There is a connection between the new analysis of blackbody radiation based on finite precision computation presented in Mathematical Physics of Blackbody Radiation, and Heisenberg’s Uncertainty Principle, which I now elucidate:
As presented in Universality of Blackbody Radiation I consider a wave model with a switch from outgoing radiation to internal heating at a temperature dependent cut-off frequency defined by
where is the common temperature of all frequencies of amplitude and velocity with time and and is a finite precision measure. Using that the cut-off condition can be written
from which follows by multiplication
which can be interpreted as a form of Heisenberg’s Uncertainty Principle: The smaller the amplitude (the position) is, the larger must the velocity (the momentum) be, in order for a coherent wave to be emitted/radiated.