Dear Armin,
It is good to hear from you. I found one of Peres' papers with the title "Quaternionic Quantum Interferometry" which is substantially similar to the paper you mention, if not the same. It appears Peres was interested in a radical modification of quantum mechanics in which some complex exponentials would be replaced by unit quaternions - like QM isn't complicated enough already. The experimental technique involves the examination of nuclear scattering cross-sections. It looks like quite a difficult task to find a material with three sufficiently different scatterers required to determine whether the scattering amplitude is a complex function or quaternion. It is an interesting idea I was not familiar with, and one worth investigating in my opinion.
In contrast, my essay deals with quaternions in a way that parallels quantum mechanics (I think) by using complex exponentials. I have yet to find an example from QM but the Higgs mechanism seems promising. It is only in the last few months that I found out about the Higgs field having quaternion structure.
It is unfortunate that quaternions have a bad reputation among physicists. Here are a couple of zingers about quaternions taken from Wikipedia. Kelvin's comment is especially harsh considering Maxwell originally formed his equations as quaternions, and whose untimely death (from cancer I believe, not quaternions) had occurred over a decade previously.
"Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell." - Lord Kelvin, 1892.
"...quaternions appear to exude an air of nineteenth century decay, as a rather unsuccessful species in the struggle-for-life of mathematical ideas. Mathematicians, admittedly, still keep a warm place in their hearts for the remarkable algebraic properties of quaternions but, alas, such enthusiasm means little to the harder-headed physical scientist." - Simon L. Altmann, 1986.
Perhaps there has been a slight thaw over the last century in physicist's attitudes toward quaternions and Clifford algebras.
Your dimensional theory is the most promising idea for a theory of mass I have seen, and there are hints that dimensionality plays a role in the states of quaternion resonance. I look forward to your essay.
Colin