torsdag 13 mars 2014

Increasing Uncertainty about Heisenberg's Uncertainty Principle + Resolution

                My mind was formed by studying philosophy, Plato and that sort of thing….The reality we can put into words is never reality itself…The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts...If we omitted all that is unclear, we would probably be left completely uninteresting and trivial tautologies...

The 2012 article Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements  by Lee A. Rozema et al, informs us: 
  • The Heisenberg Uncertainty Principle is one of the cornerstones of quantum mechanics. 
  • In his original paper on the subject, Heisenberg wrote “At the instant of time when the position is determined, that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position”. 
  • The modern version of the uncertainty principle proved in our textbooks today, however, deals not with the precision of a measurement and the disturbance it introduces, but with the intrinsic uncertainty any quantum state must possess, regardless of what measurement (if any) is performed. 
  • It has been shown that the original formulation is in fact mathematically incorrect.
OK, so we learn that Heisenberg's Uncertainty Principle (in its original formulation presumably) is a cornerstone of quantum physics, which however is mathematically incorrect, and that there is a modern version not concerned with measurement but with an intrinsic uncertainty of an quantum state regardless of measurement. In other words, a corner stone of quantum mechanics has been moved. 

  • The uncertainty principle (UP) occupies a peculiar position on physics. On the one hand, it is often regarded as the hallmark of quantum mechanics. 
  • On the other hand, there is still a great deal of discussion about what it actually says. 
  • A physicist will have much more difficulty in giving a precise  formulation than in stating e.g. the principle of relativity (which is itself not easy). 
  • Moreover, the formulation given by various physicists will differ greatly not only in their wording but also in their meaning.  
We learn that the uncertainty of the uncertainty principle has been steadily increasing ever since it was formulated by Heisenberg in 1927. 

In a recent series of posts based on Computational Blackbody Radiation I have suggested a new approach to the uncertainty principle as a high-frequency cut-off condition of the form
  • $\nu < \frac{T}{\hat h}$,  
where $\nu$ is frequency, $T$ temperature in Kelvin $K$ and $\hat h=4.8\times 10^{-11}Ks$ is a scaled Planck's constant, and the significance of the cut-off is that a body of temperature $T\, K$ cannot emit frequencies larger than $\frac{T}{h}$ because the wave synchronization required for emission is destroyed by internal friction damping these frequencies.  The cut-off condition thus expresses Wien's displacement law. 

The cut-off condition can alternatively be expressed as 
  • $u_\nu\dot u_\nu > \hat h$ 
where $u_\nu$ is amplitude and $\dot u_\nu =\frac{du_\nu}{dt}$ momentum of a wave of frequency $\nu$ with $\dot u_\nu^2 =T$ and $\dot u_\nu =\nu u_\nu$. We see that the cut-off condition has superficially a form similar to Heisenberg's uncertainty principle, but that the meaning is entirely different and in fact familiar as Wien's displacement law. 

We thus find that Heisenberg's uncertainty principle can be replaced by Wien's displacement law, which can be seen as an effect of internal friction preventing synchronization and thus emission of frequencies  $\nu > \frac{T}{\hat h}$.

The high-frequency cut-off condition with its dependence on temperature is similar to high-frequency damping of a loud speaker which can depend on the level of the sound. 

11 kommentarer:

  1. There is a discussion what this means (or rather what it doesn't) at

    Observation of violation of the uncertainty principle?

  2. the wave synchronization required for emission

    What requirement of synchronization is this?

  3. Emission requires waves to be in-phase which requires synchronization by resonance which gets destroyed unless amplitude x momentum is large enough because of finite precision as a form of internal friction.

  4. Emission requires waves to be in-phase

    This I don't get. What physical principal requires this?

    Not being in-phase just leads to incoherent light, as seen in incandescent light or black body radiation.

  5. Incoherent light consists of many wave lengths and phase shifts as a collection of coherent waves and each coherent wave requires a coordinated generator, which cannot be an individual single atom and thus must consist of a web of atoms singing in-phase.

  6. which cannot be an individual single atom

    Why not from an individual atom? An emission spectrum from a dilute gas is certainly part of physical reality.

  7. A dilute gas has a discrete spectrum with each spectral line representing coordinated emission from many atoms.

  8. But a dilute gas acts like a noninteracting gas. Where is the coordination?

  9. The gas is subject to incident light which is partially coherent and the emission from the gas reflects absorption.

  10. But that doesn't hold in the case where the gas is preheated. Where is the coordination then?

  11. A preheated gas has been subject to incident radiation partially coherent.