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| Hlavní autor: | |
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| Médium: | Recurso digital |
| Jazyk: | angličtina |
| Vydáno: |
Zenodo
2025
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| Témata: | |
| On-line přístup: | https://doi.org/10.5281/zenodo.18099239 |
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- <p>This manuscript presents a first-principles derivation of the fine structure constant from pure geometry, without adjustable parameters. Starting from the eleven-dimensional M-theory framework with the compact space given by the seven-sphere quotiented by the binary icosahedral group, the theory derives the inverse fine structure constant as:</p> <p>137.035999176969186368478375917333</p> <p>This value achieves agreement with the CODATA 2022 experimental measurement at 0.22 parts per trillion, representing one of the most precise theoretical predictions in fundamental physics. The derivation requires only two input parameters: the spacetime dimension d = 11 and the number of fermion generations g = 3, both determined by mathematical consistency conditions rather than empirical fitting.</p> <p>Part I develops the complete mathematical framework underlying this result. The binary icosahedral group, containing 120 elements, connects to the exceptional Lie algebra E8 through the McKay correspondence, establishing a bridge between discrete symmetry and continuous gauge structure. The quotient space inherits a natural Riemannian metric, enabling spectral analysis through heat kernel methods. The Gilkey-Seeley coefficients, which encode geometric information in the short-time asymptotic expansion of the heat kernel, are computed explicitly for the Maxwell field on real projective four-space. This calculation reveals that the type-A conformal anomaly vanishes identically, a crucial consistency requirement. The spectral zeta function on this orbifold geometry is evaluated to fifty decimal places using the Ikeda-Taniguchi eigenvalue formula, yielding precise values for the even and odd spectral derivatives. The radius formula emerges from matching conformal anomaly coefficients between the seven-sphere quotient and real projective four-space, producing the fundamental relation R = 2 pi minus the Euler-Mascheroni constant divided by the sum of the spectral integer and pi. The spectral integer itself, equal to 137, arises as a Diophantine sum encoding the framework parameters through the identity 3 times 42 plus 11. Multiple independent derivations confirm this integer from group theory, number theory, and Lie algebra dimensions, providing strong internal consistency checks.</p> <p>Part II explores the physical implications across multiple domains. The geometric framework naturally incorporates gauge coupling unification at high energies, with the Standard Model gauge groups emerging from the E8 breaking pattern. Supersymmetry predictions place superpartner masses in ranges accessible to future colliders. The Higgs boson mass and vacuum expectation value receive geometric interpretations through the icosahedral structure. Quark and lepton mass ratios, including the Cabibbo angle and CKM matrix elements, emerge from representation-theoretic considerations with sub-percent accuracy. Cosmological parameters including the dark energy density and baryon asymmetry connect to topological invariants of the compact space. Black hole entropy calculations reproduce the Bekenstein-Hawking formula while suggesting resolutions to the information paradox through the underlying discrete structure.</p> <p>Part III establishes the minimality and uniqueness of the geometric foundation. The tetrahedron, as the simplest three-dimensional polytope, generates the icosahedron through a specific geometric construction, which in turn produces the binary icosahedral group through its symmetries. This chain demonstrates that the entire framework follows from the most elementary geometric object. The spectral correspondence theorem proves that no simpler geometry can reproduce the observed value of the fine structure constant while maintaining mathematical consistency.</p> <p>The manuscript contains 24 chapters and 24 appendices providing complete mathematical proofs, numerical validations, and detailed calculations ensuring full reproducibility of all results.</p>