Perhaps I am getting grumpy as I age, but I feel that much in science is not right. One place lies in the fallacy ad verecundiam. This is the fallacy of resorting to authority. As the motto of the Royal Society puts it, nullius in verba. Now, nobody expects you to personally check everything, and if someone has measured something and either clearly shows how he/she did it, or it is something that is done reasonably often, then you take their word for it. Thus if I want to know the melting point of benzoic acid I look it up, and know that if the reported value is wrong, someone would have noticed. However, a different problem arises with theory because you cannot measure it. Further, science has got so complicated that any expert is usually an expert in a very narrow field. The net result is that because things have got so complicated, most scientists find theories too difficult to examine in detail and do defer to experts. In physics, this tends to be because there is a tendency for the theory to descend into obscure mathematics and worse, the proponents seem to believe that mathematics IS the basis of nature. That means there is no need to think of causes. There is another problem, that also drifts over to chemistry, and that is the results of a computer-driven calculation must be right. True, there will be no arithmetical mistake but as was driven into our heads in my early computer lectures: garbage in, garbage out.
This post was sparked by an answer I gave to a chemistry question on Quora. Chemical bonds are usually formed by taking two atoms with a single electron in an orbital. Think of that as a wave that can only have one or two electrons. The reason it can have only two electrons is the Pauli Exclusion Principle, which is a very fundamental principle in physics. If each atom has only one in such an orbital, they can combine and form a wave with two electrons, and that binds the two atoms. Yes, oversimplified. So the question was, how does phosphorus pentafluoride form. The fluorine atoms have one such unpaired electron each, and the phosphorus has three, and additionally a pair in one wave. Accordingly, you expect phosphorus to form a trifluoride, which it does, but how come the pentafluoride? Without going into too many details, my answer was that the paired electrons are unpaired, one is put into another wave and to make this legitimate, an extra node is placed in the second wave, a process called hybridization. This has been a fairly standard answer in text books.
So, what happened next? I posted that, and also shared it to something called “The Chemistry Space”. A moderator there rejected it, and said he did so because he did not believe it. Computer calculations showed there was no extra node. Eh?? So I replied and asked how this computation got around the Exclusion Principle, then to be additionally annoying I asked how the computation set the constants of integration. If you look at John Pople’s Nobel lecture, you will see he set these constants for hydrocarbons by optimizing the results for 250 different hydrocarbons, but leaving aside the case that simply degenerates into a glorified empirical procedure, for phosphorus pentafluoride there is only one relevant compound. Needless to say, I received no answer, but I find this annoying. Sure, this issue is somewhat trivial, but it highlights the greater problem that some scientists are perfectly happy to hide behind obscure mathematics, or even more obscure computer programming.
It is interesting to consider what a theory should do. First, it should be consistent with what we see. Second, it should encompass as many different types of observation as possible. To show what I mean, in phosphorus pentafluoride example, the method I described can be transferred to other structures of different molecules. That does not make it right, but at least it is not obviously wrong. The problem with a computation is, unless you know the details of how it was carried out, it cannot be applied elsewhere, and interestingly I saw a recent comment in a publication by the Royal Society of Chemistry that computations from a couple of decades ago cannot be checked or used because the details of the code are lost. Oops. A third requirement, in my opinion, is it should assist in understanding what we see, and even lead to a prediction of something new.
Fundamental theories cannot be deduced; the principles have to come from nature. Thus mathematics describes what we see in quantum mechanics, but you could find an alternative mathematical description for anything else nature decided to do, for example, classical mechanics is also fully self-consistent. For relativity, velocities are either additive or they are not, and you can find mathematics either way. The problem then is that if someone draws a wrong premise early, mathematics can be made to fit a lot of other material to it. A major discovery and change of paradigm only occurs if there is a major fault discovered that cannot be papered over.
So, to finish this post in a slightly different way to usual: a challenge. I once wrote a novel, Athene’s Prophecy, in which the main character in the first century was asked by the “Goddess” Athene to prove that the Earth went around the sun. Can you do it, with what could reasonably be seen at the time? The details had already been worked out by Aristarchus of Samos, who also worked out the size and distance of the Moon and Sun, and the huge distances are a possible clue. (Thanks to the limits of his equipment, Aristarchus’ measurements are erroneous, but good enough to show the huge distances.) So there was already a theory that showed it might work. The problem was that the alternative also worked, as shown by Claudius Ptolemy. So you have to show why one is the true one.
Problems you might encounter are as follows. Aristotle had shown that the Earth cannot rotate. The argument was that if you threw a ball into the air so that when it reached the top of its flight it would be directly above you, when the ball fell to the ground it would be to the east of you. He did it, and it wasn’t, so the Earth does not rotate. (Can you see what is wrong? Hint – the argument implies the conservation of angular momentum, and that is correct.) Further, if the Earth went around the sun, to do so orbital motion involves falling and since heavier things fall faster than light things, the Earth would fall to pieces. Comets may well fall around the Sun. Another point was that since air rises, the cosmos must be full of air, and if the Earth went around the Sun, there would be a continual easterly wind.
So part of the problem in overturning any theory is first to find out what is wrong with the existing one. Then to assert you are correct, your theory has to do something the other theory cannot do, or show the other theory has something that falsifies it. The point of this challenge is to show by example just how difficult forming a scientific theory actually is, until you hear the answer and then it is easy.