Friday, May 11, 2007
The Quantization of Electromganetic Energy
Isn't it strange that there is no theoretical proof till now of the quantization of electromganetic energy ? The Planck hypothesis was accepted since it yielded the correct spectral distribution of the blackbody radiation energy. Poincare showed that quantization is a necessary and a sufficient condition to obtain the correct blackbody formula. In QED, the field is quantized in an analogous way to the quantum harmonic oscillator, it is not a still a theoretical proof for quantization. In quantum optics, many experiments verify the quantization hypothesis, but still no theoretical proof !!
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Agreed. On the aesthetic ground, the light quanta prevent the untraviolet divergence too (beside yielding the correct energy spectrum per Planck). The question is: why does light "know" to quantize to save us from this potential catastrophe?
Regarding the quantization on EM wave, let's say - as the standard procedure - we MODEL it after the quantization of a harmonic oscillator. 3 methods known so far: enforce ladder operators, solve Schrodinger wave equation, and sum up the path integral. [For EM wave quantization, only the ladder operator and field quantization are suitable.] Still, one question keeps lingering ever since to me: is there an intuitive explanation to how the quantized energy levels arise?
All 3 known methods, especially the two former, are machinery. Path integral - as appealing as it is - does not directly show me how quantized energy levels arise. One does the sum of paths, then bang... the partition function shows a discrete energy spectrum. Ok, but why so?
Perhaps, one could view the harmonic oscillator in terms of path integral in a two-dimensional phase space (x, p) using coherent state representation (since x and p do not exist simultaneously). From then, IF one can argue that discrete energy levels arise from the different winding of the path around the origin of the (x,p) plane, I would be satisfied. At least, that would explain the source of quantization in terms of homotopy. That would offer some assurance that the quantization is inevitable....
But I'm not aware of any derivation in that line which suits my math limitation. Geometric, holomorphic, Bergman representation, etc. are way above my head...
Perhaps there are other intuitive answers awaiting to be uncovered...
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