Is Particle-Wave Duality a Topological Transformation?

[Rade]

Question. Suppose a particle {o} that is a topological entity [see:http://en.wikipedia.org/wiki/Topology] so that it can take an extended form {...o o o o o o o o o ...} to infinity. Now, suppose the transformation to exist as a wavefunction--is this then a correct view of particle-wave duality--e.g., that the two are nothing more than a topological transform ? Thanks for any comments.

 

[Farsight]

http://en.wikipedia.org/wiki/Topology

If I can comment: Take a look at Suppose a particle.... You've already got the beginnings of a problem here, at least in layman's language. A "particle" is commonly thought of as some little speck or mote or grain, a tiny hard little thing. It doesn't sound anything like a wavefunction. Then to bridge the gap, along comes "transformation". Why should anything be transforming at all? Maybe it just us looking at it in different ways. For example, picture a wave in the sea. Now ask yourself this: how would a blind man in the surf picture the wave that knocked him flat on his back?

But anyhow. I do like the word "entity". It ought to let us think about things without the linguistic baggage that creates wave/particle problems. Which means your question might read Suppose an entity is topological in nature and can take an extended form... and maybe the question has gone away.