## söndag 16 mars 2014

### Uncertainty Principle, Whispering and Looking at a Faint Star

The recent series of posts on Heisenberg's Uncertainty Principle based on Computational Blackbody Radiation suggests the following alternative equivalent formulations of the principle:
1. $\nu < \frac{T}{\hat h}$,
2. $u_\nu\dot u_\nu > \hat h$,
where $u_\nu$ is position amplitude, $\dot u_\nu =\nu u_\nu$ is velocity amplitude of a wave of frequency $\nu$ with $\dot u_\nu^2 =T$, and $\hat h =4.8\times 10^{-11}Ks$ is Planck's constant scaled with Boltzmann's constant.

Here, 1 represents Wien's displacement law stating that the radiation from a body is subject to a frequency limit scaling with temperature $T$ with the factor $\frac{1}{\hat h}$.

2 is superficially similar to Heisenberg's Uncertainty Principle as an expression of the following physics: In order to detect a wave of amplitude $u$, it is necessary that the frequency $\nu$ of the wave satisfies $\nu u^2>h$. In particular, if the amplitude $u$ is small, then the frequency $\nu$ must be large.

This connects to (i) communication by whispering and (ii) viewing a distant star, both being based on the possibility of detecting small amplitude high-frequency waves.