tisdag 18 mars 2014

Quantum Mechanics from Blackbody Radiation as "Act of Despair"

Max Planck: The whole procedure was an act of despair because a theoretical interpretation (of black-body radiation) had to be found at any price, no matter how high that might be…I was ready to sacrifice any of my previous convictions about physics..For this reason, on the very first day when I formulated this law, I began to devote myself to the task of investing it with true physical meaning.

The textbook history of modern physics tells that quantum mechanics was born from Planck's proof of the universal law of blackbody radiation based on an statistics of discrete lumps of energy or energy quanta $h\nu$, where $h$ is Planck's constant and $\nu$ frequency. The textbook definition of a blackbody is a body which absorbs all, reflects none and re-emits all of incident radiation:
  • A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. (Wikipedia)
  • "Blackbody radiation" or "cavity radiation" refers to an object or system which absorbs all radiation incident upon it and re-radiates energy which is characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it. (Hyperphysics)
  • Theoretical surface that absorbs all radiant energy that falls on it, and radiates electromagnetic energy at all frequencies, from radio waves to gamma rays, with an intensity distribution dependent on its temperature. (Merriam-Webster)
  • An ideal object that is a perfect absorber of light (hence the name since it would appear completely black if it were cold), and also a perfect emitter of light. (Astro Virginia)
  • A black body is a theoretical object that absorbs 100% of the radiation that hits it. Therefore it reflects no radiation and appears perfectly black. (Egglescliff)
  • A hypothetic body that completely absorbs all wavelengths of thermal radiation incident on it. (Eric Weisstein's World of Physics
But there is something more to a blackbody and that is a the high frequency cut-off, expressed in Wien's displacement law, of the principal form 
  • $\nu < \frac{T}{\hat h}$,
where $\nu$ is frequency, $T$ temperature  and $\hat h$ a Planck constant, stating that only frequencies below the cut-off $\frac{T}{\hat h}$ are re-emitted. Absorbed frequencies above the cut-off will then be stored as internal energy in the body under increasing temperature,

Bodies which absorb all incident radiation made of different materials will have different high-frequency cut-off and an (ideal) blackbody should then be characterized as having maximal cut-off, that is smallest Planck constant $\hat h$, with the maximum taken over all real bodies. 

A cavity with graphite walls is used as a reference blackbody defined by the following properties: 
  1. absorption of all incident radiation
  2. maximal cut-off - smallest Planck constant $\hat h\approx 4.8\times 10^{-11}\, Ks$,     
and $\hat h =\frac{h}{k}$ is Planck's constant $h$ scaled by Boltzmann's constant $k$. 

Planck viewed the high frequency cut-off defined by the Planck constant $\hat h$ to be inexplicable in Maxwell's classical electromagnetic wave theory. In an "act of despair" to save physics from collapse in an "ultraviolet catastrophe", a role which Planck had taken on,  Planck then resorted to statistics of discrete energy quanta $h\nu$, which in the 1920s resurfaced as a basic element of quantum mechanics. 

But a high frequency cut-off in wave mechanics is not inexplicable, but is a well known phenomenon in all forms of waves including elastic, acoustic and electromagnetic waves, and can be modeled as a disspiative loss effect, where high frequency wave motion is broken down into chaotic motion stored as internal heat energy. For details, see Computational Blackbody Radiation.

It is a mystery why this was not understood by Planck. Science created in an "act of despair" runs the risk of being irrational and flat wrong, and that is if anything the trademark of quantum mechanics based on discrete quanta. 

Quantum mechanics as deterministic wave mechanics may be rational and understandable. Quantum mechanics as statistics of quanta is irrational and confusing. All the troubles and mysteries of quantum mechanics emanate from the idea of discrete quanta. Schrödinger had the solution:
  • I insist upon the view that all is waves.
  • If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.
But Schrödinger was overpowered by Bohr and Heisenberg, who have twisted the brains of modern physicists with devastating consequences... 

5 kommentarer:

  1. I think you have forgotten two important characteristics 1/ a black bodies applies to a solid surface (see for example definitions in Perry's Chemical Engineering Handbook P 5-34 (section on heat and mass transfer). It can not apply to a gas which has no surface or a liquid where phase change (eg evaporation) can take place because then radiation absorption will not equal radiation emission. 2/ Strictly, a black body should also be in a vacuum. As Fourier wrote when there is an atmosphere everything changes- a) the atmosphere may absorb some radiation intended for the black body surface and b) convection occurs at the surface so absorption no longer equals emission. A vacuum of course can cause phase change (or evaporation ) of a liquid. This is used in refrigeration. ( I am sure you know that the work input by the compressor does not oppose the second law of thermodynamics- the compressor heats the gas so it can be cooled and liquified, this then is expanded to cool and evaporated by the vacuum at the inlet of the compressor- heat always flows from high to lower temperature.)
    keep strong cementafriend

  2. Claes, Did Planck himself ever use the expression Energy quanta ? In his 1900 paper there is a reference to the quanta of electricity. Elsewhere he talks about quantum of action.

  3. No, Planck dis not believe in any physical material reality of quanta of whatever, only as a form of conceptual "trick" to get rid of infinities popping up in theory.

  4. Have you read his submission for the 1911 solvay conference?


    French translation of the proceedings of the 1st Solvay conference held in Brussels in 1911.

    Plancks submission:

    The Theory of black body radiation

    Page 100

    "Let us search therefore to examine intensely the physical nature of the constante h. It poses immediately a fundamental question: This element of action does it possess a physical signficance for the propagation of radiant energy in the vacuum, or does it not come by its very nature in the phenomena of production and destruction of radiant energy, in emission and absorption? Following the response given to that preliminary question, the later development of the theory must follow completely different paths.

    The first point of view has been adopted by A. Einstein in his hypothesis of the quanta of light"