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If you think of a sphereical symmetric diffraction ring, the intensity is constant for each sphereical section (intensity doesn't vary for theta or phi), but it varies kind of like a sine wave in the r dimension from zero to zero with a maximum in the middle of the ring. So that if you think about a vector as being an object that has an energy intensity defined throughout the entire ring, such as another diffraction pattern imbedded in the ring, then I beleive that the distance between two such imbedded patterns can be defined as the enrgy overlap of the patterns. Since the ring sphereically symmetric but thinned out in the r direciton, I believe that it can be thought of as having two eliptical and one hyberbolic dimension. Moving into the r dimension makes things farther apart because the energy overlap becomes less.

Accordingly, I'm thinking that a similar four dimensional diffraction pattern should provide three eliptical and one hyperbolic dimension for determining the closeness of embedded diffraction/distributed energy patterns, which I think should follow the Minkowski metric.

although, I'm not quite sure how to define the energy distributions to make it all work out.

I was just rying to work out the idea of what Minkowski spaces are but it seems to me know that it is the expansion of space with time that causes the Minkowski nature of space.

Accordingly, I'm thinking that a similar four dimensional diffraction pattern should provide three eliptical and one hyperbolic dimension for determining the closeness of embedded diffraction/distributed energy patterns, which I think should follow the Minkowski metric.

although, I'm not quite sure how to define the energy distributions to make it all work out.

I was just rying to work out the idea of what Minkowski spaces are but it seems to me know that it is the expansion of space with time that causes the Minkowski nature of space.

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