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February 9th, 2017, 10:06 PM   #1
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Planck blackbody fermion emission

What would happen to the derivation of Planck's constant if its blackbody emitted classical particles or fermions, instead of bosons (photons)?
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February 10th, 2017, 01:41 AM   #2
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What would happen to the derivation of Planck's constant if its blackbody emitted classical particles or fermions, instead of bosons (photons)?
The typical black body experiment uses photons, which are bosons, so if we try it out for fermions we will end up getting different statistics. But there is another crucial point to be made here: photons are massless. We do not have to worry about any stray momentum effects as there is no mass term mucking up the energy spectrum.

In order to get fermions out the blackbody we also want use massless fermions, which pretty much means you are talking about neutrinos. That also means you are going to have one heck of a time setting up your experiment: the Sun acts as such a black body and I can't think of any smaller source to give out a large enough neutrino cross-section to work with. You would also have to surround the Sun with detectors which would give you some slight problems.

As far as "classical" particles are concerned right up until the final point in the calculation the particles coming out were considered to be classical...Light wasn't considered to be particles in those days, they were thought to be waves. Planck's genius was to realize that if he summed the calculated spectrum instead of integrating it (like he should have) then he got the correct results. But he thought the "corpuscular" nature of the radiation from the body had something to do with the walls of the chamber, not due to the radiation coming from it. To find the classical result he would have had to do the integration, not the summation.

In short: The three different kinds of particles (bosonic, fermonic, classical) have the same black body derivation right up to the last summation or integration of the energy spectrum.

What this boils down to is that we have the summation for the bosonic case (which is Planck's result), the classical case (from doing the integration, not the summation) gives a curve with singularities, and frankly I don't know how to do the fermionic case off the top of my head but I'm sure it can be done.

-Dan
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Last edited by topsquark; February 10th, 2017 at 01:44 AM.
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February 10th, 2017, 10:27 AM   #3
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Fantastic work, topsquark! Do the results have anything to do with B-E, F-D and M-B statistics?
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February 10th, 2017, 11:26 AM   #4
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Fantastic work, topsquark! Do the results have anything to do with B-E, F-D and M-B statistics?
Intimately. Boson statistics and fermion statistics are sort of the extreme ends of the statistics. Classical particles (MB) sort of sit on the fence. Just about any problem we do "macroscopically" deals with the Maxwell-Boltzmann statistics. (There are the occasional Bose-Einstein condensates that blur the issue. An example is superconductivity...We get Cooper pairs on a macroscopic scale that act as Bose-Einstein condensate.) It is an unproven statement that, on the Quantum level, particles are either bosons or fermions. I don't think anyone doubts this but we are lacking a rigorous proof.

As a general rule the ground state in the bosonic case is that all particles are in the same state. Fermions are a lot trickier than that and only one fermion per state is allowed. Bosons are usually easy to work with, but trying to sum the energy states in a fermion system that is not in its ground state is problematic to say the least...we have no good rule to tell us which levels become populated if we aren't in the ground state.

-Dan
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February 26th, 2017, 09:40 PM   #5
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Dan,

I learned significantly from your last post.

Loren
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