Hypothesis: Gravity & Electromagnetism Start Within the First Spheres.

Fourier transforms Electromagnetism⬄Gravity
by Bruce E. Camber (a working draft, initiated April 5, 2022, the foundation for hypostatics)

The hypothesis is that within our most infinitesimal scale (currently either the Planck scale, a Stoney scale or a new ISO scale), the Fourier Transform imparts gravitational or electromagnetic qualities within each infinitesimal, primordial sphere ^[1]. If our working hypotheses are true and there are 539-to-4605 tredecillion spheres per second (one primordial sphere per primordial unit of time), this is a most-basic process within the very earliest universe. Not yet recognized within the academic community, each sphere has a natural functionality of continuity-symmetry-harmony as given within pi (π) and her Fourier transform.^[2] Here the finite-infinite boundary (or bridge) is defined.^[3] Here each sphere manifests with its own flavors and functions which we further hypothesize begins as an attractor or repeller.^[4] As our universe expands very rapidly, those first 64 notations are the beginnings of Langlands programs, string-and-M theory, hypothetical particles, SUSY, and so much more.

Some of these speculations have had a relatively short history within this website:

August-September 2018: The first exploration of the nature of gravity within this website was in late summer 2018. The URL for that homepage is: https://81018.com/gravity-2018/

The tagline is Radical Chic! Gravity Chic! and its headline, “Gravity, Oh Gravity… Why Such Gravity?” The Fourier Transform is not mentioned. None of the integral transforms are mentioned.

October 22, 2018: Obviously on my mind, this homepage soon followed yet its focus is to engage quantum gravity. That URL is: https://81018.com/quantum-gravity/

The tagline is: On defining a dynamical behaviour of spacetime geometry on all scales. And, the headline is “What comes before Quantum Gravity?” Again, neither the Fourier Transform nor any other integral transform is mentioned.

Friday, March 1, 2019: Work on the Fourier transform was inspired by Steve Strogatz and his 2015 Pi Day article in The New Yorker magazine. I didn’t discover the article until March 2019. Almost immediately, upon looking more deeply within every infinitesimal sphere (again, all 539 tredecillion spheres per second using PlanckTime and up to 4605 tredecillion spheres per second using StoneyTime), the Fourier transforms — part of integral transforms — came alive. It was easy to postulate that gravity is created within one spin state and electromagnetism within another. In May 2021, the Fourier came out of the closet within this website. Here are key references on the lead up to this page:

• The Fourier Transform See #6 (gravity is not mentioned once)
• The magic of the sphere is the Fourier transform (no mention of gravity).
• In search of the essential universe See #6 (no mention of gravity)
• The many faces of the Fourier transform (first mention of gravity in May 2021)
• The most basic transformations (many references to gravity, May 2021)

Sunday, February 21, 2021: If you assume one infinitesimal sphere for each unit of infinitesimal length and time, the numbers become self-evident. Though hard to fathom, Planck’s and Stoney’s range is from 539-to-4605 tredecillion spheres per second; mathematics is mathematics!

An Emergent Level of Understanding

Friday, April 8, 2022: Our advantage or handicap going into these analyses are the following five assumptions: (1) 202 base-2 active notations outline the universe, (2) there is an always-active finite-infinite relation defined by continuity, symmetry and harmony, (3) there is a domain of perfection in the earliest notations which begin to encapsulate geometric gaps that become quantum fluctuations first measured within Notations 65-to-67, (4) infinitesimal (primordial) spheres generated from within Notation-0 to Notations-1-to-3 fill the emergent universe, and (5) point particles are redefined as infinitesimal, primordial spheres that emerge within Notations-1-to-3. Within this domain these spheres are the vertices of classic geometries, yet here these vertices have all the functionalities of the sphere. So, yes, within this redefinition of vertices, each becomes part of the functionality of everything finite. There are no less than 64 doublings so an entire science of vertex functionalities at each notation could begin to emerge.

Of course, these five points are all idiosyncratic, unconventional, and a necessary paradigm shift; here gravity and electromagnetism begin to be created in the first notation. Each results from a Fourier Transform and attractors-repellers and these transforms are scale invariant.

Thank you. -BEC

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May 2021: Hidden within these representations of the Fourier transform is a formal relation between electromagnetism and gravity. Many have started such an analysis over the years, yet none of our scholars have had (1) the 202 active notations, (2) a finite-infinite relation defined by continuity, symmetry and harmony, (3) a domain of perfection, and (4) an aether defined by infinitesimal (primordial) spheres where fields are within fields and everything, everywhere for all time is related to everything, everywhere for all time. Link: https://81018.com/starts-6/

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Endnotes/Footnotes

[1] Each infinitesimal, primordial sphere. Somebody has to postulate it! An attractor sphere (even more fundamental than a hypothetical particle) or repeller (or repellor) sphere. As crazy as it sounds, why not? It was in this discovery of the attractor scholarship that I also discovered one of its primary thinkers, Steve Smale of the University of California, Berkeley. Immediately I began to think he might be able to shed light on my questions about the current work by David Kaiser of MIT and Karen Uhlenbeck of IAS.

In that process the work of John Milnor to define an attractor helped to move it into the infinitesimal scales. Within our base-2 chart of the universe, the infinitesimal scale begins within quantum fluctuations within Notation-67 and then drops below all thresholds of direct measurements. The inclination today is to assume that Notation-1 is the manifestation of the first infinitesimal sphere and Milnor and Smale’s work describes part of the processes within that sphere.

[2] The Fourier transform. Scale invariant, these infinitesimal spheres adopt what amounts to attractor and repeller functionalities and these functionalities, building upon each other, manifest differently in each notation. The possibilities for complexity and uniqueness are staggering and most bewilderingly. Much more to come…

[3] The finite-infinite boundary (or bridge). Pi is under-appreciated and little understood. The absolute mystery of pi is that it defines both the finite and the infinite with three concepts (not 3000 volumes). The inexplicable never-ending, never-repeating, always-changing, always-the-same qualities is beyond comprehension yet is summarized in a word, continuity, and it is order. A simple formula that renders the most complex qualities is enigmatic enough, pi-and-its-sphere defines space uniquely and perfectly and that is called symmetry and it is the first working relation. The majesty of that perfection is barely grasped and is profoundly unappreciated. The third quality has only been engaged for a short time in human history, perhaps a bit by Kepler, Euler, Fourier, and Poincaré, but it is so little understood even today. That is the dynamics of a moment, particularly the deepest, most intimate dynamics of motion that brings everything alive within what is best summed up as harmony. Everything qualitative is infinite and everything quantitative is finite. A bridge of other dimensionless constants connect the two. We have so much to learn and even more to begin to understand and truly appreciate. More… Even more…

[4] Spherical functionalities: From attractors and repellers, to electromagnetism and gravity. The functionalities of spheres is a young science within one of our oldest studies, that of pi (π). Its most-basic functionality is within the first 67 notations (of the 202 that currently encapsulate the universe). Of those 67, the first ten notations are the foundations of a new science. It is well beyond the domain of quantum fluctuations and any direct measurements. As the foundations under the foundations, we have referred to this domain as hypostatic, for “that which stands under” and here we take that to be continuity, symmetry, and harmony. Here are the essences, the first principles, and the starting point for every possible application and understanding of spherical functionalities.

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References & Resources

• Auslander, J., Bhatia, N.P., Seibert, P.: Attractors in dynamical systems, Bol. Soc. Mat. Mex. 9, 55–66 (1964) 4
• Mohsen Khodadi, Kourosh Nozari & Fazlollah Hajkarim, On the viability of Planck scale cosmology with quartessence, Eur. Phys. J. C 78, 716 (2018). https://doi.org/10.1140/epjc/s10052-018-6191-4
• John Willard Milnor (1985). “On the concept of attractor”. Communications in Mathematical Physics. 99 (2): 177–195. doi:10.1007/BF01212280 (excellent bibliography). Wikipedia
• Steve Smale The Emergence of Function, ArXiv, 2016
• Steve Smale, The mathematics of time Springer-Verlag, New York-Berlin, 1980. ISBN 0-387-90519-7