Thank you for your response. It gives me chills of delight.
In my search for an answer to this question for a few decades, I have become convinced that either, (1)the answer was too complex for me to understand and that people like Ed Witten and Stephen Hawking were able to comprehend some concepts that were beyond their capability to explain to someone with a brain as limited as mine, or (2) that they really didn't comprehend the situation either and were grasping at inadequate straws such as "compactification of dimensions".
Before your response, I was nearly resigned to accept number (1). Now, I feel that there is a possibility that (2) may be correct.
If so, it seems to me important to give a fair hearing to the argument that there is no need to compactify dimensions, if the only reason to do so is to explain why we can't detect or access them. The topological properties of manifolds embedded in higher dimensional spaces explains that fact in a natural easy-to-comprehend way.
If we consider the possibility of the real existence of 10, or so, full-size extended spatial dimensions, with our accessible three forming a 3D manifold in that space, I think there are more than sufficient possibilities for complex configurations of structures within it to explain all phenomena in our manifold, including the results of the Aspect experiment.
Consider Flatlanders existing on the surface of one of our oceans. Since waves on the ocean curve their space in a non-Euclidean way, the wave action would be detectable to them in many different ways. But in addition, think of all the 3D structures we are familiar with (ships, fish, sonar, e/m radiation, fishing line, periscopes and binoculars, human beings, etc.) which can influence what those Flatlanders might experience, with no need whatsoever to "roll up" the surface of the ocean in order to do so.
I would like to be in a position to be able to challenge people like Hawking, Greene, Witten, et. al. to defend their reasons for insisting on Klein's corruption of Kaluza's excellent idea. I have written a couple letters to a couple of these guys, but of course, I got the response one would expect -- none.
I think that once it is seen that there is no necessity to "compactify" dimensions, the absurd contortions of Calabi-Yau spaces can be abandoned in favor of nice simple Euclidean Geometry in 10 or so dimensions. I would expect this to lead directly to some new insight and some breakthrough ideas.
I'm excited! What do you think?