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It is generally believed that any quantum theory of gravity should have ageneric feature --- a quantum of length. We provide a physical ansatz to obtainan effective non-local metric tensor starting from the standard metric tensorsuch that the spacetime acquires a zero-point-length $\ell _{0}$ of the orderof the Planck length $L_{P}$. This prescription leads to several remarkableconsequences. In particular, the Euclidean volume $V_D(\ell,\ell_{0})$ in a$D$-dimensional spacetime of a region of size $\ell $ scales as $V_D(\ell, \ell_{0}) \propto \ell_{0}^{D-2} \ell^2$ when $\ell \sim \ell_{0}$, while itreduces to the standard result $V_D(\ell,\ell_{0}) \propto \ell^D$ at largescales ($\ell \gg \ell_{0}$). The appropriately defined effective dimension,$D_{\rm eff} $, decreases continuously from $D_{\rm eff}=D$ (at $\ell \gg\ell_{0}$) to $D_{\rm eff}=2$ (at $\ell \sim \ell_{0}$). This suggests that thephysical spacetime becomes essentially 2-dimensional near Planck scale.

Spacetime with zero point length is two-dimensional at the Planck scale