Originally posted by KazetNagorra I don't see the conflict - if you regard a black body at t = 0 and wait for a photon to be emitted at exactly 744 nm it won't happen. The wavelength of an emitted photon will contain an infinite string of random numbers in decimal representation and even though the infinite string of all zeros is not any less likely than any other particular infinite st ...[text shortened]... safe to say a black body will never emit a 744 nm photon (or "almost sure", if you insist).
The conflict is that adam's statement was perfectly correct and precise.
Your corrections are therefore out of place and, worse, are more imprecise with the wording.
It's false to say that events of probability zero won't happen. It's as simple as that. In fact, all future wavelength emissions have probability zero of happening, yet they will happen.
Originally posted by KazetNagorra You don't analyze the case L = 0, since that doesn't allow any EM mode. You start with some finite L, which allows wavenumbers (in 1D, generalization to 3D is straightforward) k = 2*pi*n/L with n integer. Taking the limit of L to infinity allows a continuum integral formulation appropiate for thermodynamics, and allows photons will arbitrarily low energies instead of the lower limit corresponding to k = 2*pi/L in the finite L case.
Shame on me for writing L=0. But good thing you understand what I meant.
By the way: wrong answer.
Read up on probability theory, statistical mechanics, and quantum mechanics. 😉
There has been a sub-discussion in this thread about probability zero. On argument states that "events of probability zero may happen". If find this impossible.
An event that has probability zero cannot happen!
If p=0 can happen, than anything can happen.
The probability that the sun is gone and been gone from the time Earth was into being has zero probability. It's there, we see it, we can measure it, th whole life on earth is dependant that it's there. If someone says that even if the probability is zero that it's gone, it might be that the suns is gone, I will object.
If the probability that the sun is gone tomorrow, is zero, then it will surely be there tomorrow. If it's even the slightest is > zero, then it might be gon tomorrow, but when b=0, and exactly =0, then it will be there tomorrrow too, rely on that.
If we calculate that the probability of that the sun is gone tomorrow is exactly zero, and it actually isn't there tomorrow, then we have made an error in our calculation.
Bottom line: An event that has probability zero cannot happen!
Originally posted by FabianFnas There has been a sub-discussion in this thread about probability zero. On argument states that "events of probability zero may happen". If find this impossible.
An event that has probability zero cannot happen!
If p=0 can happen, than anything can happen.
The probability that the sun is gone and been gone from the time Earth was into being has zer ...[text shortened]... ror in our calculation.
Bottom line: An event that has probability zero cannot happen!
Physicists these days don't seem to understand anything of probability theory.
How to calculate radiance emitted?
16 May '09 10:43
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