How is the red-shift of CMB obtained?

[Doctor Strange]

The value for the red-shift of the CMB is 1090 according to the latest Plank study. How do they arrive at this number? You can look at how hydrogen lines of supernovae light are shifted, but how do you tell how far light is shifted when looking at the light from a primordial soup? Is there some absorption lines or do we know at what temperature Hydrogen becomes stable (and thus neutral and thus transparent), calculate the age of the universe and then use the age to calculate the red-shift?

 

[Orodruin]

You can compute the temperature of the universe at CMB release. The rest is a matter of dividing that number by the currently observed temperature.

 

[Doctor Strange]

You can compute the temperature of the universe at CMB release. The rest is a matter of dividing that number by the currently observed temperature.

Would you know what temperature (I'm guessing the temperature at which hydrogen becomes stable) was used to arrive at z=1090.43?
Also, I'm trying to perform the calculation myself and working backwards. I'm guessing you would use the Ideal Gas Law, but that only works if you either know the pressure or the volume. Would you mind connecting the dots for me.

 

[Bandersnatch]

Take the temperature at which hydrogen plasma recombines to form atoms(3000 K). The released radiation is that of a black body at that temp.
Use Wien's displacement law to calculate the shift to the observed 2.7K.

 

[Doctor Strange]

Take the temperature at which hydrogen plasma recombines to form atoms(3000 K). The released radiation is that of a black body at that temp.
Use Wien's displacement law to calculate the shift to the observed 2.7K.

Thanks, I think I'm getting close. Wien's Displacement law is:$$\lambda_{MAX}=\frac {b}{T}$$The red-shift due to metric expansion is expressed as:$$z=\frac {\lambda_{OBS} - \lambda_{REC}}{\lambda_{REC}}$$If we substitute Wien's Law in we get:$$z=\frac {\frac {b}{T_{OBS}} - \frac {b}{T_{REC}}}{\frac {b}{T_{REC}}}$$$$z =\frac {T_{REC}}{T_{OBS}} - 1$$Where $T_{REC}$ is the temperature of recombination and $T_{OBS}$ is the current (observed) temperature.
Is this the general idea?

 

[Orodruin]

Is this the general idea?

Yes, this is more or less the general idea. Also note that $\lambda$ is proportional to the scale factor $a(t)$ at the respective times. The 1 in the expression for $z$ is essentially negligible in comparison to the large quotient between the temperatures.

 

[Igael]

It doesn't mean that these values are absolutely relevant, which is for popular sciences articles. It is only what it can be said today with a medium confidence according to some models checked by Wmap and Planck ( best fitting model's model ). Most of them incorporate dark matter and energy as overlays. When dark matter will be identified and/or dark energy understood, the models will evolve and surprises may arise, in particular around what was theorized between the singularity and the end of the inflation.

 

[Doctor Strange]

It doesn't mean that these values are absolutely relevant, which is for popular sciences articles. It is only what it can be said today with a medium confidence according to some models checked by Wmap and Planck ( best fitting model's model ). Most of them incorporate dark matter and energy as overlays. When dark matter will be identified and/or dark energy understood, the models will evolve and surprises may arise, in particular around what was theorized between the singularity and the end of the inflation.

A cosmologist who places the Earth at the center of the solar system will be absolutely convinced that there must be some mysterious force pulling Mars backwards as it travels through the sky. They will spend their entire career searching for this force and writing endless papers about the attributes of this force. There's not a single cosmologist alive today who's capable of doing what Copernicus did: place the sun at the center of the solar system and forget about the fact that you need retrogrades to explain the motion of Mars. The failure of LUX and LHC to find Dark Matter is a clear indication that we're dealing with the exact same issue.

 

[Igael]

A cosmologist who places the Earth at the center of the solar system will be absolutely convinced that there must be some mysterious force pulling Mars backwards as it travels through the sky. They will spend their entire career searching for this force and writing endless papers about the attributes of this force. There's not a single cosmologist alive today who's capable of doing what Copernicus did: place the sun at the center of the solar system and forget about the fact that you need epicycles to explain the motion of Mars. The failure of LUX and LHC to find Dark Matter is a clear indication that we're dealing with the exact same issue.

I know that the Planck collaboration had considered a very very large options panel. The best fitting model theory is a good guide to further researches, the only possible error being to take the intermediate results as absolute truths

 

[Chronos]

The only thing constrained by failure in direct detections of dark matter experiments is the parameter space and properties of the particles for which the experiment was designed to detect. The evidence for dark matter remains far more robust than any detection failure can refute. The problem with all direct detection experiments to date is they are forced for things like electroweak interactions because we can, in principle, detect those things. Its like the man searching for his keys under the parking lot light - Attendant 'So, where you think you lost them, buddy?' Man, 'Over by my car', he replies pointing toward the far side of the parking lot. Attendant 'So why you looking over here?' Man 'It's dark over there, I'll never see them.'

 

[Doctor Strange]

The only thing constrained by failure in direct detections of dark matter experiments is the parameter space and properties of the particles for which the experiment was designed to detect. The evidence for dark matter remains far more robust than any detection failure can refute. The problem with all direct detection experiments to date is they are forced for things like electroweak interactions because we can, in principle, detect those things. Its like the man searching for his keys under the parking lot light - Attendant 'So, where you think you lost them, buddy?' Man, 'Over by my car', he replies pointing toward the far side of the parking lot. Attendant 'So why you looking over here?' Man 'It's dark over there, I'll never see them.'

In every other field, we would have taken the resounding failure of LUX to find a single collision as a disproof of the "Dark Matter" theory. But because cosmology has decided to leave the scientific method behind, the faithful move the red line again. "Dark Matter" is no longer disprovable and, therefore, not a valid scientific theory. You might as well say that God is responsible for the velocity curve in galaxies. The next time an experiment fails to find it, you'll simply put another letter in front of your supersymmetry model and say, "we've got to look for it here now."

Like I said, someone who places the Earth at the center of the solar system will never be able to understand a model that doesn't include retrogrades. You think in a linear way, as all cosmologists do, so you're unable to critically examine the assumptions of your model. Dark Matter is to λCDM what retrogrades were to Geocentrism.

 

[Igael]

There are hundreds dark matter theories. It is a a broad concept where you can find disproof the applicability of the virial theorem, hidden ordinary matter, matter in other dimensions, super symmetric particles, etc. One of the solutions must explain the observed presumed failures.

 

[PeterDonis]

A cosmologist who places the Earth at the center of the solar system will be absolutely convinced that there must be some mysterious force pulling Mars backwards as it travels through the sky.

Not if he's applying GR correctly, which cosmologists do as far as I can see. Mars is following a geodesic of the spacetime geometry it's in; that's true whether you choose coordinates centered on the Sun or the Earth or Alpha Centauri or anywhere else. Since it's following a geodesic orbit, it is not subject to any force and there's no point in looking for one; that's also true regardless of what coordinates you choose.

Perhaps you, placed in the position of someone forced to look at the solar system in geocentric coordinates, would be unable to appreciate these facts. But that does not give you any license to accuse cosmologists of such a thing.

 

[Doctor Strange]

Perhaps you, placed in the position of someone forced to look at the solar system in geocentric coordinates, would be unable to appreciate these facts. But that does not give you any license to accuse cosmologists of such a thing.

Excellent point. However, I stand by my statement that (nearly) all cosmologists are unable to critically examine the assumptions of their models. That's the reason your model misses the observed universe by 95%. Where I come from, we call this a dismal failure, not a success. "Hey boss, our budget is off by 95%, but if we use this Monopoly Money, then we're nailed it!"

 

[rootone]

The name 'dark matter' is a placeholder name for something which ought to exist according to our present best models.
Something unseen accounts for galaxies hanging together by providing additional gravity, but otherwise is not visible.
WIMPS (super symmetry particles) has been the favourite horse in the race for a while, but nobody found them yet.
I still think MACHO objects (baryonic stuff we can't detect, or even remnant primordial black holes ) can't be discounted as a possibility.

 

[Doctor Strange]

The name 'dark matter' is a placeholder name for something which ought to exist according to our present best models.
Something unseen accounts for galaxies hanging together by providing additional gravity, but otherwise is not visible.
WIMPS (super symmetry particles) has been the favourite horse in the race for a while, but nobody found them yet.
I still think MACHO objects (baryonic stuff we can't detect, or even remnant primordial black holes ) can't be discounted as a possibility.

What I'm saying is that you are convinced that there must be a placeholder because your (the cosmologists) thinking is linear. If your brain is only able to handle $5 x = 25$ when there is no scientific foundation for $x$, you'll still search in vain for $x$ because you can't go back and revisit your initial assumptions. You'll create entire industries devoted to describing the attributes of $x$. When Cosmologists are able to think non-linearly, they'll be able to understand that sometimes $5^2 = 25$. There is no $x$.

 

[rootone]

I am only convinced that something is going on that looks gravity, but we don't know what it is.
I have no doubt that the mathematical square function has useful applications
though I doubt that it offers an explanation for the puzzle of dark matter.

 

[Doctor Strange]

I am only convinced that something is going on that looks gravity, but we don't know what it is.
I have no doubt that the mathematical square function has applications, but I doubt that it offers an explanation for the puzzle of dark dark matter.

You're convinced that it looks like gravity so you'll never be able to critically examine the assumptions that got you there. You're convinced that GR is the foundation for a cosmology, so you'll never be able to wrap your head around a quadratic solution.

 

[rootone]

I'm open minded, if you want to provide a link for the quadratic solution you talk of.
I'm off here for now though, probably will login tomorrow at some point.

 

[PeterDonis]

a quadratic solution

Please give an acceptable reference for such a solution (by PM, as this thread is closed per my note at the end of this post). If you don't think the current models are correct, you're entitled to your opinion, but discussion of it is off topic here unless you can provide acceptable references to an alternative theory that makes testable predictions different from the current model.

And with that, this thread is closed since the actual question in the OP has been answered.