Science in Action – or Not

For my first post in 2019, I wish everyone a happy and prosperous New Year. 2018 was a slightly different year than most for me, in that I finally completed and published my chemical bond theory as an ebook; that is something I had been putting off for a long time, largely because I had no clear idea what to do with the theory. There is something of a story behind this, so why not tell at least part of it in my first blog post for the year? The background to this illustrates why I think science has gone slightly off the rails over the last fifty years.

The usual way to get a scientific thought over is to write a scientific paper and publish it in a scientific journal. These tend to be fairly concise, and primarily present a set of data or make one point. One interesting point about science is that if it is not in accord with what people expect, the odds on are it will be ignored, or the journals will not even accept it. You have to add to what people believe to be accepted. As the great physicist Enrico Fermi once said, “Never underestimate the joy people derive from hearing something they already know.” Or at least think they know. The corollary is that you should never underestimate the urge people have to ignore anything that seems to contradict what they think they know.

My problem was I believed the general approach to chemical bond theory was wrong in the sense it was not useful. The basic equations could not be solved, and progress could only be made through computer modelling, together with as John Pople stated in his Nobel lecture, validation, which involved “the optimization of four parameters from 299 experimentally derived energies”. These validated parameters only worked for a very narrow range of molecules; if they were too different the validation process had to be repeated with a different set of reference molecules. My view of this followed another quote from Enrico Fermi: I remember my friend Johnny von Neumann used to say, “with four parameters I can fit an elephant and with five I can make him wiggle his trunk.” (I read that with the more modern density functional theory, there could be up to fifty adjustable parameters. If after using that many you cannot get agreement with observation, you should most certainly give up.)

Of course, when I started my career, the problem was just plain insoluble. If you remember the old computer print-out, there were sheets of paper about the size of US letter paper, and these would be folded in a heap. I had a friend doing such computations, and I saw him once with such a pile of computer paper many inches thick. This was the code, and he was frantic. He kept making alterations, but nothing worked – he always got one of two answers: zero and infinity. As I remarked, at least the truth was somewhere in between.

The first problem I attacked was the energy of electrons in the free atoms. In standard theory, the Schrödinger equation, when you assume that an electron in a neutral atom sees a charge of one, the binding energy is far too weak. This is “corrected”througha “screening constant”, and each situation had its own “constant”. That means that each value was obtained by multiplying what you expect by something to give the right answer. Physically, this is explained by the electron penetrating the inner electron shells and experiencing greater electric field.

What I came up with is too complicated to go into here, but basically the concept was that since the Schrödinger equation (the basis of quantum mechanics) is a wave equation, assume there was a wave. That is at odds with standard quantum mechanics, but there were two men, Louis de Broglie and David Bohm, who had argued there was a wave that they called the pilot wave. (In a recent poll of physicists regarding which interpretation was most likely to be correct, the pilot wave got zero votes.) I adopted the concept (well before that poll) but I had two additional features, so I called mine the guidance wave.

For me, the atomic orbital was a linear sum of component waves, one of which was the usual hydrogen-like wave, plus a wave with zero nodes, and two additional waves to account for the Uncertainty Principle. It worked to a first order using only quantum numbers. I published it, and the scientific community ignored it.

When I used it for chemical bond calculations, the results are accurate generally to within a few kJ/mol, which is a fraction of 1% frequently. Boron, sodium and bismuth give worse results.  A second order term is necessary for atomic orbital energies, but it cancels in the chemical bond calculations. Its magnitude increases as the distance from a full shell increases, and it oscillates in sign depending on whether the principal quantum number is odd or even, which results when going down a group of elements, that the lines joining them zig zag.

Does it matter? Well, in my opinion, yes. The reason is that first it gives the main characteristics of the wave function in terms only of quantum numbers, free f arbitrary parameters. More importantly, the main term differs depending on whether the electron is paired or not, and since chemical bonding requiresthe pairing of unpaired electrons, the function changes on forming bonds. That means there is a quantum effect that is overlooked in the standard calculations. But you say, surely they would notice that? Recall what I said about assignable parameters? With four of them, von Neumann could use the data to calculate an elephant! Think of what you could do with fifty!

As a postscript, I recently saw a claim on a web discussion that some of the unusual properties of gold, such as its colour, arise through a relativistic effect. I entered the discussion and said that if my paper was correct, gold is reasonably well-behaved, and its energy levels were quite adequately calculated without needing relativity, as might be expected from the energies involved. This drew almost derision – the paper was dated, an authority has spoken since then. A simple extrapolation from copper to silver to gold shows gold is anomalous – I should go read a tutorial. I offered the fact that all energy levels require enhanced screening constants, therefore Maxwell’s equations are not followed. These are the basic laws of electromagnetism. Derision again – someone must have worked that out. If so, what is the answer? As for the colour, copper is also coloured. As for the extrapolation, you should not simply keep drawing a zig to work out where the zag ends. The interesting point here was that this person was embedded in “standard theory”. Of course standard theory might be right, but whether it is depends on whether it explains nature properly, and not on who the authority spouting it is.

Finally, a quote to end this post, again from Enrico Fermi. When asked what characteristics Nobel prize winners had in common: “I cannot think of a single one, not even intelligence.”

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!