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In "Ueber das Gesetz der Energieverteilung im Norrnalspectrum".

When Planck write "u dν statt E dλ", what is the difference between "u " and "E ", as all two are radiation energy ? Malypaet (talk) 05:54, 3 July 2023 (UTC)[reply]

We've had that before, haven't we? If I remember correctly u is flux (or was it energy density?) per frequency interval (in modern notation something like ${\displaystyle u_{\nu }}$), whereas E is flux per wavelength interval (${\displaystyle u_{\lambda }}$). They're related by ${\displaystyle u\,\mathrm {d} \nu =E\,\mathrm {d} \lambda }$. --Wrongfilter (talk) 06:01, 3 July 2023 (UTC)[reply]

Thank's, u and E are energy accounted for 1 second (power/c), so in W-s or Joules, if you prefer . So Why not E dλ = E dν ? Malypaet (talk) 07:54, 3 July 2023 (UTC)[reply]

Because they are not the same, they are different quantities! Question: Do you know what dλ and dν mean? Do you know any calculus at all? --Wrongfilter (talk) 08:24, 3 July 2023 (UTC)[reply]

Also, are you aware of the concept of dimension of a physical quantity? Dimensional analysis can save one from some of the worst blunders. The dimension of ${\displaystyle \lambda }$ is ${\displaystyle {\mathsf {L}},}$ while that of ${\displaystyle \nu }$ is ${\displaystyle {\mathsf {T}}^{-1}.}$ It follows that ${\displaystyle E}$ and ${\displaystyle u}$ have different dimensions, and therefore cannot be the same quantity. In fact, ${\displaystyle \operatorname {dim} E={\mathsf {ML}}^{2}{\mathsf {T}}^{-2},}$ but ${\displaystyle \operatorname {dim} u={\mathsf {ML}}^{3}{\mathsf {T}}^{-1}.}$  --Lambiam 09:49, 3 July 2023 (UTC)[reply]

Thanks, I understand better.

So "E dλ" == "ML³ T-²" and "u dν" == "ML³ T-²".

"E" is energy ("Joule" == "ML² T-²"), "E dλ" and "u dν" are energy per unit volume, or energy density.

"u" == "ML² T-²" * (c/ν²) == "ML² T-² LT-¹ T²"

"u" == "ML³T-¹" == "ML³ T-²" * "T".

So "u" is already an energy density multiplied by a unit of time and when we multiply by "dν" we eliminate this unit of time.

What does an energy density multiplied by a unit of time correspond to in physics, in nature? Malypaet (talk) 13:05, 4 July 2023 (UTC)[reply]

What looks like "multiplied by a unit of time" is actually "divided by a unit of frequency". ${\displaystyle u\,\mathrm {d} \nu }$ is the energy density (J/m³) that is carried by radiation in the frequency interval of width ${\displaystyle \mathrm {d} \nu =\nu _{2}-\nu _{1}}$ (I'm writing a finite interval here, because I'm not convinced that you know about infinitesimal quantities - nothing to be ashamed of); u is the energy density divided by that frequency interval, it's called a spectral energy density with units J/(m³ Hz). E is similar to that, but instead of a frequency interval it uses the corresponding wavelength interval ${\displaystyle \mathrm {d} \lambda =\lambda _{1}-\lambda _{2}={\frac {c}{\nu _{1}}}-{\frac {c}{\nu _{2}}}}$. For infinitesimal quantities, this becomes ${\displaystyle \mathrm {d} \lambda ={\frac {c}{\nu ^{2}}}\mathrm {d} \nu }$. --Wrongfilter (talk) 14:09, 4 July 2023 (UTC)[reply]

Realy, do you know what is a frequency and a unit of frequency ?

On wikipedia:

"The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second." Malypaet (talk) 16:09, 4 July 2023 (UTC)[reply]

(very tired) What is your problem now? We could use wave numbers as well, if you wish. --Wrongfilter (talk) 17:36, 4 July 2023 (UTC)[reply]

The term "unit" is not really applicable. A quantity like ${\displaystyle 2.45\,{\text{ms}}}$ is not a unit of time, but a time value denoted by a dimensionless value (${\displaystyle 2.45}$) multiplied by a unit of time (${\displaystyle {\text{ms}}}$).  --Lambiam 16:21, 4 July 2023 (UTC)[reply]

So when you have:

(a dimensionless value "2" multiplied by a time unit "s")

divided by

(a dimensionless value "1" multiplied by a time unit "s")

What is going on ?

For example in electricity, if we have a constant power (an energy flow per unit time), if we multiply it by a certain dimensionless value and a unit of time we obtain a dimensionless value multiplied by kilowatt-hours, therefore energy in joules where the initial unit of time has disappeared. Malypaet (talk) 21:04, 4 July 2023 (UTC)[reply]

I don't see a problem. Given a dimension, it is somewhat meaningless to ask what a physical quantity with that dimension "corresponds to". For example, both work and torque have the dimension ${\displaystyle {\mathsf {ML}}^{2}{\mathsf {T}}^{-2},}$ but are incomparable quantities. For a more mundane example, the efficiency of a loom may be expressed as the area of cloth produced in a given amount of time, having dimension ${\displaystyle {\mathsf {L}}^{2}{\mathsf {T}}^{-1}.}$ It would be peculiar to call this the "flux" of the loom.  --Lambiam 09:21, 5 July 2023 (UTC)[reply]

In context, it is often quite pertinent to ask what a physical quantity with a given dimension "corresponds to". The oft-quoted example being vehicle fuel consumption measured, as it is in most of Europe, in litres per kilometer has dimensions of ${\displaystyle {\mathsf {L}}^{2}}$ - an area which has a perfectly reasonable physical interpretation. 2A01:E0A:D60:3500:7DF3:344F:2C91:F813 (talk) 08:40, 10 July 2023 (UTC)[reply]

Actually I disagree, 2.45 ms can also be decomposed into a dimensionless value 2.45 multiplied by a time unit of 1 ms, as the number 1 is neutral. Similarly for a frequency unit of 1 Hz == 1 cycle / 1 s, with a dimensionless value for the number of cycles divided by a time unit of 1 s. Malypaet (talk) 09:07, 5 July 2023 (UTC)[reply]

My aim was to point out that the conventional way of expressing the nature of quantities that are rates of change is potentially confusing. For example, according to the article Speed, "the speed ... of an object is ... the magnitude of the change of its position per unit of time". But is it? There are many units of time, and the magnitude of the change of position of a snail per fortnight will not be the same as the magnitude of the change of its position per megasecond, even if our snail proceeds in a straight line at a constant rate. To express the rate of progress we can use units with the dimension ${\displaystyle {\mathsf {LT}}^{-1}}$ such as the knot (unit). Otherwise, we need to choose both a unit of length and a unit of time. The use of the term "unit" in the definition of speed is a red herring.  --Lambiam 09:46, 5 July 2023 (UTC)[reply]

It is a common pattern of speech, though. It may be a bit imprecise but I don't really see it as problematic. My answer to "what unit of time?" has always been "pick whatever unit is appropriate for the situation". The same for the distance even if the word "unit" is not mentioned there. It should be obvious to everyone that two velocities should be expressed in the same units when they are being compared... Note that while dimensional analysis is certainly useful, it provides only very limited information on the physical significance of a quantity. In the definition of the Jansky (an article that might actually be helpful for Malypaet's understanding) the product s·Hz occurs in the denominator. Dimensional analysis would cancel those: ${\displaystyle {\mathsf {T}}{\mathsf {T}}^{-1}=1}$ obscuring the fact that this comes from a product of a time interval and a frequency interval. --Wrongfilter (talk) 20:31, 5 July 2023 (UTC)[reply]

I agree it is a common pattern of speech; I called it "the conventional way of expressing" rates of change. It becomes problematic if one is doing dimensional analysis while not realizing such expressions are imprecise, and also if one does not quite grasp the concept of dimensions. Responding by "pick whatever unit is appropriate for the situation" is then not helpful. Assume I am clueless about dimensions but need to report the speed of Beep-beep, my racing snail. The animal being blindingly fast, I pick the second as being an appropriate unit. In that time, it moves a whopping 2.4 mm. Now, applying the definition in the article Speed literally, substituting my hand-picked unit of the second for the indeterminate "unit of time", I report its speed as being the distance it progresses per second and so report Beep-beep's speed as being 2.4 mm. If you think people wouldn't actually make such mistakes, you probably haven't been a teacher.

The jansky has the same dimension as units of acceleration, such as g-force (which is not a unit of force). So it is another nice illustration of the fact that it is somewhat meaningless to ask what physical quantity corresponds to a given dimension.  --Lambiam 10:30, 6 July 2023 (UTC)[reply]

The dimension of the Jy is ${\displaystyle {\mathsf {M}}{\mathsf {T}}^{-2}}$, not ${\displaystyle {\mathsf {L}}{\mathsf {T}}^{-2}}$ as for g-force...--Wrongfilter (talk) 13:09, 7 July 2023 (UTC) [reply]

You are making a mistake, Wrongfilter is right, the jansky is TT-¹ and not T-² as g-force (watt divided by Hz). Malypaet (talk) 04:20, 7 July 2023 (UTC)[reply]

I did not say that, read again. --Wrongfilter (talk) 05:27, 7 July 2023 (UTC)[reply]

Sorry, but Hz is only a SI derived unit of T-¹, so Hz-¹ is == T that is the Si base unit.

In wikipedia:

"... The hertz is an SI derived unit whose expression in terms of SI base units is s⁻¹, meaning that one hertz is the reciprocal of one second..."

you realy writed :" TT-¹" ! Malypaet (talk) 12:05, 7 July 2023 (UTC)[reply]

You may be tired, reciting is easy, but explaining the unexplainable is bound to be challenging. Malypaet (talk) 12:07, 7 July 2023 (UTC)[reply]

I was talking about the product s·Hz in the denominator, not about the entire unit Jy. Franchement, cette discussion va nulle part. --Wrongfilter (talk) 12:41, 7 July 2023 (UTC)[reply]

Sorry, but for me the jansky only brings confusion. A watt is a flow of energy for 1 s and here the Hz brings a number of cycles during this same second. So we shouldn't have Hz in the denominator, but a dimensionless number of cycles because it's measured in the same time interval. We should rather have a matrix with a column for the irradiance and a column for the frequency, it seems to me that it would be more coherent, especially since we have two distinct simultaneous measurements. Malypaet (talk) 22:38, 6 July 2023 (UTC)[reply]

I would have thought that it was obvious that spectral density or irradiance are functions of frequency, ${\displaystyle u_{\nu }=u_{\nu }(\nu )}$ (is that what you mean by your "matrix"?). But the units/dimensions of ${\displaystyle u_{\nu }}$ are not affected by that at all. --Wrongfilter (talk) 05:27, 7 July 2023 (UTC)[reply]

Very strictly speaking, the latter infinitesimal equality should be be ${\displaystyle |{\text{d}}\lambda |={\frac {c}{\nu ^{2}}}|{\text{d}}\nu |,}$ since ${\displaystyle \lambda }$ decreases as ${\displaystyle \nu }$ increases, but in the context it is clear that we are not interested in the sign but solely the magnitude.  --Lambiam 16:14, 4 July 2023 (UTC)[reply]

I have removed an incomplete reference from Protistology article. The reference was named 'The Flagellates', but it had no contents. Would be nice if someone familiar with the topic can fix the problem. Please see Talk:Protistology#Invalid reference removed for more details. --CiaPan (talk) 20:26, 3 July 2023 (UTC)[reply]

Looks like the talkpage is well on the way to solving this. DMacks (talk) 00:56, 4 July 2023 (UTC)[reply]

@DMacks: Yup, just like I hoped. But the subject may be not that widely interesting like sports or politics, so despite pinging the author at the talk page I wanted to gather some more attention. Just in case the original author does not response. My bad, may be I should have rather checked whether the author is still active and ask her/him directly, and come here if that have failed.
Anyway, the ref is fixed now, thanks to you and Snoteleks, so I mark this thread as Resolved. CiaPan (talk) 11:17, 4 July 2023 (UTC)[reply]