Finite Precision Blackbody Radiation vs Uncertainty Principle

· blackbody radiation
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.

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