tisdag 11 mars 2014

Wikileaks: Heisenberg's Uncertainty Principle Fundamentally Misleading!

Wikipedia gives the following information about Heisenberg's uncertainty principle:
  • In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously.
  • Though widely repeated in textbooks, this physical argument is now known to be fundamentally misleading. While the act of measurement does lead to uncertainty, the loss of precision is less than that predicted by Heisenberg's argument; the formal mathematical result remains valid, however.
  • Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology. 
  • It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer.
  • Thus, actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.
The uncertainty principle, which in current text books on quantum mechanics serves a fundamental role, is in fact fundamentally misleading. Wow! This must be a leak from a true Wikileaks whistleblower. Imagine what will happen if this message is understood by the scientific community.

The leak opens to a fresh look at the uncertainty principle as in Computational Blackbody Radiation suggesting the following fundamental property of atomistic quantum systems: Finite precision computation introduces a high frequency cut-off as expressed in Plank's law:
  • $\nu < \frac{T}{\hat h}$ where $\hat h =\frac{h}{k}$, 
with $\nu$ frequency, $h$ Planck's constant, $k$ Bolzmann's constant and $\hat h =4.8\times 10^{-11}\, Ks$. Planck's constant $\hat h$ is then determined by the reference blackbody as the blackbody with maximal cut-off frequency (smallest $\hat h$) = peep hole of empty box with graphite walls.

The high frequency cut-off can alternatively be expressed as a restriction on wave length $\lambda$ of the form
  • $\lambda > \frac{c}{T}\hat h$,
which can be seen as a smallest coordination length required for emission of radiation from atomistic oscillation subject to finite precision.

To see the connection to Heisenberg's uncertainty principle, consider a wave of frequency $\nu$ of amplitude $u_\nu$ with $\dot u_\nu \equiv\frac{du_\nu}{dt}=\nu u_\nu$ and $T =\dot u_\nu^2$ for which the high-frequency cut-off condition $\nu < \frac{T}{\hat h}$, can be expressed as
  • $\dot u_\nu u_\nu  >  h$.
We see that high-frequency cut-off from finite precision computation can be seen as a substitute for an uncertainty principle which today is viewed as fundamentally misleading. 

We note that the idea of viewing the uncertainty principle as a relation between a function and its Fourier transform also seems to be fundamentally misleading. 

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