# Finite Precision Blackbody Radiation vs Uncertainty Principle

Authors

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 $\nu$ defined by

• $\nu =\frac{T}{h}$

where $T$ is the common temperature of all frequencies of amplitude $u_\nu$ and velocity $\dot u_\nu \equiv \frac{du_\nu}{dt}$ with $t$ time and $T =\dot u_\nu^2$ and $h$ is a finite precision measure. Using that $\dot u_\nu\approx \nu u_\nu$ the cut-off condition can be written

• $\dot u_\nu^2=h\nu$ or $u_\nu^2 \approx \frac{h}{\nu}$

from which follows by multiplication

• $\vert \dot u_\nu\vert \vert u_\nu\vert \approx h$,

which can be interpreted as a form of Heisenberg’s Uncertainty Principle: The smaller the amplitude $\vert u_\nu\vert$  (the position) is, the larger must the velocity $\vert \dot u_\nu\vert$ (the momentum) be, in order for a coherent wave to be emitted/radiated.