### Do we really live in four or in higher dimensions?

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In Einstein gravity, gravitational potential goes as $1/r^{d-3}$ in $d$ spacetime dimensions, which assumes the familiar $1/r$ form in four dimensions. On the other hand, it goes as $1/r^\alpha$ with $\alpha=(d-2m-1)/m$ in \emph{pure Lovelock gravity} involving only one $m$th order term of the Lovelock polynomial in the gravitational action. The latter offers a novel possibility of having $1/r$ potential for the dimension spectrum given by $d=3m+1$. Thus it turns out that in the two prototype gravitational settings of isolated objects like black holes and the universe as a whole -- cosmological models, there is \emph{no way to distinguish} between Einstein in four and $m$th order pure Lovelock in $3m+1$ dimensions, i.e., in particular $m=1$ four dimensional Einstein and $m=2$ seven dimensional pure Gauss-Bonnet gravity. As envisaged in higher dimensional theory, all matter fields, e.g., Electromagnetic field, remain confined to the usual four dimensions while gravity is however free to propagate in higher dimensions. But it cannot distinguish between any two members of the dimension spectrum, then one wonders, do we really live in four or in higher dimensions?