Is science sometimes in danger of getting tunnel vision? Recently published ebook author, Ian Miller, looks at other possible theories arising from data that we think we understand. Can looking problems in a different light give scientists a different perspective?

Relativitistic Effects In Valence Electrons?

Nullius in verba (take nobody's word) is the motto of the Royal Society, and it should be the motto of every scientist. The problem is, it is not. An alternative way of expressing this comes from Aristotle: the fallacy ad verecundiam. Just because someone says so, that does not mean it is right. We have to ask questions of both our logic and of nature, and I am far from convinced we do this often enough. What initiated this was an article in the August Chemistry World where it was claimed that the “unexpected” properties of elements such as mercury and gold were due to relativistic effects experienced by the valence electrons.
 
If we assume the valence electrons occupy orbitals corresponding to the excited states of hydrogen (i.e. simple solutions of the Schrödinger equation) the energy E is given by E = Z2Eo/n2h2. Here, Eo is the energy given by the Schrödinger equation, n gives the quanta of action associated with the state, and Z is a term that at one level is an empirical correction. Thus without this, the 6s electron in gold would have an energy 1/36 that of hydrogen, and that is just plain wrong. The usual explanation is that since the wave function goes right to the nucleus, there is a probability that the electron is near the nucleus, in which case it experiences greater electric fields. For mercury and gold, these are argued to be sufficient to lead to relativistic mass enhancement (or spacetime dilation, however you wish to present the effects), and these alter the energy sufficiently that gold has the colour it has, and both mercury and gold have properties unexpected from simple extrapolation from earlier elements in their respective columns in the periodic table. The questions are, is this correct, or are there alternative interpretations for the properties of these elements? Are we in danger of simply hanging our hat on a convenient peg without asking, is it the right one? I must confess that I dislike the relativistic interpretation, and here are my reasons.
 
The first involves wave-particle duality. Either the motion complies with wave properties or it does not, and the two-slit experiment is fairly good evidence that it does. Now a wave consistent with the Schrödinger equation can have only one frequency, hence only one overall energy. If a wave had two frequencies, it would self-interfere, or at the very least would not comply with the Schrödinger equation, and hence you could not claim to be using standard quantum mechanics. Relativistic effects must be consistent with the expectation energy of the particle, and should be negligible for any valence electron. 
 
The second relates to how the relativistic effects are calculated. This involves taking small regions of space and assigning relativistic velocities to them. That means we are assigning specific momentum enhancements to specific regions of space, and surely that violates the Uncertainty Principle. The Uncertainty Principle argues the uncertainty of the position multiplied by the uncertainty of the momentum is greater or equal to the quantum of action. In fact it may be worse than that, because when we have stationary states with nh quanta, we do not know that that is not the total uncertainty. More on this in a later blog.
 
On a more personal note, I am annoyed because I have published an alternative explanation [ Aust. J. Phys. 40 : 329 -346 (1987)] that proposes that the wave functions of the heavier elements do not correspond exactly to the excited states of hydrogen, but rather are composite functions, some of which have reduced numbers of nodes. ( The question, “how does an electron cross a nodal surface?” disappears, because the nodes disappear.) The concept is too complicated to explain fully here, however I would suggest two reasons why it may be relevant.
 
The first is, if we consider the energies of the ground states of atoms in a column of elements, my theory predicts the energies quite well at each end of a row, but for elements nearer the centre, there are more discrepancies, and they alternate in sign, depending on whether n is odd or even. The series copper, silver and gold probably show the same effect, but more strongly. The “probably" is because we need a fourth member to be sure. However, the principle remains: taking two points and extrapolating to a third is invalid unless you can prove the points should lie on a known line. If there are alternating differences, then the method is invalid. Further, within this theory, gold is the element that agrees with theory the best. That does not prove the absence of relativistic effects, but at least it casts suspicion.
 
The second depends on calculations of the excited states. For gold, the theory predicts the outcomes rather well, especially for the d states, which involve the colour problem. Note that copper is also coloured. (I shall post a figure from the paper later. I thought I had better get agreement on copyright before I start posting it, and as yet I have had no response. The whole paper should be available as a free download, though.) The function is not exact, and for gold the p states are more the villains, and it is obvious that something is not quite right, or, as I believe, has been left out. However, the point I would make is the theoretical function depends only on quantum numbers, it has no empirical validation procedures and depends only on the nodal structure of the waves. The only interaction included is the electron nucleus electric field so some discrepancies might be anticipated. Now, obviously you should not take my word either, but when somebody else produces an alternative explanation, in my opinion we should at least acknowledge its presence rather than simply ignore it.
Posted by Ian Miller on Aug 26, 2013 3:58 AM Europe/London

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