Why would three orthogonal directions of rotation be required to "close off" the universe? And why does this necessitate "extra" dimensions? Furthermore, when you speak of the intrinsic spin imparted by such a rotation, are you indeed equating it with the traditional quantum "spin" characteristic, or introducing something new and orthogonal to that, but similar in function?
Ooooh... good question. First point is that I am not taking the "easy" path in TOE's. It is not popular at the moment to take the quantum out of things that have been traditionally quantized. I am a "practical" elf and I take some points up because I see a more immediate benefit from this approach than some others. Consider for one moment that "String Theory" does not start out with strings of 23 or 24 dimensions anymore. This is not because they do not have those 23 or 24 dimensions. The reason is it is "easier" to deal with 10 or 11 dimensions. Will the Theory of Everything be any worse for that "simplification"... probably not since the concept is these "excess" dimensions are more tightly curled up than the others and are definitely in a range of energies too high to reach by human engineering .... forever. I say that quite confidently.
In the same way it may be possible to deal with gravity and mass as a particle theory and quantize those quantities but knowing the practical limits of quantum gravity I would be very surprised to find any measure of quantum "levels" in our measurable part of the Universe. There is a theory that these effects may be visible at about 1/10th millimeter dimensions if gravity is able to "penetrate dimensions" as postulated in one of those theories on quantum gravity. I somehow doubt it... if a "differential" effect was observable at this level of the Universe it would have affected "other" experiments by now. So I am "happy" with the idea that we can deal with Gravity "safely" as a non-quantized phenomenon. This means that it will be incompatible with quantum phenomena.... we have almost always known this. So I have taken a "look ahead" and believe that quantum phenomena will not be the ultimate solution to the Universe but the Universe has a hidden state we have known about for quite a long time. This state is when the "quantized" particle is unable to be observed for significant periods due to some peculiarity of the means of observation.
You will be well aware of "Bohmian Mechanics" if you have been following me. What this says is that the quantum particle is unobserved and is somewhere else for much of its travels. For instance light quanta which travel at © cannot be observed unless you destroy the qubit. This action drags the "particle" from out of some "higher space" where it is not being observed and then it is able to be "scattered". Good Elf does not say this is any of his ideas because it has been "developed" in the years since Bohm has passed away. I am convinced by the argument that this is one paradigm that may work. It will not be the only paradigm that can work but it is "ready" and "willing" to mount the "bull" and try to hold on by its horns.
The spaces of quantum physics and "real" linear space are not the same beast and this is where the problem occurs. You need a "configuration space" as an intermediate to map the quantum events into our spacetime of 3D + T. The reason this is required is because there are more dimensions. Both General Relativity and Quantum Mechanics do not have enough dimensions to describe our Universe. The theory can be made to work but while the particle... a quantum of any sort... is out of view "mankind" is going to have to come to grips with the sad fact that it will be out of range of our observation. What happens is that the particle's trajectory are described by "simple" kinematics familiar to all (well mostly). The actual positions where observations are made represent points on that trajectory. This observation mostly destroys the game though it is not necessarily the case.
The important point is that particles becoming invisible is not the "end". If the particle is big enough it may carry a probe and make observations in the frame of reference of the quantum process (from within the quantum). This will mean that after the 'trip" clocks and times and positions may be compared to determine the Physics is still OK.
We can make macroscopic quanta even now such as a BEC. This is a single quantum state. A "probe" could potentially be inserted inside this "cloud". The logical place to do this sort of experiment is in free fall. I will not elaborate here.
How can "rotation" close off a space like our Universe. Firstly I interpret the length contraction of Einstein/Lorentz as a rotation "out" of 3D + T spacetime. It can be shown (see numerous texts) that in stereoscopically derived visualizations of length contraction the contracted object is rotated "away" from all bystanders... even on both sides of the observed phenomena. This is mathematically provable and is actually standard theory. What I would like to say is this "phenomena" is effectively a "projection" of a particle traveling partially in "Uberspace"... those extra dimensions spoken of in String Theory. The partial "removal" of the particle from our visible Universe is accompanied by be Broglie Wavelength and "length contraction" which is like the moving particle "going around an invisible hyperdimensional corner". This you see from all vantage points in 3D spacetime. This two dimensional projective surface of a brane is spoken of by Ed Witten in the Geometric Langlands Program that I have recently been discussing on this forum. It is also the projective "surface" that is the only expression of the higher dimensional neutral EM "spiral" is traveling in, and it is the "shadow on the wall" that we see as the "charges" and the electric and magnetic oscellating fields associated with it. Waterbreath... you were following this idea earlier this year.
What it is all saying is that Special Relativity, General Relativity, Electromagnetism, and the Quantum are all facits of the one thing.... this one thing is "higher dimensions". That is what all those theories lack... too few dimensions to describe reality. So if you accept this idea... that there is a need for more dimensions... is it any wonder why we cannot observe everything happening in our Universe by simple observation? We are banging our "metaphysical" brains out against a wall trying to fit the Universe into only 4 dimensions. To do it everything had to be "banged flat" with a hammer to fit into the Universe we "think" we know.
And what of "closure" for our Universe? If length contraction is a rotation into a higher space it is a "curl" in those extra dimensions it is moving into. These "non bulk" dimensions "apparently" are curving very near to us in our 3D + T braneworld (flatland) we inhabit. These dimensions are only the slightest distance "away" from our "flatland" of 3D + T. All 6 extra dimensions "touch" the empty spaces of our bosonic "bulk" ... everywhere (the empty space). This is the 6D surface of our universe. Actually there are nine spatial dimensions and they "all" ultimately curl up. We can't touch it but if we had any "thickness" at all we could climb out of it into higher spaces... right where you are sitting now "onto the outside of our Universe". You would move via a brane connection through a 2D surface, leaving your "flattened" image on its surface as you went. There may be more than one way to do this... you can start to do this with sheer speed near © and Special Theory of Relativity, but it will not allow you to escape. Or you can just "pop out" as a quantum. To do this just increase your de Broglie wavelength...

= h/mv where m can approach 0. Then you will quantum tunnel into higher dimensions.
Once on the "outside" of our "petal" Universe you will see our Universe which is spinning in six or more dimensions in a scale that boggles the mind... as a tiny quantum "boson". The rotation of the Universe on the "inside" causes the periphery to "spin" nearly as fast as light and could shrink to almost zero diameter. See that former post above with the simple calculations about rotation of our Univese to cause it to "wrap up" like a cosmic lotus flower. On the "inside" the "bulk" is a huge 3D + T "flatland" called a braneworld we are inhabiting. This is observed through the 2D surface of the brane on the outside of our Universe. A "ball"... more correctly a Calabi-Yau Space object. The information about the entire "interior" is "stored" as a dynamic energetic "string" on the
surface of that 2D "ball".... "electromagnetically" as a layer of "impulse" h whose "parametric thickness" is in "reciprocal frequency".... a two dimensional fourier hologram of our entire Universe on the inside of that higher dimensional space. This is beautifully and simply expressed as...
E = hf.
The Universe and all other Universes are "holographic". They are other "smaller" ones "inside " our Universe as well (they look smaller to our perspective). Not just quarks but there are many types of branes probably some we have not even begun to understand yet and they are not all the same dimensionality either.
Ed Witten speaks of a Black Hole being a D-Brane and the information of the interior of the Black Hole is stored on the surface as an energetic string. In fact this is repeated on both sides of these surfaces everywhere they occur. Bubble Universes. But true to form, being bosonic the information is "quantum" and invisible... he he he!
Those higher dimensions we can't see but we know they spin since we know quarks spin... is a repeated "motif" for other bosons such as our Universe (we are inside that one) and the "radiation pattern" of radio antennas. This is a lower (broken) dimensional equivalent of what is happening in atoms and their Bosonic supersymmetric partners... the "so called" electronic shells of atoms. I have previously expressed in other posts Schrodingers Equation in purely Electromagnetic Terms (not my idea though but fits the bill). These shells exist even when you do not have electrons. They are the "shadow companion" of the particles in the Nucleus... a mixing if you will (supersymmetric s-particles). This naturally results in the Schrodinger Equation if you had all those assumptions and projected everything happening there onto a 3D "flatspace". The truth is the Bosons are "rich" higher dimensional objects, a place for other "bosons" and quantum particles (electrons) to "hide" as they do in our Universe.
Now about all that spin.... In three spatial dimensions you can only spin in one plane at a time. If you have six spatial dimensions you can spin in three planes all at once... this is not something you can do in only 3D + T without "disruption". For instance an object can be doing all that in 6 dimensions but in 3D + T you would not notice anything going on at all. Alternatively it can fall or accelerate "linearly" into those directions while it sits on your table "looking at you" and doing apparently "nothing at all". It is "intrinsic spin" or acceleration that is "invisible" but it will result in relativistic effects since this is potentially a reflection of the "outside of our Universe" traveling at near the speed of light. Because it is invisible it is a quantum process. There is a long story associated with this and fourier transforms... frequency domains and time domains are part of it. Suffice to say go watch "Dr Who" and brush up on your Time and Relative Dimension in Space (TARDIS) Travel... he he he!
Is this global spin of the Universe a quantum spin?.... yes through T-Duality properties. The spin of the Universe is reflected in every tiny particle (separately I hope). The scales are mapped as "inverse". The property of curvature of Spacetime is the same property that curves and closes sub-atomic particles. One produces gravity in the extrinsic Universe and the other leads to mass in the intrinsic Universe. It is "all" curvature... just differing levels of it.... mixed with "acceleration" or "spin".
Humans have intuitively "discovered" all this before and now all this is happening again... this time it is happening to 'Good Elf".

(Apologies to James M. Barrie).
I think this is all I have time for tonight. Thanks for listening.
PS: If you want to catch up on what I have been doing... this trick is a good one. Click on my Name to the top left of the post then when you see my window under my name click on "Find all posts by this member". This shows a reverse sequence listing of all my posts ... nearly 1000 of them. Obviusly the later ones are more important to catch up on this but I suspect it will be too much to bear.
Cheers