An Infinitesimal Universe – Open For Exploration
BY BRUCE E. CAMBER RELATED REFERENCES: INFINITY, REFORMULATING SPACE, TIME, AND INFINITY
- This universe, from the first moment in time until this moment in time, is outlined within 202 base-2 notations (progressive doublings) of the Planck base units. The model begins at the Planck scale and goes to the Age of the Universe today.1
- This model, by definition, contains everything, everywhere, and for all time. This model is 100% predictive, mathematical, logical and rational.
- The first 64 notations, an infinitesimal universe below our thresholds for measurement, have never been studied by academics, scholars or scientists. Yet, these base-2 numbers of the Planck units tell many stories.
- This simple model appears to be able to absorb discoveries since 1927 when Georges Lemaître proposed his theory of a primeval atom.2 That work became big bang cosmology.
- This model opens time symmetry; Max Planck redefined the very nature of light-space-time but big bang cosmology blocked our view of it.
Our history is rather brief. These ideas and concepts are based on a natural progression of numbers from the Planck Length to the size of the universe. It requires doubling mechanisms and mathematics that goes from the most simple to the most complex.
Also, it seems that only by becoming more precise about our definition and understanding of infinity will we begin to understand the very nature of this universe.
To that end, some of the work done over the years is outlined and linked:
1. All the Numbers: A Highly-Integrated Mathematical Model. These 202 base-2 doublings outline the universe; and, by definition these notations include everything, everywhere, for all time. However, it is a base-2 exponential expansion from Planck Time. The first second doesn’t emerge until between notations 143 and 144 and the first light year between notations 168 and 169. The first million years is between 188 and 189 and the first billion years between 198 and 199. Notation 201 encapsulates 5.49 billion years; and given that the aggregation of all notations up to 201 is also 5.49 billion years, the 202nd notation encapsulates 10.9816 billion years. Given the universe is between 13.78 and 13.81 billion years old, it follows that we are in the earlier part of the 202nd notation (no more than 2.8284 billion years into it).
- Natural Inflation. This progression of the four Planck base units delineates a natural inflation and a thrust that mimics big bang cosmology.
- Each notation (doubling) defines a boundary; and, logic tells us that each is always active and never the same because of all the dimensionless constants involved.
- The Now. Here is a fullness of time that is quantitative, derivative, and finite. This model does not support absolute space and time.
- Max Planck’s formulas: In 1899 Max Planck redefined the basics.
- The sphere, it would seem, is the first manifestation of space-and-time-and-charge-mass.
- The first 67 doublings. Particularly, the first 64 doublings are all below the thresholds of physical measurement, yet these are all still very physical. I call it a hypostatic domain, the foundations of the foundations. It is purely based on mathematics and logic and it redefines our small-scale universe and the infinitesimal.
- The first 64 notations provide a primary outline for a sub-grid of mathematical physics whereby Langlands, Wilczek et al (with 31 dimensionless constants), Rees (Just Six Numbers), Weinberg, Witten and a rather sizable group of others might find a few helpful numbers to interpret the very early universe and infinitesimals.
3. Unified Theory of Mathematics. The simplicity of this model encourages the development of an extensible platform starting with the most simple mathematics and geometry that build to include the two Standard Models, Langlands programs, string theory, dark matter/energy…
- Euler. The universe is fundamentally exponential. Euler’s identity is universal.
- In process: Each notation will be analyzed, notation by notation. It will be within this format this unified theory could possibly unfold. Wouldn’t the role of prime numbers be to determine when new mathematical systems can be introduced?
- Continuity. Order / numbers, first within the dimensionless constants, never-ending, never repeating, and then with the progression of spheres.
- Symmetry. Relations / Geometries, first with the symmetry of the spheres, then the symmetry within the tetrahedrons and octahedrons that are generated.
- Harmony. Dynamics / Space-time where two symmetries actively interact as a moment of space-time; it is a qualitative moment we experience as harmony.
5. The qualitative opens the way to value and ethics. Perhaps the most controversial conclusion of all, it seems to follow from the abstractions within harmony.
 Big Bang. If Georges Lemaitre had studied with Max Planck, he may have begun thinking that his primeval atom was there on the baseline of Planck’s equations. It is. For now, we call it a plancksphere.
What shall we do with this simple construction? Why does it work? Why doesn’t it work?
The 202nd notation encapsulates over 10.9 billion years!
Within a notation there appears to be time asymmetry, but once integrated with the first 201 notations, it becomes part of “the Now” and time symmetries become evident.
We do not know the answers so we reach out to scholars who might. For this homepage, we have asked Alexander Vilenkin of Tufts, Claus Kiefer of Cologne, and Steve Adler of the Institute for Advanced Studies (click on their pictures above). If any allow us to post their comments, we will. Thank you. – BEC