6533b82efe1ef96bd12931eb

RESEARCH PRODUCT

Duality-invariant Einstein-Planck relation and the speed of light at very short wavelengths

subject

description

We propose a generalized Einstein-Planck relation for photons which is invariant under the change $\ensuremath{\lambda}/a{l}_{P}$ to $a{l}_{P}/\ensuremath{\lambda}$, $\ensuremath{\lambda}$ being the photon wavelength, ${l}_{P}$ Planck's length, and $a$ a numerical constant. This yields a wavelength-dependent speed of light $v(\ensuremath{\lambda})=c/(1+{a}^{2}({l}_{P}/\ensuremath{\lambda}{)}^{2})$, with $c$ the usual speed of light in vacuo, indicating that the speed of light should decrease for sufficiently short wavelengths. We discuss the conceptual differences with the previous proposals related to a possible decrease of the speed of light for very short wavelengths based on quantum fluctuations of the space-time, as well as its consequences on Heisenberg's uncertainty principle up to second order in ${l}_{P}$.