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

[exchemist]

Well, I'll make a last try, using Planck's and Wien's formulae, and some definitions:

 

Monochromatic Irradiance or Spectral Flux Density at the aperture in the cavity: Radiance of a surface per unit frequency or wavelength per unit solid angle. A directional quantity and differs from Planck's formula by (c/4). This is sometimes confusingly called "spectral intensity". (Note: I use L instead of the symbol for Lambda)

 

L_e(L,T) = (c/4).W_e(L,T) = 2hc²L^-5(e^ch/kLT-1)^-1    [units:  Watt.m^-2.m ^-1.sr^-1]

 

Using L_e(L,T) for a single measurement at COBE (or WMAP or PLANCK), and assuming that the measured value is X, then:

 

X = 2hc²L^-5(e^ch/kLT-1)^-1

 

Extracting T (the temperature that is derived from Planck's formula), you have:

 

T(L)  = (kL/ch) ln [1 + (2hc²L^-5) X^-1]  , in Kelvin degrees

 

In this way temperatures from 6,144 spots (COBE), 234,541 spots (WMAP) and 703,524 spots (PLANCK), is calculated. With this data, average temperature of the CBR is calculated, and a differential map (after filtering anomalies) is presented.

 

Using Wien's displacement law, and assuming that the average temperature obtained is about 2.73 Kelving deg,

 

_Lmax = b/T   , being b = 2900 m.K^-1

you have

 

_Lmax = 1.067 mm

 

at peak frequency

 

f(_max ) = 282.4 GHz

 

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

 

I hope that the above explanation can help to understand HOW thermal radiation temperature is CALCULATED,

and is only by using a derivation of Planck's formula.

 

As you can see, Planck's formula is everywhere, when it is about CBR measurements.

 

To my understanding, there is not any other formula used, as Planck's formula is the ultimate expression

for thermal radiation density WITHIN a Black Body Cavity, as the Universe is assumed to be.

 

These formulae also prove why Planck's BBR generators are VITAL for instruments calibration.

 

And if you wonder HOW did I obtain the amount of spots (actually reduction of domes to small plane areas),

I obtained it from NASA's Planck details, and NASA's WMAP and ESA's PLANCK deails from ESA sources.

 

I don't know what else to do to probe the usage of Planck's formula everywhere, whithin the BB cavity that

the Universe was assumed for these projects.

 

My original question at the topic stands, because I strongly dissagree that the Universe be interpreted as

a Black Body Cavity.

 

And if you wonder the role of the BBRG on board, think with an analogy.

 

Suppose that you are at a MIT lab, and you are measuring a voltage with your 8 digits

state of the art voltmeter, and have to measure the accuracy of a third order reference

of 1.0000000 volts.

 

But you read 0.9347581 volts.

 

Then you use your first order voltage reference for 1 volt (with 10^-10 accuracy), and

it results that you recalibrate your voltmeter to have a 1.000000 volts reading.

 

But, for whatever be the cause, your premium reference has shifted to a value 5% lower

and you don't know about this error.

 

Your's voltmeter calibration will render a measurement of 1.000000 volts, but actually the

true value is 0.950000 volts.

 

So, obeying your reference, you adjust your equipment and measure a wrong value.

 

This is what happens with the on-board BBRG calibrations. You follow the master reference

and, doing so, you are following Planck's law.

 

And this is a "petitio principii" fallacy. Of course that your values will follow exactly Planck's formula.

 

You've forced the whole system to follow the indications of the BBRG calibrator.

They measured differences from Planck's law.  This is described in the paper I linked to in post 67.

[OceanBreeze]

 

 

My original question at the topic stands, because I strongly dissagree that the Universe be interpreted as

a Black Body Cavity.

 

And if you wonder the role of the BBRG on board, think with an analogy.

 

Suppose that you are at a MIT lab, and you are measuring a voltage with your 8 digits

state of the art voltmeter, and have to measure the accuracy of a third order reference

of 1.0000000 volts.

 

But you read 0.9347581 volts.

 

Then you use your first order voltage reference for 1 volt (with 10^-10 accuracy), and

it results that you recalibrate your voltmeter to have a 1.000000 volts reading.

 

But, for whatever be the cause, your premium reference has shifted to a value 5% lower

and you don't know about this error.

 

Your's voltmeter calibration will render a measurement of 1.000000 volts, but actually the

true value is 0.950000 volts.

 

So, obeying your reference, you adjust your equipment and measure a wrong value.

 

This is what happens with the on-board BBRG calibrations. You follow the master reference

and, doing so, you are following Planck's law.

 

And this is a "petitio principii" fallacy. Of course that your values will follow exactly Planck's formula.

 

You've forced the whole system to follow the indications of the BBRG calibrator.

 

 

Now I cannot take you seriously. Nobody in their right mind recalibrates their instrument according to a random measurement. Surely, as a retired “electronic engineer” you should know that! I should not even need to explain that the BB generators are used as the reference for calibration and then when the Input was switched to the CMBR no significant difference could be seen. To use your analogy, the multimeter is calibrated to a known reference of 1 Volt and when the unknown voltage is measured no difference is seen. Nobody calibrated the instrument to the unknown CMBR! The calibration was done to the known BB generator.

 

Here is an explanation that contradicts what you are claiming:

 

"The FIRAS instrument on COBE had a large conical horn for collecting the cosmic microwave background. There was only a small hole in the end of the horn to let the radiation into the instrument. But FIRAS also carried a microwave absorber, the external calibrator or XCAL, that could be inserted into the horn like a trumpet mute, and heaters that could make the whole horn+plus absorber cavity isothermal.

 

When the XCAL was in the horn FIRAS observed a very good blackbody cavity, but when the XCAL was out FIRAS observed the CMB. No signifcant difference could be seen. The CMB is very close to a blackbody with temperature 2.725 K. The FIRAS results are shown below in units of intensity (power per unit area per unit frequency per unit solid angle) vs. frequency and/or wavelength."

 

 

 

 

"Eric Adelberger would like me to point out that the fundamental FIRAS measurement is the residual plot at the bottom. This is what FIRAS actually measured: the difference between the CMB and the best fitting blackbody. The plot at top shows this residual added to the theoretical blackbody spectrum at the best fitting XCAL temperature, based on the function derived by Planck in 1900. The three curves in the bottom correspond to three fairly likely non-blackbody spectra: the grey curve shows a body with a reflectivity of 100 parts per million instead of zero, and the red and blue curves show the effect of hot electrons adding an excess 60 parts per million of energy to the CMB either before (blue) or after (red) 1000 years after the Big Bang. These curves show the maximum distortions allowed by the FIRAS data."

[exchemist]

Hi, I've searching for alternate theories about the origin of the CBR.

 

Please, take this with care as I'm not proposing any theory here. Just pure and simple

research over the Internet about people or groups which have a different proposal

than the currently accepted.

 

To be clear. and as far as I know (source:Dear Professor Dyson: Twenty Years of Correspondence

Between Freeman Dyson):

 

1) CBR was proposed in 1948 by Alpher and Herman, who estimated a 5 ºK as the

    average temperature of an expanding universe, originated in a Big Bang.

    They considered that the whole universe should be filled with Planck's radiation in

    the microwave region (Watt/m3), as rests of the original explosion and that this could

    be measured at present day, heavily red-shifted due to the Hubble constant (it was larger by then).

    There was no interest in cosmology by then, even when they tried for 15 years to convince

    astronomers, but they thought this radiation couldn't be measured.

 

2) In 1948, Hoyle, Gold and Bondi proposed an alternative: The steady Universe.

    They didn't like the Big Bang, the CBR and the primordial singularity. Their model was based on

    the constant number of galaxies per volume and an unexplained model for matter creation as

    the universe was expanding (they accepted that, due to Hubble's constant).

 

3) In a radio program, in 1950, Hoyle and Gamow were discussing about cosmology. At this program,

    Boyle introduced the term "Big Bang", mocking about Gamow's position.The name stuck.

 

4) In 1964, Penzias and WIlson discovered, accidentally, a steady low level radiation everywhere at

    the observed sky, while playing with an antenna given to them for spatial explorations in radioastronomy.

 

5) Everything slowly expanded around the CBR and the Universe's average temperature since then.

 

6) 25 years after Penzias-Wilson, and with many experiment around the CBR (on Earth, balloons, etc.),

    the COBE (Cosmick Background Noise Explorer) was launched in 1989. WMAP followed in 2001, with

    more advanced technology and finally PLANCK was launched in 2009 with the most advanced tech

    available by then. Since 2009, there is no other plan for an observatory after Planck satellite, and,

    since 2014, the original teams (WMAP and PLANCK) were dismembered, without explanations.

 

    Members of each of the three teams had to get a new job at other areas.

 

    It seemed that Planck's anisotropies were insuficient to explain the rol of galaxies in the creation

    of new matter, as well as the roles of the dark matter and dark energy. Now, the subject is in suspended

    state.

 

This is a simplified history of the perception of the CBR as Planck's radiation. It was born in 1948.

 

The CBR is out there, even when some people doesn't believe in the isotropy of the radiation, nor

about its origin. This persons, as the Hoyle's team did think, believe that that there was no Big Bang,

BUT they accept that the CBR exists (one way or another).

 

This is a link to one of these theories, and is based on the Oort Cloud, which is understood as an

spherical shell that encloses the solar system and that could be capable of produce something like the CBR:

 

They, apparently, believe that such an spherical shell could have the properties of a Planck's cavity and follow

the values of the Planck radiation.

 

http://aoi.com.au/OortSoup/index.htm

 

I don't believe nor deny this possibility, as I know very little about the Oort thing. But I know that scientists know

very little about this Oort shell, also.

 

It has been rather ignored by the astronomer's community.

 

I stop here. I'll keep searching for alternate explanations,which tipically are originated by not-believers of the Big Bang.

 

I, for many reasons, don't believe in the BBT either. But, even with several doubts that a initial singularity creates, it

seems that the BBT is adopted by consensus, like herd's behavior, just to stay "on" in the community. The BBT also

fails explaining several major doubts about acceleration of expansion, calculations about real amount of matter (which

forced the invention of dark matter and dark energy) and the future of the universe, among others.

Well it is something that you acknowledge the CMBR is real, at any rate.

 

On your difficulty accepting that the early universe behaved like a black body cavity, I should have thought that would not be too difficult to accept. According to the theory, the early universe was small and filled with plasma, until 380,000yrs after the big bang. During that phase it was a closed system in which matter and radiation were in thermal equilibrium. This is just what a black body cavity is.

 

The CMBR, according to the theory, comes from the "surface of last scattering", which was the point at which the plasma condensed into atoms, which only absorb and emit at certain frequencies, thus uncoupling the radiation flux from matter for the first time. The effective temperature of the radiation has dropped as the universe has expanded further.

 

This "herd" stuff is rather unfair. After all, the big bang model is quite successful so far. But it is only a model and can always be overturned by someone with convincing evidence against it. Have you researched the evidence against it and can you summarise any of that here for us?        

[exchemist]

IF Planck's formula for perfect black body cavity fits perfectly COBE's measurements of CBR spectra, which are the emitters and the absorbers of radiant energy, in order to correctly assimilate CBR to Planck's enviroment?

The charged particles that form the plasma.

 

The radiation became "frozen" at the time of the so-called "surface of last scattering", estimated in the model to have occurred about 380,000yrs after the big bang itself. It became frozen because that was the time at which the adiabatic cooling due to expansion first allowed neutral atoms to form.

 

Once the matter was in the form of neutral atoms, the emission and absorption would obviously have taken the form of line spectra, rather than a continuum, so it would no longer have followed the black body continuum curve. At all wavelengths other than those at which line emission or absorption took place, the universe would have been, for the first time, transparent to radiation. Hence the radiation simply travelled round and round the universe from that point onward, being gradually shifter to longer wavelength as the universe expanded. 

Edited May 11, 2019 by exchemist

[exchemist]

It's not a mathematical function at all!

 

It's a final expression of 41 years of research for the Kirchoff's theorem for thermodynamics, which occupied

the most privileged minds in that period, and that merge results from electromagnetism, statistical mechanics,

theory of radiant heat and the second law of thermodynamics. Planck himself invested six years developing it!

 

 

You can read the entire historical development of the black body radiation formulae at this link:

 

https://physictheories.blogspot.com/

 

Another thing is that you didn't identify which elements work as emitters and which ones work as absorpters of EM radiation.

Don't forget that only primordial radiation has to apply, as this is the proof that CBR is the remain of energy that wasn't transformed

into matter, after the initial blast.

None of that stops it being a mathematical function: a function that happens to be followed very exactly by the CMBR spectrum.

[exchemist]

No, exchemist.

 

The primordial plasma soup is gone long time ago, with its charged particles that formed primordial atoms.

 

The CBR is (according to current interpretations, with which I disagree) the remnant of radiation that couldn't be transformed

into matter when the temperature of the Universe descended from millions °K up to 3,000 °K.

 

By the, at 3,000 °K and a much smaller Universe, the remnants had a peak wavelength of about 1 micrometer, which is the

region of FAR INFRARED, just below the visible light.

 

When the Universe cooled off and expanded, the 3,000 °K CBR elongated its wavelength up to 1 mm peak, which correspond

to the current 3° K radiation.

 

And this radiation is present everywhere (according to current understanding), with an energy density of radiant modes equal to:

 

         N = 8.Pi.f².c^-3 , in units of number of resonance modes per unit volume per unit frequency.

 

having each mode the average energy:

 

        E_avg = hf/(e^hf/(kT) - 1)  , in units erg-seconds

 

and this is the final work of Planck: The spectral distribution of energy in a black body cavity under thermal equilibrium is:

 

       u = N . Eavg = 8.Pi.h.f³.c^-3 (e^hf/(kT) - 1)^-1

 

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

 

So, CBR photons are everywhere at the current Universe, with a calculable amount of photons per cubic meter per Hertz.

I quote, from https://en.wikipedia.org/wiki/Cosmic_microwave_background :-

 

"CMB is landmark evidence of the Big Bang origin of the universe. When the universe was young, before the formation of stars and planets, it was denser, much hotter, and filled with a uniform glow from a white-hot fog of hydrogen plasma. As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral hydrogen atoms. Unlike the uncombined protons and electrons, these newly conceived atoms could not absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog.^[3]"

 

So my explanation is correct, unless you are challenging the Wiki article, in which case I can easily find another saying the same thing.

 

And if you do not consider that 380,000years after the big bang i.e. about 14bn years ago, is a long time ago, I don't what would be. 

 

I don't understand why you are trying to work all this "radiant modes" stuff into the discussion when the black body that emitted the radiation ceased to exist 14bn years ago.  

Edited May 11, 2019 by exchemist

[exchemist]

Color by color:

 

1) The "radiant modes" stuff has to be with the DENSITY of BB energy per unit volume that permeates the ENTIRE SPACE.

    I just wrote the Planc's formula with his two constituents:

 

      1.1) The density per unit volume (N/m³) of radiating modes that exist within an arbitrarily sized black body cavity.

      1.2) The individual energy per mode, E_avg, which had two acceptions:

 

             1.2.1)   E_avg = kT (which correspond to the June 1900's Rayleigh solution).

             1.2.2)   E_avg = hf/(e^hf/(kT) - 1) , which correspond to the December 1900's Planck solution.

 

2) In a perfect black body cavity, the energy stay in there FOREVER. It's emitted, then absorpted, then emitted again, and so on.

    This occurs IF the black body cavity is in thermal equilibrium.

 

    Theorists say (and also said that they proved it with COBE) that the Universe behaves as a perfect black body cavity.

    NOT ME, AS I DISAGREE WITH THIS!

 

    They also affirm that the Universe WAS BEHAVING as a BBC when it cool off, reaching 3,000 °K.

 

    So, scientists state that the Universe was behaving as a perfect BBC 13.5 billion years ago AND that is behaving as a perfect BBC

    RIGHT NOW, while the Universe average 2.75 °K.

 

    Then, blame them and not me for these interpretations.

   

 

3) I don't challenge that Wiki excerpt. I just remark to you that such excerpt doesn't explain how the remnant of

    the Big Bang appeared, once the Universe cooled off.

 

    Maybe you forgot to copy and paste another part of the Wiki's article.

You are still missing the point. The universe has not been a black body since 14bn years ago. It ceased to be one when the plasma condensed into neutral atoms. So there is no calculation of radiant modes to be done. It's irrelevant. There are no radiant modes, of anything, radiating or absorbing. 

 

And yes the explanation does explain why the remnant is there. Once the universe became transparent to radiation, it stopped absorbing it. That is what transparent means. So the radiation just persists, everywhere, as a......cosmic background.  

Edited May 11, 2019 by exchemist

[exchemist]

exchemist, you have to read this short article from NASA, of which I'll extract an excerpt.

 

There, you'll find ground for your position and I find ground for my position (and maybe we just have

a communication problem, and that's the basis of our differences).

 

https://map.gsfc.nasa.gov/universe/bb_tests_cmb.html

 

I extracted from the article this picture, as I found it very didactical, among the complexities we are dealing here.

 

 

 

What I found as extraordinary is that this article is the first one from NASA (or ESA) that has the courage

to risk numbers about the size of the universe when CBR started to permeate it, from a site different from

academic places, where I found more daring and precise numbers.

 

 

Excerpt from the link provided above: Tests of Big Bang: The CMB ------------------------------------------------------------------------

 

The Origin of the Cosmic Microwave Background

 

One of the profound observations of the 20th century is that the universe is expanding. This expansion implies the universe was smaller,

denser and hotter in the distant past. When the visible universe was half its present size, the density of matter was eight times higher

and the cosmic microwave background was twice as hot. When the visible universe was one hundredth of its present size, the cosmic

microwave background was a hundred times hotter (273 degrees above absolute zero or 32 degrees Fahrenheit, the temperature at

which water freezes to form ice on the Earth's surface). In addition to this cosmic microwave background radiation, the early universe

was filled with hot hydrogen gas with a density of about 1000 atoms per cubic centimeter. When the visible universe was only one

hundred millionth its present size, its temperature was 273 million degrees above absolute zero and the density of matter was

comparable to the density of air at the Earth's surface. At these high temperatures, the hydrogen was completely ionized into free

protons and electrons.

 

End of excerpt --------------------------------------------------------------------------------------------------------------------------------------------------

 

As far as I researched about theories for black bodies being used currently in astrophysics (as sacred dogmas), I found that

the three main theories (converted in laws, actually) were originated between Kirchoff's theorem (1859) and Planck's theory (1900).

 

During those 41 years, three theories (two of them with a Nobel Prize awarded to their authors) are:

 

1) Stefan's Law (or Stefan-Boltzmann Law): It is applied since 1877 to perfect black body surfaces (watts per square meter units).

2) Wien's Displacement Law: It is applied since 1893 to perfect black body cavities (peak micrometers . °Kelvin units).

3) Planck's Black Body Cavity Radiation Law: It is applied since 1901 to perfect black body cavities (Joules per cubic meter per Hertz units).

 

1. Part of this post using the Wien's Displacement Law:

 

   Using NASA's article data:

 

   Peak wavelength of CBR (380,000 years after the BB)     = 2,900/3,000 micrometers = 0.9667 micrometers.

   Peak wavelength of CBR (13.7 billion years after the BB) = 2,900/2.75 micrometers = 1.05 millimeters.

 

   So, peak wavelength of the CBR has increased almost 1,000 times since it appeared. Explanations that are

   given, relate this displacement to the expansion of the universe.

 

 

 

2. Part of this post using the Stefan-Boltzmann's Law:

  

 j = T⁴

   where is 5.67x10^-8 Watt.m^-2.K^-4

 

   At this link:  https://physictheories.blogspot.com/    , there is a complete explanation of the three theories.

 

   As j is power per unit area, it allows to calculate (astrophysics and industrial applications) the total power emitted by a perfect BB surface.

 

   So, j = P/A and, in the case of the inner surface of an spherical shell, j = P/(4.PI.r²),  where r is the radius of the spherical shell.

 

   It can be derived that

 

                                                   P = (4.PI.r²),.T⁴

 

  and a quotient between two different values is (dividing side by side)

 

                                                   P_M/P_N = (r_M/r_N)² . (T_M/T_N)⁴

 

From NASA's article, we can write down the given data in a different form:

 

1) Visible universe (r₁: 13.7.10⁹ yl):  density 10^-5 atoms/cm³ and T₁ = 2.73 ºK

2) Visible universe (r₂: 6.85.10⁹ yl):  density 8.10^-5 atoms/cm³ and T₂  = 5.46 ºK

3) Visible universe (r₃: 137.10⁶ yl):  density: 1000 atoms/cm³ and T₃  = 273 ºK

4) Visible universe (r₄: 137 yl):         density: 2.53 x 10³¹  atoms/cm³ and T₄ = 273 millions ºK

 

 

In this way, using Stefan-Boltzmann's Law, we can calculate (for the entire Universe):

 

P₁/P₂ = (r₁/r₂)² . (T₁/T₂)⁴ = 2² . 0.5⁴ = 0.25              (It means decrease in CBR energy, in joules per second units)

Atomic density decrease (per cm³): 1/8

Missing parameter: Time elapsed between 1) and 2). If expansion was linear, the value is 6.85 billion years.

 

P₁/P₃ = (r₁/r₃)² . (T₁/T₃)⁴ = 100² . 0.01⁴ = 10^-4        (It means decrease in CBR energy, in joules per second units)

Atomic density decrease (per cm³): 10^-8

Missing parameter: Time elapsed between 1) and 3).  If expansion was linear, the value is 13.56 billion years.

 

P₁/P₄ = (r₁/r₄)² . (T₁/T₄)⁴ = (10⁸)² . (10^-8)⁴ = 10^-16  (It means decrease in CBR energy, in joules per second units)

Atomic density decrease (per cm³): 3.95 . 10^-37

Missing parameter: Time elapsed between 1) and 4).  If expansion was linear, the value is almost 13.7 billion years.

 

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

 

CONCLUSION: According to data supplied by NASA at the above link, the total energy of the initial CBR is  NOT A CONSTANT.

Apparently, this energy is dissipating as time passes by, so the conclusion is: The Universe doesn't behave as a perfect

black body cavity.

 

Maybe I'm wrong in my extrapolation of power into energy along the time passed, but the application of two out of the

three fundamental laws for perfect black bodies is correct as they are widely used in astrophysics and cosmology.

 

The third law for BBR (Planck's one) could be applied in the form of a double integral of the spectral flux density (first in spheric space

units and then in Hertz units). The result has to be equal to the Stefan-Boltzmann's law (area under Planck's curve and over 4PI radians).

 

L_ʋ(ʋ,T) = (c/4).W_u(ʋ,T) = 2hʋ³c^-2(e^hʋ/kT-1)^-1    [units:  Watt.m^-2.Hz^-1.sr^-1]

 

Anyone can check this on the section Radiometric Quantities of the given blog link, which is unrelated with astrophysics or cosmology,

and deals only with theories of classic thermodynamics applied to black bodies.

Maybe what you and I are saying is starting, very slowly, to converge. 

 

You are of course perfectly right that the universe today is not a black body. But that is not what what the Big Bang model contends. The model proposes that the universe WAS a black body, but only for the first 380,000 years of its existence.

 

At that point atoms formed and so it became generally transparent to radiation for the first time. Once it was generally transparent to radiation (i.e stopped absorbing and re-radiating at most wavelengths), clearly matter and radiation could no longer be in thermal equilibrium with one another, which is a requirement for a black body. 

 

So the situation at that point was that the whole universe was filled with black body radiation which was, suddenly, no longer being absorbed. What would have happened to it? It could not be absorbed and it could not disappear, seeing as the universe is closed. A photon going in one direction would just go all the way round the universe and get back to where it started. There is no escape.  

 

So it just continued to exist, throughout space. However, since the metric of space continued to expand, the wavelength of the radiation got longer and longer, shifting the energy distribution to lower and lower frequencies while still maintaining the characteristic black body profile it had from the surface of last scattering.  

Edited May 12, 2019 by exchemist

[OceanBreeze]

 

 

From NASA's article, we can write down the given data in a different form:

 

1) Visible universe (r₁: 13.7.10⁹ yl):  density 10^-5 atoms/cm³ and T₁ = 2.73 ºK

2) Visible universe (r₂: 6.85.10⁹ yl):  density 8.10^-5 atoms/cm³ and T₂  = 5.46 ºK

3) Visible universe (r₃: 137.10⁶ yl):  density: 1000 atoms/cm³ and T₃  = 273 ºK

4) Visible universe (r₄: 137 yl):         density: 2.53 x 10³¹  atoms/cm³ and T₄ = 273 millions ºK

 

 

In this way, using Stefan-Boltzmann's Law, we can calculate (for the entire Universe):

 

P₁/P₂ = (r₁/r₂)² . (T₁/T₂)⁴ = 2² . 0.5⁴ = 0.25              (It means decrease in CBR energy, in joules per second units)

Atomic density decrease (per cm³): 1/8

Missing parameter: Time elapsed between 1) and 2). If expansion was linear, the value is 6.85 billion years.

 

 

 

 

A couple of things you might want to consider:

1. The presently accepted radius of the observable universe is about 46 billion lyr, not 13.7 billion lyr.
2. The expansion of the universe is not linear, but accelerating.

[OceanBreeze]

I'm aware of the concept of "observable" universe, which is explained at many sites (Wikipedia included) as a theoretical observable

universe, and is conceived as the universe that we COULD observe today IF we had the technology, and that is caused by expansion.

 

As it's explained, within the observable universe, with the radius that you wrote, there is the VISIBLE universe. This one is the universe

that we, using  our current state of the art technology, can observe and even register with instruments. The visible universe has a radius

of 13.77 billion ligth-years, which is almost the maximum reach of the Hubble's telescope.

 

Don't blame me, because I don't understand how come the concept of "observable" universe appeared, and astronomers insist that it could

be measured at the edge IF we had the proper technology. For me, this is an utter nonsense. It involves not only the BBT but also the GTR,

co-moving and proper distances and a lot of denominations with which I don't agree.

 

NASA talks about visible universe, and that is the reason by which I adopted the 13.7 billion ly as a radius.

 

Excerpt from Wikipedia: Observable universe, at https://en.wikipedia.org/wiki/Observable_universe

 

The word observable in this sense does not refer to the capability of modern technology to detect light or other

information from an object, or whether there is anything to be detected. It refers to the physical limit created by

the speed of light itself. Because no signals can travel faster than light, any object farther away from us than light

could travel in the age of the Universe (estimated as of 2015 around 13.799±0.021 billion years^[5]) simply

cannot be detected, as the signals could not have reached us yet.

 

Sometimes astrophysicists distinguish between the visible universe, which includes only signals emitted since

recombination (when hydrogen atoms were formed from protons and electrons and photons were emitted)—

and the observable universe, which includes signals since the beginning of the cosmological expansion

(the Big Bang in traditional physical cosmology, the end of the inflationary epoch in modern cosmology).

 

End of excerpt -------------------------------------------------------------------------------------

 

As you can read about, weird concepts for me but not for BBT, Inflation and GTR believers.

 

This image is from:  The Observable Universe, at the site: http://theuniverse.is/the-observable-universe/

 

 

 

I suggest you read the Wiki page again and this time don't allow cognitive dissonance to block out any part you do not want to see!

 

Here, I will help you.

 

 From the same link you quoted from:

 

"Sometimes astrophysicists distinguish between the visible universe, which includes only signals emitted since recombination—and the observable universe, which includes signals since the beginning of the cosmological expansion (that is, the end of the inflationary epoch in modern cosmology). The radius of the visible universe, is about 14.0 billion parsecs (about 45.7 billion light years), while the comoving distance to the edge of the observable universe is about 14.3 billion parsecs (about 46.6 billion light years),^[2] about 2% larger"

 

As much as you want the radius of the visible universe to be 13.799 lyr, that is not correct! That is the AGE of the universe, not the size.

 

Since you used the same Wiki page to support your claim, will you now use it to concede your mistake?

[exchemist]

I hope so.

 

But there are many issues that even scientists are discussing and contradicting themselves by today. So, what if left for us, then.

 

Greetings,

 

Richard

Well that's where science differs from engineering :) .At the leading edge there is always a lot of uncertainty and rival hypothesis. What is left for us is to follow the evolution of these ideas, as new observations come in that enable science to start to discriminate between the rival hypotheses. I am currently quite intrigued by dark matter. The astronomical evidence for it is considerable but the particle physicists seem stumped. Dark energy strikes me as a lot more hypothetical. I'll take more of an interest in that when there are more observations to tie down what it might be.

[exchemist]

Thanks to OceanBreeze, who provided me this link:

 

 

New Aspects of Photon Propagation in Expanding Universes

 

https://arxiv.org/pdf/1610.05609.pdf

 

I can see that not only scientists at NASA and ESA used Planck's formula for their COBE, WMAP and PLANCK

missions.

 

I can see that Cosmologists are totally lost without using the formulae developed by Planck and, before him,

Stefan and later Boltzmann. We are talking about theories for the BB Cavity Radiation that are, to the least,

120 years old and that are the CORE of any speculation of what happened after the BB with CMB radiation

(which is the strongest radiation out there, in terms of energy density and unknown origin).

 

Even when they mix a little of GTR (mandatory in the BB aftermath), they are lost without a planckian world.

 

Meanwhile, a NON-RELATIVISTIC and undisputable formula is eating their bodies from inside out, and is the

simple relationship with the Hubble's constant that gives the radius of the visible universe:

 

As simple as this:   R(Hubble's universe) = c/H₀

 

and nobody know squat what happens BEYOND this limit.

 

Yet more, none of the thousand of theories for behavior BEYOND this frontier can be measured (proved).

 

Conclusion: They (cosmologists) know nothing. NOTHING!

I expect they are "lost" without Newton's laws of motion and Mendele'ev's Periodic Table, too. Why is that a criticism of them?  

[exchemist]

They are. This are the modified Laws of Motion from Newton:

 

Definition of law of motion

1 : a body at rest remains at rest and a body in motion remains in uniform motion in a straight line unless acted upon by an external force.

 

    New: a body at rest remains at rest and a body in motion remains in uniform motion in a geodesic line unless it's affected by accelerations

             produced by the curvature of space-time, under the presence of a massive body.

 

2: the acceleration of a body is directly proportional to the applied force and is in the direction of the straight line in which the force acts.

 

   New: the acceleration of a body is somehow proportional to the curvature of space-time due to the presence of a massive body and is

           in the direction of the geodesic line traced in the curved space-time.

 

3: for every force there is an equal and opposite force or reaction.

 

    New: for every acceleration that a body suffers due its motion in the curved space-time, there is a change in the curved space-time that

             induce opposite accelerations in such a developed gravitational field that is carried by gravitons.

 

4th postulate (new): Mass is what used to be m = F/a since the dawn of life on Earth. It holds true until it be found what really mass is.

 

:spin:

Yeah yeah, but they still use Newton's laws for orbital mechanics etc, just as we all do to build bridges.

 

 

You seem to have some sort of bee in your bonnet about c.19th science, as if it is somehow significant whether or not concepts from that era are still used today. I do not understand why. We make use a of  lots of concepts from a variety of eras. If they are good models for the situation at hand, we use them. 

[exchemist]

Physics desintegrated as a science between 1912 and 1929 (Rutherford's proton, Le Maitre`s Big Bang, Schrodinger's wave function and Hubble's constant).

 

Today is a compartmentalized body of knowledge with more than 100 different disciplines, many of which contradict others, and there is not a Master

to correct it.

 

As a building, it's broken because it's allowed that false knowledge spread with a speed given by the Bradford's law of dispersion 1:n:n² (and I would add n³).

 

It's said that the amount of available information doubles every 2 years and it's accelerating, like galaxies' speed with the Hubble constant.

Today, it's calculated that the information being around is in excess of 800 exabytes (10²⁰ bytes) and grows without control or sense.

 

I'd like a reset at physics, technology and at the industry of multimedia, but....................

 

We are doomed to live towards Idiocracy.

 

I find your reply interesting, psychologically speaking. c.20th physics does seem to be hard to take, for some older engineers. I was in fact taught physics in the 1st yr 6th form by a man who claimed to be agnostic about the existence of molecules!  He had read Engineering at Cambridge. He was actually an excellent teacher and very solid on c.19th "classical" physics (optics, electromagnetism, thermodynamics etc.) But for the 2nd year we needed a different teacher of course.

 

You remind me of that comment by Richard Feyman: "You don't like it? Go somewhere else! To another universe! Where the rules are simpier, philosophically more pleasing, more psychologically easy."  This seems to me to be exactly what you are trying to do.  

 

Best of luck with that. 

Edited May 16, 2019 by exchemist

[exchemist]

Always using the "downplaying card" as a last resort, exchemist. I've made a living working with state of the art electro-optical and electromagnetic systems

until 2011, at large national and international telecomm systems. And I kept informed on these fields since then.

 

The duality wave-particle is essential at long range fiber optic systems that encircle the globe at Terabits/sec, with repeaters that are separated almost

1,000 Km, Light travel as a wave, is codified in spectral slots (DWDM) and amplified as if it behave as photons.

 

Do you know something about light amplification using EDFA and nextgen amplifiers?

 

And, by the way, I only see you criticizing other's people posts.

 

When are you going to post an original thought of yours, if you have one? :sorry:

If you look back in the history of topics on the forum, to the days when there were more people who were not cranks posting, you will see what I am like when there is genuine science to discuss. At the moment, though, a large proportion of the active posters here are cranks. Such original thoughts as I have are mostly issues I have realised I do not understand, as I do not as a rule go in for putting forward half-arsed notions that claim well-established science is wrong. There is no point in asking my questions here, obviously, though I do so on some of the other forums I belong to.  

Edited May 17, 2019 by exchemist

[Dubbelosix]

I would like to clear something up, at some point I marked that it was possibly Lorentz that discovered the energy mass equivalence, but my memory appears to be not working as well as I thought, it was in fact Poincare.

[exchemist]

Thanks for your sincere explanation. I believe you and it is obvious that you somehow mutated from a good thinker to a troll.

 

I'm good with my intuition, by which I profiled you since day 1.

 

What I wonder is why do you troll here and are a serious poster at other forums, but it's OK with me. It's part of your character

and your private jokes.

 

I propose you that you rise your trolling level by using emoticons according to the depth of your hidden sarcasm or fine irony,

so the lesser aware can decide if they reply to you or not.

 

This would be a decent thing to do, instead of using this forum as a social laboratory for your intelligence, while dragging

naive but intelligent people behind your trail. Maybe you can enlight people over here as you do at more "serious" forums,

and contributing in that way to make this place "better" for you and for the rest of us.

 

I'll show you just a little sampling of your character: It's impossible for you, when there is a thread, not to have the last word.

In you are engaged in any thread, it's just something that you can't do. Your nick has to be the last one at the listing of threads

at which you have posted some distorted opinion. It's compulsive on your nature.

 

I believe, and always did, that everyone deserves respect as a person. I also believe that if someone, who believe himself being

intelligent in some degree, reply to other person who's posting something which is genuine but wrong (for you), this person deserve

either a decent reply. If you can't do it, because the post violates your beliefs, then the most decent attitude is TO BE SILENT and

not playing with that other person for your little joy.

 

I invite you to reply this assertion of mine, well connected with my OP here.

 

IF there is true and valid that Planck's formulae (the final one and derivatives like Stefan-Boltzmann's)

can be applied to the almost initial Universe, then it's valid only for the surface of the Hubble's Sphere.

 

Otherwise, if the CBR measured today belongs to the edge of the OBSERVABLE universe, then it would

imply that the speed of light in such universe is 3.77  times the known value of c₀.

 

This is because the acceptable age of the universe is 13.77 Byears, while the "accepted" radius of the

"observable" universe is 46.5 Bly, so the CMB reached satellite's instrument after travelling at 3.77 c₀.

 

But, being the radius of the VISIBLE universe (Hubble's radius) 13.5 Bly and the CMB originated as a

left over of the Big Bang, 0.27 By AFTER this event, then the real c₀ involved is 13.5 Bly/13.5 Byears,

what results in the known universal c₀.

 

So, the question is: did the CMB background source is located today at the edge of the Hubble's Sphere

or at the edge of the OBSERVABLE universe?

 

In adition to a selection of the second choice: If true, then can we observe today stellar objects at (say)

19 Byl far away or not?

 

I hope that these questions may fit within your range of selective choice of well-established science.

 

Please, enlight me before shinning of wisdown elsewhere.

OK. Your question assumes that there is a "source", somewhere in the universe, for the CMBR.

 

There isn't.

 

The CMBR pervades the whole of the universe. 

 

That is why it is called "background" radiation. 

 

I have already explained earlier that it was left behind, rattling round the universe, when the universe first became transparent to radiation and ceased to behave like a black body. 

 

I find it extraordinary that you still cannot understand this.