Dear Israel,
Thank you for your feedback on my essay. It is regrettable that you approached it with some preconceived notions and also lacking certain understanding of the 4D geometry, which is clear from your following comment:
"You are supporting the view that the 3D space we experience everyday is some sort of solid embedded in another physical space of 4D, likewise as a sheet of metal could be embedded in a solid sphere. "
It appears that you do not know that the surface of a 4D object, such as a hypersphere, is 3-dimensional in the same way as a surface of a sphere is a 2D plane. The 2D surface of a sphere is not "some sort of solid embedded in another physical space of" a sphere, but is an integral part of it. Similarly, the 3D surface is an integral part of a hypersphere. It seems all your confusion about my essay stems from this lack of basic geometric awareness. In line with other multidimensional models, I called this 3D surface a membrane, instead of always referring to it as a (hyper)surface.
In addition, I am not sure what you mean by "solid dimensions" which you differentiate from "geometrical dimensions". This seems your original definitions and usage, on which I cannot comment.
Regarding the KK model predictions that you refer to, they were based on the wrong assumption that the extra dimension was equally accessible to both matter and radiation as the observed 3. The same wrong assumption was the reason why Klein invented compactification: to ensure that the extra dimension was well hidden and thus in line with the question of why we do not see it. In my essay I show that this was both wrong and unnecessary.
Regarding your question of why ether was a wrong model, first, the concept itself stems from air, which cannot support transverse waves, and second, the theory never considered the 4D nature of space, assuming that it had only 3 observed dimensions.
You also say: "... that this paradox is only valid considering that space is some sort of fluid. Today physics does not assume space as such and therefore there is no paradox for contemporary physics. My question in this respect is: don't you think that by reviving the old problem you are also contradicting current views, in particular, the general and the special relativity?"
That physics decreed 100 years ago that space was empty is in fact the topic of my essay, in which I argue that it was the wrong turn.
In no way does my model contradicts current views. You seem to have missed the part where I say that the model is the same overall as other models with large extra dimension (which are in line with relativity).
You also say: "Something that was not clear for me is whether you think that the universe was created in the Big Bang (BB) or not. ... What reasons can you provide to explain the lost of dimensions? "
In the essay I say, "in line with big bang theory, we could assume that initially the structure had infinite number of dimensions, but once it cooled off, it settled into 4D." I presume you are aware of the high energies at first instances after the BB. These high energies correspond to higher-dimensionality of space. When space cools off, its structure precipitates from higher-dimensions into lower, i.e. it looses dimensions, as if energies hidden in higher dimensions trickle down all the way to 4D, increasing the bulk and hyperssurface area, which corresponds to expansion.
Similarly, going in the direction of increasing energy, when the structure is put under too much pressure locally, because it is non-compressible, it will bulge out into an additional dimension (and by the way, in this context, the appearance of singularities is what marks the door into a higher dimension). When the local pressures let go, the energies hidden in extra-dimension trickle back into the 4D bulk, causing it to expand, which, in turn, increases its 3D surface area, causing perceived expansion of space.
Regarding the process of "precipitation into a lower D", being only an analyst, I can't adequately speak for topology. My hunch is that the method based on Hamilton-Ricci flow, quite possibly the one perfected by Grigory Perelman in his latest work, may shed some light on the specifics.
Again, thank you for your feedback.
I have read your essay today and found it interesting, even though I cannot conceive of an absolute reference frame, for which you advocate. I see absolute reference frame an abstraction that cannot exist in reality. But it is the plurality of our views is that is valued in this contest. Best regards to you!
