String theory grew out of attempts to find a simple and elegant way to account for the diversity of particles and forces observed in our universe. The starting point was to assume that there might be a way to account for that diversity in terms of a single fundamental physical entity (string) that can exist in many “vibrational” states. The various allowed vibrational states of string could theoretically account for all the observed particles and forces. Unfortunately, there are many potential string theories and no simple way of finding the one that accounts for the way things are in our universe.
One way to make progress is to assume that our universe arose through a process involving an initial hyperspace with supersymmetry that, upon cooling, underwent a unique process of symmetry breaking. The symmetry breaking process resulted in conventional 4 dimensional extended space-time AND some combination of additional compact dimensions. What can mathematics tell us about how many additional compact dimensions might exist?
One of the chief features that have caught my mind is the way in which extreme curvature might have been enlisted to take us a to a place where the infinities have been curtatiled to a way of thinking. You need a model in which to do this, if you are to think that the events in the unverse are to be considered out of what the pre big bang era might have entailed had ths action been defined properly?
So immediately one see’s the benfit of cyclical unverses being developed as well as understanding that the particle reductionistic views were well within the range to consider superfluids as part of the working of this interior blackhole? How did one get there?
A splitting of five-dimensional spacetime into the Einstein equations and Maxwell equations in four dimensions was first discovered by Gunnar Nordström in 1914, in the context of his theory of gravity, but subsequently forgotten. In 1926, Oskar Klein proposed that the fourth spatial dimension is curled up in a circle of very small radius, so that a particle moving a short distance along that axis would return to where it began. The distance a particle can travel before reaching its initial position is said to be the size of the dimension. This extra dimension is a compact set, and the phenomenon of having a space-time with compact dimensions is referred to as compactification.
So first and formeost gathering a perpectve that could immediate take us into the understanding of how these circles could ahve gained value in conceptual models. Of course every one wants the truth and mathematics is saying okay where the heck do we find the matematics that is so pure that by the very means enlisted would take us from the states of superfluids and their capabilities?
That was the problem we had to solve. In order to count microstates, you need a microscopic theory. Boltzmann had one–the theory of molecules. We needed a microscopic theory for black holes that had to have three characteristics: One, it had to include quantum mechanics. Two, it obviously had to include gravity, because black holes are the quintessential gravitational objects. And three, it had to be a theory in which we would be able to do the hard computations of strong interactions. I say strong interactions because the forces inside a black hole are large, and whenever you have a system in which forces are large it becomes hard to do a calculation.
So it is very important that if such views are taken down to these extreme levels that some method be adopted to maintain what might have emerged from the basis of the reality where such pure states as superfluids, may have simplified, immmediate symmetry breaking as arisng from some geoemtrical method?
The general theory of relativity is as yet incomplete insofar as it has been able to apply the general principle of relativity satisfactorily only to grvaitational fields, but not to the total field. We do not yet know with certainty by what mathematical mechanism the total field in space is to be described and what the general invariant laws are to which this total field is subject. One thing, however, seems certain: namely, that the general principal of relativity will prove a necessary and effective tool for the solution of the problem for the toal field.
Out of My Later Years, Pg 48, Albert Einstein
Lubos reminds us in the “strominger linked statement” about the understanding that there is no physics, but I would like to work towards gathering perspective as I am to lead us to the theory in the thinking. What concepts made this thinking valuable might have arisen in the previous years might have found itself explained over and over again.
Where does the pure mathematics changes it’s form?
If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost ‘context’ is indistinguishable from the innermost ‘content’ – a structure for which we coined the term ‘liminocentric’.
The drive to tke this down to such levels of perception and wipe away all the faces of our concepts seems a hard struggle yet I think it a very capable thing in any mind that would move to the forms of pure math? What are these?
Such a simple psychological thinking that would have maintained our views, and find that enlightenment is just a few short steps away. Some mathematics might emerge that will unfold into our everyday world that wil bring together so many things?
So from where in all the probabilstic states could such thinking reveal the smoothness of topological fucntions and relayed the working of all the states havng been reached in the blackhole? Travels of the circle measured in te radius of that same cicle gives inherent energy valution to the concept of the blackhole being multiplied to seeing the macroscopic view of the universe having been driven to it’s current state?
The familiar extended dimensions, therefore, may very well also be in the shape of circles and hence subject to the R and 1/R physical identification of string theory. To put some rough numbers in, if the familiar dimensions are circular then their radii must be about as large as 15 billion light-years, which is about ten trillion trillion trillion trillion trillion (R= 1061) times the Planck length, and growing as the universe explands. If string theory is right, this is physically identical to the familiar dimensions being circular with incredibly tiny radii of about 1/R=1/1061=10-61 times the Planck length! There are our well-known familiar dimensions in an alternate description provided by string theory. [Greene’s emphasis]. In fact, in the reciprocal language, these tiny circles are getting ever smaller as time goes by, since as R grows, 1/R shrinks. Now we seem to have really gone off the deep end. How can this possibly be true? How can a six-foot tall human being ‘fit’ inside such an unbelievably microscopic universe? How can a speck of a universe be physically identical to the great expanse we view in the heavens above?
(Greene, The Elegant Universe, pages 248-249)
So what particles will have emerged from such a process and we find ourselves facing the gluonic phases of sight, and what level should we assign these energy values in relation to the supersymmetrical state now recognized, and moved from in the symmetical breaking that is to be accomplished?
It is from these positions as I am making them clear, that even in face of the perspective shared by the Krausss’s and Woit, that the continued efforts of LUbos and all the young minds might do as Peter Woit askes and bring the demands of the recognition of things, that emerge from this process, into full regalia.
For those who were skeptical, hopefully this sets up your minds as to what is being accomplished, and what is being said, is quite beautiful. I find this process very beautiful indeed.