Wikipedia:Reference desk/Archives/Science/2023 June 17

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June 17

Planck's law simplification

On "On the Law of Distribution of Energy in the Normal Spectrum", chapter "Introduction of Wien’s Displacement Law" , §7, Planck made a simplification from :

u.dv=ϑ...(...).dv

to:

u=ϑ...(...)

am I to understand that u.dv is a product and it simplifies equality by dividing by dv, or is it another operation? Malypaet (talk) 13:51, 17 June 2023 (UTC)

Yes, that's essentially correct. --Wrongfilter (talk) 17:10, 17 June 2023 (UTC)

This simplification is allowed when the relation between the two differentials is an identity. Let $f$ and $g$ be two functions with primitives $F$ and $G$, so $\textstyle {\int f(x)dx=F(x)+C_{1}}$ and $\textstyle {\int g(x)dx=G(x)+C_{2}}.$ The differential identity $f(x)dx=g(x)dx$ only implies the identity of their primitives up to an additive constant of integration. But this does not matter; we have

$f(x)-g(x)={\frac {d}{dx}}F(x)-{\frac {d}{dx}}G(x)=$ ${\frac {d}{dx}}(F(x)-G(x))=$ ${\frac {d}{dx}}(C_{2}-C_{1})=0.$

So we may conclude that $f(x)=g(x).$  --Lambiam 18:25, 17 June 2023 (UTC)

So, if "u.dv" is a volume density of a spectral slice between v and v+dv, what does "u" represent once dv removed? Malypaet (talk) 19:34, 17 June 2023 (UTC)

u is called "spectral energy density" (at least where I come from, i.e. astrophysics; I'm not linking because that would lead to an article that discusses a somewhat different concept of "spectral"), it has dimensions of energy per volume per frequency interval (units e.g. ${\frac {\mathrm {J} }{\mathrm {m} ^{3}\,\mathrm {Hz} }}$). By contrast, $u\,\mathrm {d} \nu$ is an energy density (${\frac {\mathrm {J} }{\mathrm {m} ^{3}}}$) but only the density of photons with frequency between $\nu$ and $\nu +\mathrm {d} \nu$. The total energy density is the integral of that expression over all photons. --Wrongfilter (talk) 19:56, 17 June 2023 (UTC)

So going back to E, we have a spectral energy density in J/m3.wavelength. That is to say that in the black body we measure the power/m2 for a wavelength, power divided by this wavelength and the speed of light to obtain a spectral energy density, or is it different? Malypaet (talk) 06:11, 18 June 2023 (UTC)

In detail it's more complicated (and a hell of a confusing subject with varying nomenclature in different fields; look at the bewildering variety of quantities in radiometry) but you're partially on the right track. Note that E is not the usual notation that we would use nowadays; I'd write it as $u_{\lambda }$ (as opposed to what we had before, which would be $u_{\nu }$). You're right with the division by c (physical reason is that photons passing through a given area in the time interval $\mathrm {d} t$ come from a maximum distance $c\,\mathrm {d} t$. You're wrong about the division "by this wavelength". In fact it's impossible to go from bolometric power to spectral density. Working forward from spectral density, you need to integrate over all wavelengths such that power is proportional to $\int _{0}^{\infty }u_{\lambda }\,\mathrm {d} \lambda$. You're really better off trying to find a modern text book where this is explained systematically and in a clearer and more didactic way that in Planck's original paper. --Wrongfilter (talk) 08:07, 18 June 2023 (UTC)

Sorry, but I always prefer the original to a copy, here with you and the original I got the answer I was looking for. Malypaet (talk) 22:14, 18 June 2023 (UTC)

So when you write "spectral energy density" , as you don't divise by frequency or wavelength, how can you have a dimension by hertz for example ? Do you use a vector with 2 attribut (energy density, frequency), a matrice with 2 élément (energy density, frequency) or what else ? Malypaet (talk) 05:03, 19 June 2023 (UTC)

For the bolometer, it seem that in experiment, in front of it you can apply a filter (a crystal) to select a very fine slice of wavelenth, isn't it ? So Why don't divise by wavelength ? Malypaet (talk) 05:09, 19 June 2023 (UTC)

You don't divide by wavelength but by a wavelength interval. For "bolometric" look at, I don't know, it just means "integrated over all wavelengths". You can always observe through a filter, than you only measure radiation within some wavelength window of some width Δλ. And so on. We'd have to write a text book for you to explain all this. I'm not going to do this. --Wrongfilter (talk) 14:17, 19 June 2023 (UTC)

Once you succeed in understanding the derivation of Planck's law as presented in a modern textbook, you'll probably have a much easier time following Planck's original paper.  --Lambiam 19:32, 19 June 2023 (UTC)

Thank you, I already had the original version which allowed me to recreate a complete and translated version with the same format, after importing the pdf indicated by Wikipedia into Google docs. It was very useful for me to understand the original spirit of this theory.

What I'm looking for now is a modern or old article that contains the raw data on black body measurements. A theory and any interpretation have value only if they can be corroborated by experimentation. Malypaet (talk) 07:40, 21 June 2023 (UTC)

Escaped genetic experiment

Read something years ago about this but I can't remember all the details. Apparently some geneticists in South Africa were messing around with locusts back in the day, splicing their genes with god knows what in an attempt to create a less aggressive, less voracious, less swarmy version. But someone screwed up and the resulting organisms escaped into the wild. These organisms are huge, slow, placid bugs, the size of mice, flightless and seem to enjoy eating human garbage, but are otherwise harmless, except that they look scary and are a minor annoyance to people. So the government just left them alone. Does this sound familiar to anyone? I remember a South African person online telling me that the District 9 movie was kinda based on the premise of "what if these things were sentient?". — Preceding unsigned comment added by 146.200.128.34 (talk) 22:20, 17 June 2023 (UTC)

A popular urban legend, propagated by April Fools' Day articles published by the Johannesburg newspaper The Star, claims that the Parktown prawn was the result of a genetic experiment by students from the University of the Witwatersrand in the 1960s ...  Card Zero  (talk) 23:52, 17 June 2023 (UTC)

Thank you. So this creature is entirely a creation of nature? 146.200.128.34 (talk) 00:40, 18 June 2023 (UTC)

Well yes. Myths have arisen regarding this species: some people feel it is an alien invader or the result of a freak mutation. But it's just one of the Anostostomatidae.  Card Zero  (talk) 12:03, 18 June 2023 (UTC)

Sounds like a mixed up version of the real origin of Africanized bees. Matt Deres (talk) 20:43, 18 June 2023 (UTC)