Conjoint Orthogonal Projections of 9 Superstring Dimensions on a 10th Dimension Explain with Considerable Precision (0.8%) the Percentage of Observable Matter and Energy: Theoretical Value 4.86% Compared with the Empirically Derived Value 4.9%

 

Conjoint Orthogonal Projections of 9 Superstring Dimensions on a 10th Dimension Explain with Considerable Precision (0.8%) the Percentage of Observable Matter and Energy: Theoretical Value 4.86% Compared with the Empirically Derived Value 4.9%

 by Stefan Geier (27.09.2023: First open version asking for critique, and discussion)

 

Scientific cosmology of the second and third decade of our century suggests that ordinary matter we can encounter, see, feel, and measure sums up to 4.9 % of all matter and energy (ESA: Planck reveals an almost perfect Universe. https://www.esa.int/Science_Exploration/Space_Science/Planck/Planck_reveals_an_almost_perfect 21/03/2013, rertr. 17.IX.2023). Less interactive energy and matter are called dark energy (68.2%), and dark matter (26.9%). We will now give a theoretically consistent explantion of the percentage of ordinary matter, also called white matter-energy, based on string theory and the existence of gravitons with spin 2hdash obeying the principles of Richard FEYNMAN’s quantum corrections. Our appoach is based on the mathematical concept of the orthogonal projector.

The orthogonal projector is the most basic principle of HEISENBERG’s matrix mechanics (e.g. eigenwerte and eigenstates of typically HERMITIAN matrices in the HILBERT space are used in HEISENBERG’s quantum mechanics, and the spectral theorem allows to express self-adjoint HERMITIAN matrices respective operators as a sum of orthogonal projectors onto their eigenstates) which stands at the beginning of quantum physics. It is also included in the SCHRÖDINGER equation as well as in the DIRAC equation by the basics of complex numbers (e.g. the i-axis is orthogonal to the real axis).

On our journey from a summer holiday at Venice visiting the Bienale Architectura 2023 „The Laboratory of the Future“ and at Albarella back to Rosenheim we made a stop at Citadella, Veneto. After having an Italian Cafe Shacerato at the nice Cafè ai Portici we went to the ancient town hall nearby. In the loggia we were impressed by a piece of sculptured art (Photo). A so called Genesa Crystal. These Genesa Crystals were made popular by Derald LANGHAM in the 1970s, and they are in this remote context “somewhat esoteric” to us. However, the 4 rings of the sphere associatively induced the idea how to project 2 respective 3 rings or 2 respective 3 orthogonal dimensions on a third respective fourth, and how to project a six-dimensional CALABI-YAU manifold on this fourth ring or dimension, too. As the orthogonal projector is familiar to me (especially in the analysis of associations using Jean-Paul BENZÈCRI’s Correspondence Analysis and Principal Component Analysis according to Sigmund FREUD, and James DEESE) I used the concept of an orthogonal projector in my imagnation: How to project the basic unit of 3 standard space dimensions and 6 CALABI YAU dimensions on a 10th dimension, and how to quantify those projections. Of course, an angle bisector was the first consideration for the 10th axis respective dimension as an angle bisector maximizes intuitively the equidistance of the axes to the new axis projected onto (by representing the principal component axis in mathematics).

 

Photo: A Genesa Crystal in the ancient Town Hall of Citadella, Veneto, Italy

 

Now we show that an at least 10*space + 1*time orthogonal dimensional theory (e.g. string theory in form of M-theory with 11 dimensions, or F-theory with 12 dimensions) on gravitation, the electromagnetic force, the weak force, and the strong force explains with a theoretically derived value of 4.86 the 4.9 matter-energy percentage of ordinary matter in relation to dark matter plus dark energy by an interactive equi-relevance consideration (angle of pi/4 between the brane space dimension ant the other 9 dimensions) of the 9 non-brane space dimensions with 1 more brane-related space dimension:

This is because:

Orthogonal projector of one basic unit of one dimension on a second axis (the 10th space dimension, or brane dimension) with angle of pi/4 gives by othogonal projection the following reduction of the basic unit (according to the basics of linear algebra, and sin or cos functions):

½*2^1/2 ≈ 0.707106781.

 

Nine iterative orthogonal projections on the 10th brane dimension because of 9 non-brane every orthogonal dimensions based on every pi/4 combine by the 9th power:

(½*2^1/2)^9 ≈  0.707106781^9 ≈ 0.04419417.

 

One percent of FEYNMAN graviton distraction according to GEIER et al. August 2021[1] must be taken into account for every one of the 10 space dimensions:

0.04419417 + 1 percent * 10 = 0.04419417 + 0.004419417 =
= 0.048613587

 

4.9 is the percentage of ordinary matter-energy according to empirical data (https://www.esa.int/Science_Exploration/Space_Science/Planck/Planck_reveals_an_almost_perfect).

This fits well to 4.86: q.e.d. .

 

 

In addition pi/4 reflects the speed of light in the MINKOWSKI diagram or PENROSE diagram, too. This is in accordance with EINSTEIN’s theory of special relativity, and with the speed of light c for photons, and the speed „of light“ c for gravitons, too. Furthermore, pi/4 thus connects very consistently the 10 space dimensions with the 1 time dimension of M-Theory (Edward WITTEN and others), and the 2 orthogonal time dimensions of F-Theory (Cumrun VAFA and others). Our data and theory on NEWTON’s Cradle and the Bifilar Pendulum are consistent with 2 orthogonal time dimensions; however, our data also fit M-Theory allowing to embrace Superstring Theory, M-Theory, and F-Theory with an adapted F-Theory with an optional complex time dimension being the most consistent, and testable (Sic! Please, see Karl POPPER’s falsification principle is open now for string theories) theory of our unisverse.

 

Constraint (in retrospect): Our analysis is based on the assumption that all 9 space dimensions contribute equally to the existence of ordinary matter. The impressing small delta of 0.386 (%) suggests that this not explicit assumption is valid.

 

Additional hypothesis: The relevance of orthogonal projectors in human associations might reflect an adaption of humans to a respective the nature surrounding humans and given in humans dominated by the principles of quantum physics including orthogonal projections and eigenvalues (Werner HEISENBERG’s matrix mechanics etc.).

I invite scientists to discuss the presented insight. The implications, if scientific critique can be rejected, are important.

Additum 01.12.2023:The PLANCK data 2015 measure an empirical value of 0.0486 ± 0.0010 for Baryonic Matter which fits our theoretical value of 0.0486 extremely well providing very strong evidence for our theory: Planck 2015 results. XIII. Cosmological parameters by Planck Collaboration: P. A. R. Ade et al., 2016, arXiv:1502.01589, p. 32, table 4, last column, calculated from Ωbh^2 and h = H0 / (100 km s^−1 Mpc^−1).
Please, compare with Wikipedia "Lambda-CDM model".

SG

[1] https://www.researchgate.net/publication/353658741_Gravitons_with_Spin_2h_in_the_Classical_Pendulum_Quantum_Physics_Fits_Newton's_Classical_Physics?utm_source=twitter&rgutm_meta1=eHNsLUtVZ1I2dFRwRExCb2tWd3ZvVU1rY0ZWS0Y3d1BIREx0L2hkck5mOG1Sekw0dnJycXA1RjF5WUZ6YnROM2NNZlpvWmxCQ3NLU1hLM3pvQm9Ta0QwMHkrYz0%3D