive amount of data was added to the literature, but there was little that really grabbed my attention. This may say more about me than the year.
 
One example that struck me was Curiosity rover on Mars. What struck me the most was that everything we have heard so far is more or less what we might have predicted. The dust has the same composition as dust analysed elsewhere, the rocks were the same basalt as seen elsewhere, there was evidence of water, but the evidence was more or less what would have been predicted. So what is the problem? For me, if you send the same set of instruments, you will get the same set of results, and the instruments are designed to be sure to get results. There will be no gene sequencing equipment because we do not believe there are genes to sequence. Nevertheless, do we really need more billion dollar dust analyses? Could the money have been better spent? Worse, there was evidence of organic material, but only because we detected carbon dioxide, methylene chloride and chloroform after pyrolysing the sample. What does that tell us about Mars? (Other than there is a strong oxidizing surface and chlorine present, which we knew.)
 
Another recent event was that in Chemistry World, the question of why chemists are more likely to be climate sceptics was raised, and the answer – chemists are ornery. At the risk of being labelled ornery, perhaps I should mention that I am sceptical, but not about the planet being warming. I am sceptical about the relevance of computations, and of the effectiveness of politicians. Regarding the modelling, models consistently state that as the climate warms, Australia will get progressively drier. The trouble is, observation says that rainfall at Alice Springs has actually increased steadily since about 1930. Regarding effectiveness of politicians, gas emissions are steadily increasing. Carbon trading might seem a solution to economists, but is it not just another excuse to generate paper, and derivatives, and make lots of money?
 
Finally, this will be the last post for the year. (As a partial ex-seaweed chemist in the middle of summer, the beach calls!) However, I should leave readers with something to think about, especially those buried in the depths of winter. In my view, science is not about generating data, although that is necessary, but rather it is about drawing conclusions from them. So, a quick commercial and a problem. I have also published at Amazon some fictional ebooks in which I try to show something about science, and the latest, Athene's Prophecy, has this problem: a young Roman soldier must prove the heliocentric theory. He starts by reviewing the literature (as available in the first century) he does a couple of experiments to correct one of Aristotle's mistakes (Aristotle did not apply his own methodology twice!) but then he has the problem: how can he prove the Earth goes around the sun with what he could see? Could you? Try it over the festive season. Meanwhile, I shall post again in mid January.
 
Merry Christmas to you all, and may the molecules behave as desired through 2014.
 
Posted by Ian Miller on Dec 16, 2013 12:54 AM GMT
In my new ebook entitled Guidance Waves, An Alternative Interpretation of Quantum Mechanics, I wrote in the introduction, . . . you to tread a path that differs from the well-trodden path. Your friends will shake their heads in despair, as if to say, "What are you doing going off there?" Don't you hate it when you are right? What inspired that is that down in this part of the world we have just completed the NZIC Chemistry Conference, and at the first morning tea (and let's face it, the real benefit of conferences lies in the conversations over tea, lunch, etc) one of my oldest friends asked me what I was up to, so naturally I told him about my alternative interpretation of quantum mechanics. There was the predictable smile and the shake of the head. So why? I followed that in the ebook introduction with This is a real problem regarding quantum mechanics, because when calculations based on the Schrödinger equation always give agreement with observation, the main path is "obviously correct". The question is, is it "obviously correct"?
 
First, I must say at once that I do not dispute the Schrödinger equation; what I dispute is what it means. One of the examples I give is the particle in a box with walls with infinite wave impedance, and where the walls are close enough together to require a clear zero point energy. Let us restrict it to the one dimensional box, in which case you get a wave with one antinode in the centre and two nodes at the walls, which is the classical stationary wave. The particle now has a zero point energy because the Schrödinger equation requires the particle to have motion; it cannot be stationary with respect to the box walls. So, the motion now must go along our chosen axis, and it must go equally in each direction, averaged over sufficient time. Now, the question is, how does the particle turn around?
 
What you will initially think (and there is no evidence to suspect this is incorrect) is that it will strike the wall and bounce back – a fully elastic collision. However, that cannot happen within the Born interpretation, the reason being, the probability of a particle being at a point is proportional to the square of what I call the wave displacement (the amplitude is the displacement at the antinode). Now, at the wall there is a node, which by definition has zero wave displacement, so the surface of the wall is the one place the particle cannot be. The same argument comes through, say, the ground state of the valence orbital of the caesium atom: how does the electron cross the nodal surfaces? You cannot go from positive to negative without going through zero, and the square of zero is always zero. I would be very interested to hear a lucid statement on that point within the Born interpretation.
 
Leaving all that aside, I should add that the conference was, in my view, a success, and it showed conclusively that chemistry is not only alive and well in this rather remote part of the world, but it is also vibrant, as shown by the number and enthusiasm of the younger chemists. Finally, a reminder that the promo mentioned in last post starts this coming Friday.
Posted by Ian Miller on Dec 9, 2013 3:01 AM GMT
There were three papers in November that pleased me quite a bit because they gave additional support to my theory of planetary formation. The first (Earth Planet. Sci Lett. 385: 110) examined the Se and Te systematics of mantle derived peridotites on Earth, and showed that the ratios are not consistent with melt depletion alone. The results indicate no firm evidence for chondritic S-Se-Te signatures in the primitive upper mantle, which challenges the simplistic perception that near-chondritic Se/Te ratios may readily trace the Late Veneer composition. This is of importance because these ratios are often cited as "proof" of a massive late accretion of chondrites, which would be the source of the volatiles on Earth. In my opinion, the volatiles were accreted by other means, and it is good to see the "opposition view" have its main evidence removed. The second (Nature  503: 513 ) showed that a meteorite from Mars is a regolith breccia with zircons of an age 4.428 + 25 My. The evidence implies that Martian crust formed in about the first 100 My of Martian history, which in turn implies no magma ocean. The magma ocean is a requirement of the standard theory where massive embryos collide to form protoplanets, and the inherent gravitational energy would provide so much heat that a magma ocean is inevitable. If no magma ocean, then a different mechanism of formation is required. Finally, (Planet. Space Sci. 87: 130) a trough within Noctis Labyrinthus displays a diversity of hydrated minerals and fluvial channels, including opal, Al clays, gypsum and polyhydrated sulphates., and furthermore, these different minerals had to be laid down under different conditions. Accordingly, there should have been several periods of aqueous alteration.
 
For those interested in seeing more of my theory of planetary formation, Planetary Formation and Biogenesis will be available for 99 cents  as a special promo on Amazon.com (and 99p on Amazon.co.uk – these are the lowest prices permitted on each case) on December Friday 13, and the prices increase daily for about 5 days until they reach normal price. Also on the promo is my novel Red Gold, which is about fraud during the settlement of Mars.  This ebook was written in the early 1990s, and to expose the fraud, a surprising discovery was required. The surprise was the discovery of what remained of the Martian atmosphere, which provided the nitrogen fertilizer necessary to make the settlement viable. The very first version that led me to the theory in the first book is outlined in the appendix, so this is one of the very few examples of how a theory got started. How important this is depends on whether the theory is correct, and I would love to know the answer to that one.
 
As an aside, that is the main difference between the experimentalist and the theoretician. If the experimentalist gets the wrong idea, the evidence usually (but not always) becomes evident quickly, such as when the wrong result is obtained. For the theoretician, the required evidence may not be easily obtained, and he is kept in suspense for some time. Thus Peter Higgs had to wait from the mid 1960s until now. At my age, I cannot afford that time, so I probably will never know for sure. Of course, I am convinced!
Posted by Ian Miller on Dec 2, 2013 4:32 AM GMT
The biggest alternative interpretation must surely be of quantum mechanics. So far there are at least three major interpretations, (Copenhagen, pilot wave, many worlds) with variations, but that should not let that deter one should it, after all, who understands quantum mechanics? After more than a little tiring effort, I have finally self-published an ebook on my alternative interpretation of quantum mechanics. (If interested, see http://www.amazon.com/dp/B00GTB8LJ6 ). Why self-publish as opposed to publish a series of papers? There are a number of reasons, not the least of which is that any part of the foundation of the theory that could be condensed into a paper is not very convincing by itself, whereas any of the applications of the interpretation without the underlying foundation is more difficult to understand. There are further reasons, including at my age there is a desire to get this out rather than argue with a sequence of referees.
 
How can there be a yet another interpretation? Actually, quite easily. We start with the Schrödinger equation, from which we get a wave function. The wave function is a complex function, correct? Well, not entirely. If you take the standard wave function as seen in fundamental text books, and consider this from the point of view of Euler's presentation of complex numbers, then the wave function becomes real at the very extremes of the crest and trough of the wave. The first significant difference of this interpretation is the assumption that the wave only has physical effect on the particle when it is real.
 
If that assumption is correct, then it follows that the phase velocity of the wave has to equal the expectation velocity of the particle, so that the two can be in roughly the same place at the same time. That gives a further relationship, from which the square of the amplitude must be proportional to the kinetic energy of the particle. Since energy is proportional to mass, it follows that the probability of finding the position of a particle will roughly follow the Born interpretation. It does not quite, but that is a detail.
 
If this interpretation is correct, then all the results of the two-slit experiment follow (and a further experiment is proposed that will give a rather unexpected result), the reason why an electron does not spiral into the nucleus of an atom as expected from Maxwell's relationships follows by following Maxwell's relationships! The Uncertainty Principle and the Exclusion Principle are now derived. But the real great advantage, from my point of view anyway, is that you do not have to solve differential equations! The only physically real picture is when the action is quantized, i.e. occurs in some numbers of Planck's quantum of action. First order computations for simple systems merely require counting. The basics of chemistry are simply obtainable by requiring the quantization of action over the sum of separable components. More on this in later posts, but one final comment. Assuming I am correct, obviously action is a very important concept, but how many chemists know what it is? When is it mentioned in undergrad courses in chemistry?
 
So, why am I tired? Ever tried compiling an ebook with mathematical symbols? If you do not use Unicode (Universal code) symbols, and Microsoft Word frequently does not, almost anything can come out. And the problem is, in some cases you cannot work out whether the symbol is Unicode or not. Also, you might imagine there would be one Universal code, right? Sorry, no. And, apparently as the versions change to adopt new symbols, old ones drop out, but not all of them. Some sort of standardization would be good!
Posted by Ian Miller on Nov 25, 2013 1:25 AM GMT
The recent Chemistry World highlighted a recent publication on astatine, in which the paper predicted that due to relativistic effects on the inner electrons, it would be metallic and monoatomic in the solid state. As some may recall, in previous posts I have questioned such relativistic corrections since I had previously published a paper (  http://www.publish.csiro.au/nid/78/paper/PH870329.htm) in which I showed that ionization energies and lower excited state energies could be related through reasonably simple relationships involving quantum numbers. In this, the s electron of gold was actually more "normal", if that means agreement with the required relationship is better, than either copper or silver.
 
The reason I regard astatine as annoying comes from this consideration. In my paper cited above, the ionization potentials of valence electrons could be calculated from simple relationships involving only quantum numbers when there was only one electron in the level, while an additional term was required for others that approximated to a term only in the quantum number , but in practice was better with a minor empirical correction for each group. The important point was that this term was constant for a given column of elements in the periodic table, and there are relationships between groups. (This term is conceptually due to additional quanta of action being generated through the waves exploring all available space, and attenuates as increases because the number of orbitals to explore increases the number of cycles before the required quantum of action is completed. This lies outside standard quantum mechanics, and I shall elaborate my alternative interpretation in future posts.) Now, in principle if my alternative interpretation is correct and relativistic correction is not required, the ionization energies of the elements I did not calculate should still be given by the published relationships. (I regard the equations as predictions, even if I did not evaluate them.)
 
The relationships were not exact. There were two unexplained small regularities. The first involved a small term (st for this post) the sign of which depended on whether n and were odd or even, the magnitude of which increased with the distance from shell completion. There was also a positive term (+T for this post) that applied only to paired p electrons following d shell completion, thus Se, Br, Kr, then Te, I and Xe all required +T, as did Po. Recently ionization potentials have been measured for At and Rn, so how do my functions perform?
 
The prediction for astatine, with +T was 9.7606 ev; without it, 9.1893 ev; the observed value is 9.3175 ev. What should I make of that? Suppose we consider radon. Without +T, the predicted IP is 10.7457 ev; the observed value is 10.747 ev, which in my view, is fairly close, so my obvious conclusion is that there is some interaction with the d electrons that applies to Po when n = 6, not for Rn, and annoyingly, somewhere in between for At. In my opinion, admittedly somewhat biased since I am supporting my own theory, this would indicate that if the "non-hydrogen-like" wave functions are correct, there is no need for relativistic corrections here. Finally, it may be of interest that the IP of Fr is predicted without st to be 3.903 ev; the observed value is 3.938 ev.  These calculated values are based solely on the wave nature, without any terms for interference with other waves or resonances. The value of st required for Fr is of very similar magnitude to that for Rb and Cs, except that Cs is of opposite sign. Then, to confuse everything, the ionization potential for radium is such that some further effect might be operating, and that could be relativistic in origin.
 
What relativistic corrections are suggested? In one account (Chem. Rev. 112: 371-384) without relativistic corrections, the ionization potential of gold was 7.057 ev, and with it, 9.147 ev (observed, 9.2254 ev). Thus it would appear that contraction of the inner orbitals adds over 2 ev, and this should increase as the charge on the nucleus increases. I am sorry, but for me, this does not add up.
 
Perhaps chemistry would solve this issue? My calculation of the bond distance in At2 is 150 pm, and the bond energy of hydrogen astatide is 273 kJ/mol. Would that settle the question? Perhaps, but annoyingly I can't see the data coming any time soon because the most stable isotope of astatine has a half-life of 8.1 hrs. 
Posted by Ian Miller on Nov 18, 2013 4:28 AM GMT
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