måndag 28 november 2011

Renormalization in QED, Blackbody Radiation and Turbulence

There is a connection between the cut-off in Computational Blackbody Radiation and the cut-off in Renormalization of QED, namely
  • avoiding an ultraviolet catastrophe of infinite energy
  • by transforming high-frequency waves into low-frequency waves
  • in a form of reinvestment.
In the case of blackbody radiation with an absorbing body with a cut-off proportional to temperature subject to forcing from incident waves, the reinvestment comes out as heating (increasing temperature) from incident wave frequencies above the current cut-off.

There is also a connection to turbulent dissipation with high-frequency kinetic energy being transformed into low frequency internal/heat energy. The total energy as the sum of kinetic and internal energy collects the reinvestment and is thus conserved.

Renormalization thus concerns reinvestment of what is cut off, like collecting the branches cut off from a tree and using them together with the trunk of the tree so that nothing is lost.

The basic question concerns partition of energy between the trunk and branches (on branches)
and its dependence on the size of the cut-off length.

In turbulence, the total turbulent dissipation (= drag in bluff body flow) shows to be independent of the cut-off length.

In quantum mechanics the question is if the world would look the same with a different value of Planck's constant which sets the cut-off length on atomic scales.

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