Hi:

I am quite impressed with the work of Neil Turok and Paul Steinhardt. Paul sent me a note clarifying a few points about the model. They have done their homework and I believe are well on the way to a workable model of the universe with their "cyclic" model in 5D with a total 10 or 11 small dimensions. Mike Feltz was quite discouraged a few weeks ago...he must be overjoyed now!

Even though the Schwarzschild two/ sphere universe is also internally cyclic, there are many differences between the T/S proposed model and the one described on this site!

When Kalusa proposed the 5D idea as a way of unifying forces, he got the worlds attention, and a two year study was done of 5D cosmology. The upshot was that the idea was rejected because the universe would not particulate in 5D.

At that time singularity was considered a mathematical vestige, and it took a while for it to dawn on scientists that singularity WAS important to the structure of the universe. Once that idea (that singularity had a real place in cosmology) was accepted, it was a short leap to the idea that the particulate 4D reality we observe is embedded in a higher dimensional, non-particulate singular matrix of "Dark Energy" ....ie, that cosmologically the universe might NOT BE Particulate!

The model presently proposed, however, while it is an enormous step forward, is not as advanced (or as complex) as the two/sphere model of Schwarzschild.

There is no inverse mapping of matter and antimatter, no duality, and no sure protection of information and complexity in the model...only conservation of mass (a darned good first step!) and entropy (also a darned good first step!). We also see, in this model (which is just plain super!) the beginnings of a realization of the topological realities of the universe which to this point have been unhappily ignored in cosmology....I guess because the SRT, GR, Planck Realm universe is just plain spooky in its implications...regardless how "obvious" they are...

This model only contains a part of the truth about the preservation of complexity in the universe. It is acknowledged in the model that the "forms" of the next cycle are preserved in the previous "crunch"...but dimensionally, it is just not "all there".

Another of my criticisms of the model is that, so far as I can see, it has problems keeping its reference frames invariant and ignores the fact that ultimate reality is found at each invariant frame of reference in a GR universe. The fact that cosmologically the universe is NOT particulate, ( as discovered in a "backwards" kind of way by Einstein etal) but SINGULAR means that the focus of the universe is NOT on TIME, but ETERNITY.. a geometric, at least quasi-static phenomenon, which at its heart requires a more elegant symmetry than 5D with additional small dimensions.

Time, and particulation as we observe them are, and must be strictly 4D phenomena, even in higher dimensional cosmological models. The Schwarzschild two/ sphere has two 4D "tracks" or frame sets in the system within which a universe like ours can be observed. This is true even though the Schwarzschild model has a single process periodic time dimension, for the Schwarzschild model, although dual, is chiral...the laws of physics in each "hemisphere" are slightly different, and so the hemispheres would be observed (and that is the key to reality) differently. This model has only one continuous time track. Observed chirality in the universe creates special problems for the concept.

As a first impression, I think one of the most shaky assertions of the theory regards the 10 or 11 small dimensions. Quite a bit of work has already been done searching for such small dimensions and all efforts to date have been unsuccessful. 4D, as I already noted, is the cosmic formula for particulation. The universe in 5D and up is not particulate, therefore, 10 or 11 dimensions curled up in a little ball is first and foremost, a contradiction in terms. Additionally, the key to the universe is the way it is observed. Stings are not the foundation of reality...we are. At the lowest levels of scale, strings may exist, but sting theory is like the search for the Higgs Boson...sure to be fruitful, but in the end not a cosmological key. Strings are a transitional 4D frame of reference phenomenon which is much less important than the information itself...the universe we observe, and US.

We are still trying to find high order in singularity! From our frame, maybe we observe the singular realm as a kind of phase solid, liquid or even a gas as it supports, forms and surrounds our particulate world as "dark Energy" but a search for high order, is I believe conceptually in error.

We must accept the fact that GR by mathematical definition does not and cannot work in the Planck Realm. Mass YES, but NOT order! What is Quantum Mechanics all about, anyway! Where is our knowledge of geometry? The order necessary for stability in the universe lies NOT INSIDE SINGULARITY but BEYOND IT- on the other side of reality...a macroscopic bounce or fold; the two/ sphere. Dimensionally the other side is the same "size" as this side....so where does this need for small dimensions come from, conceptually?

Einstein designed GR gravity with geometric points, not a real, definite sized, massive quantum realm consisting of singularity. Because of that concept, GR gravity made sense to him.

GR gravity is therefore incredibly accurate, (to 33 places obviously) but it is not correct because it is not congruent with the universe we actually live in. The smallest scale in the universe, and the place where most of the universal mass resides is NOT a geometric point, but a volume of space (as observed from outside "frames"!) 10 to the minus 33rd of the universal whole.

The "horizon problem" is only ONE of many glaring indications that the GR gravity concept is flawed at its geometric conceptual foundations ...as an exasperated Bohr tried over and over to tell Einstein!

A final comment. Kalusa never suggested that his 5D concept would make a complete cosmology, only that such an arrangement had the effect of unifying the first two of the four "forces". The implication of course was that the four forces were ficticious and geometric in their origin. When Einstein and company investigated Kalusa's finding, and realized that the 5D system would not particulate, they proceeded no further in their work. However, now that we know of the foundational importance of a non-particulate singular condition in the real universe, it can be easily seen that as one additional dimension unified the first two "forces", a 6th dimension would unify three and seven dimensions could be expected to unify all four! Understanding the universe we observe starts, not with 5D and 10 or 11 small dimensions, but with 7D in a Schwarzschild two/ sphere geometry. This configuration naturally unfolds to the higher dimensional reality which is our universe.

Most important, the Schwarzschild two/ sphere has the kind of solid, engineering stability which would make PAM Dirac proud...and makes the world we live in possible!

Best Wishes,

Sam Cox