Carried along by the Hubble flow.

[yuiop]

Hi. If we fire a rocket into space at some significant fraction of the speed of light (say 0.1c) and then switch off the engines and let it cruise indefinitely, will it appear to accelerate away from us and in effect be carried along by the Hubble flow. Given a million or a billion years would it eventually appear to be receding at greater than the speed of light in the same way that distant galaxies appear to recede?

 

[Dickfore]

Unless it falls into some local gravitational well by some nearby planet or a star and falls into oblivion.

 

[yuiop]

Unless it falls into some local gravitational well by some nearby planet or a star and falls into oblivion.

So do you agree that in principle, an un-powered projectile with an initial local cruising velocity of 0.1c could (eventually) catch up with a distant galaxy receding at say 5c, if that galaxy is at rest with the local Hubble flow?

 

[Dickfore]

So do you agree that in principle, an un-powered projectile with an initial local cruising velocity of 0.1c could (eventually) catch up with a distant galaxy receding at say 5c, if that galaxy is at rest with the local Hubble flow?

no, if both the galaxy and the rocket are at rest with respect to the co-moving reference frame, they can never meet.

 

[yuiop]

no, if both the galaxy and the rocket are at rest with respect to the co-moving reference frame, they can never meet.

Yes, but the rocket is not at rest with the Hubble flow. Initially and locally it is moving at 0.1c relative to the local reference frame / CMBR / Hubble flow. Does it somehow get slowed down to come to rest with the Hubble flow?

P.S. Just thought. Isn't everything at rest with its own co-moving reference frame by definition?

 

[Dickfore]

Yes, but the rocket is not at rest with the Hubble flow. Initially and locally it is moving at 0.1c relative to the local reference frame / CMBR / Hubble flow. Does it somehow get slowed down to come to rest with the Hubble flow?

P.S. Just thought. Isn't everything at rest with its own co-moving reference frame by definition?

If the engines of the rocket get stopped, it starts moving along a geodesic, which, in FLRW metric, are the world lines of "Hubble flow".

 

[yuiop]

If the engines of the rocket get stopped, it starts moving along a geodesic, which, in FLRW metric, are the world lines of "Hubble flow".

Shouldn't then everything (un-powered) including the Moon going around the Earth, the Earth going around the Sun and the Sun going around the Galaxy all grind to a halt because they have peculiar velocities relative to the local Hubble flow?

 

[marcus]

It's an intriguing discussion! Thanks both.

Y: So do you agree that in principle, an un-powered projectile with an initial local cruising velocity of 0.1c could (eventually) catch up with a distant galaxy receding at say 5c, if that galaxy is at rest with the local Hubble flow?[/QUOTE]

D: no, if both the galaxy and the rocket are at rest with respect to the co-moving reference frame, they can never meet.[/QUOTE]

Y: Yes, but the rocket is not at rest with the Hubble flow. Initially and locally it is moving at 0.1c relative to the local reference frame / CMBR / Hubble flow. Does it somehow get slowed down to come to rest with the Hubble flow?
P.S. Just thought. Isn't everything at rest with its own co-moving reference frame by definition?[/QUOTE]

D: If the engines of the rocket get stopped, it starts moving along a geodesic, which, in FLRW metric, are the world lines of "Hubble flow".[/QUOTE]
===============

I'm not sure how I would analyze or reply. Dick's intuition is absolutely right (I'm sure though not an expert myself.)
But I'm not sure how I would respond on a detailed level. There is something called the "cosmic event horizon" which is around 16 billion LY. If today you send a flash of light at a galaxy that is 16 Gly from here it will never get there. And those guys are not even receding at 5c. They might be receding at 1.2c or something modest like that. I will check.

And if they sent us a message today, it would never reach us. That is what the CEH is about. It is in some ways like a BH event horizon.

 

[Dickfore]

P.S. Just thought. Isn't everything at rest with its own co-moving reference frame by definition?

In GR, a reference frame has a different meaning than in Special Relativity. Namely, it is a set of (curvilinear) coordinates which uniquely determine an event. The space-time interval is given by the quadratic form:
<br /> ds^2 = g_{\mu \nu} \, dx^{\mu} \, dx^{\nu}<br />
If we choose a system of coordinates in which:
<br /> g_{0i} = 0, \ (i = 1, 2, 3), \ g_{00} = 1<br />
then dx^{0} = d\tau the temproal coordinate coincides with the proper time, and the metric becomes:
<br /> ds^{2} = d\tau^{2} - \gamma_{i k} dx^{i} \, dx^{k}<br />
This kind of coordinate system is what I mean by a co-moving frame.

 

[Dickfore]

Shouldn't then everything (un-powered) including the Moon going around the Earth, the Earth going around the Sun and the Sun going around the Galaxy all grind to a halt because they have peculiar velocities relative to the local Hubble flow?

Well, the celestial bodies are actually "powered" by the extra gravitational pull from the local variations in the mean density of the Universe caused by nearby celestial bodies. That was my point about the rocket falling in a "local gravitational well".

The FLRW assumes a homogeneous and isotropic space. If you look at the night sky, you can easily confirm this is not the case. But, you have to bear in mind that the FLRW metric is "averaged out" over length scales of the order of magnitude of several intergalactic distances. Then, the "lumpiness" gets evened out.

 

[yuiop]

This kind of coordinate system is what I mean by a co-moving frame.

OK, I think I sort of get that and I assume it is something like the concept of a Momentarily Co-moving Inertial Reference Frame used to analyse accelerating systems in SR. The point is I don't get why inertial objects should come to rest with the local Hubble flow or CMBR if you prefer. Let's switch the scenario around. Let's say for the sake of argument that our galaxy is at rest with the local CMBR. Some distant freak Supernovae event hurls a huge star in our direction at 0.9c. Would it not be odd if we were saved because the speeding star came to a stop just short of colliding with us because it is un-powered and required to slow to the local Hubble flow/CMBR. What is that slows this projectile down, while other objects continue to orbit etc without any noticeable slow down?

 

[marcus]

YUIOP, you asked an interesting question, it uncovers intriguing considerations. Counterintuitive things you might not expect. Here is something you should realize: expansion causes things to lose momentum relative to the CMB.
So if you send a rocket off at .1c (relative to ancient light) it will eventually slow down (relative to ancient light).
Not because of gravity, although if there is gravity pulling it back that would slow it also, but because of expansion.

Expansion bleeds momentum from a flash of light as well. It keeps going the same speed but its wavelength lengthens, which means its momentum is drained also. Just like happened to the rocket.

However this is a slow effect. Don't worry about it, neglect it. But do realize it is there.
=====================

Another thing. the CEH is not the same as the Hubble distance. The present Hubble distance is something like 13.8 Gly.
The CEH is something like 16 Gly.
Try dividing 13.8 by sqrt(0.73) and see what it comes to. We are working with standard model LCDM as usual with "dark energy fraction" 0.73.
=======================

Oooops! I see you guys are still busy conversing. I had better be quiet and come back later so as not to spam up the thread with extra posts.

 

[yuiop]

But I'm not sure how I would respond on a detailed level. There is something called the "cosmic event horizon" which is around 15 or 16 billion LY. If today you send a flash of light at a galaxy that is 16 Gly from here it will never get there. And those guys are not even receding at 5c. They might be receding at 1.4c or something modest like that. I will check.

OK, to eliminate the CEH issue from the analysis, I will settle for an un-powered projectile with a local peculiar velocity of 0.1c catching up with a distant galaxy receding at something more modest like 0.9c (but locally at rest with the Hubble flow/CMBR). Is that possible?

By the way, thanks Marcus (and Dickefore) for your detailed contributions, despite some of them being a bit too advanced for me. I am trying to establish if there is any drag effect (positive or negative) from the Hubble flow and expansion. So far the answer seems to be negative. Perhaps one way to get at the crux of the problem is put the question like this. If we launch an unpowered projectile at 0.1c and wait a long time, will it ever appear to be exceeding 0.1c as it recedes from us. (Please ignore any local gravity wells and assume the projectile is aimed at largely empty space).

P.s. Will the projectile even catch up with a not too far away Hubble flow object that appears to be receding at 0.1c now?

 

[marcus]

Just to complete CEH talk with rough estimates. A galaxy with a redshift of 1.8 is at the CEH and it is currently receding with speed 1.17 or 1.2 (I'm using Jorrie's calculatorhttp://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc_2010.htm
with redshift z=1.8 plugged in.

Dickfore was showing you something, I just butted in. I'll wait a while and then see about your galaxy that is receding at 0.9c. "more modest" as you say [redshift in that case would be z=1.2, and distance would be 12.4 Gly at the present moment.]
I think Dick would say it still could not be reached by the rocket leaving today, and I would agree. Details later.

Over to you, D.

 

[marcus]

Well, D. left, let's see what we can do with this new galaxy.
First of all be sure you know how to use:
http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc_2010.htm

It is very easy. Just put in 1.2 into the box labeled "redshift of source" or something like that.

You should get that the current recession speed is 0.9c. Or 0.896, but we can round up to 0.9.

You should also be getting that the current distance is 12.4 billion LY (Gly). that is the socalled proper distance now, which you would get if you could stop expansion, freeze it, so you'd have time to measure with some conventional means like radar or string. Of course that takes a long time 24.8 billion years for the radar round trip, but you don't care because you have frozen expansion in its tracks so you have plenty of time to do the measuring. That is what proper distance at a given moment in time means.

I'll see if you are still around. Say uh-huh or something.

 

[yuiop]

Oooops! I see you guys are still busy conversing. I had better be quiet and come back later so as not to spam up the thread with extra posts.

Hey! Its a public forum. Your contributions, knowledge and insights are always very welcome .

I will give it a break now and slow things down and hopefully come up with more considered responses. Hopefully you guys will also have time to consider my revised questions in post #13.

 

[marcus]

I am trying to establish if there is any drag effect (positive or negative) from the Hubble flow and expansion. So far the answer seems to be negative.

Perhaps one way to get at the crux of the problem is put the question like this. If we launch an unpowered projectile at 0.1c and wait a long time, will it ever appear to be exceeding 0.1c as it recedes from us. (Please ignore any local gravity wells and assume the projectile is aimed at largely empty space).​

P.s. Will the projectile even catch up with a not too far away Hubble flow object that appears to be receding at 0.1c now?
​

I think the answer to the blue question is YES! That should not be too hard to figure out. (There IS a drag effect in the CMB rest frame but as I said earlier you should neglect it. Too small to worry about.)

71/3.26 = about 22. Hubble constant is about 22 km/sec per Mly (per million LY)

So after your projectile has traveled a million years it will be more than 100,000 LY away and it will be receding at 2.2 km/second PLUS its projectile speed of .1c. So it will be departing from us at a little bit MORE than 0.1c. 2.2 km/s is not a lot more but it is something.
==============

your red question is harder. i am used to thinking about light signals, whether or not they reach the target. Not projectiles going 0.1c. But my intuitive hunch is NO! it does not ever reach the galaxy. You say the galaxy is receding 0.1c so it has redshift about z=0.102 which we can round to 0.1.

for small redshifts like 0.1 the redshift is almost the same as the recession speed as a fraction of light.

So put that in the calculator and find out how far away the darned thing is!
http://www.einsteins-theory-of-relativity-4engineers.com/cosmocalc_2010.htm
It comes out around 1.4 billion LY. And the projectile is only going .1c

It is going to take roughly 14 billion years for the projectile to get where the galaxy USED TO BE when the projectile started. And by that time the galaxy will have moved on. It does NOT look good for the projectile.

Someone else more wide awake than I am may step in and set up an equation and solve it. I'm just doing the approximate scribble on scrap paper.

[EDIT: I really was quite sleepy last night when i wrote that. My hunch was WRONG. The projectile sent at .1c towards a target receding at rate .1c actually does make it! For the same reason (linearly scaled down) that we could today send a flash of light to a galaxy at Hubble distance, i.e. receding at rate c, and it would eventually get there. See the post #21 further down the page.]

 

[Chronos]

Expansion never exceeds the speed of light in any local reference frame, so it appears to me photons eventually escape all regions of the universe, but, at a price - redshift. This appears to explain how we can still observe galaxies that were receeding at superluminal velocities when they emitted the photons we now observe.

 

[marcus]

...photons eventually escape all regions of the universe, ...

"Regions of the universe" are typically described as co-moving volumes. Consider a ball with comoving radius 16 billion LY, centered at our galaxy. Or just to be sure make it 17 billion LY.
If today you flash your flashlight up into the sky those photons are never going to escape from that region.

If you have a link to something online that says they escape all regions I'd be happy to look at it.

the fact that photons are reaching us today from galaxies which were receding faster than light when they emitted the light is due to the fact that the Hubble constant has been shrinking rapidly (and the Hubble radius growing) for most of the past 13.7 billion years.

That is not going to be happening so much in the future according to LCDM. H constant will tend to stabilize at around 60 km/s per Mpc. So I think its pretty clear you will NOT be seeing much of that. If you consider light emitted from now on, eventually we will not see any that was emitted by galaxies receding >c.

Expansion never exceeds the speed of light in any local reference frame, so it appears to me photons eventually escape all regions of the universe, but, at a price - redshift. This appears to explain how we can still observe galaxies that were receeding at superluminal velocities when they emitted the photons we now observe.

 

[Dickfore]

Just as a note, what I called a co-moving frame should be called a synchronous frame.

 

[marcus]

Hi Dickfore!
just had an insight. The answer to the most recent question is YES the projectile CAN make it.
That was the case where the target is currently receding at .1c and the projectile is sent off towards it at .1c.

I'm glad you got back to this thread.

I had a mistaken hunch last night that the answer was no, for that case, so I want to correct my mistake. It just barely makes it.

What happens is for a long time it kind of hovers at the same proper distance from the target, just barely hanging on. Because its speed .1c just exactly cancels the rate the thing is getting farther way.

But the Hubble constant is still decreasing! According to standard LCDM it is now around 70.4 and destined to decline slowly and level out at (asymptotic) value of around 60 km/s per Mpc.

As soon as H gets appreciably below its present value the projectile will begin to slowly gain ground!

But for a long time it is just hanging in there, staying approximately 1.4 billion LY from the target. The target receding at .1c and it going towards at .1c, so no change. Then finally beause of declining H, the recession speed at that 1.4 billion LY distance will get slightly less, like .95c. And then the projectile will begin to creep towards it at 0.05c. From then on it is assured of getting there.

Just as a note, what I called a co-moving frame should be called a synchronous frame.

Interesting. if time permits I'll try to understand what you were saying earlier with that change, but so far have been distracted by other stuff and haven't tackled it
================

YUIOP, I think the fastest-receding galaxy which your .1c projectile could catch would be a galaxy that is currently receding at rate around .11c.
Then it would at first slowly lose ground (at around 0.01c) but eventually its determined persistence would be rewarded by Mother Nature who would graciously reduce H enough so that it would begin to shorten the distance between itself and target.

I'm pretty sure that it could NOT catch a galaxy receding at 0.12c. And I don't have an exact figure for the critical recession speed, just something around .11c

 

[Chronos]

I should have clarified I was speaking about the observable universe, which includes everything inside our particle horizon. We still receive photons emitted from the surface of last scattering, which I assume we all agree was receeding at superluminal velocity when the photons we now observe were emitted. Davis and Lineweaver explained this in http://arxiv.org/abs/astro-ph/0310808

A quote of interest from section 3.3. of the paper
"Our teardrop shaped past light cone in the top panel of Fig. 1 shows that any
photons we now observe that were emitted in the first ∼ five billion years were emitted
in regions that were receding superluminally, vrec > c. Thus their total velocity was
away from us. Only when the Hubble sphere expands past these photons do they move
into the region of subluminal recession and approach us. The most distant objects
that we can see now were outside the Hubble sphere when their comoving coordinates
intersected our past light cone. Thus, they were receding superluminally when they
emitted the photons we see now. Since their worldlines have always been beyond the
Hubble sphere these objects were, are, and always have been, receding from us faster
than the speed of light."

 

[marcus]

You have just explained why what you said here in post#18 is wrong. The Hubble sphere is slated to expand much more slowly in future (in the usual LCDM model) and so photons will NOT range as freely as in in the past.

Expansion never exceeds the speed of light in any local reference frame, so it appears to me photons eventually escape all regions of the universe, but, at a price - redshift. This appears to explain how we can still observe galaxies that were receeding at superluminal velocities when they emitted the photons we now observe.

I just described the same mechanism facilitating photons getting here in the past, the mechanism you quote Lineweaver Davis explaining---H decreasing or the Hubble distance c/H increasing.

None of this is effected by whether you meant universe or currently observable portion, either is way larger than the regions that today's photons can NOT get out of. (Because the decline of H has slowed enormously and is slated to essentially stop.)

I should have clarified I was speaking about the observable universe, which includes everything inside our particle horizon. We still receive photons emitted from the surface of last scattering, which I assume we all agree was receeding at superluminal velocity when the photons we now observe were emitted. Davis and Lineweaver explained this in http://arxiv.org/abs/astro-ph/0310808

A quote of interest from section 3.3. of the paper
"Our teardrop shaped past light cone in the top panel of Fig. 1 shows that any
photons we now observe that were emitted in the first ∼ five billion years were emitted
in regions that were receding superluminally, vrec > c. Thus their total velocity was
away from us. Only when the Hubble sphere expands past these photons do they move
into the region of subluminal recession and approach us. The most distant objects
that we can see now were outside the Hubble sphere when their comoving coordinates
intersected our past light cone. Thus, they were receding superluminally when they
emitted the photons we see now. Since their worldlines have always been beyond the
Hubble sphere these objects were, are, and always have been, receding from us faster
than the speed of light."

 

[Chronos]

I think this may be a case of semantical dissonance. Again, from the paper -
"... Most observationally viable cosmological models have event horizons and in
the CDM model of Fig. 1, galaxies with redshift z ∼ 1.8 are currently crossing our
event horizon. These are the most distant objects from which we will ever be able to
receive information about the present day. The particle horizon marks the size of our
observable universe. It is the distance to the most distant object we can see at any
particular time. The particle horizon can be larger than the event horizon because,
although we cannot see events that occur beyond our event horizon, we can still see
many galaxies that are beyond our current event horizon by light they emitted long
ago."

 

[marcus]

Chronos, anybody can quote intelligent authors' stuff. It does not do any good if you don't understand the implication of what you are quoting. You say this

photons eventually escape all regions of the universe,..

I've explained that photons emitted today are not going to be as free-ranging as those emitted during much of the past. So there are galaxies that we observe now, which are part of our observable universe, which today you could not send a flash of light that would get there. Most of the galaxies observable today, in fact, are OUTSIDE THE REACHABLE REGION.
We are surrounded by a region from which photons we emit today cannot escape.

You are quoting nice articles which I admire and know well and that's nice, but you don't seem to understand why what you said is wrong and inconsistent with the articles. So I'm inclined to give up and not try to explain further. Please excuse if I don't reply to you every time you quote Lineweaver and Davis.

The basic reason what you said is wrong is the positive cosmo constant---accelerated expansion. Its a feature of the standard LCDM model.

 

[Chronos]

Marcus, what part of 'photons eventually escape all regions of the universe [within our particle horizon - as clarified]' do you fail to comprehend? You appear to be reading something into the Davis and Lineweaver paper I failed to notice. Your insulting tone was beneath your usual standards of dignity.

 

[marcus]

You appear to be reading something into the Davis and Lineweaver paper I failed to notice. ...

I imagine you are right that you failed to notice something! You may not have noticed that whereas the particle horizon goes out to past z = 1100 (and is the radius of the observable region, galaxies, etc.) they mention z = 1.8 as the event horizon.

Any galaxy beyond z = 1.8 is not reachable by a light signal you send today.

Most galaxies that we observe are beyond redshift z = 1.8. They have redshifts like 2,3,4, 5, etc.

Most of of the currently observable universe, overwhelmingly most of it, is OUTSIDE the region that we can reach by a light signal that we send today.

Photons we send today are quite restricted to which galaxies they can reach. They cannot escape the confines of a comoving volume defined by that, in other words.

 

[marcus]

I guess to put it really simple terms, Davis and Lineweaver talk about the event horizon at z=1.8 which is I guess around 16 billion LY. That defines the reachable region: includes the target galaxies and other matter we could eventually reach with a signal sent today. They explain this.

And the radius of the currently observable is around 46 billion LY, that includes all the matter galaxies gasclouds etc that we are currently looking at. 46 billion LY is called the particle horizon.

So the volume of the observable universe is about 27 times the volume of the reachable.

That is, the radius is about 3 times longer, so cube 3.

Based on D&L if you like, or just ordinary logic, if you pick a galaxy at random in the observable universe it is overwhelmingly unlikely that we could reach that galaxy with a light signal sent today, even if it traveled forever. Our light signals are *confined* in what they can reach, to a much smaller set of destinations, represented by a region whose volume is roughly 1/27 of the observable.

Try plugging z=1.8 that Davis Lineweaver give us into a calculator to check that it it corresponds to comoving radial distance 16 billion LY. I think that's about right. Yeah, I checked, almost exactly 16.
http://www.astro.ucla.edu/~wright/CosmoCalc.html. This is the essential thing I've been trying to get across.

It's important because it the clearest or one of the clearest results of the 1998 discovery of socalled "dark energy" (or "positive cosmological constant"). The 16 billion LY event horizon, much closer than the radius of the observable, appears because of the accelerated expansion. That is what puts the limit on the range of targets today's photon can reach. Before 1998 the standard cosmic model HAD the property you attribute--there was no such limit, no event horizon.

photons eventually escape all regions of the universe,..

...photons eventually escape all regions of the universe [within our particle horizon - as clarified]...

Note that "within particle horizon" doesn't make any difference. Still wrong. Particle horizon 46 billion LY describes a vastly bigger volume.

 

[Chronos]

You are overstating the significance of accelerated expansion. See D&L Appendix B, item 14, page 108. While it is true we will never received photons emitted TODAY from galaxies at z > 1.8, we will continue to receive older photons emitted from within our particle horizon until the source reaches our particle horizon, at which point the photons will be infinitely redshifted.

 

[marcus]

... it is true we will never received photons emitted TODAY from galaxies at z > 1.8,...

So photons emitted today, from them, do not escape the region around them---do not get to US.

The same is true reciprocally from our point of view. A photon we send to them today will never get there. Will never escape the region defined around us by the same event horizon distance.

You made a general statement about photons (which includes those emitted today). The statement was incorrect. That's all I wanted to point out. It is important for beginners to understand this---that the event horizon exists, because of acceleration, so the highlighted statement is wrong and I could not let it pass. The other stuff you are talking about appears not related to this simple point, and not to require discussion.

Thanks for acknowledging the above---"that we will never receive..." etc. This is progress and might be a good point at which to conclude.

 

[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...