I was wondering whether fractional dimensions have any applications in physics as a whole. I found this photo which suggests:
The dimensions observed in any physical system are not absolute but depend on the observer’s perspective, particularly the distance and angle relative to the object being observed in fractional dimensional space. This axiom introduces a relativistic element to dimensionality itself, suggesting that the dimensional nature of space could vary based on how it is measured or observed, adding a layer of complexity to physical observations and experiments.
Consider an observer in coordinate system $S$ and an object in system $S′$. The angle between these systems becomes acute as the distance increases, reaching 90 degrees when the distance approaches infinity (or when the object disappears from the observer’s view) [...] An object in the $S′$ coordinate system appears smaller as it moves away from the observer in the $S$ system. This observation can be understood by considering the trajectory of the $S′$ coordinates, where $S′$ is not orthogonal to $S$ and forms a specific angle at each space-time position.
