The c=ℏ=G=1—question

•The notion of physical quantity is defined including multidimensional quantities.•The notion of dimensional fundamental constant is defined.•Geometric structure of space–time is constructed from time measurements only.•Quantum mechanics is formulated without quantization and without ℏℏ.

The question whether the invariant speed c  , Planck constant ℏℏ, and gravitational constant G can be put equal to 1 is analyzed. The discussion is based on fundamental considerations concerning the notion of physical quantity. It is found that the issue is not a matter of appropriate unit selection. Further it is shown that classical space–time geometry and quantum mechanics can be formulated in such a way that the invariant speed and the action quantum are truly one and do not have to be set equal to one.