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

[rhertz]

The formula that Planck presented on December 14, 1900, to the German Physics Society (date celebrated as the birthday of Quantum Physics) is the final answer to the Kirchoff's 1859 challenge to the physics community: to find the spectral formula for his relationship between emissivity e(L) = J(L, T), with absorptivity a(L) being equal to one in a perfect black body cavity. I use L as Lambda (wavelength).

Edited June 19, 2019 by rhertz

[Dubbelosix]

There's a lot of complicated issues, but really, to describe it in the simplest sense, Planck's law is universal. We apply it to black body's of all types.

[Dubbelosix]

But why protest which works in even an approximate sense? Science isn't always about being absolute, but it a lot of it has to do with equations which best fit ..... Unless of course an equation can manifest better answers.

[Dubbelosix]

I might be having a senior person day, but plancks constants is based on the hypothesis light has frequency like maxwells equations for radio waves. This is not necessarily the case for photons.  A photon of Light is a packet of energy with inertia, it causes a fluctuation in a field as it moves through space, it has no electric charge or magnetic field, it can be polarized ie it has spin 1. This is not an oscillatiing wave with frequency. The idealized picture a photon that goes in exactly in straight lines through space, with mystical properties of wave particle duality is likely a misunderstanding on how photons moves. 

 

There is no way of measuring photons without interfering with them. The way in which it is measured affects the results. All we can really say is it leaves point A and arrives at point B. It is not affected by electric charges or magnetic fields, both of which are ascribed to virtual photons under qed. 

 

Example throw an invisible particle into a pool and you will observe ripples, throw the same particle into sand, and you will observe a hole caused by a particles.  

 

Red Shift indicates a reduction in energy of the photons received, which is analogous to the doppler effect, but it could equally be a tired light effect. Photons losing energy due to loss of momentum instead of by increased wavelength. Would be both measured in the same way, ie its a photon which just arrived at point B with an amount of energy. 

 

Ascribing the doppler effect to red shift might be an incorrect assumption ?

 

Oh the final question WHY it was maybe the ultraviolet catastrophe. https://en.wikipedia.org/wiki/Ultraviolet_catastrophe that the mathematical jiggery pokery of planck resolved.  

 

 

By far you are the biggest thinker here, and you are able to collect idea's coherently, maybe not always right, but If I had taken a student on, you'd be the type I'd take on.I'll try and get back to all these posts, but you ask many complicated questions which require... a push in the right direction.

[OceanBreeze]

For me, it's very simple: to make a map with spatial observatories like COBE, WMAP and Planck (1989 - 2003), an extraordinary number

of events have to be ELIMINATED by digital filters and interpolations in powerful computers.

 

Have in mind that every one of these satellites measure the sky in an spherical perception, with a sphere with no radius (or infinite, if you like)

centered at the satellite.

 

The entire spherical "surface" of 4Pi steraradians is explored with a very narrow apperture with the satellite antennae, which requires thousands

of measurements about the electromagnetic radiation that is captured.

 

The main problem is that, to obtain the background NOISE, emissions from our galaxy (the Milky Way) has to be substracted! And the energy values

from our galaxy are over a million times more powerful than the backgroud noise, and also is anisotropic!

 

Also, difractions caused by clouds of gases and plasma, and gravitational effect have to be discounted.

 

I don't believe that the results are VALID, because it requires to obtain an unknown value, which has a negative signal to noise ratio bigger than

- 60dB. And this, with stocastic processes that are the basis of radio transmission and reception, is directly IMPOSSIBLE.

 

You can detect a signal whose energy is under the capture signal by several dB, if you know HOW this energy behaves,

 

This is tha basis for Spread Spectrum modulation (military) and for CDMA coding mobile telephony (commercial), because

the pseudo-random signal below the noise level has a known pattern.

 

But, with analog signal with random values, it's impossible to rescue signal from high values of noise.

 

Then, I think that NASA and ESA are fudging results in order to fit the expected data (Planck's formula).

 

And adding to this, I think that it's incorrect to apply the Planck's formula to the Universe, assuming that

it behaves as a black body cavity, because it violates the original Kirchoff's law (1859), which leads to

Planck and others by 1900.

 

 

Why would NASA and ESA and everyone else engage in a conspiracy about the CMB?

 

Do you believe the moon landings were faked too?

 

Measuring the CMB is very easy to do, and I have done it several times myself.

 

We have several microwave/satellite dish antennae on board ship, the largest is 5 m diameter. With that dish I get about 4 K excess antenna T which can only be due to the CMB. I could probably do a better measurement if I had the time and inclination to do so, but I mainly am concerned with making sure the equipment is in good working order and measuring the CMB is a fun way of doing that.

 

Basically, the low noise amplifier’s equivalent noise temp NT is first characterized by switching the input between a cold load (liquid nitrogen) and ambient temperature. The “Y” factor and a little basic math gives the NT of the LNA. The antenna Temp is determined by pointing at a known radio source such as a radio star, the moon or a bore sight source. The system NT is the sum of the LNA T and the antenna T plus waveguide or coax losses.

 

Everything can be calculated beforehand and then compared with measurement.

 

When looking at what should be “cold sky” the system noise T is always higher than it should be by about 4 K in my case. That is the CMB signal that Penzias and Wilson accidentally stumbled on in 1964, much the same way that I see it; as excess antenna noise. In fact, it was predicted decades earlier and actually measured in 1941 to be 2.3 K by Andrew McKellar. It has been measured countless times using extremely accurate equipment and we now know it is about 2.7 K.

 

There is no conspiracy to see here!

[exchemist]

Engineers still use newtons theories which are simpler than relativity and Maxwells equations which are simpler than QED. But QED and relativity gives a more accurate solution than Maxwells and Newtons equations.

 

A Photon we know has no electromagnetic properties it is has no charge and no magnetism. Virtual photons in  QED would be the same but might not even exist. 

 

Until we get to extremely high energies photons dont interact with each other, https://en.wikipedia.org/wiki/Two-photon_physics These sort of energies are not normally observed on earth, unless you have a particle accelerator to hand.

 

I agree classically the maths works for maxwells equations but he is modelling a wave, generated from an alternating source with frequency. The source uses electricity or  magnetism to generate the wave, he assumes an electric field and magnetic field travel through space with the wave. But the wave does not interact with other waves as it travels through space. It is therefore wrong to view the wave as having electro magnetic properties. The wave is charge neutral, like a Photon. The only it is moving energy is via a wave which moves the electrons in the receiver, by imparting inertia to the electrons. Not unlike a real photon being absorbed by an atom and raising it to a higher energy level.

 

Photons being emitted from a source at 1/sec could be ascribed a frequency of 1 Hz. The energy of those photons is likely better described by Einsteins E=pv, rather than Plancks E=hf.

 

I understand using fourier analysis or digitising a wave anything can be ascribed a range of frequencies, but it does not give an accurate picture of the wave/quantum fluctuation unless you understand what the maths is trying to model. Currently photons are considered to be both waves and particles. Some people even think photons have magical electro magnetic properties, not realizing they have no charge or magnetic field, and are not influenced in anyway by other fields except gravity. The only force they carry is momentum.  

 

There is absolutely no evidence I can find that shows a photon has frequency. Would you agree it is an assumption which comes from Maxwells Electro magnetic equations?

 

PS the speed of light is not constant in a gravitational field, Einstein said so in about 190?. c is only constant in free space away from gravitational fields.  

I would not agree with that a photon has no frequency and certainly not that Maxwell had anything to do with this.   

 

A photon has an energy and a momentum, both of which imply a frequency, because of Planck's relation (E=hν) and De Broglie's relation (p =h/λ.) Both of these are relations from quantum theory. Maxwell's theory was a pre-QM, classical theory and so, by definition, did not involve photons.

 

What you may be thinking of is the problem that position and frequency cannot be simultaneously known, due to the Principle of Indeterminacy. Thus if one has a photon with an exactly known momentum (and thus frequency), one cannot know where it is in space, while conversely if one knows its location exactly, it is a Fourier superposition of infinite different frequencies and thus has an indeterminate momentum (frequency). In practice however one can can know both position and momentum (frequency) approximately, subject to a standard deviation of each given by:   σ(x) . σ(p) >/= h/4π .  

Edited April 26, 2019 by exchemist

[OceanBreeze]

I don't see how a photon can exist if it has no frequency.

[exchemist]

Good post, nice to read!

 

Please, refer to the subject in my OP. It's about the use of Planck's spectral formula for thermal radiation within

a black body cavity (100% absorptivity of thermal energy).

 

What I question is the claim (NASA, ESA) that CBR perfectly fit the spectral values of Planck's formula using

frequency as variable, peaking at 160 GHz, assuming that the Universe behaves as a black body cavity.

 

Doing this, they equated what happens at a graphite cavity having a volume of 2,000 cm^3 with what happens

at the volume of the observable universe (8.7x10^69 Km^3). And this, besides violating Kirchoff's postulate, is

an utter nonsense (for me).

 

Penzias-Wilson measurements were made at a frequencies around 4.5 Ghz, which is probably close to the range

at which you conducted your on-ship measurements. But neither them, nor you did scan the entire spectrum, did you?

 

It is sad for me that, being a fact that science don't have a better formula to use than a 120 years old one (valid only at

a very restricted enviroment), the results are being published as if the verification of Planck's formulae at the entire

Universe is a breakthrough discovery. I think that this is false, misguiding for the general public and for autosatisfaction

of the people involved.

 

It's scary to register "things that happens out there" and not know what is it. But, trying to grab to something known here,

even WHEN IT'S NOT TRUE, is more scarier, because it is a sample of how far "the community" is willing to collude in

order to have peace of mind and keep getting public funds. Not to mention the fact that the CBR radiation is the single

more important support for the big bang theory.

 

I'd prefer that other means were used instead of black body cavity.

 

And regarding the term "conspiracy", with all the negative sides that it carries is far

from my thoughts. The meaning is (Google): "a secret plan by a group to do

something unlawful or harmful".

 

I prefer collusion: "secret or illegal cooperation in order to deceive others."

 

The world actually with collusion. My best example is the financial world and the

QE of money to hide economical depression. Or Big Pharma and statins, etc.

 

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

background noise right behind Milky Way radiation. Impossible.

 

It's similar to use algorithms to find the location of a given stellar object that is behind the

radiating edge of the Sun, by filtering the Sun's light at those places.

 

If such an impossible task were possible, we could be testing General Relativity any day,

any time, instead of waiting the screening of the Moon to measure light bending by gravity.

And this isn't happening, is it?

 

So, my original question stands firmly: Why Planck's formula is being used to validate the CBR?

 

There is a hidden agenda behind this. Not conspiracy, just collusion.

Why would anyone collude? The fact is we can observe the spectral distribution of the radiation and it follows the black body radiation curve. That is an observational fact and does not depend on any formula. https://en.wikipedia.org/wiki/Cosmic_microwave_background#/media/File:Cmbr.svg

 

Given that the radiation takes the form of a black body distribution, it is logical to treat it according to the formula for, er, a black body. N'est ce pas? 

 

Regarding the difference in size between a lab black body and the universe, as someone who clearly reads a fair bit of historical physics you ought surely to appreciate that the physical size of the body has little or nothing to do with the shape of the radiation curve it emits. A tungsten filament bulb is a pretty good black body emitter.

 

So I don't really understand what your beef is with using Planck's Law. It is merely the applicable law for any black body emitter.  And we know, from observation, that the CMBR is a black body radiation distribution. 

 

Or am I missing your point? 

Edited April 26, 2019 by exchemist

[exchemist]

I do not see how it can have a frequency, it carries spin, polarization, and momentum at <=c. Nothing else can be confirmed about it. Frequency implies oscillation. No measurement has ever confirmed a photon has frequency. 

A photon is an oscillation in the electric and magnetic fields. 

 

But, more generally, all QM entities have both particle and wave nature to them. An electron has a frequency, too. If it did not, we could not have the orbitals in atoms that correspond to standing wave patterns. 

 

You say a photon has momentum. Well that means it has a wavelength, given by p=h/λ, and thus it has a frequency. This is basic quantum theory. Why do you think this is wrong?  

[exchemist]

I would agree there is more than one way of viewing radio waves. 

 

A minor correction electro magnetic radiation / radio waves consist of virtual photons, not photons. 

That is untrue. Radio waves consist of real photons, as does any form of EM radiation. 

Edited April 26, 2019 by exchemist

[exchemist]

exchemist, I've read your historical posts and I found that you are a very knowledgeable person

in your field of expertise and beyond.

 

So am I.

 

Please, make a deeper search about how data from satellite's readings are computed, read a bit

about the decomposition in monopoles, dipoles, cuadrupoles, etc,, AFTER a thorough data filtering,

interpolation, extrapolation, etc. and then came here to tell me about observational facts.

 

The amount of computing time and meetings to agree with coincidences or discrepances about the

final data is extraordinary,

 

There is not a Galilei there, discovering Jupiter moons as an observational fact.

 

It's the same as if you tell me that ANY composed "photograph" of any distant galaxy is as it comes out

of the CCD camera, and it's not true that is heavily doctored to compose wavelengths from mm to nm,

covering a wide spectrum of microwaves, infrared, visible light, UV and X-Ray radiation.

 

And, as a final touch, an artist renders the final picture with a beatiful assignment of colors to make

the picture look more "beautiful".

 

This is a link to the basic theory behind the CBR mapping:

 

https://en.wikipedia.org/wiki/Spherical_harmonics

 

Greetings,

 

Richard

 

P.S.: Please, read again your final comment about direct observations and mere applications of Planck's law.

        And yes, you are missing my point, but you are entitled to think differently, So let us to agree that we desagree.

 

Excerpt from your post:

 

So I don't really understand what your beef is with using Planck's Law. It is merely the applicable law for any black body emitter.  And we know, from observation, that the CMBR is a black body radiation distribution. 

 

Or am I missing your point?

What on Earth do spherical harmonics have to do with CMBR? 

[OceanBreeze]

I would agree there is more than one way of viewing radio waves. 

 

A minor correction electro magnetic radiation / radio waves consist of virtual photons, not photons. 

 

That’s an interesting point of view!

 

However, about the only place you will ever see virtual photons is on a Feynman diagram, as they only exist as force-carriers for the Electromagnetic force that exists directly between charged particles. So, they only exist in static fields and are not detectable nor do they have energy or momentum.

 

 

 

Obviously, radio waves must consist of real photons as they do carry energy and momentum and are detectable.

[exchemist]

This complete map of CMB with detectable anisotropy of CBR, showing thermal variations in the order of 10^-4 Kelvin degrees.

(Wikipedia: All-sky mollweide map of the CMB, created from 9 years of WMAP data)

 

Read carefully these articles from Wikipedia and will understand what spherical armonics have to do with it (there are more sources if you search about it):

 

https://en.wikipedia.org/wiki/Cosmic_microwave_background

 

https://en.wikipedia.org/wiki/Cosmic_Background_Explorer

 

 

 

No, I'm not going on a wld goose chase through these articles to hunt for an answer to my own question.

 

You are the one claiming spherical harmonics have some connection with CMBR. So you can tell me, in your own words, what that connection is. Or alternatively you can quote the most relevant paragraph of the articles you are relying on, to give me an idea.   

[exchemist]

From

 

https://en.wikipedia.org/wiki/Cosmic_microwave_background

 

Data reduction and analysis

Raw CMBR data, even from space vehicles such as WMAP or Planck, contain foreground effects that completely obscure the fine-scale structure of the cosmic microwave background. The fine-scale structure is superimposed on the raw CMBR data but is too small to be seen at the scale of the raw data. The most prominent of the foreground effects is the dipole anisotropy caused by the Sun's motion relative to the CMBR background. The dipole anisotropy and others due to Earth's annual motion relative to the Sun and numerous microwave sources in the galactic plane and elsewhere must be subtracted out to reveal the extremely tiny variations characterizing the fine-scale structure of the CMBR background.

 

The detailed analysis of CMBR data to produce maps, an angular power spectrum, and ultimately cosmological parameters is a complicated, computationally difficult problem. Although computing a power spectrum from a map is in principle a simple Fourier transform, decomposing the map of the sky into spherical harmonics, in practice it is hard to take the effects of noise and foreground sources into account. In particular, these foregrounds are dominated by galactic emissions such as Bremsstrahlung, synchrotron, and dust that emit in the microwave band; in practice, the galaxy has to be removed, resulting in a CMB map that is not a full-sky map. In addition, point sources like galaxies and clusters represent another source of foreground which must be removed so as not to distort the short scale structure of the CMB power spectrum.

 

Constraints on many cosmological parameters can be obtained from their effects on the power spectrum, and results are often calculated using Markov chain Monte Carlo sampling techniques.

 

-----------------------------------------------

 

With this, I'm done with this topic in our interaction.

Ah OK I see now, just about, why you bring in spherical harmonics. But can only be relevant to an angular Fourier transform decomposition of the signal. So, as I read it, they relate only to attempts to measure the angular anisotropies, not the CMBR signal itself. For that, you obviously do not need anything with the angular dependence characteristic of a spherical harmonic.

 

These anisotropies are very tiny indeed, corresponding to temperature variations of the order of 10⁻⁴ K, which is why it is a challenge to measure them, i.e. they are close to zero.  

 

So none of this calls in question the observation that the CMBR spectrum very accurately corresponds to a black body, which is why Planck's law is used to describe it.

[exchemist]

This might be of interest on this thread ref sources of cosmic back ground radiation  https://phys.org/news/2019-04-bright-space.html?utm_source=nwletter&utm_medium=email&utm_campaign=daily-nwletter and https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.161601

 

A sort of cherenkov radiation caused by magnetic fields around pulsars via interaction with virtual particles in space. If I read it correctly  :unsure:

Yes, but this phenomenon is quite separate from the CMBR.

 

It is not black body radiation, is not part of the background and involves emission of far higher frequency radiation than the CMBR. 

[exchemist]

 Spherical harmonics is a mathematical tool used to analyze data of any kind at spherical surfaces, in spectral terms.

They are the equivalent to Fourier analysis for one-dimensional data.

 

A sphere is analyzed as being a bi-dimensional surface, which has a curvature. Because of that curvature, bi-dimensional

Fourier analysis can't be performed.

 

As CMB data is collected as broadband temporal information about power density over a dome, wich is the cap of the solid

angle at which the radio measurement is performed, THEN Spherical Harmonics DECOMPOSITION is applied over this

specific dome's reading by the antenna. The bi-dimensional information, captured as a single temporal data, HAS TO be

decomposed into spectral components in order TO UNDERSTAND what are the major components of this sample of the CBR.

 

The use of Spherical Harmonics decompose the signal as having components called n-poles. Then you have monopoles, dipoles,

quadrupoles, octupoles, etc.

 

You can analyze each sample of the solid angle that is captured the antenna either as one single value, which poses not so much

value, or decompose the sample and study the contribution of each part of the spectrum in the tridimensional space.

 

After you have the thousands of samples of CBR, solid angle per solid angle, UNTIL you complete the scanning of the

spherical perspective of the universe, you make complex computations over each single sample and make corrections

to: eliminate undesired sources of radiations (like the Milky Way, weird zones at space with nebular aspect, artifacts (noise)

of different types and as many other undesired influences). Once you have completed this, using spherical harmonics, you

can transform the power samples into temperature samples (by using the PLANCK'S FORMULA).

 

Then, with thousand of pieces at your disposal, you can create a single 2D projection, placing each sample at his correct place.

 

THEN, you have to perform a digital low SPATIAL FILTERING of the whole data, in order to eliminate ARTIFACTS that appears at

the edges of each sample, when they are placed togheter.

 

THEN, you have choice: 1) present the whole map, which is not a good idea; 2) present a differential map, substracting the cosmic

average temperature of the background noise (the most popular version for laymen); 3) analyze the source of anisotropies by

decomposing (AGAIN) the radiation in monopoles, dipoles,quadrupoles, etc., for the ENTIRE UNIVERSE and analyz the contributions

of each n-pole, trying to figure out the sources of anisotropies.

 

There is much more behind this work, which is far beyond the capability of this forum to publish,

 

Here you have the best simplified explanation about CBR spectrum, the use of Spheric Harmonics and more.

 

It worth the effort to read it:

 

An introduction to the CMB powerspectrum

 

http://folk.uio.no/hke/AST5220/v11/AST5220_2_2011.pdf

Yes thanks. But if you read my post 30, you will see my understanding of the relevance of this is that it ONLY applies to analysis of the minute angular anisotropies of the CMBR, not the CMBR signal itself. 

[exchemist]

Well, your understanding of the relevance of spherical harmonics in the CBR analysis is just plain wrong.

 

I think that you like to argue just for the sake of it, and not for a valid scientific doubt. Also, I note that your

way to addressing to me is a little bit tilted to the downplaying game, to prove that you're the smartest child

in the block (you're far from being a child, of course).

 

So, this is mi final attempt to give you insights about the complex mechanisms behind the measurement of

the Cosmic Backgroud Radiation. I'll base this simple explanation on the final analysis of the data of COBE,

which was written by 18 scientists involved in the posterior evaluation of the data recopiled by COBE FIRAS.

 

As the final paper is heavily protected to readings by non-members, as it is in custody of the American

Astronomical Society, I've managed to get a link to a photographic copy at this link:

 

Measurements of the Cosmic Background Spectrum by the COBE FIRAS Instrument

 

http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1994ApJ...420..439M&db_key=AST&page_ind=0&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES

 

But also, I searched a copy of a derivate paper at this link, which is written by the same 18 scientists, and is

less protected (if you select PRINT to a virtual PDF printer will obtain the document):

 

Cosmic Background Dipole Spectrum Measured by the COBE FIRAS Instrument

 

http://adsabs.harvard.edu/full/1994ApJ...420..445F

 

--------------------------------------------------------------------------------------------------------

Some explanations to make it easier to understand:

 

1) The Universe was measured as a black body spherical cavity by COBE, 30 years ago,

    As the capabilities of FIRAS to make accurate measurements over small areas was low,

    scientists invented (specifically for COBE) the reduction of a sphere to a "cube), which

    was called: quadriteralized spherical cube.

 

   

 

 

This cube was decomposed into 6144 macropixels, to make average measurements over each one of them (they only could

measure 90% of the total).

 

2) The measurements covered the band between 60 and 660 Ghz (THIS has to make your eyebrows to raise). It was

     EQUIVALENT to measure wavelengths between 0.2 mm and 2 mm.

 

    What was measure was a "fluctuating thermal radiation" using a wideband bolometer. The measurements were a total

    TEMPORAL AVERAGE per macro-pixel, and were stored (thousands of them) to further and heavy post-processing

    here, at Earth,

 

    And this is a KEY FACTOR. The Planck's formula is an SPECTRAL formula, not a TEMPORAL formula, and is based

    on statistical averages (Boltzmann, Planck).

 

    To obtain the SPECTRAL data of a macro-pixel, you HAVE TO make a spectrum transform of bidimensional order,

    But each macropixel is not a cartesian area, but a 2D representation of a 3D surface, so you HAVE TO apply

    spherical harmonics transforms to EACH macropixel (either to analyze power or to its derivate temperature, which is

    obtained FROM Planck's formula. Or Rayleigh's formula, as frequency is very low).

 

3) Having your thousands of samples per each of the 6144 pixels, you need to ELIMINATE distortions (galactic noise,

    cosmic noise - difficult to define, instrument's missbehaviors, glitches, etc).

 

    To do that, you use the spectral spherical decomposition in monopoles, dipoles, quadrupoles, etc., and HEAVILY

    DOCTOR the data to eliminate what you don't like.

 

4) Finally, you have to SHOW to the audience HOW GOOD is the job COBE did, by proving that CBR is fully compliant

    with Planck's law for a black body cavity,

 

    But you have A PROBLEM:

 

   Planck's formula is about DENSITY of thermal radiation that fills the cavity, wich is a volumetric measurement.

 

   But you only have 6000+ pieces of spectral data (heavily doctored) and you need to MAKE PUBLIC a single

   chart (measured radiation intensity that escapes from a small hole at the Planck's cavity versus wavelength).

 

   Then, what you do is A WEIGHTED SPECTRAL AVERAGE of 6000+ spectral data (with a wide range of wavelengths)

   and PRESENT IT as a SINGLE spectral formula, like Planck did.

 

   Then, when you fitted data to your target, you present it to the general audience, which cheers you and the mission

   and recover their faith on science and its reconciliation with history: Planck tell us that CBR is exactly as he predicted,

   He's the father of quantum physics, so the man knows and, also, the COBE results HAVE TO be true,

 

I end it here, as I'm sicked of this, But remember that I claimed for "petitio pricipii" sophistic mechanism behind COBE, WMAP

or Planck satellite; The calibrations of the antenna and the measurement instrument use not one, but two Black Body radiation

generators,

 

So, going back to this topic and my OP: "Why Planck's formula for black body radiation is used to measure the CBR?"

 

THE END

No, I think you've misunderstood this.

 

Here is a description of the detector used when the CMBR was originally measured in 1964.https://en.wikipedia.org/wiki/Microwave_radiometer#History

There is no reference here to Fourier transforms, still less to spherical harmonics. They just used a heterodyne method to convert the microwave frequency to a lower one they could put through a conventional amplifier. 

 

Oceanbreeze has told you he has detected the CMBR himself, for fun, on his research ship. He did not need to futz about with Fourier analysis and spherical harmonics to do that. 

 

I repeat: spherical harmonics can only be relevant to evaluating angular dependence of the signal. Whereas the CMBR can be - and was originally - detected just by looking in some direction and assessing the microwave background, without considering any angular variation. 

 

Anyway, you have my answer to your final (and original) question: Planck's formula is used because the radiation has a black body spectrum, i.e. it is black body radiation, so that is the appropriate formula to use.  

Edited April 28, 2019 by exchemist