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When there is a wave, something is undulating. In the example of a rope, the rope is what undulates. In the case of a ripple on a pond, the water is undulating, and when a sound wave propagates, the air is undulating. The question is: in the case of a particle, what undulates?

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Your question was a little messy at first, but I thought it would be much clearer to remove some parts, so I edited them out. If the question in its current version doesn't accurately represent what you are asking, you can always edit it again. –  David Z Aug 30 '11 at 21:04
    
@jormansandoval what would you consider to be the thing undulating when looking at light, since it is a wave? –  luksen Aug 30 '11 at 21:09
    
The undulations are in 6 dimensions for two particles and in 9 dimensions for three. –  Ron Maimon Aug 30 '11 at 21:14

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The undulations are of the probability amplitude for the particle to be someplace. The notion of probability amplitude is fundamental, and cannot be reduced to anything more primitive. It is described on Wikipedia under "superposition principle". The undulations are in the space of all possible universes, so that two particles are described by undulations in the 6 dimensional space of all possible pairs of positions, three particles are described by undulations in 9 dimensions. There is no physical way of making it like waves on water or sound in air, because physical waves travel in three dimensions of space.

If you are asking about classical fields, like E and B fields, there are not undulations in anything either. They are the primitive things out of which things like atoms and water are built. You can make classical fields out of particles if they have the right statistics, and these fields, when they are made of matter, are called Bose-Einstein condensates or superfluids, depending on the density.

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