måndag 10 mars 2014

New Objective View of Heisenberg's Uncertainty Principle

Heisenberg's Uncertainty Principle stating a lower bound of accuracy in observation of position $x$ and momentum (velocity) $p$.

Computational Blackbody Radiation gives a new view on Planck's constant $h$ as effectively a high-frequency cut-off: Only frequencies $\nu$ such that
• $\nu < \frac{T}{\hat h}$,
will be radiated, where $T$ is temperature in Kelvin K, and $\hat h =\frac{h}{k} \approx 4.8\times 10^{-11}\, Ks$ where $k$ is Planck's constant. The cut-off condition can alternatively be expressed as
1. $u_\nu\dot u_\nu > \hat h$
where $u_\nu$ is amplitude of wave frequency $\nu$ and $\dot u_\nu=\frac{du}{dt}=\nu u$ and $\dot u_\nu^2 =T$.

This relation 1 is similar to Heisenberg's Uncertainty Principle as a lower bound on the product of position (amplitude) and velocity, but with a different physical meaning. Whereas Heisenberg's Uncertainty Principle concerns the product of errors in position $\Delta x$ and momentum/velocity $\Delta p$ vs Planck's constant $h$, the relation 1 concerns the product of amplitude and velocity vs the scaled Planck constant $\hat h$.

The relation expresses that radiation of a certain frequency $\nu$ requires either a sufficiently large amplitude $u_\nu$ or velocity $\dot u_\nu$, as a requirement for coordinated oscillation under finite precision computation.

We thus replace uncertainty in observation by finite precision in actual physics, which reduces the subjective observer aspect of Heisenberg's Uncertainty Principle.  There is a connection to observation in finite precision computation cut-off of high frequencies, in the sense that only frequencies which effectively are emitted, can be observed. It is here not the observer who sets limits of observational accuracy by interacting with the observed object, but rather the object itself.

We recall that the central idea is to view physics as analog finite precision computation, which can be simulated by digitial computation allowing observation without interference and thus eliminates a basic difficulty in quantum mechanics.