Continuity and symmetry, the very heart of homogeneity and isotropy

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Notwithstanding, homogeneity and isotropy originated with Newton (Principia, 1687).

Our Homogeneous And Isotropic Universe

by Bruce Camber    Initiated on December 18, 2019 IN PROCESS: a working composite of articles since 2011

Our Very-Simple, Mathematically-Integrated, Base-2 Model of the Universe. Also known as a Quiet Expansion (as opposed to the Big Bang), it all begins at the Planck scale and doubles through sphere stacking of all the infinitesimal spheres that follow a primeval sphere defined within Notation 1. This model organizes all the sphere stackings as doubles. Cubic-close packing of equal spheres engages. In just 202 doublings, you will have started at the first moment of time and come up to the current time (right now, today). You will have included everything, everywhere, for all time.  And, by definition, this universe has continuity and symmetry, therefore it is homogeneous and isotropic. This model accounts for quantum fluctuations through very simple geometries, particularly the five-tetrahedral complex.

Yet, history is history. Homogeneity and isotropy began within Newton’s cosmological principle; he was observing the large scale universe. And, within his introduction of absolute space and time (ostensibly a new definition of infinity), a sense of the scientific began to emerge.

Within our model, the universe is fundamentally defined by continuity, symmetry and harmony. Here is the very nature of infinity, the finite-infinite relation, and the deepest roots of homogeneity and isotropy.

Yet, within our current scholarship regarding quantum fluctuations, there is a lack of homogeneity and isotropy. We know that our sciences are incomplete; and as a thinking people, we’re not quite on track yet.

There are conceptual silos of information everywhere within our scholarly world. Two of the more fundamental studies are string theory within theoretical physics and the Langlands programs within mathematics. Neither has easily fit in with the current foundations of knowledge, yet both are very robust studies. Neither starts simply, yet both use the first principles of continuity (order) and symmetry (relations). So, those first 64 notations of the 202 could provide the necessary bandwidth to build the relational bridges between them and with our current wave-particle physics.

In our preliminary studies, the first ten notations are for fundamental forms. Both string theory and Langlands engage specialized concepts of forms. In much the same way, both proceed with structures, substances, qualities, relations and systems. These are also the foundations for homogeneity and isotropy.

As simplicity becomes increasingly complex, all sorts and flavors of what are currently consider theoretical objects emerge. Things like axions, branes, and gravitons-and-gravitinos have had years of work to define them, but no place to go within a grid so all are still considered hypothetical. The currently-recognized grid that starts with particles and waves is just too limiting.

Our grid is huge — no less than 64 doublings of the Planck base units.

Unlike the Big Bang inflationary cosmology there is no need to project (as MIT’s inflationary universe scholar, Alan Guth, did) an infinitesimally short period of exponential growth to smooth out any and all irregularities from their infinitely hot start known as the Big Bang. Our first 64 notations start cold and  are the product of exponential growth. It has smoothness (continuity and symmetry) right from the start.

Of course, within the base-2 model, chaos must come at some point before the 67th notation. Also known as quantum fluctuations, perhaps the five-star tetrahedral cluster with its pentastar gap is the source whereby the imperfect fitting creates a new domain for creativity, chance, randomness, and, yes, even free will.

Also, as a result of engaging these first 67 notations since 2011, I believe that the homogeneity-and-isotropy within our universe reflects the very nature of the infinite while chance, randomness, creativity, and free will reflects the very nature of the finite. If the instantiation of that five-star cluster is the marker, I suspect it is not a static location, but actually floats within a range of notations.

Assumed by most of the scholarly community, these two seminal words — homogeneity and isotropy — bind our universe as a single system. Notwithstanding, there is no currently-recognized cosmology that starts with, and then builds, upon those two concepts. Obviously, this nascent model is an attempt to do so.

Here the cosmological constant are those continuity equations that cross the finite-infinite bridge to open the way for all the dimensionless constants. It is good to have the 31 identified by Wilczek and Aguirre, Rees, Tegmark (W-ART) as a starting point. They are clear to say that all are necessary for the standard models of particle physics and cosmology (ArXiv PDF: page 2, Table 1), yet they are top-down particle-wave physicists. With their 31 as a goal, it seems that it might be much more interesting to use them to build basic forms, then structures, that are purely mathematical yet begin to manifest with infinitesimal values for time and length and very small values for mass and charge.

We will continue to try to encourage bottom-up construction of our universe and not our current top-down thinking.



Initiated in private on Monday, December 8, 2019
Protected posting: Tuesday, December 9, 2019
A first-draft homepage: Wednesday, December 11, 2019
Most-active editing: December 9 to December 11, 2019
Last update: 2 April  2021