CMB creation, distance measurement question

[artis]

How do we know it;s redshift for certain? because unlike with stars the CMB doesn't have spectral lines nor other "similar" objects to compare to as it is everywhere and the same.

From what I understand first came the theory and model of the Big bang, then Hubble saw that distant galaxies are moving away from us in every direction, then in 1965 they first experimentally verified the CMB by accident and from there we got it's current temperature,
then we plotted this temperature against the temperature at which neutral plasma can form Hydrogen atoms , aka the point at which the energy falls low enough for recombination to occur.
I read that even though the first energy low enough for hydrogen formation is about 13.6 eV that at this energy still only a fraction of the plasma formed hydrogen so the energy had to drop still lower where the majority of the matter became neutral atoms at which point the CMB photons could fully decouple.

So would I be correct in stating that we cannot observe the CMB redshift experimentally(because experimentally we just see radiation at specific wavelength) but instead have deduced it from secondary sources like lab experiments with hydrogen and plasma from which we have calculated the energy levels of hydrogen electrons and the energy and corresponding temperature of the point where such plasma can form atoms.

If so far is so good then I have one more question,
so we come to the conclusion that the temperature at which decoupling of the CMB happens is 3000K and now in present day we see that the temperature is 2.7K,
Can we then estimate how long it took for the space to expand solely on this information , the decoupling temperature and the current temperature?

 

[PeroK]

So would I be correct in stating that we cannot observe the CMB redshift experimentally(because experimentally we just see radiation at specific wavelength) but instead have deduced it from secondary sources like lab experiments with hydrogen and plasma from which we have calculated the energy levels of hydrogen electrons and the energy and corresponding temperature of the point where such plasma can form atoms.

Yes, exactly. When you observe radiation you measure a single quantity (wavelength or frequency) and that is all you get. If you find a spectrum that looks like hydrogen but is shifted, then you may infer that the radiation was produced by hydrogen and has been shifted due to some relationship between you (the observer) and the source.

How do we know it;s redshift for certain? because unlike with stars the CMB doesn't have spectral lines nor other "similar" objects to compare to as it is everywhere and the same.

What we do have is the energy density distribution of the black-body spectrum. This has a characteristic shape and a peak energy density relating to the temperature. We also need a theory that explains the point at which the universe became transparent to light. Up to a certain time the temperature was too high to allow photons to travel indefinitely, then, as the universe cooled, there came a time when photons could travel unimpeded.

A critical part of the calculation, therefore, is to determine the temperature at which this "decoupling" happened. This is not a simple calculation.

If we put these two things together we have an estimate of how much the universe has expanded since decoupling: we get the temperature at decoupling by some calculation and by measuring the temperature of the CMDB today we get the expansion since that time.

If so far is so good then I have one more question,
so we come to the conclusion that the temperature at which decoupling of the CMB happens is 3000K and now in present day we see that the temperature is 2.7K,
Can we then estimate how long it took for the space to expand solely on this information , the decoupling temperature and the current temperature?

To estimate the time we need the Friedmann equation, which relates the expansion of the universe to the energy density. Solving the Friedmann equation gives the time for the expansion.

 

[PeterDonis]

unlike with stars the CMB doesn't have spectral lines

We actually can measure spectral lines in the CMB, just not with very high precision.

 

[artis]

If you find a spectrum that looks like hydrogen but is shifted, then you may infer that the radiation was produced by hydrogen and has been shifted

When you say like hydrogen but shifted , well radiation is radiation as you said it has wavelength and frequency so if you increase or decrease the frequency either above or below the characteristic spectra of an element I would assume you get close to the one for another element , so the deviation is small enough to be thought to be from the same element just doppler shifted?

CMDB

Oh and by the way what is this?
Ok but to rephrase a bit differently , if we did not have our "standard candles" and some other measures if all we had was the CMB map from our few satellite missions as we have , could by the CMB alone we could extrapolate back in time , apart from knowing at which energy it decoupled from the opaque plasma because that we know simply from Hydrogen experiments and knowing that ordinary matter is mostly Hydrogen.
But this decoupling energy alone doesn't give us the redshift data for us to know the time that has passed? I mean suppose the universe began as per big bang theory , then decoupling happened and then say the universe expanded as much as it has but all at once and suddenly and then stopped , as long as it expanded the current amount the redshift of CMB would still be z=1100 as of today ?

 

[artis]

@PeroK Ok I get the CMDB is CMB

 

[PeroK]

@PeroK Ok I get the CMDB is CMB

CMDB is Configuration Management Database. But, of course, in I meant CMB.

 

[PeroK]

When you say like hydrogen but shifted , well radiation is radiation as you said it has wavelength and frequency so if you increase or decrease the frequency either above or below the characteristic spectra of an element I would assume you get close to the one for another element , so the deviation is small enough to be thought to be from the same element just doppler shifted?

The hydrogen spectrum is a whole pattern of different characteristic wavelengths. You can look this up here for example:

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

I mean suppose the universe began as per big bang theory , then decoupling happened and then say the universe expanded as much as it has but all at once and suddenly and then stopped , as long as it expanded the current amount the redshift of CMB would still be z=1100 as of today ?

The Friedmann equation alone can be used to estimate the age of the universe. But, of course, it's good to have data from the evolution of the universe that corroborates the predictions of the equation. The Friedmann equation should be able to join all the dots, as it were.

And, indeed, it's that data that pointed to the dark energy factor that is required in the Friedmann equation to explain the recent acceleration in the expansion rate.

 

[Ibix]

The hydrogen spectrum is a whole pattern of different characteristic wavelengths. You can look this up here for example:

Just to expand on this, @artis, Doppler shift is a multiplication - the shifted frequency, $\nu'$, is related to the emitted frequency, $\nu$, by $\nu'=k\nu$, where $k$ is some frequency-independent number. In flat spacetime where Doppler only depends on relative velocity, $$k=\sqrt{\frac{c+v}{c-v}}$$In cosmology $k$ depends on distance, time, and extraordinary velocity (at least), but is still frequency-independent.

The spectrum of an element such as hydrogen is a sequence of spectral lines that is characteristic of the element. Meeasure the frequencies of hydrogen lines in the lab and you'll get some frequencies $\nu_1$, $\nu_2$, $\nu_3$, etc. Measure them in a redshifted source and you'll get $\nu'_1$, $\nu'_2$, $\nu'_3$, etc, which is different. But remember that $\nu'=k\nu$. That means that $\nu'_i/\nu'_1=k\nu_i/k\nu_1=\nu_i/\nu_1$ for any $i$ - so we can recognise the ratios of the frequencies of the lines even when they're Doppler shifted.