Hi:

Thanks for your note. About halfway though the text of this response is only one of many sources regarding the assertion I made about particulation (invariant frames) being possible only on 4D surfaces. I include it because, it gives you some verification, almost from "the horses mouth" of what I said.

The world we live in; the reality we know and understand, is particulate. We are particulate beings. So far as can be observed, the universe is constructed in such a way that observers are particulate in their being, occupy invariant frames, embody complexity (require structure) and have a unique personal identity.

Quite a bit of scientific work has been done on this matter of particulation. Any good cosmological theory works at both the microscopic and macroscopic levels of the universe, and explains slews of observations about the universe, in every area of scientific study- from atomic physics to galactic structure. A perfect model explains everything.

What we have learned from Kalusa's work is important, but it points to a more advanced concept. Even in a seven dimensional cosmology like the two/ sphere of Schwarzschild, the 5th spatial dimension is there, lets face it, doing its work. The failure of a 5 dimensional cosmology lies not in its incorrectness, but rather its incompleteness. Kalusa himself fully recognized this incompleteness. He knew there were 4 forces, not two, and that his cosmological idea unified only the first two.

Source below:

If you wish to study this matter, just type in any combination of key words in Google and hit search. There are probably a million words presently posted on the Internet on this subject...

98. Ibid., p.225; A similar statement is found in Jagdish Mehra, ed., A Physicist's Conception of Nature, (Dordrecht-Holland: D. Reidel, 1973), pp.69-70.

"Theories with a fifteenth variable are a possible generalization of Kaluza's five-dimensional approach. Einstein and I considered, what is today rightly known as the Jordan-Thiry theories, in the late thirties. We did not publish this attempt, as it did not achieve Einstein's objective, to yield a classical model of elementary particles."

One last comment...toward the end of his life, Einstein, as he worked at Princeton began to realize that his goal of a unified field theory would only be achieved in some higher dimensional structure. Nevertheless, at that point in history the practical reality of singularity and its importance in cosmology were still undiscovered. As we have seen, Einstein understood well, from careful study that cosmologies above 4D would not particulate. Even though he understood the concept of embedded ness, it is easy to see why he and his contemporaries failed to seriously consider the 7D Schwarzschild two/ sphere, in spite of the fact that the solutions to GR which followed from that geometry were the first to fit his famous theory!

Even in Schwarzschilds two/ sphere geometry, particulation occurs only on 4D surfaces, but it occurs on TWO 4D tracks. There are positive and negative three spaces sharing a single, single process, but periodic time dimension. This single periodic time dimension separates the two 4D particulate sides of the universe, and protects them from destruction by placing singularity (and dilated cosmological time) between them. The inverse mapping of antimatter and matter thus possible is one of the many engineering triumphs of Schwarzschild geometry. I can say without hesitation that cosmology over the past 80 years has come by astronomical observation to ever more convincingly confirm Schwarzschilds (and Diracs) work

Best Wishes,

Sam Cox