Carried along by the Hubble flow.

[Naty1]

Question...As a matter of interest, and something that does not change any of the conclusions above,

I recently posted an article from Tamara M. Davis [of Lineweaver and Davis]
here:

https://www.physicsforums.com/showthread.php?t=613208

Is the Universe leaking Energy?
http://www.physics.uq.edu.au/downloa...iAm_Energy.pdf

and she said the following [approximately]:

Photons traveling in an expanding universe appear to lose energy via cosmological redshift. What about matter: You find that the de Broglie wavelength of particles increases by exactly the same proportion as a photon’s wavelength does! Thus light and matter seem to behave in exactly the same way when it comes to 'energy loss'.

What had not occurred to me when reading the article, and that as Marcus alreadly posted in this discussion

...expansion causes things to lose momentum relative to the CMB...

well, for light [like CMBR] it means a change in color, not speed...and eventually it redshifts so much it gets really really weak and eventually we won't be able to detect it;
but what about for a distant particle...seems like all the 'momentum' it has to give up is velocity...how does it know when to stop slowing down...or does it fall behind its distant local expansion...like it is losing speed...

 

[marcus]

Question...As a matter of interest, and something that does not change any of the conclusions above,

I recently posted an article from Tamara M. Davis [of Lineweaver and Davis]
here:
https://www.physicsforums.com/showthread.php?t=613208
Is the Universe leaking Energy?
http://www.physics.uq.edu.au/downloa...iAm_Energy.pdf
and she said the following [approximately]:

What had not occurred to me when reading the article, and that as Marcus alreadly posted in this discussion

"...expansion causes things to lose momentum relative to the CMB..."
...
well, for light [like CMBR] it means a change in color, not speed...and eventually it redshifts so much it gets really really weak and eventually we won't be able to detect it;
but what about for a distant particle...seems like all the 'momentum' it has to give up is velocity...how does it know when to stop slowing down...or does it fall behind its distant local expansion...like it is losing speed...

This is another really interesting question! Thanks! I guess it's wellknown that matter that is MOVING RELATIVE TO CMB rest will lose speed relative to CMB. Steven Weinberg has a Cosmology textbook and he derives this. I saw a paper on arxiv that purports to give a simpler derivation of that fact, might be able to find the link. Author had a name like Song He.

This does not involve distance expansion rates. If I'm at CMB rest here and a distant particle is at rest over there the distance between us continues to increase according to Hubble law. There is no "drag".

...expansion causes things to lose momentum relative to the CMB...

If you are already AT REST relative to CMB, which means you are participating exactly in the Hubble law expansion pattern, then you have no momentum to lose.

The "drag" if you want to (inaccurately) picture it that way, only operates to reduce local individual motion and bring you closer to being at rest relative to the ancient light or as one used to say the Hubble flow.

Distance expansion is not like ordinary familiar motion in the sense that nobody gets anywhere by it, everybody just gets farther apart. And the ancient light is spread out and cooled by the same process.

It is really good that this slowing down of local motion happens because it affects DARK MATTER PARTICLES TOO and serves to help them coalesce into wisps and blobs that then help (less abundant) ordinary matter condense into structure (like clusters of galaxies and individual galaxies).

The condensation of DM has formed the framework or armature for largescale ordinary matter structure to form, like barnacles and seaweed gathering on old sunken piers, wrecks, re-bar, junk. And DM has no way to dump energy so the only thing that can slow it bleed off excess kinetic energy and let it condense is this expansion slowing that we're talking about. It can't RADIATE the excess kinetic energy.

So in a sense the Earth and sun are here and life is here BECAUSE of this expansion slowing effect that allowed the DM to form structure (so that much less abundant ordinary matter could gather.)

Google "Smoot TED" to see computer animations of the gathering of DM into structures, ordinary matter is so relatively scarce that it doesn't even show up in the picture until later.
DM condensation is a vital precondition, and expansion promotes it, by helping slow DM down.

 

[Naty1]

...I guess it's well known that matter that is MOVING RELATIVE TO CMB rest will lose speed relative to CMB. Steven Weinberg has a Cosmology textbook and he derives this... expansion causes things to lose momentum relative to the CMB... This does not involve distance expansion rates.

You mean neither is related to distance expansion?? That piece makes sense because distance expansion is inapplicable to a galaxy or solar system distance...

Not that I am any judge, and I sure don't doubt Weinberg is correct, but that seems NUTS! [The lose speed part]

If it is not 'distance expansion related' why is it related to Hubble law:

If you are already AT REST relative to CMB, which means you are participating exactly in the Hubble law expansion pattern, then you have no momentum to lose.

Ah HA, maybe not so nuts??: ...Do you think it is related to the fact that if I shine some light on something I can get it to change momentum? Or is this the 'drag' idea??

edit: If the above idea applies it seems this loss of momentum effect should decrease over time as the CMB weakens [redshifts]??

 

[marcus]

Hi Naty,
I found that paper.
http://arxiv.org/abs/0808.1552
Note on the thermal history of decoupled massive particles
Hongbao Zhang
(Submitted on 11 Aug 2008)
This note provides an alternative approach to the momentum decay and thermal evolution of decoupled massive particles. Although the ingredients in our results have been addressed in [Weinberg, Cosmology], the strategies employed here are simpler, and the results obtained here are more general.
4 pages, published in Classical and Quantum Gravity (2008)

It is a purely geometrical effect (just like cosmological redshift of photons is) and shouldn't really be thought of as a physical "drag".
There is a universal rest concept that people can call by different words: being at rest with respect to the expansion process with respect to the ancient matter in its nearly uniform early universe state---or being at rest relative to the ancient light from that matter which we use as a kind of lighthouse beacon or marker of that stillness.

So if you have some massive particle with a certain momentum p measured relative to universal rest and if it is flying free not interacting much if any with other stuff then its momentum will tend to taper off gradually to zero and it will decline as 1/a where a(t) is the scale factor.

So that is what you see in Hongbao Zhang's paper, the equation p ~ 1/a
or "p goes as one over the scale factor"
This is Hongbao Zhang's equation (2.7)

If the universe expands by a factor of 3, say, while the neutrino is flying then the neutrino's momentum has to go down by a factor of 3, and since it is a massive particle that essentially means that its SPEED has to go down by a factor of 3.

beautifully enough that is exactly what happens to a photon of light except that a photon has to keep going the same speed, so its momentum is reduced by having its wavelength extend by a factor of 3. Light does have momentum, a flash of light gives a mirror or a solar sail a kick, and a photon's momentum is inverse proportional to wavelength. So the same effect on momentum whether it is a massive particle or a photon.
It is just REDSHIFT either way.

In math there tend to be different equivalent ways to say the same thing (Yogi Berra would have found a better way to say this) and there aren't MORE OR LESS CORRECT there are MORE OR LESS CONVENIENT ways. And a nimble mathematician could find a way to describe this using an infinite number of very small Lorentz transformations all along the particle's path. Two reputable academics, Bunn and Hogg, have analyzed redshift that way WITHOUT using the universal rest concept---as an infinite number of infinitesimal Doppler shifts all along the photons path. This is equally correct but I think it sucks because it is conceptually complex. More convenient to simply measure momentum relative to universal rest (or "CMB rest") and just say that it falls off like 1/a.

Good questions

 

[marcus]

Convenient language is so important! I've been keeping track of Hongbao Zhang (and a frequent co-author named Song He) for several years---Perimeter Institute connections, Potsdam Max Planck Institute connections, and they somehow stand out. I like how Zhang uses the phrase measured by isotropic observers here right around equation (2.7)

==quote Zhang==
...the magnitude of momentum of massive particle measured by the isotropic observers. Whence we know that for a freely traveling massive particle in an expanding FLRW universe, it is its momentum rather than energy that goes like¹
p ~ 1/a (2.7)
It is noteworthy that this result is also obtained in [Weinberg], where, however, the method employed seems somewhat complicated, and some approximations are also made.

3. Thermal Evolution
Let us assume that during the evolution of our universe, there exists a last scattering surface at the time t_L when some kinds of massive particles such as neutrinos and antineutrinos suddenly went from being in thermal equilibrium to a decoupled expansion.

Footnote 1: Of course, the momentum of a massless particle shares the same behavior...
==endquote==
Isotropic observers would be ones for whom the CMB looks the same temperature in all directions (no Doppler hotspot), and the recession rate pattern of galaxies looks the same in all directions. IOW the isotropic observers are the ones who are not moving relative to background. They are at universal rest.

So it is momentum measured by isotropic observers which very gradually tapers off as the spatial geometry expands. That is a good way to put it, that is not so bewildering I think as saying momentum as measured by observers "at rest with respect to the Hubble flow". The "Hubble flow" is not motion in the ordinary sense (nobody gets anywhere) so calling it a "flow" is a linguistic disaster which makes listeners imagine motion. The "Hubble flow" means everybody stays at their own latitude and longitude on the balloon, everybody stays PUT. It is an oldfashioned expression used mainly before 1970. after that people knew about the CMB so they could say as measured by observers "at CMB rest".

But I think saying "as measured by isotropic observers" may even beat that, convenience-wise.

 

[Naty1]

Marcus:

So if you have some massive particle with a certain momentum p measured relative to universal rest and if it is flying free not interacting much if any with other stuff then its momentum will tend to taper off gradually to zero and it will decline as 1/a where a(t) is the scale factor...beautifully enough that is exactly what happens to a photon of light ..

yes, So that explains the Tamara Davis one liner :

...matter particles have the same proportional redshift as photons...

or something very close...

very nice!

Marcus:

...So it is momentum measured by isotropic observers which very gradually tapers off as the spatial geometry expands. ...as 1/a...

I will try and read, er, that is, 'understand', the Zhang paper but before I do, can you confirm that this result is applicable for all cosmological time...in other words, in earlier matter dominated expansion as well as our current energy dominated expansion...a[t] varies over time so the redshift pattern of momentum decline [redshift] also varies over time, right...that also provides a nice insight about the cumulative effects of expansion on redshift that I did not really appreciate previously.

edit: sure. it is ok for varying cosmological time periods and the Hubble parameter is related since H[t] = a'[t]/a[t]...

[This almost makes sense!.]

PS: Wasn't that you who previously mentioned 'isotropic observers' in another thread??...no "hotspots'...anyway, somebody did and that perspective made it into my personal notes! [ If you try and deny it I will be forced to look it up in my notes and see if I have an attribution!]

 

[marcus]

I wouldn't urge anyone to read Hongbao Zhang's paper, too technical. But on page 2 it has equation (2.7) which says that, as measured by isotropic observers
p ~ 1/a

After that, he goes into how the distribution of energies remains THERMAL which is kind of interesting. But not essential.
You know that lop-sided bell curve mound that Planck discovered describes the distribution of energies of photons in thermal equilibrium (say in a hot box).
It is a kind of beautiful fact that the CMB still has that thermal shape after all these years.
The shape was established when the photons actually were in equilibrium with hot gas. But they have kept that same distribution for 13.7 billion years during which they have NOT been in contact and have not been thermalized and made to be in equilibrium with anything. Just flying free.

Well, he goes thru some math to show that neutrinos, even though they lose energy and momentum differently, would ALSO retain a thermal distribution. If we could ever see the cosmic neutrino background, we would find that it too (like the CMB) had a nice lopsided bellcurve distribution.

But that, tho nice to know, is not essential. I would just read (2.7) and glance at some verbal context, and be lazy about the rest. Life is short.

In answer to your questions: I confirm as well as I can (as non-expert retired guy who loves cosmology) that equation (2.7) would work for all the time that cosmology normally covers.

(Up to near the start of expansion where the classical GR geometry fails and you need a quantum cosmology extension.)

And I don't recall having used the phrase isotropic observers before, but I could have and forgotten. You might find the phrase in your notes if you took the time to look. It's great you keep notes.

 

[Naty1]

I wouldn't urge anyone to read Hongbao Zhang's paper, too technical.

I skimmed the paper...if you like advanced math, go for it; otherwise, there are few additional insights described beyond what Marcus posted...