"π/2 Spherical CPT Symmetry" ... : Comment on ANDERSON et al: Observation of the effect of gravity on the motion of antimatter. Nature 621, 716–722 (2023). https://doi.org/10.1038/s41586-023-06527-1

 

Here an extended comment focussing on a tiny breaking of CPT Symmetry by “a(antimatter) = 0.75 a(matter)” probably caused by “π/2 Spherical CPT Symmetry“ (see endnotes) solving some problems in physics elegantly, too:

On the Specific Difference between NEWTON’s Cradle and the CERN ALPHA-g Experiment 2023 by Focussing on the Time Dimension of Antimatter According to Richard FEYNMAN and on CPT Symmetry

or

An Explanation for the 0.75 ratio of Antimatter/Matter Gravitation Experimentally Derived by the CERN ALPHA-g Experiment (Nature 621, 716–722 (2023). https://doi.org/10.1038/s41586-023-06527-1) “a(antimatter) = 0.75 a(matter)” and a Connection to “π/2 Spherical CPT Symmetry“

Very Valuable and Ingenous Birthday Essay for
Caroline Geier and Stephanie Geier
22^nd Birthday March 03, 2024
by Stefan Geier

Our concept, and theory (GEIER et al., 2019 to 2023) on gravitation allows to explain the ratio 0.75 of the gravitational force of antimatter compared with matter demonstrated in the CERN ALPHA-g Experiment 2023 by a difference in gravitation-relevant space-time dimensions for matter and antimatter (CERN ALPHA-g Experiment https://alpha.web.cern.ch/... :, ANDERSON EK et al., 2023). Matter is related to 3 orthogonal space dimensions x, y, z, and 1 time dimension t in Isaac NEWTON’s concept. In Albert EINSTEIN’s concept the four dimensions are treated equally, and all four dimensions are orthogonal to every each other. Therefore we can write in a first approximation

[4 space and time dimensions of antimatter (e.g. CERN's ALPHA-g antihydrogene)] /
[4 space and time dimensions of normal matter (e.g. steel balls of NEWTON's Cradle)]
= 1.00

while assuming space and time are equal in matter and antimatter.

However, in our experiments on NEWTON’s Cradle we demonstrated that the damping of NEWTON’s Cradle is related to 1/t^1/2 with t time in seconds (Figure 1); this square root demonstrates that for backward proper time according to Richard FEYNMAN as it is necessary for the concept of antimatter the backward time and which is negative (< 0) and thus according to „(-1)^1/2 = i“ is asymmetric just by the imaginary number i, respective basic unit i to the forward time of normal matter we are used to. Thus, in the complex number plane the antimatter backward time of Richard FEYNMAN (FEYNMAN graphs, see Roger PENROSE 2007, pp 638), and of the concept of CPT Symmetry (Gerhart LÜDERS, Wolfgang PAULI) provides a second time dimension orthogonal to the standard forward time dimension of matter, and orthogonal to a backward time dimension described by a rotation by π (i induces a rotation by π/2¹; see, too: Roger PENROSE 2007, Fig 25.10: rotation by π/2 and point symmetry of particle-antiparticle pair annihilation and COMPTON scattering providing equivalence). By assuming that we are not able to measure this “i backward proper time of antimatter” with our standard instruments of measurement (1^st premise) there is 1 dimension with gravitation flux missing (this is another premise) in the CERN ALPHA-g experiment. Thus the ratio above gets rid of one dimension, namely the standard forward time dimension we are used to measure. The numerator becomes 3, the ratio becomes ¾ = 0.75:

[3 space-time dimensions of antimatter (e.g. CERN's ALPHA-g antihydrogene)] /
[3 space and 1 time dimensions of normal matter (e.g. steel balls of NEWTON's Cradle)]
= 3/4 = 0.75 .

This would explain the measured CERN ALPHA-g ratio of 0.75 as an expected value (expectation operator, real value).

With this point of view – based on our experiments on NEWTON’s Cradle, complex numbers, Richard FEYNMAN’s backward time, and CPT Symmetry -, the CERN ALPHA-g experiment becomes a proof for Richard FEYNMAN’s backward proper time concept in the FEYNMAN diagrams, and a proof for CPT Symmetry; furthermore, the CERN ALPHA-g experiment becomes a (at least somehow „blinded“) not T-theoretic proof (in the sense of not-falsification, respective corroboration) for our experiments and results on the bifilar pendulum and the corresponding NEWTON’s Cradle, and of our thereof derived theory on 2ħ gravitons and 11 (or 12, this latter being somehow T-theoretic but most consistent) dimensional string theory, in addition.

This is underlined by the fact that our equation y_space = constant * (1/t_time^0.5) (see Figure 1) for Phase 1 of the elastic collisions^{2, 3} of NEWTON’s Cradle allows to write i°*°y = constant * i/i (1/∣t_time∣^0.5) = constant * ∣t_time∣^-0.5) for Richard FEYNMAN’s negative proper time t < 0 by applying the mathematics of complex numbers by multiplying both sides with i. However, in contrast to mathematics (and the typical interpretation of SCHRÖDINGER’s equation) the multiplication by i in physics has to be interpreted as a rotation of (at least) one standard NEWTON-EINSTEIN space axis by π/2 (90°) which changes the concept of NEWTON-EINSTEIN space by adding a new space dimension pointing at the 5th KALUZA-KLEIN dimension, CALABI-YAU dimensions, quantum loop theories, string theories with 11 or 12 dimensions⁴. I actually assume that a 12-dimensional concept of reality with 10 space dimensions and 2 time dimensions fits the actual empirical data and mathematical calculus best; note that Cumrun VAFA with F-Theory and the introduction of anticommutative GRASSMANN coordinates (a^2 = 0; a = additional dimension) comes to the same conclusion starting at a different point of thinking about reality. Furthermore, our equation can be seen as most eased realization of the NAMBU-GOTO action or POLYAKOV action bringing string theory to NEWTON’s physics and HERTZ’s Contact Law. Again, it’s important to see that 1/t_time^0.5 is the second derivative of HERTZ’s Contact Law with x_{radius compression of the ball}^3/2 - instead of HOOKE’s Law⁵ with x_compression¹ - representing the Quadrupole Concept of Albert EINSTEIN’s General Relativity⁶ for the steel balls of NEWTON’s Cradle providing very substantial evidence for our considerations. So we can conclude that the specific difference between NEWTON’s Cradle and the CERN ALPHA-g experiment is attributed to the dimension of time of the four equally treated NEWTON-EINSTEIN dimensions by being positive for matter and negative for antimatter; the negative time of antimatter causes according to Phase I of the damping of NEWTON’s Cradle a rotation of the time axis by i respective π/2 making the time dimension for the used methods of measurement unmeasurable and thus causing a ¼ reduced local CERN ALPHA-g best fit gravitational acceleration given with 0.75g: (4-1) /4 = a(antimatter) / a(matter) = 0.75.

 

 

Literature:

ANDERSON E. K. et al.: Observation of the effect of gravity on the motion of antimatter. Nature. 621, pages716–722 (2023). https://www.nature.com/articles/s41586-023-06527-1#edit-6379357076

CASTELVECCI Davide: Antimatter falls down, not up. Nature, Vol 622, 5 October 2023, 14-15

CERN ALPHA: https://alpha.web.cern.ch/ retr. 30.I.2024

CERN ALPHA-g Experiment: The ALPHA-g Antihydrogen Gravity Magnet System. https://alpha.web.cern.ch/p... retr. 30.I.2024PENROSE Roger: The Road to Reality. Vintage 2004, 2007

HERRMANN F, SEITZ M: How does the ball‐chain work?. Am. J. Phys. 50, 977–981 (1982). https://doi.org/10.1119/1.12936

POHL Randolf: Fundamental symmetry tested using antihydrogen. Nature, Vol 578, 20 February 2020, 369-370 -15

REICHERT, Stefanie: Gravity is attractive. Nat. Phys. 19, 1549 (2023). https://doi.org/10.1038/s41567-023-02292-0

SOTER Anna: Free-falling antihydrogen reveals the effect of gravity on antimatter. Nature 621, 699-700 (2023); doi: https://doi.org/10.1038/d41586-023-02930-w;

VAFA Cumrun: Puzzles to Unravel the Universe. Harvard University, Amazon, TXu002192151, 2020

 

Literature concerning NEWTON’s experimental Law and e in footnote 3:

GUSEV V G, SOBOLKOV A V and ABORKIN A V: Determination of the coefficient of restitution upon contact of a steel ball with aluminum and steel surfaces. Intelligent Information Technology and Mathematical Modeling 2021 (IITMM 2021) Journal of Physics: Conference Series 2131 (2021) 032087 IOP Publishing doi:10.1088/1742-6596/2131/3/032087

 

Our literature:

GEIER Caroline, and GEIER Stephanie: Untersuchungen zur Newton Schaukel. Poster at VDE School Award Bayern 2019, Ignaz-Günther-Gymnasium Rosenheim.

GEIER Stefan: Facebook: Answer to Abraham Mjm Einsteig (12. January 2020) concerning Nobel Prize, 14. September 2019, Nobel Prize, Gravitational Waves #LIGO.

GEIER Stefan: Facebook: Please, look at the relation between David WINELAND's photons (quanta; see facebook Nobel Prize 22 h ago), and GEIER's interpretation of NEWTON's cradle: (25. Februar 2021) concerning Nobel Prize, 22. September 2021 10:27, Nobel Prize, David WINELAND.

GEIER Stefan: 2ħ Graviton Quantum Correction on W Boson Mass Measurements is Feasible, and Necessary. APR. 18, 2022. eLetter to Science VOL. 376, NO. 6589, 7 Apr. 2022, pp. 170-176. AALTONEN T. et al.: High-precision measurement of the w boson mass with the CDF II detector. DOI: 10.1126/science.abk178

GEIER Stefan, GEIER Caroline, GEIER Stephanie, GEIER Katharina, and GEIER Constantin: Gravitons with Spin 2ħ in the Classical Pendulum: Quantum Physics Fits Newton's Classical Physics. Research Gate, August 2021, DOI: 10.13140/RG.2.2.35308.69769

GEIER Stefan, GEIER Caroline, GEIER Stephanie, GEIER Katharina, and GEIER Constantin: Newton's Cradle, the Damped Harmonic Oscillator, and Planck's Constant h: A Quantum Physics Solution for a Mechanical Ball Chain System. August 2021, ResearchGate: https://www.researchgate.net/publication/353762880_Newton's_Cradle_the_Damped_Harmonic_Oscillator_and_Planck's_Constant_h_A_Quantum_Physics_Solution_for_a_Mechanical_Ball_Chain_System

GEIER Stefan: 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%. Blogger, September 27, 2023. https://humanistischebetrachtungen1.blogspot.com/2023/09/conjoint-orthogonal-projections-of-9.html

Etc.

 

Figure:

Figure 1. Damping of the 1st sphere of NEWTON’s Cradle composed of steel balls in Phase 1 (Caroline Geier and Stephanie Geier: Untersuchungen zur Newton Schaukel. VDE Award 2019, Rosenheim): Richard FEYNMAN's backward (negative) proper time (t(antimatter) < 0) brings in i: t(antimatter) = t(FEYNMAN's backward time) = f(i*t(matter)^0.5) = i f(t(matter))

Endnotes: 

¹ An equilateral triangle ABC on a sphere (you can see the three CPT domains as the three vertices on this sphere) gives you a π/4 rotation by translation of a tangent along a geodäsic and shifting at a vertice to the next edge. Walking on the edges back to the starting point you get an overall angle of 3π/4 giving an π/4 angle deviation of the tangent to the geodesic and a π/2 angle between the tangents when reaching the starting point; in this sense our rotation of the time axis of π/2 related to i is consistent with CPT Symmetry and the uniterian theories of Albert EINSTEIN, Hermann WEYL and Erich SCHRÖDINGER. The term „π/4+ π/4 = π/2 Spherical CPT Symmetry“ might be appropriate and ready for discussion and introduction combining `three-valued respective 3-dimensional logic of CPT Symmetry´ with a sphere and π/2. This CPT Symmetry on a sphere with a π/2 rotation of vectors in the sense of the LEVI-CIVITA connection and the RIEMANN curvature tensor is appropriate to be the wanted tiny asymmetry - important at the Big Bang (e.g. Randolf POHL, 2020) - between matter and antimatter and is a conceptual starting point to explain the differences in the amount of the measurement of matter and antimatter in our universe till now.
Note that this consideration is consistent with i^1/2=e^i*π/4, and thus with the concept of the orthogonal projector we successfully introduced in PLANCK satellite data based cosmology given by (e^i*π/4) = Re(½*2^1/2)_orth.proj. = Im(½*2^1/2)_orth.proj. = |½*2^1/2|. In addition, by π/2 the AdS/CFT correspondence is included by the anti-DeSITTER Space with the substrate border located at |π/2| allowing a link to the concept of AdS/CFT correspondence and the holographic principle.
In addition, it is noteworthy to see that the concept of the radius of curvature of the osculating circle and total curvature include a power of ^3/2 equivalent (equivalence class) to the power of ^3/2 in HERTZ’s Contact Law being one starting point on our considerations on NEWTON’s Cradle (F. Herrmann; M. Seitz. Am. J. Phys. 50, 977–981 (1982). https://doi.org/10.1119/1.12936 ); the by us used concepts of Symmetry Breaking, Emmy NOETHER, π, Werner MAURER, Max PLANCK’s h, Paul DIRAC’s ħ, Richard FEYNMAN, Roger PENROSE … followed later by logical and emiprical consequences and analyses. The equivalence of the power of ^3/2 in total curvature (the curvature of spacetime in general relativity; in general relativity theory Albert EINSTEIN’s spacetime is a pseudo-RIEMANNian manifold) and HERTZ’s Contact Law underlines the relevance of our considerations.

 ² For inelastic collisions with polyacryl balls in NEWTON’s Cradle we obtain an equation of about y_space = constant * (1/t_time^0.56) being excellently approximated by y_space = constant * (1/t_time^0.5) (1/t_time^0.05) (1/t_time^0.005) (1/t_time^0.0005) (1/t_time^0.00005) (1/t_time^0.000005) … suggesting an iterative quadrupole collision interaction in the material causing unelastic collisions (suggesting collisions of intrinsic, nested ball elements which become smaller and smaller). Thus, the backward negative time concept with an i related antimatter time holds at least for some forms of inelastic collisions, too.

 ³ Furthermore, remember that NEWTON’s Experimental Law from 1687, and the coefficient of restitution e - often demonstrated by bouncing balls - is described as a ratio of velocities, and as a square root function of the ratio of kinetic energy, as well as of potential energy respective heights being similar to the derivative of HERTZ’s Contact Law in our perspective as e can be seen as a difference quotient of velocities dx/dt before and after the impact in calculus. It is important to notice that our data on NEWTON‘s Cradle (equation y = k t^-1/2 in Figure 1) as well as our concept on 11 to 12 dimensional spacetime can be applied to the coefficient of restitution e, NEWTON’s Experimental Law, and the concept of strain energy (shape changing work of the engineers) related to 1 – e² - with equal masses of the balls - by

 

e² = y₂ / y₁ = k t₂^-1/2 / k t₂^-1/2 = (t₁ / t₂)^1/2

 

with t₁ = 1 second, t₂ = 2 seconds by

 

e² = (½)^1/2 = 0.7071

(a normalized to doubling coefficient of restitution of NEWTON’s Cradle in Phase 1 therefore is (½)^1/4 = 0.842 compared with ≈ 0.88 in empirical studies by V G Gusev, A V Sobolkov and A V Aborkin 2021 suggesting an approximated energy loss of 1 - (½)^1/2 / 0.88^1/2 = 1 - 0,913094 = 0.087 and a momentum loss of 0.842/0.88 = 1 - 0.9568181 = 0.043 remembering of the 4% respective 20% criterion of v²/c² respective v=0.2*c for the need of application of special relativity), and

sin^-1(½)^1/2 = cos^-1(½)^1/2 = π/4 = 45°

representing the angle bisector describing the basic unit orthogonal projector of space, respective spacetime in our text „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%“ (https://humanistischebetrachtungen1.blogspot.com/2023/09/conjoint-orthogonal-projections-of-9.html). This extremly high – absolutely unexpected to me - consistent relation back to NEWTON’s original thinking in 1687 – and the relation to Albert EINSTEIN’s spacetime, Richard FEYNMAN’s backward antimatter time and CPT Symmetry - underlines the relevance of our data and theory. (GEIER et al., in preparation, and footnotes 1 and 4)

 ⁴ It is noteworthy, that our approach is confounded with the metric signature problem but is different from the metric signature problem by adding a second time dimension. Furthermore, our data and theory suggest that HILBERT-EINSTEIN action should be written as a multiples of ħ, 2ħ and/or 2ħπ = h while comparing the integrand -g^1/2 in the HILBERT-EINSTEIN action with our equation y_space = constant * (1/t_time^0.5) which can be seen as a function of the second derivative of the HILBERT-EINSTEIN action, and of HERTZ’s Contact Law related to Quadrupoles simultaneously linking Gravitation from now on to 2ħ, respective ħ and/or 2ħπ = Max PLANCK’s h!

 ⁵ HOOKE’s Law is most often applied to NEWTON’s Cradle, and to simulations and models of NEWTON‘s Cradle. Friedrich HERRMAN and Manfred SEITZ: How does the ball‐chain work? Am. J. Phys. 50, 977–981, 1982, caused our focus on Heinrich HERTZ’s Contact Law from 1882.

 ⁶ Note that the integrand „-g^1/2“ in the HILBERT-EINSTEIN action fits as 1^st derivative of a Ball Quadrupole described by HERTZ‘ Contact Law by being equivalent to our equation y = k t^-1/2 in Figure 1 as a 2nd derivative of the HILBERT-EINSTEIN action, as well as HERTZ‘ Contact Law.

 

_~  finis operis  _~

 

 

Critique welcome!
Yours Stefan Geier, Haidholzen

(The text above was classified by Nature's Disqus platform as spam a few minutes ago. Therefore, I post the text here.)
(However, I was able to post the extended comment on Nature's Disqus platform by "Stefan A Geier" in the meantime; I think that's highly appropriate even when looking at the length of the extended text.)