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In three spatial dimensions, the Compton wavelength $(R_C \propto M^{-1}$)and Schwarzschild radius $(R_S \propto M$) are dual under the transformation $M\rightarrow M_{P}^2/M$, where $M_{P}$ is the Planck mass. This suggests thatthere could be a fundamental link -- termed the Black Hole UncertaintyPrinciple or Compton-Schwarzschild correspondence -- between elementaryparticles with $M < M_{P}$ and black holes in the $M > M_{P}$ regime. In thepresence of $n$ extra dimensions, compactified on some scale $R_E$ exceedingthe Planck length $R_P$, one expects $R_S \propto M^{1/(1+n)}$ for $R_P < R <R_E$, which breaks this duality. However, it may be restored in somecircumstances because the {\it effective} Compton wavelength of a particledepends on the form of the $(3+n)$-dimensional wavefunction. If this isspherically symmetric, then one still has $R_C \propto M^{-1}$, as in the$3$-dimensional case. The effective Planck length is then increased and thePlanck mass reduced, allowing the possibility of TeV quantum gravity and blackhole production at the LHC. However, if the wave function of a particle isasymmetric and has a scale $R_E$ in the extra dimensions, then $R_C \proptoM^{-1/(1+n)}$, so that the duality between $R_C$ and $R_S$ is preserved. Inthis case, the effective Planck length is increased even more but the Planckmass is unchanged, so that TeV quantum gravity is precluded and black holescannot be generated in collider experiments. Nevertheless, the extra dimensionscould still have consequences for the detectability of black hole evaporationsand the enhancement of pair-production at accelerators on scales below $R_E$.Though phenomenologically general for higher-dimensional theories, our resultsare shown to be consistent with string theory via the minimum positionaluncertainty derived from $D$-particle scattering amplitudes.

Does Compton/Schwarzschild duality in higher dimensions exclude TeV quantum gravity?