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?

Physical Wave Functions: Theory Is Not Yet Finished So Why Not Participate?

If your goals include getting rich, getting promoted, winning prizes etc, time spent developing theories appears to be time wasted. Nevertheless, if you are really interested in science, there are two good reasons to do so. The first is, you do not need expensive equipment, although you certainly need access to a good library, and you can do it in your spare time. Einstein did his most productive work as a patent clerk. The second is, while all scientists experience emotional highs (success!) and lows (oops, another failure!), for the experimentalist these usually come at the end of the experiment. For the theoretician the highs can come at almost any time later, and from most surprising sources. Further, after a time you do not suffer lows; if you are found to be wrong after a reasonable length of time, at least you can persuade yourself that you persuaded someone to do something they would not have otherwise done, hence you have advanced science a little, even if not for the best of reasons. I hope the reader will forgive me because I would like to illustrate how unexpected emotional rewards can come with something that has happened to me. This arose from what I regard as a most unexpected experimental result, which goes to the heart of quantum mechanics.
 
Up until last week, I believe most physical scientists would have stated that the wave function is not a physical entity, but rather a mathematical construct whose square represents a probability distribution associated with the outcome of a determination. After all, how else does renormalization make sense? You cannot renormalize a bucket of water! That was before Lundeen et al. (Nature, 474, 188-191) published a clearly remarkable achievement: they measured the wave function of photons, determining the real part through a rotation of the polarization and the complex part through the ellipticity. Effectively, the authors say, you could construct a "wave function meter", and they propose that you could measure the wave function associated with electron motion in atoms and molecules.
 
I have two reasons to be excited. The first is, to make a measurement of both the real and complex parts of the wave surely it has to be something, and not simply a construct. As the cover of Nature said, "Direct measurement prompts the question, what is it?" The relevance to me is that in my ebook, I have over 70 problems for exercises in the development of theory, and in the more difficult ones, there is a sequence that develops yet a further interpretation of quantum mechanics (there are at least 6 others) in which the reader is offered the chance to obtain quantum mechanics from one deeper principle, including obtaining the Schrodinger equation, the Uncertainty Principle, the Exclusion Principle, and also to note why the Complementarity Principle could in principle be got around, which is what these authors did. In the solutions I give, the wave is a physical entity, the square of the amplitude of which represents the energy associated with the particle (the square of the amplitude of all other waves represents the energy associated with the vibration), although it probably vibrates in additional dimensions, thus taking it into the concepts of string theory. This theory may or may not be correct, but as far as I am aware, it is the only one for which the wave function is "something" with a clearly physical and determinable variable associated with it.
 
The second reason is that I am an advocate for atomic orbitals of multi-electron atoms that differ from the usual wave functions that correspond to excited states of hydrogen [Aust. J. Phys. 40 : 329 -346 (1987)] in that the ground state orbitals do not have radial nodes (thus solving the problem, how do electrons cross them!) and the resultant excited states have the nodes required for excitation added to them. I doubt that the methodology outlined by Lundeen et al. will really work on atomic orbitals, but if one thing is clear in science these days it is that if there is no sound reason why something cannot be done, sooner or later it will be. There is real excitement in the realization that something you proposed could be proven true one day. (Yes, it could be proven false, but that is just one of those chances you have to take.)
 
The point that I want to make is that for young scientists starting their career, while it may not help your social standing, especially in the short term, there is the possibility of experiencing quite unique feelings. And if you think there is nothing left to theorize about, if something as fundamental as the standard interpretation of the quantal wave function can be overturned by an experiment, so can a lot of other "tablets of stone". You may or may not be right, but you will stay interested.
Posted by Ian Miller on Jun 14, 2011 3:25 AM Europe/London

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