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Re: continuous spectra



At 11:38 PM 5/18/00 -0700, Bernard G. Cleyet & Nancy Ann Seese wrote:
IOW Heisenberg uncertainty is irrelevant?

That's a dangerous question. If you answer "yes" or "no", it will be taken
out of context, resulting in confusion. Here's an analogous "relevance"
discussion:
1) To describe the collision of pucks on an air table under ordinary
conditions, it is not directly relevant to apply the HUP to the
position/momentum of the pucks.
2) OTOH, the argument that leads to a proof of the HUP is intimately
connected with the argument that leads to an estimate of the size of
atoms. Somebody could argue that if you didn't have the HUP, atoms would
shrink to zero size and your pucks would disappear, along with the air
table and everything else. So in that sense the HUP is always indirectly
relevant.

> Also, the continuousness of a "line" is the same as the
> continuousness of the spectrum of
> a "hot" solid or a "free" electron neutralizing an ionized atm.

A) Formally speaking, there is only one definition of
"continuous". Continuous means continuous, and that's all there is to
it. Formally speaking, all spectra are continuous under all conditions.

B) OTOH in informal conversation, people make a distinction between "line
spectra" and "continuous spectra". The distinction is meaningful if the Q
of the lines is large relative to whatever else is going on. But the
terminology stinks, and cannot be reconciled with the formal definition of
"continuous".

Or are they like pigs?

Pigs stink, too. But I have no idea why you bring it up.



"John S. Denker" wrote:

> At 02:48 PM 5/11/00 -0400, GARY HEMMINGER wrote:
> >The question has arisen in one of my classes - are continuous
> >spectra truly continuous?
>
> Then at 11:12 PM 5/11/00 -0500, Ludwik Kowalski wrote:
> >
> >I think the spectra are really continous. Why do you doubt?
>
> I agree with Ludwik.
>
> To be even more explicit: All spectra are continuous under all
> circumstances. The things we call "lines" are resonances. They have a Q
> which might be large but cannot be infinite. Off-peak transitions are
> always possible.
>
> To continue, at 02:48 PM 5/11/00 -0400, GARY HEMMINGER wrote:
> >
> > I'm wondering about this from both a
> >theoretical and practical point of view.
>
> OK....
>
> > Does theory say that there
> >are an infinite number of wavelengths emitted in the visible range for
> >example by a black body,
>
> Yes.
>
> Nitpickers note that "infinite" means the usual thing, namely that there is
> no meaningful finite upper bound.
>
> > Is the limited resolution of our equipment an issue?
>
> It doesn't change the underlying physics.
>
> OTOH suppose the frequency resolution is poor and the noise floor is high.
> Then a Q of 1000 will be indistinguishable from a Q of ten zillion. The
> center of the resonance can't be resolved and the "wings" of the resonance
> are lost in the noise. Such an instrument might fool you into not caring
> about the off-peak behavior of your resonances.