Is the supply of the observable CMB radiation limited?

[PeterDonis]

I cited the paper for its mathematical demonstration

The issue is not that mathematical demonstration. The issue is your erroneous claims based on it.

You are claiming that the presence of an event horizon is inconsistent with the CMB being black body radiation. You have provided no reference that supports that claim.

You are also claiming that "expansion of space" is somehow necessary for a redshifted black body to still be a black body. You have provided no reference that supports that claim either. Your reference says that "expansion of space" is sufficient. It does not show that it is necessary.

 

[JimJCW]

No, it is true.

Do you have any reference that actually supports your claim that redshift alone preserves the blackbody distribution?

 

[PeterDonis]

Do you have any reference that actually supports your claim

Sure; see here:

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Doppler_effect_on_intensity

The derivation is elementary and can probably be found in many textbooks.

that redshift alone preserves the blackbody distribution?

It's not "redshift alone". It's "redshift in any spacetime geometry". Or, more generally, "redshift due to any state of motion in any spacetime geometry".

For example, the "expansion of space" derivations you quote are for comoving observers in FRW spacetime. But we on Earth are not comoving observers; we see a dipole anisotropy in the CMB, whose magnitude and direction changes over the course of a year as the Earth orbits the Sun. In other words, relative to a comoving observer in Earth's vicinity, we see a redshifted CMB in some parts of our sky, and a blueshifted CMB in other parts. And yet we observe the CMB to be a black body in all parts of the sky (just with its temperature redshifted or blueshifted from the nominal 2.7 K that is the "corrected" value after the dipole anisotropy is removed, i.e., the value that would be observed by a comoving observer in Earth's vicinity).

 

[JimJCW]

Sure; see here:

https://en.wikipedia.org/wiki/Relativistic_Doppler_effect#Doppler_effect_on_intensity

The derivation is elementary and can probably be found in many textbooks.It's not "redshift alone". It's "redshift in any spacetime geometry". Or, more generally, "redshift due to any state of motion in any spacetime geometry".

For example, the "expansion of space" derivations you quote are for comoving observers in FRW spacetime. But we on Earth are not comoving observers; we see a dipole anisotropy in the CMB, whose magnitude and direction changes over the course of a year as the Earth orbits the Sun. In other words, relative to a comoving observer in Earth's vicinity, we see a redshifted CMB in some parts of our sky, and a blueshifted CMB in other parts. And yet we observe the CMB to be a black body in all parts of the sky (just with its temperature redshifted or blueshifted from the nominal 2.7 K that is the "corrected" value after the dipole anisotropy is removed, i.e., the value that would be observed by a comoving observer in Earth's vicinity).

In Wright’s Errors in Tired Light Cosmology, he demonstrates that redshift alone in tired-light model without space expansion cannot retain the blackbody distribution.

 

[PeterDonis]

In Wright’s Errors in Tired Light Cosmology, he demonstrates that redshift alone in tired-light model without space expansion cannot retain the blackbody distribution.

What he demonstrates is that the tired light model's claimed mechanism for the redshift cannot retain the blackbody distribution. But that mechanism is not "redshift alone without space expansion". It's "redshift that is not due to spacetime geometry and relative motion". What he is actually showing is that only redshift due to spacetime geometry and relative motion will preserve a blackbody radiation spectrum. But you can have that in flat spacetime with an ordinary Doppler shift (as the reference I already gave you shows); there is no requirement for "space expansion" to produce the effect (though of course it is still present in FRW spacetime with "space expansion", including spacetimes with a positive cosmological constant and an event horizon, as in the $\Lambda C D M$ model).

 

[Dale]

This paper does not appear to me to represent the current mainstream understanding of the CMB

Hindawi is a low quality publisher. In the past it was included on Beal’s list of predatory publishers, but it may have improved some of its most unethical practices since that time. In any case, I would not consider a claim made only in a Hindawi publication to be credible. Also, this specific journal is not even indexed by the Clarivate master journal list.

 

[Dale]

No, it is true.

Are you sure about that. I vaguely remember doing such a calculation once and finding that was not the case. But it is a vague memory so I am not at all confident about it.

 

[PeterDonis]

Are you sure about that.

The basic idea of the calculation for the Doppler shift preserving a blackbody spectrum is in the Wikipedia article I referenced. As I noted in response to the OP, it's an elementary calculation and probably appears in many textbooks.

 

[Ibix]

Are you sure about that.

There was a recent discussion about gravitational redshift for a star where I think we concluded that the power detected scaled as the redshift factor squared, if that's what you're thinking of?

 

[Dale]

it's an elementary calculation

Hmm, I must have done it wrong then. Oh well.

 

[George Jones]

Are you sure about that. I vaguely remember doing such a calculation once and finding that was not the case. But it is a vague memory so I am not at all confident about it.

The basic idea of the calculation for the Doppler shift preserving a blackbody spectrum is in the Wikipedia article I referenced. As I noted in response to the OP, it's an elementary calculation and probably appears in many textbooks.

Here is Weinberg's cosmological argument (from his 2008 book "Cosmology"):

 

[JimJCW]

Here is Weinberg's cosmological argument (from his 2008 book "Cosmology"):

I think Weinberg’s cosmological argument is the same as that given by Fahr and Sokaliwska, Remaining Problems in Interpretation of the Cosmic Microwave Background:

Starting from a blackbody CMB, (the cosmological redshift) + (change of CMB photon density due to space expansion) can maintain the blackbody nature of the CMB.​

 

[PeterDonis]

Here is Weinberg's cosmological argument (from his 2008 book "Cosmology"):

Note that, while this argument is framed as a specific argument for the claim that the blackbody temperature of the CMB goes as the inverse of the scale factor, because the redshift factor $1 + z$ goes as the inverse of the scale factor, it actually provides a fully general argument that a blackbody source with redshift factor $1 + z$, from whatever source (ultimately it's just the inner product of the 4-momentum of the light and the 4-velocity of the receiver) still appears as a blackbody, with temperature redshifted by the redshift factor. The latter claim is the one I have been referring to.

 

[PeterDonis]

I think Weinberg’s cosmological argument is the same as that given by Fahr and Sokaliwska

It is framed as an argument specific to FRW spacetime, but, as I noted in post #48 just now, it actually provides a fully general argument that a redshifted blackbody still appears as a blackbody. The crucial step in the argument is in the paragraph between equations 2.1.2 and 2.1.3; this step applies to any redshift factor due to spacetime geometry and relative motion.

 

[JimJCW]

It is framed as an argument specific to FRW spacetime, but, as I noted in post #48 just now, it actually provides a fully general argument that a redshifted blackbody still appears as a blackbody. The crucial step in the argument is in the paragraph between equations 2.1.2 and 2.1.3; this step applies to any redshift factor due to spacetime geometry and relative motion.

In an infinite, non-expanding universe, if there was a starting CMB in blackbody and the photons were redshifted later by, for example, a tired-light mechanism, the blackbody nature of the CMB would not be able to maintain because there was no dilution of the photon density.

 

[PeterDonis]

In an infinite, non-expanding universe, if there was a starting CMB in blackbody and the photons were redshifted later by, for example, a tired-light mechanism, the blackbody nature of the CMB would not be able to maintain because there was no dilution of the photon density.

A "tired light" mechanism would not maintain the blackbody nature of the CMB even in an expanding universe. You have already given references that show that. The reason has nothing to do with "no dilution of the photon density"; it has to do with the fact that a "tired light" mechanism does not produce a redshift due to spacetime geometry and relative motion; it produces it by an interaction with intervening matter. That is why, every time I have said that a redshifted blackbody is still a blackbody, I have qualified it by saying that the redshift must be due to spacetime geometry and relative motion.

Your original question has been answered, repeatedly, and how redshifting of a blackbody works have been discussed in some detail. Enough is enough. Thread closed.