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By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program--to make sure it is free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. You can apply it to your programs, too.\r\nWhen we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for them if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free works, and that you know you can do these things.\r\nTo protect your rights, we need to prevent others from denying you these rights or asking you to surrender the rights. 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The analysis utilizes the Python library sympy for symbolic mathematics, allowing us to define, manipulate, and analyze the dimensions of various physical quantities and equations.\r\n\r\nTheoretical Background\r\nThe Super Force (SF) is theorized to be the unification of all four fundamental forces—gravitational, electromagnetic, strong nuclear, and weak nuclear—at the Planck scale. The dimensional analysis aims to verify the consistency of the Super Force with known physical dimensions and to explore its relation to other fundamental forces.\r\n\r\nAnalysis Setup\r\nThe analysis is conducted using the following key physical constants and variables:\r\n\r\n�\r\nG: Gravitational constant\r\n�\r\nc: Speed of light in a vacuum\r\nℏ\r\nℏ: Reduced Planck's constant\r\n�\r\n�\r\nLP: Planck length\r\n�\r\n�\r\nmP: Planck mass\r\n�\r\n�\r\nMU: Unified mass (hypothetical)\r\n�\r\n�\r\nRU: Unified radius (hypothetical)\r\n�\r\nα: Fine-structure constant\r\n�\r\nq: Elementary charge\r\n�\r\nk: Coulomb's constant\r\n�\r\n0\r\nϵ \r\n0\r\n​\r\n : Vacuum permittivity\r\n�\r\n0\r\nμ \r\n0\r\n​\r\n : Vacuum permeability\r\n�\r\nμ, \r\n�\r\nϵ: Generalized permeability and permittivity in unified field theory\r\nEquations and Dimensional Consistency\r\nThe Super Force is represented by the equation \r\n�\r\n�\r\n=\r\n�\r\n4\r\n�\r\nSF= \r\nG\r\nc \r\n4\r\n \r\n​\r\n , which is dimensionally equivalent to force. The analysis extends to other forces at the Planck scale, including the strong nuclear force (FSN), electromagnetic force (FEM), and gravitational force (FG), with the following relations:\r\n\r\nStrong Nuclear Force (FSN): \r\n�\r\n�\r\n�\r\n=\r\n�\r\n4\r\n�\r\nFSN= \r\nG\r\nc \r\n4\r\n \r\n​\r\n \r\nElectromagnetic Force (FEM): \r\n�\r\n�\r\n�\r\n=\r\n1\r\n�\r\n⋅\r\n�\r\n2\r\n�\r\n�\r\n2\r\nFEM= \r\nk\r\n1\r\n​\r\n ⋅ \r\nLP \r\n2\r\n \r\nq \r\n2\r\n \r\n​\r\n \r\nGravitational Force (FG): \r\n�\r\n�\r\n=\r\n�\r\n⋅\r\n�\r\n�\r\n2\r\n�\r\n�\r\n2\r\nFG=G⋅ \r\nLP \r\n2\r\n \r\nmP \r\n2\r\n \r\n​\r\n \r\nThe Schrödinger and Dirac equations are also considered to explore the quantum mechanical aspects of the Super Force theory:\r\n\r\nSchrödinger Equation: \r\n�\r\nℏ\r\n∂\r\n�\r\n∂\r\n�\r\n=\r\n−\r\nℏ\r\n2\r\n2\r\n�\r\n∂\r\n2\r\n�\r\n∂\r\n�\r\n2\r\n+\r\n�\r\n�\r\niℏ \r\n∂t\r\n∂ψ\r\n​\r\n =− \r\n2m\r\nℏ \r\n2\r\n \r\n​\r\n  \r\n∂x \r\n2\r\n \r\n∂ \r\n2\r\n ψ\r\n​\r\n +Vψ\r\nDirac Equation: \r\n�\r\n�\r\n2\r\n=\r\n�\r\n0\r\n2\r\n�\r\n4\r\n+\r\n�\r\n2\r\n�\r\n2\r\nET \r\n2\r\n =m \r\n0\r\n2\r\n​\r\n c \r\n4\r\n +p \r\n2\r\n c \r\n2\r\n \r\nDimensional Analysis Results\r\nThe dimensional analysis confirms that the dimensions of the Super Force and related forces are consistent with the dimensions of force, as summarized below:\r\n\r\nSuperforce (SF): Dimensions {Dimension(G): -1, Dimension(c): 4}, consistent with force \r\n[\r\n�\r\n�\r\n�\r\n−\r\n2\r\n]\r\n[MLT \r\n−2\r\n ].\r\nStrong Nuclear Force (FSN): Identical dimensions to SF, as expected from the equation provided.\r\nElectromagnetic Force (FEM): Dimensions {Dimension(LP): -2, Dimension(k): -1, Dimension(q): 2}, aligning with the force in electromagnetism.\r\nGravitational Force (FG): Dimensions {Dimension(G): 1, Dimension(LP): -2, Dimension(mP): 2}, consistent with gravitational force.\r\nConclusion\r\nThe dimensional analysis provides a foundational check for the dimensional validity of the equations related to the Super Force theory. 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