In the May edition of “Chemistry World” there was an item regarding “leaps of faith” in quantum mechanics, and this item quoted a paper published in Proc. Nat. Acad. Sci. showing how the Schrodinger equation can be arrived at from the classical Hamilton Jacobi equation. What puzzled me was, why was this published? After all, in the chapter “Classical Mechanics” in “Fundamental Formulas of Physics” (Dover, 1962), essentially the same thing was published, and no claim to originality was made. The book was a summary of well-known physics, so this was presumably well-established by then.
 
So, why is quantum mechanics so weird? One possibility is that it is not at all weird, and requires no great leaps of faith at all. The only problem is that we do not understand it, which in turn might mean nothing more than there is more to sort out. One problem was that we were deeply committed to Newtonian mechanics, so anything non-Newtonian was, perforce, weird. Within its set of assumptions, Newtonian mechanics are, in my view, completely correct, but as I noted in my ebook, Elements of Theory 1, there are two statement implied by Newtonian mechanics that are not correct. The first is, force acts instantaneously at a distance. By far Einstein’s greatest contribution to science was to propose that that was wrong, and force is mediated at a velocity. Further, the statement that when you see something, you cannot say, “It is there,” but rather, “It was there when the photons set off.” The second erroneous assumption is inherent to Newton’s first law. Newton’s first law is often regarded as a bit redundant, because it is essentially the second law with a zero applied force. However, there is one further part to Newton’s first law, and that is that motion is continuous. In more detail, what the physicists call action is continuous. In my opinion, that is wrong, and it is where the problems in comprehension lie. Instead, I regard action as discrete, and specifically, in units of Planck’s quantum of action. That, as far as I can tell, is the only required difference between classical and quantum mechanics. The derivation of the Schrodinger equation immediately follows from the Hamilton-Jacobi equation if the quantum of action defines a period of the wave. The Uncertainty Principle and the Exclusion Principle also follow.
 
I think another problem in understanding what is going on follows from an obsession with another part of Hamiltonian mechanics, namely the canonical equations. You will often see that these partial differential equations enable us to represent momentum, p, and positional coordinate, q, as equivalent, from which we can make phase space diagrams, etc. However, action is an integral of motion, and if the discreteness of action is the fundamental essence of quantum mechanics, then some care has to be taken with conclusions based on partial differentials. An example I gave in the ebook is this. ∫pdq has a simple meaning: a particle travelling along a coordinate with uniform momentum. Now, consider ∫qdp; a particle at constant position with a continual change of momentum? Strictly speaking, both integrals give you action, except one is ridiculous. As for the first, ∫pdq, consider that if you integrate over a period you should get a wavelength. If so, pλ = h, the quantum of action, and we have the de Broglie equation. Action can also be represented as ∫Edt, where E is the energy. If τ is the periodic time, then it follows again that Eτ = h, from which, bearing in mind frequency is 1/τ, then E = hν, as required. This does not require "leaps of faith", and is reasonably straightforward, but how many chemists get shown things like that in their courses on quantum mechanics? Oh no! What tends to happen is that massive equations get put up, or obscure formalism using the "Sledge Hammer" approach: "Trust me, I know what I am doing."
 
Feynman said that nobody understands quantum mechanics. What I think he meant was that nobody as yet completely understands quantum mechanics, but I think you can get a lot closer to it if you take the trouble to get a few things in order. Ask what is really fundamental, and watch what follows.

Recently we have seen on the American Chemical Society website a sign  “Publish Be Found or Perish”. This rings a bell with me because there is a similar discussion going on with book authors. Yes, you have to write something that is worth reading, either with books or with scientific papers, but the whole exercise is a waste of effort unless someone reads the work, and by definition, quality has nothing to do with the first reading because if you do not know what is in the paper or book, you do not now whether it has quality or not.
 
So, how, as a scientist, do you get discovered? The short answer from me is, I do not know. With books, the best answer seems to be, “Get lucky!” The second best option is, “Be persistent!” This is, of course, what you have to do to maximize your chances of getting lucky. For any given time you do something, there is a certain chance that it will be noticed, so the more you do, the more chances. Publishing scientific papers in top journals probably helps. If you have a sequence of papers in one journal that is well-read in that topic, your name will eventually be recognized. Conference presentations probably help, because by circulating, people put a face to your name.
 
Does anyone see a problem here? What you end up with is the people being found are the academics with lots of students working for them, and with good budgets for going to conferences. The problem is, those who are found that way are those who are known anyway. It becomes very difficult for the young scientist to be discovered, other than through being associated with someone famous. To be discovered by association means the discovered has almost certainly adopted the workings of his mentor, otherwise his name will not be on the papers. This reinforces the workings of “normal science” as defined by Kuhn, but the question then is, is that the way we want science to work? Do we want to have uniform acceptance of the current paradigm, or do we want to see whether we are missing something? The ones more likely to be original are the young scientists, because they have less invested in the current paradigm, but they are also the least likely to be found.

I recently became involved in a discussion on how to write a scientific paper, and the first thing I had to concede was that on the whole we do not do this well, and sometimes it is written almost as if the author said to him/herself, "Nobody will read it anyway." In many cases it may not matter. Many papers are written to archive an observation, or a procedure, such as how to synthesize something. These involve putting things down in the order that they were done, and making sure all terms are defined. The writing style probably does not matter much, because the only people who will read this are those who wish to either use the observation or to follow the synthesis. The first group will accept the statement and the second will have to work through it, no matter what.
 
More difficult is when you have to interpret what you found. An obvious example is the structural determination. The problems include the fact that there will be several interpretations of any given observation. The usual approach is to eliminate them one by one, usually in a sequence of experiments, and if that is what you did, so must you report it. The major problems include a failure to eliminate all possible alternatives, in which case the report is unconvincing, or alternatively, the alternatives are eliminated, but the eliminations are scattered, and it is too difficult to keep them all in mind, in which case the argument runs the danger of being confusing. A common problem is the presentation of data that supports your hypothesis. It may, but equally it may support something else.
 
Time for a confession! I once wrote a series of papers on the substitution patterns of red algal galactans. Prior to writing these, structural elucidation was very difficult. These initial procedures involved the molecules or substituted derivatives being broken down into fragments, following which a sequence of fragments were further fragmented, and from the resultant structures, the overall structure was inferred. Because there were so many different aspects that had to be kept in mind, in one paper I wrote with two others, in parts the sentences became so complicated that later even I had trouble working out what they meant. So I came up with an answer: represent everything mathematically. Rather than get to the structure linearly, I carried out a number of different operations on the parent molecule, and from nmr spectral data, each operation was consistent with a set of structures. The real structure was given when the intersection of all sets gave one element. I then wrote papers representing structural units as matrices and data as ordered sets. Mathematical manipulation was unambiguous. The problem was, the rather restricted audience was not very happy with discrete mathematics, and eventually an editor told me to stop doing that or else the papers would be rejected.  As it happened, I did not care so I stopped publishing. I was self-employed, and this activity was to bring no income, so the decision to stop was not that difficult. The real shame was that the methodology was just becoming productive
 
Nevertheless, this raises the problem, what concessions should be made to the reader? My view at the time was, the statement of what I believed the structure to be should be put down in the simplest form possible. However, while how I deduced them should be as clear as possible, I thought it is not unreasonable to expect some effort to be made by those who wished to question the structure. My view was that to put down mathematically the arguments leading to the structures was optimal because all logic steps are explicit and unambiguous. There is no question of acceptance; to disagree you must show some step does not follow. However, many scientists did not agree with such an approach, and prefer comfortable sentences, which will generally be read without questioning them. What do you think? Be unambiguous, but have few readers, or be comfortable but with questionable ability to convince?

My ebook, "Planetary Formation and Biogenesis" was first published on Amazon 1 year ago, it argues that quite a lot of the standard theory needs rethinking, in particular that initial accretion is dependent on chemistry, not gravity, and while I have found a number of otherwise puzzling observations for the standard theory, as far as I can tell, nothing I have found contradicts my propositions. Readers may forgive me, but I find that rather satisfying. Part of the reason, of course, might be that the year has been relatively quiet regarding discoveries. That will change, because it is inevitable that sooner or later a large number of papers will come out regarding findings from Curiosity. That will be far more critical as far as my ideas go. A further possibility is that the theory is somewhat elastic, and hence difficult to falsify. That is true in some ways. There are a number of options for planets, but once one is chosen, there are very specific consequences. Unfortunately, some of those are as yet too difficult to test, which may also be why the theory has survived!
 
The most interesting evidence came from the Kepler satellite. It discovered (Science 340: 262) that Kepler 62 has five planets that range from half to twice Earth's diameter. These are at 0.715, 0.427, 0.12, 0.929, 0.055 A.U., around a star of 0.69 times the sun's mass. It is estimated that the outer one is in the centre of the habitable zone, and the next inner one possibly. The problem then is, are these truly rocky planets or ice planets sent inwards according to one of the possible mechanisms proposed? If they are all rocky planets, and were spaced according to my "expectation prediction" (which requires the star to have accreted at a rate proportional to its stellar mass squared, which in turn is observed, but only loosely, so there should be a range from the expectation position) the typical planet equivalents should be Mars-type  0.58, Earth-type 0.328, Venus-type (if there is one, and this is somewhat flexible) 0.22, Mercury-type 0.12. (This also assumes the secondary accretion rate, critical for exactly how the rocky planet evolves, was similarly scaled to our star, and observational evidence shows a possible order of magnitude deviation each way.) If the outer one is the Earth-type, then the theory predicts that accretion was significantly faster, and any Venus-type should be at 0.47 A.U., and  Mercury at 0.22 A.U. and there should be a Mars-type at about 1.14 A.U. Additional inner planets (Vulcans, which are predicted to be Mercury-like) would seem unlikely as the temperatures would grow too hot over a shorter radial difference. If the 0.427 A.U. planet is an Earth-type, then accretion was slower, and more material was available, in which case the Mars-type should be at about 0.68 A.U., the Venus-type at about 0.28 A.U., and the Mercury-type at 0.15 A.U. This agreement is not too bad, and the slower accretion rates could permit Vulcans. On the other hand, some of these bodies could be quite different, without violating the theory because if the accretion is slow, a variety of additional options might arise. Their densities should define their nature.
 
Slower stellar accretion rates permit planetary bodies to grow bigger, at which point they interact chaotically. It is generally considered that one major body (Theia) collided with Earth and formed the Moon. However, it is possible that modest-sized bodies might have collided and retained much of their structure provided collisions were not too violent. There is evidence this occurred (Science 340: 22-24). The Earth's deep mantle behaves as if there are two major piles of different composition, one below Africa and one mainly below the South Pacific. Plumes rise from the edges of these and give rise to the volcanic islands. These piles are thousands of kilometers across, but their composition remains unknown. An important point is that these "piles" are denser than much of the remaining mantle. Within my proposition, this is suggestive that they accreted closer to the star than the bulk of the Earth, which increases the pyroxene content, they differentiated, then eventually collided with Earth. The increased density arises through shedding aluminosilicates during collisions, including shedding them to Earth's crust. Is that right? That is unknown, but it is an interesting thought, at least for me.