In the classical theory of electromagnetism, Maxwell formulated four sets of partial differential equations that bear his name: Maxwell’s equations of the electromagnetic field. These equations describe the propagations of electromagnetic waves. This classical theory is based on the experiments performed by Faraday asserting the physical existence of the electric field and the magnetic field. Their mutual orthogonal interactions produce waves that radiate at the speed given by 1/Ö(em) where e is defined as the absolute permittivity and m the absolute permeability of the space-time continuum (classically called the vacuum). Equivalently, this speed is also elegantly given as the product of a defined frequency and a defined wavelength: c=nl where n signifies frequency and l signifies wavelength. In a space-time continuum devoid of matter, this speed is a constant. In media of increasingly varying mass density this speed is decreasingly less than its vacuum value. In space-time regions of infinite mass density this speed is exactly zero.
The idea of infinite mass density is topologically equivalent to the idea of a twist of a one-sided Möbius topology. This twist applied to the space-time continuum becomes the big bang singularity. This space-time singularity is zero dimensional. However, in the infinitesimal neighborhood of this singularity, the transformation of one dimension to zero dimensions is the space-time contraction of a Hopf link. Each cycle of one complete loop reveals a fundamental frequency of zero-point energy. It is physically and mathematically logical to set the associated fundamental wavelength equal to the Planck length. In the event that the Planck length approaches the value of zero, the corresponding vacuum frequency approaches infinity. This infinite frequency implies that a quantum of the space-time continuum can be found here often, while approaching zero Planck length implies that the quantum of the space-time continuum is here always. The multiplicative product of often and always (infinity and zero) remains a constant called the speed of light. But this implies that the Planck length can never reach the exact value of zero since zero multiplied by any quantity is still zero, which suggests that the one dimensional Hopf topology remains valid at the infinitesimal region of the space-time continuum.


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