Yes, the Planck length and its multiples are believed to be meaningful in higher dimensions within the context of some theories, such as string theory and certain versions of quantum gravity.
The Planck length, denoted by "ℓP," is a fundamental length scale in physics. It is defined as approximately 1.616 × 10^(-35) meters and represents the smallest length that can be meaningfully discussed within our current understanding of the laws of physics.
In higher-dimensional theories, including string theory, the Planck length can still play a significant role. These theories often propose that the fundamental nature of spacetime and the geometry of the extra dimensions are intrinsically linked to the Planck scale.
In particular, the presence of the Planck length in higher-dimensional theories can have implications for the size and structure of these additional dimensions. For example, in some models, the size of the extra dimensions can be on the order of the Planck length or its multiples. This suggests that at these extremely small scales, the effects of quantum gravity become important, and the smooth and continuous picture of spacetime breaks down.
It's important to note that the precise details of how the Planck length and higher dimensions are related depend on the specific theory or model being considered. Since these theories are highly mathematical and currently lack direct experimental confirmation, the exploration of the Planck length in higher dimensions remains an area of ongoing research and investigation in theoretical physics.