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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I apologize for the font-size in the last post. This was done from my laptop while on vacation, and for some reason, with different software, I got the wrong outcome. Sorry.

Let me now revisit my first paper for the last time. This paper was cursed by the referees: they accepted it without comment! Nevertheless, it is a paper that is an example of how not to publish a new concept, and it might be of help to young chemists to consider these errors, so as not to make them themselves. For those interested in the paper itself, see Tetrahedron 25 : 1349-1360 (1969).

The first error was that I put both the strain formulae and the means of explaining the dipole moments into one paper. I should have submitted two. The reason is, with two points to make that may be of value to different audiences, one of the points will be embedded in the paper, and the audience for that paper will never find it. I did not wish to be accused of not having enough material, or of unnecessarily trying to increase my publication count. That is silly thinking. There were a number of other papers out there relatively short on substance, and in any case, if both papers were submitted at the same time, let the referees/editor suggest merger.

The second error was that I did not state clearly, separate from the rest, what I had found. The basic point was that the changes of dipole moments were caused by enhanced electron density over normal alkanes, and the "compression" of the electron cloud present was proportional to the work done "compressing" the electron cloud. I relied on the fact that someone would follow what I had done by reading the paper, and by drawing the obvious conclusion from the table, but that is not good enough. If you want to persuade an audience, say it in the abstract, start the introduction with why you have to say it, say it in detail in the text, show it in the table, and say it again in the summary.

The title, "Ring strain and the negative pole" was, I thought, clever, because it related ring strain to the polarization field in the shortest space. Advice to young scientists: if you think of a clever title, try it out on some other scientists and see what they think. It may merely make them shake their heads!

Perhaps the biggest mistake was that I failed to explain fully what I was doing. The last thing I wanted to do was irritate "the real chemists" by labouring the obvious. What I did not realize was that what was obvious to me was not necessarily obvious to anyone else! I had taught myself physics, and I had bought the cheapest suitable books, which happened to be produced by Mir publications in Moscow. What I had not realized was that what was considered to be interesting additional information in Moscow was simply not present in the more expensive western textbooks. (I do not care what anybody says; for me, Landau and Lifshitz’ Mechanics is still by far the best book for learning about Lagrangian mechanics.) Accordingly, I assumed any physics in a textbook I could follow was well known, and I did not want to be accused of padding the paper with trivia. I thought that taking a divergence of a polarization field to get a pseudocharge (the pole) would be obvious. Obviously I should have said exactly what I was doing, but I was young and unguided. Worse, I did not want it rejected for being too long, which, of course, was all the more reason to submit two papers. I suppose also I was rather pleased with myself for finding a way to get an analytical solution that avoided insoluble partial differential equations.

So what happened? Apparently some chemists thought I was generating charge, which violates a variety of conservation laws. Of course I was not: I was merely trying to give an easier way of putting a numerical cause to the changes in the electric field that must arise when energy is stored in it. Since my undergraduate training in chemistry had given me no enlightenment to Maxwell’s electromagnetic theory, I should have realized it was wrong to assume everyone else would understand.
 
So, I hope young chemists might find something helpful from this. If nothing else, try to get someone else to read your paper and tell you what you said. That way, you will know whether it is comprehensible.
Posted by Ian Miller on Feb 17, 2013 10:18 PM GMT

As outlined in a previous post, my PhD  results meant that I had to find a way to account for the strange properties of the cyclopropane ring without invoking conjugation. What I came up with was to account for them through a polarization field that was generated through the work done moving orbitals towards the centre of the strained ring. Thanks to the dimensional equivalence of a polarization field and a displacement field, and thanks to Maxwell’s electromagnetic theory, I could represent the movement of charge (the real cause of  the polarization field) in terms of the addition of a pseudocharge to orbitals that had not moved (equivalent to a change of displacement field). I could do that similarly with increased charge density, and the reason for doing this was that it permitted a known solution to the partial differential equations, with only one constant required to be set. I used the electric moment of cyclopropyl chloride to set that constant, and hence the pseudocharge. Now, the question was, would the same pseudocharge properly account for the stabilization of adjacent positive charge?

 

The cyclopropylcarbinyl cation was known to be stabilized compared with corresponding alkyl cations through studies of solvolysis of tosylates, etc, but these studies were of lesser value because there was the problem of solvation energies. There was also an issue that the cyclopropylcarbinyl cation is also unstable and promptly rearranges. (This is the famous bicyclobutonium "non-classical" carbenium ion.) Substitution can stabilize it, but that adds complications. Then, luck! Well, sort of. The stability of the cyclopropylcarbinyl cation was published in a PhD thesis, and reported in some books on mass spectrometry, but for some reason it never seemed to have made its way into a paper. Someone else was having trouble getting supervisors to publish! 

 

However, I had a reported value for the gas phase cation and I could use my pseudocharge to calculate the energy of the interaction of such a polarization field with the cationic centre. Obviously, this would be a fairly crude calculation, and there would be a number of minor effects overlooked, but I needed to know whether I was even in the right ball park. To my surprise, the agreement with observation was very good.

 

Of course, there was an easier way of doing this calculation. If the strain energy arose through charge in orbitals moving closer together and thus raising repulsive energies, and if four of the six moved closer to the substituent, then the cationic charge would neutralize the repulsive energy on these, hence the maximum energy of interaction with adjacent charge would be 2/3 the strain energy, plus any additional standard stabilizations that would occur in any carbenium ion. However, as far as I was concerned, the triumph was that the same value of my pseudocharge gave correct values for a completely different type of observation for which there was no obvious relationship other than the proposed theory. Being young and inexperienced in the ways of the world, I  thought I was making headway.

Posted by Ian Miller on Feb 10, 2013 8:54 PM GMT
January was mainly a good month for my theory of planetary formation because two papers were published that strongly supported two of the proposals in my ebook that are not generally accepted. There was a third paper that is also highly relevant.
 
The first relates to where the volatiles of the rocky planets came from. There are two propositions that are usually debated: the volatiles were delivered by comets, or by chondrites. A review written by Halliday (Geochim. Cosmochim. Acta, 105, 146-171) showed the ratios of H/C/N are inconsistent with any ratio of these. All my review could do was to say that only minor miracles would permit some combination, but now even minor miracles are ruled out. My argument is that the volatiles were accreted chemically along with everything else, and the different ratios of volatiles on these planets arose because the materials from which they were made originated in different temperature zones.
 
The second paper was even more important, although I am not quite sure the authors themselves appreciated the full impact of what they discovered. One problem for planetary formation is, when the planets start forming, they form in a disk full of gas, so the question is, why do not the planets head towards the star? They are, after all, orbiting in the equivalent of a stellar "atmosphere". There are a number of papers written on this, but they generally lead to all planets ending up close to the star. What I proposed was that because the gas is falling towards the star and the azimuthal velocity is less than the Keplerian velocity at that distance, a pressure wave builds up in front of the body. That would normally cause the orbit to decay, but because there are solids in the gas, and because the gas has definite radial velocity, the planet starts spinning up, as if rolling around its orbit as material with an inwards radial velocity is accreted on the leading face. All the giants do this, although Uranus provides a problem. The body then drags gas down across its leading face, and when it becomes more gravitationally significant, it holds onto some and drags it around to its starwards side, where it strikes gas coming the other way (in its sub-Keplerian orbit). Two gas streams flowing in opposite directions cancel their velocities, in which case the gas will stream towards the star, gradually merging into the more general flow. The original angular momentum lost must be conserved, and only the orbiting body can take it up. By gaining angular momentum, it tends to move away from the star, thus offsetting the expected orbit decay.
 
The paper that excited me was due to Casassus et al. (Nature 493: 191-194). What they did was to observe the star HD 142457, which is still in the late accretionary stage, and they found two filaments of gas streaming inwards with a radial velocity greater that the azimuthal velocity by approximately 10% or greater, and further, the flows in these filaments were approximately equal to the rate of stellar accretion. It gives a surprisingly pleasant feeling to find what you predicted, as much out of desperation as anything, actually turns up.
 
There have been a variety of estimates of how much gas is present in the late stage of stellar accretion. This is important because our planetary system requires about 1% of stellar mass, and previous estimates varied by about two orders of magnitude, with only the higher end having sufficient material. In my ebook, I assumed an average, hence I required initial planetary accretion to commence earlier.  The third paper (Bergin et al. Nature 493: 644-646) provides a new means of estimating the mass in the disk by using the emissions from hydrogen deuteride, and from observations on TW Hydrae, which has a disk between 3-10 My old, the disk contains 5% of the stellar mass, which the authors state is easily enough to form planets. As it happens, this system has been reported to have a planet of about 10 Jupiter masses rather close to the star, the star continues to accrete disk gas (For TW Hydrae, approximately 1% of gas per My), and after a period, the great bulk of this disk is blown away by a stellar outburst. Further, as Casassus showed, planetary accretion must be highly inefficient if planets throw gas inwards instead of accreting it. Accordingly, I think that the odds favour my concept that planetary formation must have started earlier. Either way, though, this evidence strongly suggests that planets are more likely to form around stars than not, so the probability that we are alone in the Universe has probably just got a lot lower.
Posted by Ian Miller on Feb 3, 2013 11:00 PM GMT
From the material in the two previous posts, I now had the concepts necessary to address the issue of cyclopropane interactions with substituents. I now had to select something to apply them. What I chose was the problem of why the dipole moment of cyclopropyl chloride was about 0.4 D less than an alkyl chloride. This was important for two reasons. The first was that the generally accepted viewpoint was that this was evidence for back-conjugation, indeed it was the only evidence for it. The second was that following classical electrostatic theory, increasing the charge density on the cyclopropane ring should repel electrons, and if my concept was correct, at first sight the dipole moment should increase. On the other hand, there was a serious reason why that classical thinking must be wrong: the dipole moments of methyl acetylene and propene, where the former was approximately twice the latter. How could that be? Conjugation did not seem to be correct here.
 
My answer invoked quantum theory, albeit a version a little at odds with the standard version. I proposed that the wave function can be factorized. (According to the State Vector formalism, it cannot!) The key is that the stationary state is determined by quantized action, which requires that the frequencies in the bond zone cannot lead to destructive interference with components outside the overlap zone, and recall, p orbitals have two lobes, only one of which overlaps. If so, when the electron density increases in the cyclopropane ring, the electron density in bonds to substituents must correspondingly increase close to the cyclopropyl carbon atom. The "back donation" was not from lone pairs, but was simply movement of charge distribution in the bond from the substituent. Interestingly, nuclear quadrapole coupling parameters indicate that there is a small but axially symmetric movement of charge towards the cyclopropane ring. Such was the power of the current paradigm, this was interpreted as indicating conjugation equally from both p orbitals. That, of course, violates all other theory of delocalization of wave functions. (Incidentally, in all reviews, textbooks, etc, this difficulty is avoided by omitting all reference to these nuclear quadrapole parameter data. We cannot have observation getting in the road of a good theory!) Anyway, as far as I was concerned, I had worked out an answer to the key problem of the dipole moment of cyclopropyl chloride.
 
The problem now was to put numbers to it. Returning to my argument that the increase in charge density due to strain is mathematically equivalent (at least in terms of the equations I intended to use) as adding a pseudocharge to the original framework, I could use cyclopropyl chloride to fix the value of that pseudocharge, (via a value for the minor radius of a torus on which the pseudocharge was placed) then apply that to a number of "strained" systems. The change in dipole moment should be equal (so I thought) to the change of dipole moment generated by adding the pseudocharge to the neutral ring. I got almost exact agreement for methyl acetylene (0.75 D) and propene (0.36 D) and close agreement for methyl cyclobutane (calc. 0.07 D, measured 0.05 D) although I overestimated the dipole moment of methyl cyclopropane. Nevertheless, I felt I had achieved something. I had explained why the lower dipole moment of cyclopropyl chloride did not necessarily indicate conjugation, which should have been self-evident from the dipole moment of methyl cyclopropane, and I had an estimate for the source of this polarization field.
 
More interesting, in my opinion, this requirement that action be quantized (a general requirement for quantum theory) and the requirement that all parts of the wave have a common frequency is one of the best ways of considering electronegativity. There is what I feel is a very important point here: in classical physics, increasing electron density in part of a molecule would tend to repel additional electrons. Because of the quantization conditions that fix the wavelengths of stationary waves, it attracts them, which is why fluorine is so electronegative. Thus in my interpretation, electronegativity is determined by the electron density about the atom, and in the bond, the dipole moment gives a measurement of the electronegativity. As you can see, that is not exactly a standard interpretation! You, the reader, understandably, will not be convinced, nor should you be. All I ask is, bear with me. In future posts you will see that this goes somewhat further than you might at first think.
Posted by Ian Miller on Jan 28, 2013 1:42 AM GMT
My next problem was that I needed a means of estimating strain energy for molecules. For cyclopropane, I could have used observed values from heats of combustion, but I wanted something for general strained molecules. It may be of some interest to see how I arrived at what I did. Assume a standard carbon-carbon single bond. Now, put the rest of the molecule in place, and consider the bent bond model of Coulson and Moffitt, Phil. Mag. 1949, 40, 1-35.) As the extra parts of the molecule are put in place, the electrons in the chosen bond move outwards, approximately to some fraction of where the orbitals would intersect if all bonds are sp3. Now, as a first guess, I put the strain energy as being proportional to the displacement from the C – C bond axis, which is proportional to sine theta/2, theta being the total deformation of the bond angle from the tetrahedral angle. (With two bonds required to make an angle, the total deformation is divided evenly between the two orbitals. The energy is force times distance, so I started by assuming a constant force as deformation progressed.) This was really more a first guess, but I was hoping the difference DELTA between observed and calculated would help me guess the manner in which the force varied. What surprised me was that this almost worked, and it worked even better if I divided by [square root (bond distance)]. Also, if I used the bond energy scheme of Cox and Pilcher (Thermochemistry of Organic and Organometallic Compounds.  Academic Press: London, 1970) it also correctly calculated the "strain energy" of ethylene and acetylene! Two membered strained rings, and fused two membered rings! Since DELTA was < 10 kJ/mol for every molecule for which I had data, and usually significantly better, I was then happy enough to use this as an empirical relationship for estimating the strain energy of a number of molecules for which no determination had been made. As an aside, this relationship gives a very large strain energy for tetrahedrane, greater than that of the strength of a carbon-carbon bond. Of course that does not mean that tetrahedrane cannot be made, because simply breaking a bond leaves the great majority of the strain still there.
 
There is clear evidence this had little effect on the scientific community. In 1984, Dewar (JACS 106, 669-82) produced an argument that, since bond bending was simple harmonic, the strain energy would be proportional to the square of theta/2, or maybe theta, which gave an enormous value of DELTA. However, molecular orbital theory showed that this energy was greatly reduced by something called sigma conjugation, and sigma conjugation exactly offset DELTA. Then, in 1985, Cremer and Cracka (JACS 107, 3800-3810, 3811-2819) announced that Dewar had the wrong force constant, and his enormous strain energy should be reduced by approximately 100 kJ/mol, leaving only a huge DELTA. But not to worry! Revised molecular orbital calculations showed that there was sigma conjugation that exactly offset this new DELTA. Two computations, using what purported to be the same methodology, got exact agreement with observation, despite the key term differing by 100 kJ/mol. How could that be? Of course, there was no mention of my work, which argued that the whole argument was spurious because there is a very big difference between the square of an angle and its sine. If I were correct, there is no huge discrepancy to explain, and no sigma conjugation.
 
Of course, when I wrote my paper, there was no thought of sigma conjugation. But the question I now have to ask myself is, should I have put this strain formula in a separate paper? On the plus side is the argument that a paper should really make only one point, and ideally the whole point of the paper can be summarized by a single statement. This makes it easier to find, particularly then when "finding" was done by reading journal contents pages, and later through Chemical Abstracts. On the negative side, and what swayed me at the time, was the thought that a complete argument should be in one place. There was also the worry that the strain relationship alone may not have been sufficient to get into a reasonable journal.  Whatever the validity of either argument, the fact of the matter is, I put the strain relationship into the middle of my first paper, and I doubt many people even know about it. 
Posted by Ian Miller on Jan 21, 2013 1:51 AM GMT
I received my PhD, but I never heard from supervisor again. He wrote up a paper (published 1969) on the amine dissociation constants and rate constants, which also reported the synthesis and properties of some new compounds, but with no amines with mesomeric withdrawing ability, he ignored the issue of conjugation. As far as I am aware, he ignored the acidities in toluene, which was really his only contribution, and which gave a critical answer but one that conflicted with the emerging consensus. Make of that what you will.
 
In the meantime, I was determined to write up my theory, which had to show how certain effects could occur without cyclopropane having delocalized electrons. The two main observations to explain were the reduced dipole moment of cyclopropyl chloride, and the stabilization of adjacent positive charge. How to go about it? The first objective was to show qualitatively how these effects could be generated.
 
If I take an electron at a distance x from a proton and move it to y, where is the energy stored? In my interpretation of Maxwell's electromagnetic theory, it is stored in the electric field. Accordingly, the stabilization of positive charge adjacent to a cyclopropane ring compared with charge adjacent to a standard aliphatic hydrocarbon fragment can arise simply from the charged site receiving a stronger negative electric field. My qualitative argument to get such a field involved the strain forcing the charge in four of the orbitals around the distal atoms to move closer to the source of charge, while there was little effect from the two geminal orbitals, because their motion was more rotatory. (That may not have been the easiest way of looking at it.  If strain in the cyclopropane ring arises because of the greater electron repulsion through the orbitals being moved closer together, then adjacent positive charge would overturn that repulsion for four of the orbital lobes.)
 
The problem now was to put numbers to the cause, and this is where I had what I thought was an inspiration. Suppose you were beside a wall, and could measure electric fields, and such a field corresponding to Do was coming from the other side of the wall. Since cyclopropyl is electrically neutral overall and has no electric moment, Do = 0. Now, suppose you experience an increase in field. This can be explained two ways. The first is that charge q has been added, in which case the displacement field increases from Do to D1. In the second case, the original charge has moved, and there are now two fields: the original displacement field Do and a polarization field P, which are dimensionally equivalent. If charge is added to the original charge, at its point location div D1 = q. But for the case of the charge having moved, since we measure an electric field we can also write,  div P = q’, and the situation is numerically equivalent to having added a pseudocharge q’. Of course, since their fields are equivalent, q' = q. 
 
Why do that? Because if we wish to calculate how far the charge moved, we must solve the Schrodinger equation, which cannot be done, but if we think in terms of adding a pseudocharge, there is a mathematical simplification. If the cyclopropane ring bonds are represented by a torus, we have an analytical solution to the otherwise impossible differential equations. The work done assembling the pseudocharge on that torus is proportional to the strain energy. There remains one unknown: the minor radius of the torus, but before addressing that there was also the issue of determining the strain energy. More next post.
Posted by Ian Miller on Jan 12, 2013 1:17 AM GMT
My alternative explanations for planetary formation survived a further two months. The reason for not giving a November update was not that I was hiding something, but there was word that a "huge announcement" would be made from the Curiosity team on December 5 so I waited. Could this fulfill one of my predictions? Er, no! The announcement was a bit of a squib: the last bit of equipment was working. Yes, this is a minor miracle, but it says nothing about planetary formation.
 
Obviously, a good number of papers were published, but very few had anything relevant to say about this theory. One of the more interesting came from Tobin et al., (Nature 492: 83-85). The protostar L1527 IRS has about 0.2 solar masses, while it is surrounded by a rotationally supported disk containing at least seven Jupiter masses, and further surrounded by an envelope containing about 1 solar mass. This is obviously a star in the early stages of formation, and as far as can be seen, it follows standard theory quite nicely. If we wait for about 3 million years we might see newly formed planets!
 
A paper by Crida and Charnoz (Science 338: 1196 – 1199) proposes that satellites form from massive rings around planets. A case is made that such rings form, then spread out beyond the Roche limit, accrete into larger bodies, and are moved out by tidal forces. It is not entirely clear, at least to me, how this works with gas accreting inwards, as gas drag should drag bodies inwards. The model is claimed to give good agreement with Neptune's inner minor satellites, the Uranian system, and Saturn's inner system. The Jovian system does not fit, and Titan is not really a good fit. One problem is that such rings must be extremely massive. The proposal differs from what I proposed, although my compositional proposal might still explain the rings, if they existed.
 
For those wondering how my theory differs from standard theory, the latter is essentially purely physical, with accretion being due to gravity and driven by gas flows, turbulence, etc that lead to collisions. I agree that these are important, and the main drivers once a certain size is reached, however standard theory cannot explain how the starting position, a distribution of planetesimals, form, because bodies up to tens of kilometers in size have negligible gravity, and collisions do not lead to binding strength. My major difference is that the initial stages are driven by chemistry, and our system is typical of such a system where the star blows out the disk within 1 My after forming. If this does not happen, planets keep accreting, and now become gravitationally unstable, which leads to a variety of different, smaller system types. By being driven by chemistry, the governing variable during the initial accretion stages is temperature.
 
Just before posting this, a new system was claimed: Tau ceti is claimed to have planets with semimajor axes at 0.1, 0.195, 0.37, 0.55 and 1.35 A.U.  I made approximate predictions for the outer part of this system, and the outcome is mixed. In my theory, the rocky planets are governed by two temperature profiles, the initial accretion, and that prior to the final removal of disk material, while the outer planets are primarily determined by the primary temperature distribution. If we interpret the planet at 1.35 A.U. as the accretor due to water ice (i.e. the Jupiter equivalent, irrespective of size), then the outer planets are about twice as close to the star as I suggested, which could arise if Tau Ceti accreted more slowly than our star, or because Tau Ceti has a lower metallicity, the accretion disk may have radiated heat better, by being somewhat more transparent. If so, and if these distances are real (see caveat below) there will be three further planets at about 2.1 A.U, 4.7 A.U., and 7.8 A.U. The one at 4.7 A.U. would be the smallest, while the one at 2.1 A.U would have formed an atmosphere similar to that of Titan. (I had predicted the second outermost one would have an atmosphere of nitrogen, if it were big enough to have an atmosphere, but because the planet is twice as close to the star, it too might have volatile methane.) The inner planets are further from the star than simple proportion, as would be expected because the second temperature profile is significantly due to stellar radiation. So is that confirmation or falsification? It may be neither, because a caveat must be noted: These planets are small; the so-called Jupiter equivalent is only 2% that of our Jupiter (although I predicted they would be small, due to the lower metallicity) and were detected at the very limit of stellar wobble. They may not be real, or may not be quite as reported.
 
Finally, I wish you all to enjoy the festive season. This will be my last blog until next year, when I shall return with some postscripts to my PhD project.
Posted by Ian Miller on Dec 21, 2012 10:13 PM GMT
The Roman festival of the Saturnalia, on the winter solstice, was where order was turned on its head. The question then is, do followers of this blog have the nerve to have their deepest beliefs challenged? For those who wish to exercise the brain over the next period, on December 21-23, there will be a free download of Aristotelian Methodology in the Physical Sciences from Amazon. The concept behind this ebook is that when Galileo threw out the bath water of Aristotle's physics, he also threw out the baby, namely Aristotle's methods for forming theories. Aristotle made at least two gigantic errors in physics but as this book shows, they arose because Aristotle forgot to use his own methodology (or he had yet to develop it; Physica was one of his earliest works.)
 
The first four chapters of Part 1 introduce the reader to my interpretation of what Aristotle was trying to say, then there are several examples of where failures to follow this advice have led to problems. One recent failure is the case of the non-classical carbenium ion, where two Nobel-prizewinners went head to head and failed to reach a conclusion. Part two then covers physics that I think a chemist should know about, which includes mechanics, waves, electromagnetic theory, quantum mechanics, and some other physics of general interest, then chemistry that I thought physicists should know about. That latter part is probably the weakest part of the book, and is largely based on explanations I have had to give to physicists I have worked with. A number of you may be able to offer suggestions for a revised edition.
 
It is the third part that is intended to offer the intellectual challenges, and it comprises 72 problems, in which the reader has to offer an alternative theory to . . .   Then, just to show it can be done, I offer answers, not all of which are beyond criticism because the second challenge is for the reader to accept or falsify my answers. Are you up to it? Examples include:
 
How could Priestley have ensured that the phlogiston theory prevailed?
 
Isaac Newton spun a bucket of water, and noticed centrifugal forces forced the water to the edges. Similarly, you can have artificial gravity in a spinning space ship. The problem is, how does the water know the bucket (or the astronaut, the space ship) is spinning? Isaac Newton appeared to fail on this, and a number of modern physics books mention the issue but provide no answer. Can you do better?
 
Yes, there is that non-classical carbenium ion. Surely you will not be put off by two Nobel-prizewinners failing to solve it?
 
I could not resist some of my own work, so one question starts off asking you to formulate an alternative interpretation of quantum mechanics. In the spirit of Christmas, a clue: Following Aristotle, either there is a wave of there is not. If there is, either it travels at the same velocity as the particle or it does not. That should get you going.
 
Finally, the interpretation I have come up with is non-local only to one wavelength, or one quantum of action. But Alain Aspect showed that entangled photons do not comply with Bell's inequality. If so, my interpretation is wrong. Your job is to falsify his claim (explained in sufficient detail earlier). Then, your last problem is to falsify my answer, which is based on the requirement that Bell's inequality must be followed if energy is conserved, and if the associative law of sets holds. As an aside, attempts to publish this argument in journals led to return by editors without peer review, except once when I was informed "This is wrong; the maths are trivial." Unfortunately, no clues as to where it is wrong, so you can help (or get help from a physicist.) Mind you, I have shown it to two professors of mathematical physics and they ducked for cover, as did a professor of theoretical physics. I sent it to a professor of theoretical physics who had written a book on Bell's inequality, he had promised to tell me where I was wrong but he never answered. My guess is you will fail on that one.
Posted by Ian Miller on Dec 15, 2012 1:57 AM GMT
In a previous blog, I discussed some misadventure, but there were other incidents of somewhat higher quality. (There had to be!)  To get to my lab from the main stairs, I had to go through the main lab. This had quite a number of benches, together with a couple of side rooms which seemed to be of more value for light entertainment when bored than anything else. However, when entering the main lab, some previous student, presumably inspired by Dante Alighieri, had ensured that one of the first things a visitor saw was a bun suspended from the ceiling by a wire. This bun was completely devoid of mould or any fungal growth! Enter not herein, for this laboratory is totally unsuitable for life!
 
One day, when I left my lab and entered the main lab, there to my right was something that I shall never forget. A friend was trying to purify a nitroazetidine by distillation, and was using a microburner on a pear-shaped flask. As I watched, suddenly there was a "pop", the top of the distillation equipment went upwards, and there was the poor victim sitting disconsolately holding the microburner while a light cloud of soot descended on him.
 
Then there was the fire alarm. A fire in a chemistry lab is a nightmare, although to be honest, I have never seen one, which says something about chemists ability to handle flammable materials. Anyway, the rules were clear. To make it easier to evacuate, those who could used the fire escape external to the building. Eventually, everybody assembled in the quad, and I received a few remarks, for I had come down the fire escape holding a lab bench drawer. In the drawer were all my precious samples and my lab book, and I was the only one who had thought to take that precaution.
 
Finally, an embarrassing scene. About the end of my second year, the Department introduced multiple choice questions for the first time, and as you might guess, the PhD students couldn't wait to get their hands on one of the papers. "What idiot set this question?" I asked, and looked up, and it was fairly clear the "idiot" was at the far end of the lab! Nevertheless, I stood by it. The question was, you are determining the molecular weight of benzene by the Victor Meyer method. If the benzene is wet, will the result be too high, too low, or about the same? I could justify each answer! Unless the experimentalist is a clod and does not introduce drops of water, the answer is, not much difference because water is essentially insoluble in benzene. If there is a drop of water, and the water stays in the vapour phase, the answer is, too low, but if the water condenses somewhere, the answer is, too high (because there is weight that does not give rise to vapour). I really hate these questions where the student cannot explain why the option was taken.
 
Slightly off the topic, but many years later I saw one of those Olympiad questions they inflict on students, and the question was, which has the higher boiling point: methyl cyclopropane or cyclobutane? When I saw this question, I thought it unreasonable, because while the former has a small dipole moment, the other has more degrees of vibrational freedom. I mentally picked the cyclobutane, but the answer the students were supposed to give was methyl cyclopropane, because of the dipole moment. The problem is, observation shows that answer is just plain wrong! People who set questions like that ought to be taken out and identified, and made to wear placards saying, "check the literature!"
Posted by Ian Miller on Dec 8, 2012 12:55 AM GMT
When writing up, I had to explain why my results were contradicting the emerging paradigm. How would you enjoy that, when future employment depends on success? My first step was to define some terms, and I interpreted "conjugation" to mean a system where a common wave function extended over more than two atoms. In particular, if cyclopropyl (Cy) conjugated with unit A, there was at least one two-electron wave function in the system Cy-A. Now, suppose there was a unit B; if Cy conjugated, then there was at least one two-electron wave function in the system Cy-B.  Thus in hexatriene, there are wave functions extending over the entire system. Now, I reasoned that if Cy-A was a delocalized system, through the virial theorem and the fact that a solution consistent with the stationary state Schrodinger equation can have only one energy, the wave function extending over the system had a common potential. The same applied to Cy-B. Therefore, if Cy conjugates, within this definition if substitution changed the potential at B, there must be a change at A. I had shown there was no mesomeric change, therefore there was no linking wave function. Now, at the very least, I had to explain how cyclopropane stabilized adjacent positive charge, why did cyclopropane give significant bathochromic shifts to certain UV spectra, and why was the dipole moment of cyclopropyl chloride reduced compared with other alkyl chlorides? Fortunately, if the first was answered, so was the second. The reason is, from Maxwell’s electromagnetic theory, light can only be absorbed if there is a change of electric moment, and if cyclopropyl stabilizes adjacent positive charge, it will stabilize the excited state when positive charge is adjacent, and by doing so, it will also increase the extinction coefficient. (In this respect, I think Pauling’s canonical structures/VB approach make these effects so much easier to understand at a lower level than MO theory.)
 
It was then that I saw what I believed was the answer. Coulson and Moffatt had proposed bent bonds. If we consider the carbon atoms to have orbitals in the sp3 configuration that overlap, in a bond, the forces from the opposing nucleus pull the orbital closer to the C-C line, the movement being opposed by the remaining four ring electrons, and an equilibrium was reached whereby the charge density of each bond was moved some distance towards the centroid of the ring. This movement of electrons might be symmetrical in cyclopropane, but it was not with respect to a substituent. Four lobes on the two distal carbon atoms moved more or less directly towards the substituent, but the two lobes on the geminal carbon atom changed their angles, but did not significantly change the electron distance to the substituent.
 
There were two ways of viewing this, and I probably chose the harder of the two, although in the event it was the way with the greatest ability to explain a wider range of observations. Both depend on the obvious: the potential energy is stored in electric fields. (That is due to Maxwell.) The first is to note that the repulsion energy on the four distal lobes will be overridden by the positive charge on the substituent. If so, the stabilization energy of a carbenium ion should not exceed 2/3 the strain energy, together with a standard polarization energy of alkane bonds. The second way of looking at it is that the four distal lobes move towards the positive charge and stabilize it. In short, at least qualitatively, the stabilization, in excess of that given by standard alkyl groups, of adjacent positive charge by the cyclopropyl group is required by Maxwell’s electromagnetic theory, and there is no necessity for special quantum effects.
 
I proposed to explain the electric moment of cyclopropyl chloride this way. Assume the linear combination of atomic wave functions. (Quantum mechanics is a linear theory. Waves always combine in a linear fashion.)  The reason alkyl chlorides have a dipole moment (as I saw it then) is that on wave interference, each orbital tries to increase its electron density by a given proportion, but the electron density is much higher around the chlorine atom before wave interference, so electron density has to move towards the chlorine after it. The higher electron density in the cyclopropane ring, which I referred to as a monopole, partly offsets that. So I had my explanations. I could write up the conclusions.
 
However, I had a minor problem: I had nobody to beta test what I was writing, because supervisor had gone to North America. This was a serious problem because I had nobody to check whether I might be going wrong somewhere, and nobody to check whether what I was writing was readily comprehensible. I was effectively saying everyone else was wrong. What should have happened was that supervisor should have sat me down in front of a physicist and straightened out what I was thinking so I could put it in a more orthodox form. That did not happen.
Posted by Ian Miller on Dec 1, 2012 2:09 AM GMT
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