: (hbarG/c3)1/2 = 1.616x10-35m

: : I have read a lot books and articles that speak of the Planck length and what it signifies, but I have never seen an explanation of why those basic constants of natural science are associated in that specific way. How did this derivation come about and is there any way of putting how they are associated into words.

Planck scales are not rigorously derived. They are simply calculated by combining the fundamental G h c etc... in a way that results in the dimension sought. For instance (hbarG/c3)1/2 results in a Length and so its called Planck Length, though some just use (hG/c3)1/2 and call that Planck length.

It turns out that the coupling "constants" describing the "strength" of the forces of nature actually vary with different particle energies or scales. It is somewhere near Planck scales that the forces become all of the same strength. It also at these scales that the quantum behavior of gravity can be investigated.

• http://www.delphi.com/sciandpara