Three Analytical Relations Giving The Speed of Light, The Planck Constant and The Fine-Structure Constant

The fundamental physical constants are at the root of physics theories, but no theoretical framework provides their experimental values. In addition, they are assumed to be independent of each other. Here, we present two valuable dimensionless numbers based on vacuum properties and fundamental constants. The value of these dimensionless numbers provokes questioning, since they are of order 101. In particular, they mean that it is possible to build a velocity and a parameter homogeneous to the Planck constant of the same order as the speed of light and the Planck constant respectively, only based on five well-known physical parameters. These formulas are very unlikely to be two coincidences and suggest that the parameters involved depend on each other. They also seem to indicate that light is a material wave and quantum mechanics is a deterministic theory. A link between these numbers and the fine-structure constant is also established.