Planck Uncertainties
by Steven Gusman My understanding is that the Planck units were discovered when Max Planck simply took the fundamental constants, c, G, and h, and algebraically manipulated them until they returned a unique length, mass, and duration (in other words, he reverse-engineered them through unit analysis). 1 Utilizing the fact that p = mv and E = mc 2 , one can further manipulate the Planck units to include a momentum and an energy. l p = (hG/c 3 ) 1/2 m p = (hc/G) 1/2 t p = (hG/c 5 ) 1/2 p p = (hc 3 /G) 1/2 E p = (hc 5 /G) 1/2 The small values, length and time, are then naturally assumed by many physicists to be quanta of those variables (or at least of the right order-of-magnitude). That combining the relativistic constants G and c with the quantum of action, h, appears to yield a quantum of space and time leads most physicists attempting to discover a theory of quantum gravity to believe that the Planck unit