12 May '09 19:11>2 edits
Originally posted by adam warlock…Why do you say that since we have a dense set of possible values of wavelengths we must have 0 photons for each wavelength? This is a wrong conclusion but nevertheless I need to know how you arrived at it.
Th energy density is not about the volume of the black body but about the volume you are considering.
If you have a black body radiating energy you can know the energy it is radiating in a given wavelength for cubic meter. So it's not about what's radiating but to where it is radiating.
[b]if so, then this is what confuses me about this; the range ...[text shortened]... velength isn't a well defined one. Remember that photons aren't conserved in this situation.
..…[/b]
Suppose there is a blackbody that is radiating out photons and suppose in a snapshot of time there are 10^10 photons in a particular cubic meter volume that all originated from the blackbody. Now the photon there that happens to have the longest wavelength (out of all the photons currently there) may be, say, 40000nm in wavelength while the shortest may be, say 400nm in wavelength. So we have a range of wavelengths but this range can be split up into many smaller ranges such as the range from 1000nm to 1001nm and each of those small ranges would have less photons existing in that smaller wavelength range in that specified cubic meter than the 4000nm to 40000nm range and each of those smaller ranges such as from 1000nm to 1001nm can be split into many even smaller ranges such as from 1000.01nm to 1000.02nm and each of those small ranges would have less photons existing in that wavelength range in that specified cubic meter than the 1000nm to 1001nm range and so on until you get to the range like from 1000.00000000000001nm to 1000.0000000000002nm where you can calculate the probability of a particular photon with a wavelength existing in that tiny range in a particular cubic meter to be small despite there being, say, 10^10 photons in that particular cubic meter. Thus considering the mathematical limits that are implied here, I conclude that the probability of there being a photon in that particular cubic meter with a wavelength of EXACTLY 1000.0000000000000155555555nm to be virtually zero because there are an infinite number of numbers between 1000.00000000000001 and 1000.0000000000002.
(sorry for using a ridiculous number of words but I am not good at explaining what I mean here)
-obviously I am missing something here.