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?

A 1960s PhD – (1) Baggage!

I have seen some blogs from young chemists starting or being involved in their PhD who seem to think they have troubles so I thought that just in case they thought previous times were a golden age, why not disillusion them! This little tale also shows why I got addicted to alternative theories, and has two further messages for young chemists. (1) Give more thought to the importance of beginnings. It makes or wrecks (or lies somewhere in between) the rest of your life, so think! (2) Be careful what you wish for; sometimes you get it! Then it is too late to work out you might be better off without it.
I started my PhD at the end of 1963, but what preceded that is relevant because I started with baggage that most students do not have to carry. During the summer of 1962-3 (southern hemisphere!) I was given employment to assist a little research. The department had been involved with the Hammett equation, and had been looking at some benzylammonium dissociation constants. I had the job of purifying some and making some measurements, which I did, and which introduced me to physical organic chemistry and put my name on a paper for the first time. Then in my honours year, selenium poisoning due to the failure of fume cupboard ducting led to my missing lectures frequently. Then came disillusionment. A lecture on the quantum mechanics of the hydrogen molecule led to an equation across the blackboard, and the lecturer said that he would try to show how progress could be made in solving it. I stopped the lecture to point out the equation had an energy minimum when the internuclear distance approached zero, and where it was supposed to be infinite. (If you want to do theory, it helps if you can mentally determine critical aspects of a function.) The lecturer did not know what had gone wrong (and he was only lecturing QM because someone had to). I suddenly discovered that lecturers did not necessarily understand what they were teaching! And they were going to determine my honours level!
I wanted to understand, so later, once again sick, I thought, if wave particle duality occurs, as in diffraction, electrons do not have an option: they must follow what the wave requires of them. After all, no particle description gets diffraction. So, if the wave determines energy and momentum, why not consider the problem as a standing wave problem? (As an aside, can you think of a good reason why not? Bet you can't!) An important point about stationary waves is that they are single-valued, i.e., they do not self-interfere, which requires the geometry of the problem to fix the location of nodes and antinodes. (In a subsequent paper I submitted, I used an organ pipe as an example. The referee could not understand the relevance.) Now, for a given energy, to a first approximation in the Coulomb field of a hydrogen atom the momentum is independent of the mix of radial/angular momentum, so consider it angular, in which case wavelength is proportional to m(thetadot)r^2. Doubling the interactions (electron pairing) is equivalent to doubling mass, hence at constant frequency (frequency had to be conserved otherwise there would be self-interference and the wave would not be single-valued) the wavelength between the nuclei should be a/root2, where a is the Bohr radius. Then from the Einstein ratio, where energy = h x frequency, the energy of the component on the bond axis, in Cartesian coordinates had to be twice the energy of those components in the free atom, hence the bond energy of the hydrogen molecule was 1/3 the Rydberg energy. Try looking up the observed values – the agreement was extraordinarily encouraging, and I had this weird feeling that I had discovered something. Then, problems! The method did not work for any other bond, so it was wrong, right? Not so fast! For the alkali metals, the errors were a clear function of the quantum number n!
Now what? The next step was to go to the library. Unfortunately, with finals about five weeks away, most of the "good" books were gone. One that was there was by de Broglie, on his "double solution". The good news was that there was someone there who felt that there was a real wave there, which although not necessary for the above reasoning, seemed to be the only way there was a physical cause. The bad news was that it was clear that I needed to learn some more physics to make sense of quantum mechanics. One more thing was clear: I had to avoid quantum mechanics in my finals! So, when finals were over, and my total neglect of quantum mechanics had paid dividends, I had a decision: progress to PhD or go back and do physics. I decided to progress, and put my efforts to learn physics to one side. I could teach myself, so I thought. It turned out to be an interesting decision because I avoided bothering about the mathematical formalism of the state vector approach, which of course specifically forbids factorizing the wave function as I did above. My next problem was simple: choose a PhD project. More soon.
Posted by Ian Miller on Oct 12, 2012 10:54 PM Europe/London

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