Why Planck's Formula For Black Body Radiation Is Used To Measure The Cbr?

[exchemist]

I agree that Planck is long dead, but his formulae (for frequency and wavelength) are the heart of the state of the art

radiometry today. The ubergenius Henri Poincaré proved in 1912, just before his death, that any approach to the

problem of thermal radiation inevitably conducts to the Planck's solution and to the quantification of EM energy in hf chunks.

 

At his 1901 paper (available for free download in English and German), Planck used the Part 3 to present his values of "h"

and "k" constants (Boltzmann's constant), with a precision that was higher not more than 3.5% of current values.

 

One is inclined to think that science, 120 years ago (even before widespread of AC energy, radio, atom and molecules

composition, etc.) was something primitive. But this was not the case.

 

Planck, Wien, Thiesen  and many other scientists between 1890 and 1910, used the experimental research conducted at

what was the most advanced laboratory in the world for physics: the PTR or Physical-Technical Reichsanstalt, at Berlin.

 

This link, devoted to the figure of one of the greatest experimental physicist at the PTR (Otto Lummer) is in german.

 

But if you place this link into Google Translation tool, Google will translate it to English very well. You'll be amazed to

read about the depth and accuracy of measurements on spectrometry and more.

 

http://www.otto-lummer.de/waermestrahlung.html

 

Lummer was just one of more than a dozen experimental physicists that, working there, made breakthrough discoveries.

Many of them were nominated for the Nobel Prize.

 

I've studied Planck's work and life very intensively, as well as developments around the 2nd. Principle of Thermodynamics,

which is a central piece in the theories about thermal radiation and black bodies since Kirchoff, in 1859, challenged his

colleagues to find the SPECTRAL formula for black body cavity radiation. It took 40 years, until Planck, and the results

remain undisputed until today.

 

I know that Planck would NEVER had accepted that his formula be used to prove that CBR is equivalent to that of a black

body radiation, because it violates the principles of the 2nd. Law of Thermodynamics, which Kirchoff stablished as

mandatory to verify with the solution of the spectral equation of BB radiation. Nor it would had been accepted by any other of the dozen

or more scientists involved, in the last decade of XIX century, in the black body problem.

 

It's just a matter of logic and common sense. Black body radiation involves emissivity and absorptivity of thermal radiation, and the main

postulate is that a PERFECT black body has to have an absorptivity equal to ONE for every wavelength under observation.

 

There is no way to assimilate the universe to a black body cavity just because it violates the principle of absorptivity. So, I don't

see possible that any physicist (even today) could agree to this license about the misuse of BBR. Only astrophysicists and

cosmologists need that this happens, because its compliance is THE MAIN SUPPORT behind the BB theory. As simple as that.

 

Thanks for your thoughtful comment.

 

Greetings,

 

Richard

But Planck's formula is NOT used to "prove" anything. 

 

Observation shows the spectral distribution to be that of a black body. 

[exchemist]

Planck's formula is the only, universally accepted for 119 years, that express

the spectral distribution of a perfect black body cavity.

 

There is no other formula, nor it will be.

 

"Planck" is inmediately related to "Black Body Cavity Radiation spectral formula".

 

Unless you want to use the FAILED Rayleigh-Jeans formula (1900-1905) which is

an approximation to Planck's formula for wavelengths bigger than 100 micrometers.

 

By the way, how are you doing with your obserbations. Have you or someone that

you know "observed" an atom?

 

I bet you'll say yes.

I'm afraid you are really not making much sense here. The spectral distribution is observed to be a curve that looks like this: 

https://upload.wikimedia.org/wikipedia/commons/c/cd/Cmbr.svg

 

To a very high degree of accuracy, this fits exactly the curve for a theoretical black body. No formula is relied on to derive this curve. It is what is observed.

 

The fact that Planck originally derived his formula, which fits any black body, and therefore fits this curve too, by considering oscillators inside a cavity, is neither here nor there. It is the formula for the radiation distribution of any black body. 

Edited April 28, 2019 by exchemist

[exchemist]

You really should be carefull writing wrong information.

 

There are two universal laws for black bodies:

 

1) Stefan's law for total surface radiation of PERFECT black bodies:

 

                            J = s.T⁴        (s= 5.67x10^-8 Watt.m^-2.K^-4 and T in Kelvin degrees), which applies as W = A.J (A: area (real or equivalent) of the surface)

 

2) Planck's law for spectral density of PERFECT black body cavities.  This is the original formula, with variant f, at his 1901 paper,

about the density of radiation inside a perfect black body cavity:

                       

                        u = 8hc^-3f³ (e^hf/kT – 1)^-1     (Joule.m^-3.Hz^-1)

 

or, derivated after his 1901 paper, as the spectral intensity of a perfect black body cavity radiation, as it is emitted

per steraradian within such a cavity.

 

                        I = u.(c/4)  = 2hc^-2f³ (ehf/kT – 1^)-1     (Watt.m^-2.Hz^-1.sr^-1)

 

For lab measurements, and measuring at an angle normal to the wall of the cavity, through a small (non-perturbatory) hole,

this formula is used being multiplied by the solid angle of the aperture (in sr).

 

1 steradian = 1 rad² = (180/π)² square degrees = 3282.8 deg² = 4.25 x 10¹⁰arcsec²

 

Current industrial black body cavity radiation generators (near perfect BB) are sold with an aperture wheel, which allows to

make measurements with different solid angles, like this portable instrument, manufactured by:

 

https://www.newport.com/p/67032

 

 

 

 

 

This is the method used by COBE, WMAP and PLANCK satellites to scan the "apparent sphere" of the Universe, step by step:

 

 

1989 COBE resolution: 7° (420 arcminute) per scan.

2001 WMAP resolution: 0.22° (13 arcminute) per scan.

2009 PLANCK resolution: better than 0.07° per scan (< 4 arcminute). Bandwith to be measured: 25-1000 GHz.

 

Use the conversions from above to obtain the solid angle aperture (sr.sr = sr²)

 

Time to complete an entire spherical scan (Planck satellite): 7.5 months (15 months doing two complete scans)

 

Source for Planck satellite:

https://frontline.thehindu.com/static/html/fl2613/stories/20090703261309700.htm

 

 

Source for WMAP satellite:

https://lambda.gsfc.nasa.gov/product/map/current/

So what? Stefan's Law has nothing to do with spectral distribution, which is what I was talking about.  

 

All this guff you have posted about cavities is irrelevant. Planck's Law applies to ANY black body, from an oven with a hole, to a star, to the tungsten filament of a traditional light bulb. For what it is is worth the CMBR is the most perfect black body radiation curve ever seen in nature. https://en.wikipedia.org/wiki/Black_body. I quote:-

"The cosmic microwave background radiation observed today is "the most perfect black body ever measured in nature".^[49] It has a nearly ideal Planck spectrum at a temperature of about 2.7 K. It departs from the perfect isotropy of true black-body radiation by an observed anisotropy that varies with angle on the sky only to about one part in 100,000."

 

Or...... are you trying to say you think Planck's law only applies to a black body that is a cavity? If that is what you are contending, please explain how you think the spectral distribution of a black body that is not a cavity differs, and what law if any governs its spectral distribution curve, according to you. 

Edited April 28, 2019 by exchemist

[exchemist]

And again:

 

No, and it's not my word. It's about Kirchoff's and Planck's words: The universal law of radiation density INSIDE a perfect black body cavity of any arbitrary form.... is: Planck's formula.

 

If the cavity IS NOT PERFECT, like being opaque or imperfectly black, then Kirchoff's law applies, affecting the density's formula by spectral emissivity and spectral absorptivity. In perfect black bodies, spectral absorptivity is 100%, under thermal equilibrium.

 

Now, cutting to the chase: YOU give me an example where Planck's formula for radiation density is not applied in black body cavities.

 

You have to be aware that there are two partially valid laws that can be derived from Planck's formula:

 

1) Wien's formula for perfect black body, valid only as an approximation for frequencies above short infrared frequencies (just below visible light, in the THz region)

 

2) Rayleigh-Jeans formula for perfect black body cavities, valid only for low frequencies (as microwave or long infrared), also an approximation.

 

This, unless you want to apply the modified Bose-Einstein approximation to Planck's formula, using photons instead of electromagnetic waves.

 

 

Pyrometers and several other instruments used in open enviroments to measure temperatures at a distance, or color equivalence of radiative

power of NON REFLECTING surfaces, like those covered with coating, use a derivation of Stefan's law, applied for measurements at an arbitrary angle different that the angle normal to the surface. And these instruments are based on the assumption of a NOT PERFECT black body surface or volume.

 

Planck is another world, as it is demonstrated by the hyphotesis and experimental proofs on cavities. It's all about the internal radiation equilibrium within a CLOSED enviroment and its dependance on wavelength and temperature.

 

WHAT IS YOUR PROBLEM WITH THIS THEORY? DO YOU REALLY UNDERSTAND IT?

 

If so, explain it to me as if I were a child, and write about practical uses of WHAT YOU'RE SAYING.

A black body does not have to be a physical cavity. It simply has to consist of a physical system in which matter and radiation are in thermal equilibrium and in which there are no specific line or band absorptions/emissions (i.e. it has to be "black"). It was first modelled by Planck as a cavity with "oscillators", because QM obviously did not exist at that time. However now that we have quantum theory, it can be seen as a consequence of Bose-Einstein statistics, applied to photons in thermal equilibrium. I quote Wiki:

 

"Planck's law arises as a limit of the Bose–Einstein distribution, the energy distribution describing non-interactive bosons in thermodynamic equilibrium. In the case of massless bosons such as photons and gluons, the chemical potential is zero and the Bose–Einstein distribution reduces to the Planck distribution."

 

(From this article: https://en.wikipedia.org/wiki/Planck%27s_law)

[sanctus]

Plus, if you read my former posts on this thread, I consider IMPOSSIBLE to rescue

background noise right behind Milky Way radiation. Impossible.

But no1 does, there are models which you can discuss which are used remove the signals from the galaxy. But if you do not you still get these images in the 5 WMAP bands:

https://wmap.gsfc.nasa.gov/media/101082/index.html

 

which are indeed anisotropies starting from l=2 (monopole and dipole removed)

 

[Dubbelosix]

My wife might disagree, she thinks I am always right:) (normally) .

 

I am open to being educated, can you tell me what is wrong with what I wrote above.

 

 

You misunderstand friend, I was not implying you made an incorrect statement in the post you made, its just that we do tend to make mistakes, but we learn from them, just as I have made incorrect statements... as you eloquently put, call it the senior moments... we all have them.

[exchemist]

But no1 does, there are models which you can discuss which are used remove the signals from the galaxy. But if you do not you still get these images in the 5 WMAP bands:

https://wmap.gsfc.nasa.gov/media/101082/index.html

 

which are indeed anisotropies starting from l=2 (monopole and dipole removed)

Sanctus, rhertz's issue seems not to be the anisotropies but something far more basic.

 

He or she refuses to accept that the CMBR follows the spectral distribution of a black body, because he or she thinks the universe (at the time of the surface of last scattering) cannot behave like a classical black body "cavity".  (Actually of course the pre-transparent early universe WAS an almost perfect black body cavity, but never mind that.) 

 

To bolster this idea, rhertz maintains that the widely used CMBR spectral profile is an artifact of computer-enhancement of the spectrum, designed to produce the result desired by Big Bang theorists - in effect, a collusion by scientists to create a myth.

 

Part of the confusion seems to be that rhertz attributes the computer enhancements that are done to identify the anisotropies (which are what cosmologists are interested in nowadays) with what is needed to record the basic CMBR spectral profile itself, which does not require any of this.

 

I've had a go at explaining this but I am not making much headway. I suspect there is some crank idea at the bottom of it which makes these misunderstandings essential to rhertz's stance.  

[Dubbelosix]

Here is a recent pop science link on how data is collected highlighting some differences. A technical paper is linked to at the bottom.

 

https://phys.org/news/2019-04-hubble-universe-faster.html?utm_source=nwletter&utm_medium=email&utm_campaign=weekly-nwletter

 

"But the true explanation is still a mystery".

 

You clearly have a lot of knowledge, it is a little unclear as to where exactly you are headed with this thread. Do you have a series of questions, involving or supporting a newer or older theory ?  Please clarify ?

 

The level of proof required in astronomy is apparently (sigmas) less than that for particle physics. This suggests there is greater room for error. 

 

What level of error are you claiming will be observed if you are correct ref what you have researched? 1,2,3,4,5,6 sigma? 

 

Don't you just need a sigma 5 statistical significance?

[Dubbelosix]

Mmm... I may have to challenge this. A sigma 5 significance level is a measure of confidence that according to a scientist, that their results are indeed significant enough that it is [not] by a chance accident. If there exists a sigma 5 relative significance, the results could only be by a chance if it is repeated, something like 4 million times -  in other words, the likelihood of that being an accident, is vanishingly small. Of course, I am open to be corrected.

[Dubbelosix]

As for your statements on the issue of cosmology, I regretfully agree... there is too much hand wavy arguments concerning cosmology, including the evaluation of statistical significance, so I certainly agree in that issue. We still need sigma 5 to be significant in cosmology, in which case, I certainly agree.

[sanctus]

Well the papers I published where at 5 sigma. (Was too detect foregrounds in CMB-WMAP data, also applied to Planck later).

All this talk about anisotropies or not does not really make sense here (I mean in this context). l=0 is the isotropic signal, l=1 movement of earth etc. l>2 we call anisotropies.  So all it is, is a decomposition into spherical harmonics of the CMB signal.

Wrt CMB being the perfect black body or not, well so far this assumption is in agreement with the observations (but I admit I was on the statistcal analysis side in Cosmology, not so much into the theoretical side). So my aitional 2 cents is simply there are sooooo many people (from profs to master-students) who worked with the different CMB-data we have (CObe, WMAP, Planck,etc.) and the obtained power spectra of the anisotropies where always coherent with each other, at least till the multipoles they were comparable. And this also consodering that they were at different frequencies. So I find it very hard to believe:
1) It is just a statistical fluke
2) And in case it were, no1 has picked it up yet

I do agree though that the behind milky-way filling of data is of limited trustability, that is why when doing my anlises the galaxy was always masked out.

[OceanBreeze]

I don’t understand what his main objection is. First, he seemed to be saying it is impossible to detect any signal at all, due to background noise, then he was objecting that Planck’s formula for BB radiation was used to analyze the data and finally he had some objection to the satellites having on board BB generators; that NASA and ESA were using to “fudge” the data! So, I count at least three objections in there and none of them make any sense to me.

 

I know, from personal experience, it is entirely possible to detect the CMB signal out of the cold sky noise. True, to do this the antenna cannot be on either the ecliptic plane nor the geostationary arc, in order to avoid galactic noise in the former and satellite signals in the latter. I also doubt that a standard-gain, small aperture backyard satellite dish antenna is suitable for the task, but the antenna I used is anything but standard. It is a high-gain shaped system with cryogenically cooled LNAs. It is probably better than the Holmdel horn antenna used by Penzias and Wilson, when they first accidentally stumbled on the CMB signal. As for Planck’s formula, it is only used for a comparison with the observed data; and the same goes for the satellite on-board BB generators. Scientists aren’t involved in some great “collusion” to fudge their data; that is an absurd idea.

 

[sanctus]

I know, from personal experience, it is entirely possible to detect the CMB signal out of the cold sky noise. True, to do this the antenna cannot be on either the ecliptic plane nor the geostationary arc, in order to avoid galactic noise in the former and satellite signals in the latter.

That is way overkill :-)

Just use an old anlaog tv, but some reserach on the net showed no1 really knows how much of the noise is CMB.

[OceanBreeze]

I think I see it!

 

[exchemist]

I have tracked down the paper publishing the findings on the shape of the primary CMBR spectrum (.e. before they got into studying anisotropies)  from the FIRAS instrument aboard COBE: http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?letter=.&classic=YES&bibcode=1994ApJ...420..439M&page=&type=SCREEN_VIEW&data_type=PDF_LOW&send=GET&filetype=.pdf

 

It is clear from this that there was no spherical harmonic analysis required (unless you count the dipole contribution). All they did, to get the most accurate spectral curve they could, was to subtract off the signal the effects of the galaxy, which they did by making a model of it by observations over 10 months, and also subtracting the "dipole" effect due to the Earth's proper motion. 

 

Planck's Law does not feature in any of this until we get to the discussion of the results, by which time it has been established, purely by observation, that the radiation spectrum is  - very accurately - that of a theoretical black body. 

Edited April 30, 2019 by exchemist

[sanctus]

Wrt to your point 3:

I do not really know how COBE measurements were done. But as I said above, in WMAP most of data analysis is done with masking of the galaxy. Here is an example of such a mask comparing WMAP7 and WMAP9:
https://lambda.gsfc.nasa.gov/product/map/current/pub_papers/nineyear/basic_results/images/med/cb9_f17_M.png

 

 

Wrt 2) and 4):
Why is composite a problem?

[sanctus]

No, not a problem at all!

 

It's the proper way to do it.

 

But 1 post before you said:

 

Then, due to points 2) and 3), I find that the curve presented at the COBE's report, claiming

full compliance with Planck's formula is just plain and simple BS.

 

 

Seems a contradiction to me