Quantum weirdness, or not?

How can you test something without touching it with anything, even a single photon? Here is one of the weirder aspects of quantum mechanics. First, we need a tool, and we use the Mach-Zehnder interferometer, which is illustrated as follows:

There is a source that sends individual photons to a beam splitter (BS1), which divides the beam into two sub-beams, each of which proceed to a mirror that redirects them to meet at another beam splitter (BS2). The path lengths of the two sub-beams are exactly the same (in practice a little adjustment may be needed to get this to work). Each sub-beam (say R and T for reflectance and transmitted at BS1) is reflected once by a mirror. When reflected, they sustain a phase shift of π, and R sustains such a phase shift at BS1. At BS2, the waves going to D1 both have had two reflections, so both have had a phase shift of 2π and they interfere constructively, therefore D1 registers the photon arrival. However, it is a little more complicated at D2. The original beams T and R that would head towards D2 have a net phase difference of π within the beam splitter, so they destructively interfere and the original beam R continues in the direction of net constructive interference hence only detector D1 registers. Now, suppose we send through one photon. At BS1, it seems the wave goes both ways but the photon, which acts as a particle, can only go one way. You get exactly the same result because it does not matter which way the photon goes; the wave goes both ways but the phase shift means only D1 registers.

Now, suppose we block one of the paths? Now there is no interference at BS2 so both D1 and D2 register equally. That means we can detect an obstruction on the path R even if no photon goes along it.

Now, here is the weird conclusion proposed by Elitzer and Vaidman [Foundations of Physics 23, 987, (1992)]. Suppose you have a large supply of bombs, but you think some may be duds. You attach a sensor to each bomb wherein if one photon hits it, it explodes. (It would be desirable to have a high energy laser as a source, otherwise you will be working in the dark setting this up.) At first sight all you have to do is shine light on said bombs, but at the end all you will have are duds, the good ones having blown up. But suppose we put it in the arm of such an interferometer so that it blocks the photon. Half the time a photon will strike it and it will explode if it is good, but consider the other half. When the photon gets to the second beam splitter, the photon has a 50% chance of going to either D1 or D2. If it goes to D1 we know nothing, but if it goes to D2 we know the photon went to the bomb. If the bomb was any good it exploded, so if it did not explode we know it was a dud. So if the bomb is good, the probability is ¼ that we shall learn without destroying it, ½ that we destroy it, and ¼ that we don’t know. In this case we send a second photon and continue until we get a hit at D2, then stop. The probability that we can detect the bomb without sensing it with anything now ends up at 1/3. So we end up keeping 1/3 of our bombs and locate all the duds.

Of course, this is a theoretical prediction. As far as I know, nobody has ever tested bombs, or anything else for that matter, this way. In standard quantum mechanics this is just plain weird. Of course, if you accept the pilot wave approach of de Broglie or Bohm, or for that matter my guidance wave version, where there is actually a physical wave other than the wave being a calculating aid, it is rather straightforward. Can you separate these versions? Oddly enough, yes, if reports are correct. If you have a version of this with an electron, the end result is that any single electron has a 50% chance of firing each detector. Of course, one electron fires only one detector. What does this mean? The beam splitter (which is a bit different for particles) will send the electron either way with a 50% probability, but the wave appears to always follow the particle and is not split. Why would that happen? The mathematics of my guidance wave require the wave to be regenerated continuously. For light, this happens from the wave itself, from Maxwell’s theory of light being an oscillation of electromagnetic waves. The oscillation of the electric field causes the next magnetic oscillation, and vice versa. But an electron does not have this option, and the wave has to be tolerably localised in space around the particle.

Thus if the electron version of this Mach Zehnder interferometer does do what the reference I say claims it did (unfortunately, it did not cite a reference) then this odd behaviour of electrons shows that the wave function for particles at least cannot be non-local (or the beam splitter did not work. There is always an alternative conclusion to any single observation.)

Polymerised Water

In my opinion, probably the least distinguished moment in science in the last sixty years occurred in the late 1960s, and not for the seemingly obvious reason. It all started when Nikolai Fedyakin condensed steam in quartz capillaries and found it had unusual properties, including a viscosity approaching that of a syrup. Boris Deryagin improved production techniques (although he never produced more than very small amounts) and determined a freezing point of – 40 oC, a boiling point of » 150 oC, and a density of 1.1-1.2. Deryagin decided there were only two possible reasons for this anomalous behaviour:

(a) the water had dissolve quartz,

(b) the water had polymerised.

Since recently fused quartz is insoluble in water at atmospheric pressures, he concluded that the water must have polymerised. There was no other option. An infrared spectrum of the material was produced by a leading spectroscopist from which force constants were obtained, and a significant number of papers were published on the chemical theory of polywater. It was even predicted that an escape of polywater into the environment could catalytically convert the Earth’s oceans into polywater, thus extinguishing life. Then there was the inevitable wake-up call: the IR spectrum of the alleged material bore a remarkable resemblance to that of sweat. Oops. (Given what we know now, whatever they were measuring could not have been what everyone called polywater, and probably was sweat, and how that happened from a very respected scientist remains unknown.)

This material brought out some of the worst in logic. A large number of people wanted to work with it, because theory validated it existence. I gather the US navy even conducted or supported research into it. The mind boggles here: did they want to encase enemy vessels in toffee-like water, or were they concerned someone might do it to them? Or even worse, turn the oceans into toffee, and thus end all life on Earth? The fact that the military got interested, though, shows it was taken very seriously. I recall one paper that argued Venus was like it is because all its water polymerised!

Unfortunately, I think the theory validated the existence because, well, the experimentalists said it did exist, so the theoreticians could not restrain themselves from “proving” why it existed. The key to the existence is that they showed through molecular orbital theory that the electrons in water had to be delocalized. Most readers won’t see the immediate problem because we are getting a little technical here, but to put it in perspective, molecular orbital theory assumes the electrons are delocalized over the whole molecule. If you further assume water molecules come together, the firsr assumption requires the electrons to be delocalised, which in turn forces the system to become one molecule. If you cannot end up with what you assumed in the first place, your theoretical work is not exactly competent, let alone inspired.

Unfortunately, these calculations involve what are called quantum mechanics. Quantum mechanics is one of the most predictive theories ever, and almost all your electronic devices have parts that would not have been developed but for knowledge of quantum mechanics. The problem is that for any meaningful problem there is usually no analytical solution from the formal quantum theory generally used, and any actual answer requires some rather complicated mathematics, and in chemistry, because of the number of particles, some approximations. Not everyone agreed. The same computer code in different hands sometimes produced opposite results with no explanation of why the results differed. If there were no differences in the implied physics between methods that gave opposing results, then the calculation method was not physical. If there were differences in the physics, then these should have been clearly explained. The average computational paper gives very little insight to what is done and these papers were actually somewhat worse than usual. It was, “Trust me, I know what I’m doing.” In general, they did not.

So, what was it? Essentially, ordinary water with a lot of dissolved silica, i.e. option (a) above. Deryagin was unfortunate in suffering in logic from the fallacy of the accident. Water at 100 degrees C does not dissolve quartz. If you don’t believe me, try boiling water it in a pot with a piece of silica. It does dissolve it at supercritical temperatures, but these were not involved. So what happened? Seemingly, water condensing in quartz capillaries does dissolve it. However, now I come to the worst part. Here we had an effect that was totally unexpected, so what happened? After the debacle, nobody was prepared to touch the area. We still do not know why silica in capillaries is so eroded, yet perhaps there is some important information here, after all water flows through capillaries in your body.

One of the last papers written on “anomalous water” was in 1973, and one of the authors was John Pople, who went on to win a Nobel Prize for his work in computational chemistry. I doubt that paper is one that he is most proud of. The good news is the co-author, who I assume was a post-doc and can remain anonymous because she almost certainly had little control on what was published, had a good career following this.

The bad news was for me. My PhD project involved whether electrons were delocalized from cyclopropane rings. My work showed they were not however computations from the same type of computational code said it did. Accordingly, everybody ignored my efforts to show what was really going on. More on this later.

Ossified Science

There was an interesting paper in the Proceedings of the National Academy of Sciences (118,  e2021636118,  https://doi.org/10.1073/pnas.2021636118 ) which argued that science is becoming ossified, and new ideas simply cannot emerge. My question is, why has it taken them this long to recognize it? That may seem a strange thing to say, but over the life of my career I have seen no radically new ideas get acknowledgement.

The argument in the paper basically fell down to one simple fact: over this period there has been a huge expansion in the quantity of scientists, research funding, and the number of publications. Progress in the career of a scientist depends on the number of papers produced. However, the more papers produced, the more likely is the science to stagnate because nobody has the time to read everything. People pick and choose what to read, the selection biased by the need not to omit people who may read your funding application. Reading is thus focused on established thinking. As the number of papers increase, citations flow increasingly towards the already well-cited papers. Lesser known authors are unlikely to ever become highly cited; if they do it is not through a cumulative process of analysis. New material is extremely unlikely to disrupt existing work, with the result that progress in large established scientific fields may be trapped in existing canon. That is fairly stern stuff.

It is important to note there are at least three major objectives relating to science. The first is developing methods to gain information, or, if you prefer, developing new experimental or observational techniques. The second is using those techniques to record more facts. The more scientists there are, the more successful these are, and over the period we have most certainly been successful in these objectives. The rapid provision of new vaccines for SARS-CoV-2 shows that when pushed, we find ways of how to do it. When I started my career, a very large clunky computer that was incredibly slow and had internal memory measured in bytes occupied a room. Now we have memory that stores terrabytes in something you can hold in your hand. So yes, we have learned how to do it, and we have acquired a huge amount of knowledge. There is a glut of facts available.

The third objective is to analyse those facts and derive theories so we can understand nature, and do not have to examine that mountain of data for any reason other than to verify that we are on the right track. That is where little has happened.

As the PNAS paper points out, policy reflects the “more is better” approach. Rewards are for the number of articles, and citations reflect the quality of them. The number of publications are easily counted, but the citations are more problematical. To get the numbers up, people carry out work most likely to reach a fast result. The citations are the ones most easily found, which means those that get a good start gather citations like crazy. There are also “citation games”: you cite mine, I’ll cite yours. These citations may have nothing in particular to add in terms of the science or logic, but they do add to the career prospects.

What happens when a paper is published? As the PNAS paper says, “cognitively overloaded reviewers and readers process new work only in relationship to existing exemplars”. If a new paper does not fit the existing dynamic, it will be ignored. If  the young researcher wants to advance, he or she must avoid trying to rock the boat. You may feel that the authors of this are overplaying a non-problem. Not so. One example shows how the scientific hierarchy thinks. One of the two major advances in theoretical physics in the twentieth century was quantum mechanics. Basically, all our advanced electronic technology depends on that theory, and in turn the theory is based on one equation published by Erwin Schrödinger. This equation is effectively a statement that energy is conserved, and that the energy is determined by a wave function ψ. It is too much to go into here, but the immediate consequence was the problem, what exactly does ψ represent?

Louis de Broglie was the first to propose that quantum motion was represented by a wave, and he came up with a different equation which stated the product of the momentum and wavelength was Planck’s constant, or the quantum of action. De Broglie then proposed that ψ was a physical wave, which he called the pilot wave. This was promptly ignored in favour of a far more complicated mathematical procedure that we can ignore for the present. Then, in the early 1950s David Bohm more or less came up with the same idea as de Broglie, which was quite different from the standard paradigm. So how was that received? I found a 1953 quote from J. R. Oppenheimer: “We consider it juvenile deviationism .. we don’t waste our time … [by] actually read[ing] the paper. If we cannot disprove Bohm, then we must agree to ignore him.” So much for rational analysis.

The standard theory states that if an electron is fired at two slits it goes through BOTH of them then gives an interference pattern. The pilot wave says the electron has a trajectory, goes through one slit only, and while it forms the same interference pattern, an electron going through the left slit never ends up in the right hand pattern. Observations have proved this to be correct (Kocsis, S. and 6 others. 2011. Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer Science 332: 1170 – 1173.) Does that change anyone’s mind? Actually, no. The pilot wave is totally ignored, except for the odd character like me, although my version is a little different (called a guidance wave) and it is ignored more.

A Different Way of Applying Quantum Mechanics to Chemistry

Time to explain what I presented at the conference, and to start, there are interpretive issues to sort. The first issue is either there is a physical wave or there is not. While there is no definitive answer to this, I argue there is, because something has to go through both slits in the two slit experiment, and the evidence is the particle always goes through only one slit. That means something else should be there. 

I differ from the pilot wave theory in two ways. The first is mathematical. The wave is taken as complex because its phase is. (Here, complex means a value includes the square root of minus 1, and is sometimes called an imginary number for obvious reasons.) However, Euler, the mathematician that really invented complex numbers, showed that if the phase evolves, as waves always do by definition of an oscillation and as action does with time, there are two points that are real, and these are at the antinodes of the wave. That means the amplitudes of the quantal matter wave should have real values there. The second difference is if the particle is governed by a wave pulse, the two must travel at the same velocity. If so, and if the standard quantum equations apply, there is a further energy, equal in magnitude to the kinetic energy of the particle. This could be regarded as equivalent to Bohm’s quantum potential, except there is a clear difference in that there is a clear value of it. It is a hidden variable in that you cannot measure it, but then again, so is potential energy; you have never actually measured that.

This gives a rather unexpected simplification: the wave behaves exactly as a classical wave, in which the square of the amplitude, which is a real number, gives the energy of the particle. This is a big advance over the probabilistic interpetation because while it may be correct,  the standard wave theory would say that A^2 = 1 per particle, that is, the probability of one particle being somewhere is 1, which is not particularly informative. The difference now is that for something like the chemical bond, the probabilistic interpretation requires all values of ψ1 to interact with all values of ψ2; The guidance wave method merely needs the magnitude of the combined amplitude.  Further, the wave refers only to a particle’s motion, and not to a state (although the particle motion may define a state). This gives a remarkable simplification for the stationary state, and in particular, the chemical bond. The usual way of calculating this involves calculating the probabilities of where all the electrons will be, then further calculating the interactions between them, recalculating their positions with the new interactions, recalculating the new interactions, etc, and throughout this procedure, getting the positional probabilities requires double integrations because forces give accelerations, which means constants have to be assigned. This is often done, following Pople, by making the calculations fit similar molecules and transferring the constants, which to me is essentially an empirical assignment, albeit disguised with some fearsome mathematics.

The approach I introduced was to ignore the position of the electrons and concentrate on the waves. The waves add linearly, but you introduce two new interactions that effectively require two new wave components. They are restricted to being between the nuclei, the reason being that the force on nucleus 1, from atom 2 must be zero, otherwise it would accelerate and there would be no bond. The energy of an interaction is the energy added to the antinode. For a hydrogen molecule, the electrons are indistinguishable, so the energy of the two new interactions are equivalent to the energy of the two equivalent ones from the linear addition, therefore the bond energy of H2 is 1/3 the Rydberg energy. This is out by about 0.3%. We get better agreement using potential energy, and introduce electric field renormalisation to comply with Maxwell’s equations. Needless to say this did not get much excitement from the conference audience. You cannot dazzle with obscure mathematics doing this.

The first shock for the audience was when I introduced my Certainty Principle, which, roughly stated, is the action of a stationary state must be quantized, and further, because of the force relationship I introduced above, the action must be that of the sum of the participating atoms. Further, the periodic time of the initial electron interactions must be constant (because their waves add linearly, a basic wave property). The reason you get bonding from electron pairing is that the two electrons halve the periodic time on that zone, which permits twice the energy at constant action, or the addition of the two extras as shown for hydrogen. That also contracts the distance to the antinode, in which case the appropriate energy can only arise because the electron – electron repulsion compensates. This action relationship is also the first time a real cause of there being a bond radius that is constant across a number of bonds has been made. The repulsion energy which is such a problem if you consider it from the point of view of electron position is self-correcting if you consider the wave aspect. The waves cannot add linearly and maintain constant action unless the electrons provide exactly the correct compensation, and the proposition is the guidance waves guide them into doing that.

The next piece of “shock” comes with other atoms. The standard theory says their wave functions correspond to the excited states of hydrogen because they are the only solutions of the Schrödinger equation. However, if you do that, you find that the calculated values are too small. By caesium, the calculated energy is out by an order of magnitude. The standard answer – the electrons penetrate the space occupied by the inner electrons and experience stronger electric field. If you accept the guidance wave principle, that cannot be because the energy is determined at the major antinode. (If you accept Maxwell’s equations I argue it cannot be either, but that is too complicated to be put here.) So my answer is that the wave is actually a sum of component waves that have different nodal structures, and an expression for the so-called screening constant (which is anything but constant, and varies according to circumstances) is actually a function of quantum numbers, and I produced tables that shows the functions give good agreement for the various groups, and for excited states.

Now, the next shock. Standard theory has argued that the properties of heavy elements like gold have unusual properties because these “penetrations” lead to significant relativistic corrections. My guidance wave theory requires such relativistic effects to be very minor, and I provided  evidence that showed the properties of elements like francium, gold, thallium, and lead were as good or better fitting with my functions as any of the other elements.

What I did not tell them was that the tables of data I showed them had been published in a peer reviewed journal over thirty years before, but nobody took any notice. As someone said to me, when I mentioned this as an aside, “If it isn’t published in the Physical Review or J. Chem Phys., nobody reads it.” So much for publishing in academic journals.  As to why I skipped those two, I published that while I was starting my company, and $US 1,000 per page did not strike me as a good investment.So, if you have got this far, I appreciate your persistence. I wish you a very Merry Christmas and the best for 2020. I shall stop posting until a Thursday in mid January, as this is the summer holiday season here.

What does Quantum Mechanics Mean?

Patrice Ayme gave a long comment to my previous post that effectively asked me to explain in some detail the significance of some of my comments on my conference talk involving quantum mechanics. But before that, I should explain why there is even a problem, and I apologise if the following potted history seems a little turgid. Unfortuately, the background situation is important. 

First, we are familiar with classical mechanics, where, given all necessary conditions, exact values of the position and momentum of something can be calculated for any future time, and thanks to Newtom and Leibniz, we do this through differential equations involving familiar concepts such as force, time, position, etc. Thus suppose we shot an arrow into the air and ignored friction and we wanted to know where it was, when. Velocity is the differential of position with respect to time, so we take the velocity and integrate it. However, to get an answer, because there are two degrees of freedom (assuming we know which direction it was shot) we get two constants to the two integrations. In classical mechanics these are easily assigned: the horizontal constant depends on where it was fired from, and the other constant comes from the angle of elevation. 

Classical mechanics reached a mathematical peak through Lagrange and Hamilton. Lagrange introduced a term that is usually the difference between the potential and kinetic energy, and thus converted the problem from forces to one of energy. Hamilton and Jacobi converted the problem to one involving action, which is the time integral of the Lagrangian. The significance of this is that in one sense action summarises all that is involved in our particle going from A to B. All of these variations are equivalent, and merely reflect alternative ways of going about the problem, however the Hamilton Jacobi equation is of special significance because it can be mathematically transformed into a mathematical wave expression. When Hamilton did this, there were undoubtedly a lot of yawns. Only an abstract mathematician would want to represent a cannonball as a wave.

So what is a wave? While energy can be transmitted by particles moving (like a cannon ball) waves transmit energy without moving matter, apart from a small local oscillation. Thus if you place a cork on the sea far from land, the cork basically goes around in a circle, but on average stays in the same place. If there is an ocean current, that will be superimposed on the circular motion without affecting it. The wave has two terms required to describe it: an amplitude (how big is the oscillation?) and a phase (where on the circle is it?).

Then at the end of the 19th century, suddenly classical mechanics gave wrong answers for what was occurring at the atomic level. As a hot body cools, it should give radiation from all possible oscillators and it does not. To explain this, Planck assumed radiation was given off in discrete packets, and introduced the quantum of action h. Einstein, recognizing the Principle of Microscopic Reversibility should apply, argued that light should be absorbed in discrete packages as well, which solved the problem of the photoelectric effect. A big problem arose with atoms, which have positively charged nuclei and electrons moving around it. To move, electrons must accelerate, and hence should radiate energy and spiral into the nucleus. They don’t. Bohr “solved” this problem with the ad hoc assumption that angular momentum was quantised, nevertheless his circular orbits (like planetary orbits) are wrong. For example, if they occurred, hydrogen would be a powerful magnet and it isn’t. Oops. Undeterred, Sommerfeld recognised that angular momentum is dimensionally equivalent to action, and he explained the theory in terms of action integrals. So near, but so far.

The next step involved the French physicist de Broglie. With a little algebra and a bit more inspiration, he represented the motion in terms of momentum and a wavelength, linked by the quantum of action. At this point, it was noted that if you fired very few electrons through two slits at an appropriate distance apart and let them travel to a screen, each electron was registered as a point, but if you kept going, the points started to form a diffraction pattern, the characteristic of waves. The way to solve this was if you take Hamilton’s wave approach, do a couple of pages of algebra and quantise the period by making the phase complex and proportional to the action divided by (to be dimensionally correct bcause the phase must be a number), you arrive at the Schrödinger equation, which is a partial differential equation, and thus is fiendishly difficult to solve. About the same time, Heisenberg introduced what we call the Uncertainty Principle, which usually states that you cannot know the product of the position and the momentum to better than h/2π. Mathematicians then formulated the Schrödinger equation into what we call the state vector formalism, in part to ensure that there are no cunning tricks to get around the Uncertainty Principle.

The Schrödinger equation expresses the energy in terms of a wave function ψ. That immediately raised the question, what does ψ mean? The square of a wave amplitude usually indicats the energy transmitted by the wave. Because ψ is complex, Born interpreted ψ.ψ* as indicating the probability that you would find the particle at the nominated point. The state vector formalism then proposed that ψ.ψ* indicates the probability that a state will have probabilities of certain properties at that point. There was an immediate problem that no experiment could detect the wave. Either there is a wave or there is not. De Broglie and Bohm assumed there was and developed what we call the pilot wave theory, but almost all physicists assume, because you cannot detect it, there is no actual wave.

What do we know happens? First, the particle is always detected as a point, and it is the sum of the points that gives the diffraction pattern characteristic of waves. You never see half a particle. This becomes significant because you can get this diffraction pattern using molecules made from 60 carbon atoms. In the two-slit experiment, what are called weak measurements have shown that the particle always goes through only one slit, and not only that, they do so with exactly the pattern predicted by David Bohm. That triumph appears to be ignored. Another odd feature is that while momentum and energy are part of uncertainty relationships, unlike random variation in something like Brownian motion, the uncertainty never grows

Now for the problems. The state vector formalism considers ψ to represent states. Further, because waves add linearly, the state may be a linear superposition of possibilities. If this merely meant that the probabilities merely represented what you do not know, then there would be no problem, but instead there is a near mystical assertion that all probabilities are present until the subject is observed, at which point the state collapses to what you see. Schrödinger could not tolerate this, not the least because the derivation of his equation is incompatible with this interpretation, and he presented his famous cat paradox, in which a cat is neither dead nor alive but in some sort of quantum superposition until observed. The result was the opposite of what he expected: this ridiculous outcome was asserted to be true, and we have the peculiar logic applied in that you cannot prove it is not true (because the state collapses if you try to observe the cat). Equally, you cannot prove it is true, but that does not deter the mystics. However, there is worse. Recall I noted when we integrate we have to assign necessary constants. When all positions are uncertain, and when we are merely dealing with probabilities in superposition, how do you do this? As John Pople stated in his Nobel lecture, for the chemical bonds of hydrocarbons, he assigned values to the constants by validating them with over two hundred reference compounds. But suppose there is something fundamentally wrong? You can always get the right answer if you have enough assignable constants.The same logic applies to the two-slit experiment. Because the particle could go through either slit and the wave must go through both to get the diffraction pattern, when you assume there is no wave it is argued that the particle goes through both slits as a superposition of the possibilities. This is asserted even though it has clearly been demonstrated that it does not. There is another problem. The assertion that the wave function collapses on observation, and all other probabilities are lost actually lies outside the theory. How does that actually happen? That is called the measurement problem, and as far as I am aware, nobody has an answer, although the obvious answer, the probabilities merely reflected possibilities and the system was always just one but we did not know it is always rejected. Confused? You should be. Next week I shall get around to some from my conference talk that caused stunned concern with the audience.

That Was 2017, That Was

With 2017 coming to a close, I can’t resist the urge to look back and see what happened from my point of view. I had plenty of time to contemplate because the first seven months were largely spent getting over various surgery. I had thought the recovery periods would be good for creativity. With nothing else to do, I could write and advance some of my theoretical work, but it did not work but like that. What I found was that painkillers also seemed to kill originality. However, I did manage one e-novel through the year (The Manganese Dilemma), which is about hacking, Russians and espionage. That was obviously initially inspired by the claims of Russian hacking in the Trump election, but I left that alone. It was clearly better to invent my own scenario than to go down that turgid path. Even though that is designed essentially as just a thriller, I did manage to insert a little scientific thinking into the background, and hopefully the interested potential reader will guess that from the “manganese” in the title.

On the space front, I am sort of pleased to report that there was nothing that contradicted my theory of planetary formation found in the literature, but of course that may be because there is a certain plasticity in it. The information on Pluto, apart from the images and the signs of geological action, were well in accord with what I had written, but that is not exactly a triumph because apart from those images, there was surprisingly little new information. Some of which might have previously been considered “probable” was confirmed, and details added, but that was all. The number of planets around TRAPPIST 1 was a little surprising, and there is limited evidence that some of them are indeed rocky. The theory I expounded would not predict that many, however the theory depended on temperatures, and for simplicity and generality, it considered the star as a point. That will work for system like ours, where the gravitational heating is the major source of heat during primary stellar accretion, and radiation for the star is most likely to be scattered by the intervening gas. Thus closer to our star than Mercury, much of the material, and even silicates, had reached temperatures where it formed a gas. That would not happen around a red dwarf because the gravitational heating necessary to do that is very near the surface of the star (because there is so much less falling more slowly into a far smaller gravitational field) so now the heat from the star becomes more relevant. My guess is the outer rocky planets here are made the same way our asteroids were, but with lower orbital velocities and slower infall, there was more time for them to grow, which is why they are bigger. The inner ones may even have formed closer to the star, and then moved out due to tidal interactions.

The more interesting question for me is, do any of these rocky planets in the habitable zone have an atmosphere? If so, what are the gases? I am reasonably certain I am not the only one waiting to get clues on this.

On another personal level, as some might know, I have published an ebook (Guidance Waves) that offers an alternative interpretation of quantum mechanics that, like de Broglie and Bohm, assumes there is a wave, but there are two major differences, one of which is that the wave transmits energy (which is what all other waves do). The wave still reflects probability, because energy density is proportional to mass density, but it is not the cause. The advantage of this is that for the stationary state, such as in molecules, that the wave transmits energy means the bond properties of molecules should be able to be represented as stationary waves, and this greatly simplifies the calculations. The good news is, I have made what I consider good progress on expanding the concept to more complicated molecules than outlined in Guidance Waves and I expect to archive this sometime next year.

Apart from that, my view of the world scene has not got more optimistic. The US seems determined to try to tear itself apart, at least politically. ISIS has had severe defeats, which is good, but the political futures of the mid-east still remains unclear, and there is still plenty of room for that part of the world to fracture itself again. As far as global warming goes, the politicians have set ambitious goals for 2050, but have done nothing significant up to the end of 2017. A thirty-year target is silly, because it leaves the politicians with twenty years to do nothing, and then it would be too late anyway.

So this will be my last post for 2017, and because this is approaching the holiday season in New Zealand, I shall have a small holiday, and resume half-way through January. In the meantime, I wish all my readers a very Merry Christmas, and a prosperous and healthy 2018.

A personal scientific low point.

When I started my PhD research, I was fairly enthusiastic about the future, but I soon got disillusioned. Before my supervisor went on summer holidays, he gave me a choice of two projects. Neither were any good, and when the Head of Department saw me, he suggested (probably to keep me quiet) that I find my own project. Accordingly, I elected to enter a major controversy, namely were the wave functions of a cyclopropane ring localized (i.e., each chemical bond could be described by wave interference between a given pair of atoms, but there was no further wave interference) or were they delocalized, (i.e. the wave function representing a pair of electrons spread over more than one pair of atoms) and in particular, did they delocalize into substituents? Now, without getting too technical, I knew my supervisor had done quite a bit of work on something called the Hammett equation, which measures the effect or substituents on reactive sites, and in which, certain substituents that had different values when such delocalization was involved. If I could make the right sort of compounds, this equation would actually solve a problem.

This was not to be a fortunate project. First, my reserve synthetic method took 13 steps to get to the desired product, and while no organic synthesis gives a yield much better than 95%, one of these struggled to get over 35%, and another was not as good as desirable, which meant that I had to start with a lot of material. I did explore some shorter routes. One involved a reaction that was published in a Letter by someone who would go on to win a Nobel prize. The very key requirement to get the reaction to work was omitted in the Letter. I got a second reaction to work, but I had to order special chemicals. They turned up after I had submitted my thesis. They travelled via Hong Kong, where they got put aside and forgotten. After discovering that my supervisor was not going to provide any useful advice on chemical synthesis, he went on sabbatical, and I was on my own. After a lot of travail, I did what I had set out to do, but an unexpected problem arose. The standard compounds worked well and I got the required straight line set with minimum deviation, but for the key compound at one extreme of the line, the substituent at one end reacted quickly with the other end in the amine form. No clear result.

My supervisor made a cameo appearance before heading back to North America, where he was looking for a better paying job, and he made a suggestion, which involved reacting carboxylic acids that I already had in toluene. These had already been reported in water and aqueous alcohol, but the slope of the line was too shallow to be conclusive. What the toluene did was to greatly amplify the effect. The results were clear: there was no delocalization.

The next problem was the controversy was settling down, and the general consensus that there was such delocalization. This was based on one main observational fact, namely adjacent positive charge was stabilized, and there were many papers stating that it must on theoretical grounds. The theory used was exactly the same type of programs that “proved” the existence of polywater. Now the interesting thing was that soon everybody admitted there was no polywater, but the theory was “obviously” right in this case. Of course I still had to explain the stabilization of positive charge, and I found a way, namely strain involved mechanical polarization.

So, where did this get me? Largely, nowhere. My supervisor did not want to stick his head above the parapet, so he never published the work on the acids that was my key finding. I published a sequence of papers based on the polarization hypothesis, but in my first one I made an error: I left out what I thought was too obvious to waste the time of the scientific community, and in any case, I badly needed the space to keep within page limits. Being brief is NOT always a virtue.

The big gain was that while both explanations explained why positive charge was stabilized, (and my theory got the energy of stabilization of the gas phase carbenium ion right, at least as measured by another PhD student in America) the two theories differed on adjacent negative charge. The theory involving quantum delocalization required it to be stabilized too, while mine required it to be destabilized. As it happens, negative charge adjacent to a cyclopropane ring is so unstable it is almost impossible to make it, but that may not be convincing. However, there is one UV transition where the excited state has more negative charge adjacent to the cyclopropane ring, and my calculations gave the exact spectral shift, to within 1 nm. The delocalization theory cannot even get the direction of the shift right. That was published.

So, what did I learn from this? First, my supervisor did not have the nerve to go against the flow. (Neither, seemingly, did the supervisor of the student who measured the energy of the carbenium ion, and all I could do was to rely on the published thesis.) My spectral shifts were dismissed by one reviewer as “not important” and they were subsequently ignored. Something that falsifies the standard theory is unimportant? I later met a chemist who rose to the top of the academic tree, and he had started with a paper that falsified the standard theory, but when it too was ignored, he moved on. I asked him about this, and he seemed a little embarrassed as he said it was far better to ignore that and get a reputation doing something more in accord with a standard paradigm.

Much later (I had a living to earn) I had the time to make a review. I found over 60 different types of experiment that falsified the standard theory that was now in textbooks. That could not get published. There are few review journals that deal with chemistry, and one rejected the proposal on the grounds the matter was settled. (No interest in finding out why that might be wrong.) For another, it exceeded their page limit. For another, not enough diagrams and too many equations. For others, they did not publish logic analyses. So there is what I have discovered about modern science: in practice it may not live up to its ideals.

What is nothing?

Shakespeare had it right – there has been much ado about nothing, at least in the scientific world. In some of my previous posts I have advocated the use of the scientific method on more general topics, such as politics. That method involves the rigorous evaluation of evidence, of making propositions in accord with that evidence, and most importantly, rejecting those that are clearly false. It may appear that for ordinary people, that might be too hard, but at least that method would be followed by scientists, right? Er, not necessarily. In 1962 Thomas Kuhn published a work, “The structure of scientific revolutions” and in it he argued that science itself has a very high level of conservatism. It is extremely difficult to change a current paradigm. If evidence is found that would do so, it is more likely to be secreted away in the bottom drawer, included in a scientific paper in a place where it is most likely to be ignored, or, if it is published, ignored anyway, and put in the bottom drawer of the mind. The problem seems to be, there is a roadblock towards thinking that something not in accord with expectations might be significant. With that in mind, what is nothing?

An obvious answer to the title question is that a vacuum is nothing. It is what is left when all the “somethings” are removed. But is there “nothing” anywhere? The ancient Greek philosophers argued about the void, and the issue was “settled” by Aristotle, who argued in his Physica that there could not be a void, because if there were, anything that moved in it would suffer no resistance, and hence would continue moving indefinitely. With such excellent thinking, he then, for some reason, refused to accept that the planets were moving essentially indefinitely, so they could be moving through a void, and if they were moving, they had to be moving around the sun. Success was at hand, especially if he realized that feathers did not fall as fast as stones because of wind resistance, but for some reason, having made such a spectacular start, he fell by the wayside, sticking to his long held prejudices. That raises the question, are such prejudices still around?

The usual concept of “nothing” is a vacuum, but what is a vacuum? Some figures from Wikipedia may help. A standard cubic centimetre of atmosphere has 2.5 x 10^19 molecules in it. That’s plenty. For those not used to “big figures”, 10^19 means the number where you write down 10 and follow it with 19 zeros, or you multiply 10 by itself nineteen times. Our vacuum cleaner gets the concentration of molecules down to 10^19, that is, the air pressure is two and a half times less in the cleaner. The Moon “atmosphere” has 4 x 10^5 molecules per cubic centimetre, so the Moon is not exactly in vacuum. Interplanetary space has 11 molecules per cubic centimetre, interstellar space has 1 molecule per cubic centimetre, and the best vacuum, intergalactic space, needs a million cubic centimetres to find one molecule.

The top of the Earth’s atmosphere, the thermosphere goes from 10^14 to 10^7. That is a little suspect at the top because you would expect it to gradually go down to that of interplanetary space. The reason there is a boundary is not because there is a sharp boundary, but rather it is the point where gas pressure is more or less matched by solar radiation pressure and that from solar winds, so it is difficult to make firm statements about further distances. Nevertheless, we know there is atmosphere out to a few hundred kilometres because there is a small drag on satellites.

So, intergalactic space is most certainly almost devoid of matter, but not quite. However, even without that, we are still not quite there with “nothing”. If nothing else, we know there are streams of photons going through it, probably a lot of cosmic rays (which are very rapidly moving atomic nuclei, usually stripped of some of their electrons, and accelerated by some extreme cosmic event) and possibly dark matter and dark energy. No doubt you have heard of dark matter and dark energy, but you have no idea what it is. Well, join the club. Nobody knows what either of them are, and it is just possible neither actually exist. This is not the place to go into that, so I just note that our nothing is not only difficult to find, but there may be mysterious stuff spoiling even what little there is.

However, to totally spoil our concept of nothing, we need to see quantum field theory. This is something of a mathematical nightmare, nevertheless conceptually it postulates that the Universe is full of fields, and particles are excitations of these fields. Now, a field at its most basic level is merely something to which you can attach a value at various coordinates. Thus a gravitational field is an expression such that if you know where you are and if you know what else is around you, you also know the force you will feel from it. However, in quantum field theory, there are a number of additional fields, thus there is a field for electrons, and actual electrons are excitations of such fields. While at this point the concept may seem harmless, if overly complicated, there is a problem. To explain how force fields behave, there needs to be force carriers. If we take the electric field as an example, the force carriers are sometimes called virtual photons, and these “carry” the force so that the required action occurs. If you have such force carriers, the Uncertainty Principle requires the vacuum to have an associated zero point energy. Thus a quantum system cannot be at rest, but must always be in motion and that includes any possible discrete units within the field. Again, according to Wikipedia, Richard Feynman and John Wheeler calculated there was enough zero point energy inside a light bulb to boil off all the water in the oceans. Of course, such energy cannot be used; to use energy you have to transfer it from a higher level to a lower level, when you get access to the difference. Zero point energy is at the lowest possible level.

But there is a catch. Recall Einstein’s E/c^2 = m? That means according to Einstein, all this zero point energy has the equivalent of inertial mass in terms of its effects on gravity. If so, then the gravity from all the zero point energy in vacuum can be calculated, and we can predict whether the Universe is expanding or contracting. The answer is, if quantum field theory is correct, the Universe should have collapsed long ago. The difference between prediction and observation is merely about 10^120, that is, ten multiplied by itself 120 times, and is the worst discrepancy between prediction and observation known to science. Even worse, some have argued the prediction was not right, and if it had been done “properly” they justified manipulating the error down to 10^40. That is still a terrible error, but to me, what is worse, what is supposed to be the most accurate theory ever is suddenly capable of turning up answers that differ by 10^80, which is roughly the same as the number of atoms in the known Universe.

Some might say, surely this indicates there is something wrong with the theory, and start looking elsewhere. Seemingly not. Quantum field theory is still regarded as the supreme theory, and such a disagreement is simply placed in the bottom shelf of the minds. After all, the mathematics are so elegant, or difficult, depending on your point of view. Can’t let observed facts get in the road of elegant mathematics!

A Further Example of Theory Development.

In the previous post I discussed some of what is required to form a theory, and I proposed a theory at odds with everyone else as to how the Martian rivers flowed. One advantage of that theory is that provided the conditions hold, it at least explains what it set out to do. However, the real test of a theory is that it then either predicts something, or at least explains something else it was not designed to do.

Currently there is no real theory that explains Martian river flow if you accept the standard assumption that the initial atmosphere was full of carbon dioxide. To explore possible explanations, the obvious next step is to discard that assumption. The concept is that whenever forming theories, you should look at the premises and ask, if not, what?

The reason everyone thinks that the original gases were mainly carbon dioxide appears to be because volcanoes on Earth largely give off carbon dioxide. There can be two reasons for that. The first is that most volcanoes actually reprocess subducted material, which includes carbonates such as lime. The few that do not may be as they are because the crust has used up its ability to turn CO2 into hydrocarbons. That reaction depends on Fe (II) also converting to Fe (III), and it can only do that once. Further, there are many silicates with Fe (II) that cannot do it because the structure is too tightly bound, and the water and CO2 cannot get at the iron atoms. Then, if that did not happen, would methane be detected? Any methane present mixed with the red hot lava would burn on contact with air. Samples are never taken that close to the origin. (As an aside, hydrocarbon have been found, especially where the eruptions are under water.)

Also, on the early planet, iron dust will have accreted, as will other reducing agents, but the point of such agents is, they can also only be used once. What happens now will be very different from what happened then. Finally, according to my theory, the materials were already reduced. In this context we know that there are samples of meteorites that have serious reduced matter, such as phosphides, nitrides and carbides (both of which I argue should have been present), and even silicides.

There is also a practical point. We have one sample of Earth’s sea/ocean from over three billion years ago. There were quite high levels of ammonia in it. Interestingly, when that was found, the information ended up as an aside in a scientific paper. Because it was inexplicable to the authors, it appears they said the least they could.

Now if this seems too much, bear with me, because I am shortly going to get to the point of this. But first, a little chemistry, where I look at the mechanism of making these reduced gases. For simplicity, consider the single bond between a metal M and, say, a nitrogen atom N in a nitride. Call that M – N. Now, let it be attacked by water. (The diagram I tried to include refused to cooperate. Sorry) Anyway, the water attacks the metal and because the number of bonds around the metal stays the same, a hydrogen atom has to get attached to N, thus we get M-OH  + NH. Do this three times and we have ammonia, and three hydroxide groups on a metal ion. Eventually, two hydroxides will convert to one oxide and one molecule of water will be regenerated. The hydroxides do not have to be on the same metal to form water.

Now, the important thing is, only one hydrogen gets transferred per water molecule attack. Now suppose we have one hydrogen atom and one deuterium atom. Now, the one that is preferentially transferred is the one that it is easier to transfer, in which case the deuterium will preferentially stay on the oxygen because the ease of transfer depends on the bond strength. While the strength of a chemical bond starts out depending only on the electromagnetic forces, which will be the same for hydrogen and deuterium, that strength is reduced by the zero point vibrational energy, which is required by quantum mechanics. There is something called the Uncertainty Principle that says that two objects at the quantum level cannot be an exact distance from each other, because then they would have exact position, and exact momentum (zero). Accordingly, the bonds have to vibrate, and the energy of the vibration happens to depend on the mass of the atoms. The bond to hydrogen vibrates the fastest, so less energy is subtracted for deuterium. That means that deuterium is more likely to remain on the regenerated water molecule. This is an example of the chemical isotope effect.

There are other ways of enriching deuterium from water. The one usually considered for planetary bodies is that as water vapour rises, solar winds will blow off some water or UV radiation will break a oxygen – hydrogen bond, and knock the hydroden atom to space. Since deuterium is heavier, it is slightly less likely to get to the top. The problem with this is that the evidence does not back up the solar wind concept (it does happen, but not enough) and if the UV splitting of water is the reason, then there should be an excess of oxygen on the planet. That could work for Earth, but Earth has the least deuterium enrichment of the rocky planets. If it were the way Venus got its huge deuterium enhancement, there had to be a huge ocean initially, and if that is used to explain why there is so much deuterium, then where is the oxygen?

Suppose the deuterium levels in a planet’s hydrogen supply is primarily due to the chemical isotope effect, what would you expect? If the model of atmospheric formation noted in the previous post is correct, the enrichment would depend on the gas to water ratio. The planet with the lowest ratio, i.e. minimal gas/water would have the least enrichment, and vice versa. Earth has the least enrichment. The planet with the highest ratio, i.e. the least water to make gas, would have the greatest enrichment, and here we see that Venus has a huge deuterium enrichment, and very little water (that little is bound up in sulphuric acid in the atmosphere). It is quite comforting when a theory predicts something that was not intended. If this is correct, Venus never had much water on the surface because what it accreted in this hotter zone was used to make the greater atmosphere.

Chemical Reactivity and the Hammett Equation

This post is being presented as a background explanation for the post above. If you have no interest in chemistry, ignore this post.

The Hammett equation is an empirical relationship that relates the effect of a distant substituent in a molecule with the reactive centre. Such a centre might react with something, or be in equilibrium with another form. An example of the latter could be an acid or an amine, which could be in equilibrium with its ionized form, thus

X – H ⇋ X- + H+

Now, further suppose X is part of a molecular structure where some distance away there is a substituent Y, in which case

Y—-X – H ⇋ Y—-X- + H+

and —- is the hydrocarbon structure separating X and Y. Now it is observed that different Y can alter the equilibrium position or rate of reaction of the function X, and the reason is, the substituent alters the potential energy of electrons around wherever it is attached, and that alters to a lesser degree the potential energy around the next carbon atom, and so on. Thus the effect attenuates with distance. There are two complicating factors.

The first is what is called (in my opinion, misleadingly) electron delocalization. It is well known that carbon-carbon double bonds can “delocalize”. What that means is, if you have a molecule with a structure C=C-C(+/-) , where (+/-) means there is either a positive or negative electric charge (or the start of another double bond) on the third carbon atom, then the molecule behaves as if it were C-C-C with two additional electrons that make the bonds effectively 1.5 bonds, and half the charge is at each end. That particular system is called allyl.

The Hammett equation

log(K/Ko) = ρσ

relates the effect of distant substituents on a reactive site. Here K is a rate or equilibrium constant, Ko is a reference constant (to make the bracketed part a number – you cannot have a logarithm of apples!) and this should give a straight line when the logarithm is plotted against the axis that measures σ. ρ is the slope of the line, which attenuates as the path between substituent and site increases provided we assume each intervening chemical bond is localized. If so, σ is a specific value for the substituent. The straight line results because the values of σ are assigned to the substituent to ensure you get a straight line provided the attenuation is dependent on the substituents always having the same values of their assigned σ. What you are doing is empirically relating the attenuation of the electric potential change caused by the substituent at one point by the time it reaches the reactive site. Of course, there is always scatter, but it should be random.

To understand why delocalization becomes relevant, we have to consider what is actually meant. In chemistry textbooks you will often see mechanisms postulated to explain what is going on, and you will see electron pairs moving about. Electrons do not hold hands and move about, and they are never “localised” in as much as they can be anywhere in the region of the molecule at any given instant. The erroneous concept comes from the Copenhagen Interpretation of Quantum Mechanics, whereby the intensity of the wave function gives the probability of finding charge. The chemical bond arises from the interference between two wave functions and the interference zone has two electrons associated with it, and if you agree with my Guidance Wave Interpretation, half the periodic time (because a wave needs a crest and a trough per period, and in the absence of a nodal surface, which is only generated in the so-called antibonds, you need two electrons to provide both in one cycle). What I consider to be localised is not the electrons but the wave interference zone. If you follow the Copenhagen Interpretation, such an interference zone represents regions of enhanced electron density. If the wave interference zone is restricted to a certain volume of space, that characteristic space in the molecule conveys characteristic properties to the molecule because there is enhanced electron density at a lower potential within that region.

Why does it become localised at all, after all the waves can go on forever. The simplest answer is that because of molecular structure, e.g. the carbon atom has four orbitals directed towards the corners of a tetrahedron because that is the optimal distribution to minimize electron repulsion between the four carbon electrons. Interference to create single bonds is “end-on”, in which case for the wave to proceed its axis has to turn a corner, and it cannot do that without a change of refractive index, which requires a change of total energy. However, the allyl system, and a number of others, can delocalize because the axes of the orbitals are normal to any change of direction, and the orbitals can interfere sideways (i.e. normal to the orbital axes) as opposed to the end-on interference in single bonds. So, to get delocalization, the bonding must involve sideways interference of atomic orbitals, while the single bonds are invariably end-on. The reason why cyclopropane was of interest is that if the atomic waves have axes directed towards a tetrahedron, and an angle of 109.4 degrees between them, and since the resultant structure of cyclopropane perforce has angles of 60 degrees between the inter-atomic axes, then either there is partial sideways interference, or the bonds are “bent”. The first should permit delocalization; The second is ambiguous.

If we now reconsider the Hammett equation, we see why it is a test for delocalization. First, if there is delocalization, the value of ρ increases because there is no attenuation over the delocalized zone (i.e. overall the distance has fewer links to attenuate in it). There is, of course, the base value of how much change a substituent can cause anyway. Now, in the cyclopropyl systems I discussed in the previous post, the cyclopropane ring gave a value of ρ that was about 30% higher than a C – C link. My argument was that this is expected if there is no delocalization because there are two routes around the ring, and the final effect should be the sum of the two routes, which is what was found.

The value of σ also changes with delocalization for a limited number of substituents, namely those that can delocalize and amplify a certain effect if demanded. An example is if the reactive site generates a demand for more electron charge, then a substituent such as methoxyl will supply extra by delocalizing its lone pairs on the oxygen, or alternatively, if the demand is to disperse negative charge, a nitro group will behave as if it takes on more. Thus the effect of a limited number of substituents can address the question of whether there is delocalization. The saddest part of the exercise outlined in the previous post is that the first time it was ever deployed to answer a proper question, those who used it on the whole did not seem to appreciate the subtleties available to them. For the ionization of the 2-phenylcyclopropane carboxylic acids, the results obtained in water were too erratic, thanks to solubility problems. The results of reactions in ethanol had an acceptable value of ρ to get a result, but the authors overlooked the effect of two routes, and did not bother to examine the values of σ.