Physical Space is a Discrete-Continuous Dual Space of Varying Connectivity Dimensionality Field that Transcends Variable- Based Mathematics

We show that developing a Theory of Everything (TOE) to unify all physical interactions requires a spacetime model having: (i) a discrete-continuous dual structure in which physical properties that could hypothetically vary continuously in some abstract sense are discretized upon measurement and (ii) a variable connectivity dimensionality field. Because this type of space transcends variable-based mathematics, we prove a TOE cannot be developed using only differential geometry and other variable-based mathematics. This completely rules out all forms of hidden variable theories. We disprove the holographic principle that posits all information contained in a volume of physical space is encoded on its boundary. Finally, we show how the variable connectivity dimensionality field gives rise to cross-dimensional projections between microstates that leads to the Second Law of Thermodynamics governing Nature’s irreversibility. We further show cross-dimensional projections are one mechanism for gauge invariance breaking. Finally, we postulate that electromagnetic fields arise from spacetime gradients in the average connectivity dimensionality deviation.