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• W4306377512 abstract "Black holes play an important role in linking microphysics with macrophysics, with those of the Planck mass ($M_P sim10^{-5}$g) featuring in any theory of quantum gravity. In particular, the Compton-Schwarzschild correspondence posits a smooth transition between the Compton wavelength ($R_C propto 1/M$) below the Planck mass and the Schwarzschild radius ($R_{rm S} propto M$) above it. The duality between $R_{rm C}$ and $R_{rm S}$ implies a form of the Generalized Uncertainty Principle (GUP) and suggests that elementary particles may be sub-Planckian black holes. The simplest possibility is that the ADM mass has the form $M + beta M_P^2/M$ for some constant $beta$ and this model can be extended to charged and rotating black holes, clearly relevant to elementary particles. Another possibility is that sub-Planckian black holes may arise in loop quantum gravity and this explicitly links black holes and elementary particles. Higher dimensions may modify both proposals. If there are $n$ extra dimensions, all with the same compactification scale, one expects $R_{rm S} propto M^{1/(1+n)}$ below this scale but $R_{rm C}$ depends on the form of the higher-dimensional wave-function. If it is spherically symmetric, then $R_{rm C} propto M^{-1}$, so duality is broken and the Planck mass is reduced, allowing the possibility of TeV quantum gravity. If the wave-function is pancaked in the extra dimensions, $R_{rm C} propto M^{-1/(1+n)}$ and so duality is preserved but the Planck mass is unchanged." @default.
• W4306377512 created "2022-10-17" @default.
• W4306377512 creator A5035611844 @default.
• W4306377512 date "2022-10-17" @default.
• W4306377512 modified "2023-10-02" @default.
• W4306377512 title "The Generalized Uncertainty Principle and higher dimensions: Linking black holes and elementary particles" @default.
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• W4306377512 doi "https://doi.org/10.3389/fspas.2022.1008221" @default.
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