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A very peculiar fact is that in a compact space THERE IS a preferred inertial system. Indeed even if locally there is no way to single out a preferred inertial system, globally you can do it. Is the topology that tells you that an observer doing a loop around a torus is topologically different from an observer moving around simply connected loops. So for ...


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A nice overview of the problem is given in arXiv:1205.3740. I'll summarise the most important points here. Let $d$ be the number of space dimensions. Then the Laplace operator is given by $$ \Delta=\frac{\partial^2}{\partial r^2}+\frac{d-1}{r}\frac{\partial}{\partial r}+\frac{1}{r^2}\Delta_S\tag{1} $$ where $\Delta_S$ is the Laplace operator on the $d-1$ ...


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Although I do not quite follow your analogy, there are a few things that can be said about mutilating spacetime in general. To be very non-technical and a little casual... Firstly, the fundamental idea of spacetime is that it is the arena of physics: within a spacetime effects propagate from place to place through time and typically if two places A & B ...


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In dimensional regularization, $d$ is a complex number, not a true dimension. The $d$-dimensional integrals of a rational function are defined for any complex $d$ with sufficiently negative real part (the threshold depending on the integrand), and therefore can be analytically continued to a (provably meromorphic) function for all $d$. For a concise, ...


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Every regularization scheme is somewhat arbitrary. There are three popular regularization schemes when it comes to path integrals and their associated perturbative divergent integrals: time slicing, mode regularization, and dimensional regularization. Time slicing is the usual procedure used to derive the path integral, and it is the discretization of time ...


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If there are eleven dimensions as M-Theory asserts Let us suppose it is true would that mean that the majority of what we are made from exists in the seven other dimensions? Define dimension: In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to ...


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A simplistic answer is, 3/11ths of us exists within the normal three dimensions, and the other 8/11ths exists in the hypothetical extra dimensions. This answer does make string theory sound silly (which personally I think it is :) , but i can't see why it should not be true.



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