A hundred years ago TK noticed that you can express the equations of EM within the formalism of differential geometry of GR. To unify EM + GR he:
1) added a 5th dimension
2) used the constant of gravitation, G, in his equations.
The results are in complete disagreement with particle properties. The right step to solve this problem is a step back: drop G in the equations. This “unifies” EM and particle physics, gravitation can be recovered by series expansion.
The results you get for particles will be in the right order of magnitude. They will be exact within the range of QED corrections if you set Spin 1/2 as boundary condition. This brings in the fine-structure constant, α, as a crucial part in the equations, due to the resulting relationship of h and the electric potential which is part of Kaluza’s ansatz.
You’ ll get:
- electroweak coupling constants
- a convergent series of particle energies quantized as a function of the fine-structure constant, α, with
electron and the Higgs VEV energy as lower and upper limit
- 6 lepton-like states, 6 quark-like states
- partial charges 1/3, 2/3
- magnetic moments of the uds-baryons
- a cosmological constant in the correct order of magnitude
- etc.
The first 2 points can be given in simple form that may in principle be checked with pencil & paper:
n={3;4}
S_N = surface area of N-D-sphere; Γ = gamma functions
n={1;2;...}
The α-part is a converging series, the σ is related to α and can be given as geometric parameter: σ_0^1/3 ~ 4πΓ(-1/3)^3 /3 (spherical symmetry) and e.g. its 1D limit σ^1/3 ~ Γ(-1/3) /3, which gives the Higgs VEV.
The model works ab initio without free parameter and allows to remove some values from the set of fundamental constants:
electromagnetic constants, h, G, α, αweak, energies of elementary particles =>
electromagnetic constants.
You can find some more information here:
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Prose:
Short: Kaluza without Klein
Medium: Theodor Kaluza's Theory of Everything: revisited
Medium (On Researchgate): Theodor Kaluza's Theory of Everything: revisited
Long: Theodor Kaluza's Theory of Everything: extended
The Movie: Kaluza without Klein
Lyric:
Medium: In 1919
Short: Attempt at a haiku
Showdown:
Standard model vs Kaluza without Klein
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