Why can we still detect the CMB ?

[bwana]

According to Wayne Hu here, http://background.uchicago.edu/~whu/intermediate/intermediate.html,
the universe started hot and dense and then expanded and cooled. In the hot, dense conditions of the early universe, photons were tightly glued to matter. When the universe was about 300,000 years old the temperature dropped below 3,000K allowing atomic hydrogen to form and releasing the photons. These photons, which traveled freely through the universe as it expanded and cooled, make up the cosmic microwave background (CMB) we see today.
Our eyes are at a specific point in the universe. A year after the universe became transparent, detectors would have measured the CMB as one light year away. The CMB which originated from matter close to us, is now long gone-it has traveled far away. At any point in time we are seeing photons from the surface of last scattering. But as time passes, we are seeing older and older photons- which originate from further and further away. And yet we think that the universe is expanding and that this expansion is accelerating. At some point the CMB should wink out of existence when the surface of last scattering becomes part of space that is moving away from us at faster than light speed. no?

 

[guywithdoubts]

As far as I know, yes, at a given time the CMB will no longer be detectable because wavelengths are stretching, which means it's getting colder and colder.

 

[Chronos]

The interesting thing about causal contact in the universe, is once something enters our cosmological horizon, it never truly escapes, it just redshifts into obscurity. We can still see the CMB because it was inside our cosmological horizon when the universe was less than about 400,000 years old. It has long since receeded beyond our cosmological horizon so we will never see it as it appears today, but, we will never lose sight of its heavily redshifted ghost from the past. It's like watching Bob fall into a black hole. You never see Bob reach the event horizon, he just keeps slowing down until he redshifts beyond detectability. Rest assured, Bob doesn't know squat about this time dilation illusion you were watching. He has a very different version of this story to tell.

 

[Ken G]

And yet we think that the universe is expanding and that this expansion is accelerating. At some point the CMB should wink out of existence when the surface of last scattering becomes part of space that is moving away from us at faster than light speed. no?

No, the point when we can no longer see any CMB would not be when the surface of last scattering is moving away from us faster than light speed, it is already doing that. This is a little hard to understand, so it is best not to think of what is happening is that the distant universe is moving away from us through a static space, instead imagine that nothing is moving except that space itself is stretching. You can get the exact same effect with ants crawling at a constant speed along a rubber sheet that is stretching (the ants are the photons, not the sources of light-- the sources of light are stuck to the rubber sheet and are not moving in that sense). Ants released from a source whose distance from us is increasing at a rate faster than the speed of ants will still get to us if the rubber sheet is being stretched at a constant rate (say someone holding the far end of the sheet is pulling it away at a constant speed). It is true that at first the ants will be getting farther away from us, so it might seem they'll never get to us, but they are always making progress along that sheet-- so eventually they do start getting closer, and later on they do reach us. So it is for light emitted from sources whose distance is increasing faster than the speed of light, even at the time the photons were emitted. In fact, all ants released anywhere on that sheet, no matter how far or how fast that sheet is being pulled, will eventually get to us-- as long as the sheet is pulled at a constant speed.

If the stretching of the sheet is being accelerated by dark energy, as we think is happening to the universe, what changes is that now we can draw a line on the sheet and say that no ants from past that line will ever get to us. The ants right on the line take an infinite time, and any ant closer than that gets to us-- but it might take a very long time. Hence we are always receiving ants-- we can always see the CMB, if we can detect a low enough intensity of extremely redshifted light.

 

[bwana]

Thank you ken. But the emission of em radiation from the universe's birth only happened once and it only became detectable when the universe became transparent 380000 yrs after it's birth. Since the source of the cmb is the surface of last scattering (sols), once the sols is far enough away so that the space containing it is expanding faster than light speed, nothing from the sols will ever reach us.

To return to your analogy, the ants hatch from eggs that were laid in a pile. The hatching doesn't start until 380000 years after the beginning. By that time the pile of ant eggs is spread out everywhere in the universe. The ants near to us wander past first. As time passes we see ants which originated from a circle a certain distance away from us. All the ants originating from closer than that circle have passed by aleady. The space between us and the 'circumference of origin' is barren. But since the rubber sheet is expanding ever faster, there will come a time when no more ants will reach us since the circle on which they are born is moving away faster than light speed. And since there are no ants between us and the 'circumference of origin', there will be no ants coming our way.

 

[mfb]

once the sols is far enough away so that the space containing it is expanding faster than light speed, nothing from the sols will ever reach us.

No. Initially the distance to this light will grow, but the Hubble constant is decreasing - at some point expansion slowed down enough for light to "catch up" and get closer to us.

The CMB light we currently see was emitted at a distance of ~42 million light years back then. Its distance first increased (because the distance between us and the emission region grew faster than the speed of light), after a few billion years this light was about 5 billion light years away, and got closer since then until it finally reaches us now.

Note that all those numbers do not matter for the general idea. You can also go the opposite way: Follow a light ray that hits us now into the past. No matter how exactly the universe has been expanding, this light ray will be at some point in space back at the time the CMB got emitted.

 

[bwana]

No. Initially the distance to this light will grow, but the Hubble constant is decreasing - at some point expansion slowed down enough for light to "catch up" and get closer to us...

The explanation here by Marcus is wonderfully clear
https://www.physicsforums.com/threads/accelerating-universe-decreasing-hubble-constant.311869/
He demonstrates that The Hubble constant may be decreasing but the universe is still expanding at an increasing rate.
Since the universe is still growing ever faster, the light will never catch up and get closer to us. For that to happen , the acceleration would have to become negative.

 

[Ken G]

To return to your analogy, the ants hatch from eggs that were laid in a pile. The hatching doesn't start until 380000 years after the beginning. By that time the pile of ant eggs is spread out everywhere in the universe.

Yes, that picture serves to give the correct answer.

The ants near to us wander past first. As time passes we see ants which originated from a circle a certain distance away from us. All the ants originating from closer than that circle have passed by aleady.

Yes.

The space between us and the 'circumference of origin' is barren. But since the rubber sheet is expanding ever faster, there will come a time when no more ants will reach us since the circle on which they are born is moving away faster than light speed. And since there are no ants between us and the 'circumference of origin', there will be no ants coming our way.

No, that is what will not happen, for the ants or for the CMB. If there is acceleration, there will be a circle beyond which we will get no ants, but we will always get ants. The eggs that are asymptotically close to that circle will always suffice to supply ants to us, for all time.

 

[bwana]

... The eggs that are asymptotically close to that circle will always suffice to supply ants to us, for all time.

1) the ant hatching only occurs once, just as decoupling only occurred once. The reason we see ants (photons) over a period of time is due to the distance between us and the distribution of eggs (hot matter) AND the fact that they have a constant finite velocity. If the rubber sheet at some distance from us stretches faster away from us than the ants can travel toward us, then ants at that distance and beyond will never reach us. And because there are no remaining eggs or new eggs being laid at that distance, the waves of incoming ants disappear a little while after the universe boundary reaches that circle (the event horizon of the universe)
2) what does asymptotically close mean when we are dealing with a finite number of discrete elements? There are only a finite number of ants- just as there were a finite number of particles cooling at the time of decoupling. At the distance from us where space is expanding linearly faster than light speed ( and volume is increasing faster than light speed cubed) there are only a finite number of photons. Just shy of that distance might not be any photons heading our way. So at some finite time after the universe reaches the event horizon, there are no more photons. How can it be otherwise?

 

[Vanadium 50]

I don't think these replies and analogies are helping.

Let's try a simpler situation. Suppose the universe became transparent all at once (it didn't) and there were people around to see this happen (there weren't) and places from them to see it from (there weren't either).

So, the universe goes transparent. A second later, we can see the moon. Can we see the sun? No - that would take another 8 minutes, because the light produced after transparency needs 8 minutes to get to us. After a few hours, we can see the solar system, and after a little less than 5 years, we can see the nearest star. OK with this? (Ignoring the fact there weren't stars, planets, people or eyes then)

If so, we have established that you always see the CMB. All that's left is to throw in the redshift. As we go later in later, we see things farther and farther away. These things are moving faster and faster away from us, so their light gets progressively more and more redshifted. By today, it's shifted all the way down to the radio? OK with this?

 

[mfb]

The explanation here by Marcus is wonderfully clear
https://www.physicsforums.com/threads/accelerating-universe-decreasing-hubble-constant.311869/
He demonstrates that The Hubble constant may be decreasing but the universe is still expanding at an increasing rate.
Since the universe is still growing ever faster, the light will never catch up and get closer to us. For that to happen , the acceleration would have to become negative.

Not clear enough apparently.
The accelerated expansion is a recent thing, expansion slowed down the first few billion years. But even if it would not have done this, it does not matter - the current position of matter that emitted the CMB we see today is irrelevant.

Did you see my example with following light rays back into the past? As the light rays don't vanish, they will be at some place at the time the CMB was emitted.

Yet another way to visualize it: the whole universe got filled with a nearly homogeneous and isotropic radiation - and it still is. It does not matter where you are. It is like being in the middle of the ocean, you will always get wet no matter where exactly you are and how fast the ocean expands.

 

[Ken G]

1) the ant hatching only occurs once, just as decoupling only occurred once.

I know, that's included in my answer. That it happened at a single time only means we get the light from a single distance at anyone time, we will still get light for all time. The same thing is true with the ants.

The reason we see ants (photons) over a period of time is due to the distance between us and the distribution of eggs (hot matter) AND the fact that they have a constant finite velocity.

No, that just isn't correct. There's nothing magical about a constant velocity, any velocity law has the property I mentioned-- all velocity laws will produce light for all time (some of the other answers can give you the reasons why, like tracing the light backwards), the only issue is whether that will eventually include all the sources or if there will be an asymptotic limit to what sources you will see. Similarly, it is impossible to see light from the same source twice, for any velocity law.

If the rubber sheet at some distance from us stretches faster away from us than the ants can travel toward us, then ants at that distance and beyond will never reach us.

The power of the analogy is that it is not really an analogy at all, it gives exactly the correct mathematics. And the rubber sheet analogy does not have the property you just mentioned. It takes a little thinking to see this, but even sources that are always moving away from us faster than the speed of ants can still get ants to us. Indeed we will see everywhere, all velocities, eventually if the expansion is constant. If it is accelerating, you must calculate the line beyond which you will never see, but that line has no relation to the place moving away from us at c at the era of recombination, just as it would have no relation to the eggs on the rubber sheet that are moving away from us at ant speed when they hatch-- indeed the line could just as easily be at an initial speed that is lower than ant speed. You can write the equations down for ants, the general relativity works out just the same way, it's a purely classical calculation and it will show you what I'm saying is true, but you need a particular velocity law to do that in detail.

2) what does asymptotically close mean when we are dealing with a finite number of discrete elements?

We are not dealing with discrete elements, our model is completely continuous. The model also uses the "cosmological principle", which means every location is the same as every other at a given age. Of course neither of those are likely to be exactly true, they are part of a mathematical model-- but no mathematical models of physical phenomena are ever exactly true, what will actually happen at infinite time is something we simply don't get to know.

There are only a finite number of ants- just as there were a finite number of particles cooling at the time of decoupling. At the distance from us where space is expanding linearly faster than light speed ( and volume is increasing faster than light speed cubed) there are only a finite number of photons. Just shy of that distance might not be any photons heading our way. So at some finite time after the universe reaches the event horizon, there are no more photons. How can it be otherwise?

Yes, the model will break down at some point. Most likely, for other reasons before we even come to that one. Remember, we don't even know what dark matter or dark energy are, one cannot extrapolate any model indefinitely into the future and expect to be correct-- one can only assert what the model says. But yes, if you put in some particular assumption about discreteness of the emission, then you will indeed get a last CMB photon if the expansion is accelerating, but it will not have any particular relation to the sources moving at c at recombination.

 

[D H]

Since the source of the cmb is the surface of last scattering (sols), once the sols is far enough away so that the space containing it is expanding faster than light speed, nothing from the sols will ever reach us.

The surface of last scattering has a redshift z≈1000. This is well outside the Hubble sphere. The Hubble sphere is not a horizon. Astronomers routinely see objects that not only are currently moving away from us at superluminal speeds, they were moving away from us at a superluminal speed at the time they emitted that light. Any light that has taken more than 9 or 10 billion years to reach us was emitted by an object that was and always will be receding from us superluminally.

The explanation here by Marcus is wonderfully clear
https://www.physicsforums.com/threads/accelerating-universe-decreasing-hubble-constant.311869/

You misinterpreted what Marcus wrote. I suggest you read this older post by Marcusthis older post by Marcus, and while you're at it, read the Davis & Lineweaver article that that post.

So at some finite time after the universe reaches the event horizon, there are no more photons. How can it be otherwise?

Read the Davis & Lineweaver article. It addresses your misconceptions.

 

[bwana]

Thank you all for your attempts to help my understanding. Obviously I am missing something basic so I will try one last time to rephrase my question. Forgive my density but I will try to make it entertaining. I hope this pleases you who have taken the time to read my question.

Imagine you are a god impervious to energy and matter. You can know everything all the time but you also decide to take human form so you can perceive things as humans do as well. You decide to do an experiment with making a new universe so you take a dense hot ball of plasma and set its initial condions so that when you let go it expands at 1 kilometer an hour but still cools pretty quickly so that it gets to 3000 kelvin an hour later. This is universe 1. After you let go you see this glowing fog expand around you. You sit in the center in human form and pretend to be as stupid as a human. One of the hardest things you do. Nothing much happens for a while but after an hour you notice a phase change and the fog disappears. In its place are a bunch of hot particles glowing white. The phase change is accompanied by a release of energy which appears as a flash of cosmic rays. These travel across the 2 kilometer diameter universe in almost an instant because lightspeed is a billion kilometers an hour. Roughly. And then the flash is gone. But the universe continues to expand. You watch the pretty glowing particles increase in separation and after a while they start to aggregate. You get bored, and trash this experiment and start over.

You do the experiment again but this time you change the initial conditions so the universe is expanding faster, almost 100 million kilometers an hour. (1/10 lightspeed). This is universe 2. You see the same thing initially, a glowing fog. An hour later, the cooling phase transition occurs. Now you see the same flash of cosmic rays start. You step out of the universe to see it as a god would and watch the cosmic rays. it isn't over instantly. The universe is almost 200 million kilometers in diameter. It will take 6 minutes for the cosmic rays to cross half this universe at lightspeed and reach the middle.(roughly) It will take 12 minutes to cross the distance of the entire universe. You step back into the center into human form and notice something odd. As the flash starts to fade, the frequency of the photons decreases. 6 minutes after you let go, the radiation is now X-rays and has crossed half the distance that the universe was when the flash started. You figure these X-rays are coming from the boundary of your universe. But the universe is now 1 hour and 6 minutes old. The radius is an additional 9 million kilometers(roughly) light will cross this distance in less than a second. So you watch the frequency of the photons decrease a little more. You think that this game of figuring out when light will cross the entire universe can be described by an infinite series. You are too lazy to construct the formula but you reason thusly: Since the universe is expanding at 1/10 light speed, the series will converge to a finite value and there will be a time when the flash will have traversed the entire universe and it will be over. The universe will continue to expand but you will not see any more photons from the flash.

You do the experiment again but this time the universe is set to expand at 10x lightspeed. This is universe 3. In an hour the phase transition occurs. From outside the universe you see the flash start. You notice that the universe is expanding a lot faster than the flash is spreading. Dark space starts to form and the flash now forms a bunch of light bubbles all of which seem to be slowly expanding(compared to how fast your universe is expanding) You realize the flash will never end because the space it can expand into is growing a lot faster than it is traveling. Large regions of dark space dwarf the expanding light bubbles. You jump into a dark region and see nothing- just inky blackness. There is no stuff here because to get particles you need a phase transition and the accompanying radiation. You jump into a light bubble and you see The particle that formed as a result of the phase transition. You look around and there are no other particles that you can see because their light cannot reach you. There is noThing when you look away from the particle.You get bored with one particle and trash this experiment.

You start over, this time you start the universe expanding slowly and speed it up. This is universe 4. You then come to the physics forums of the gods and ask all the other gods what will happen. They answer that it depends on the initial conditions. You say you start with universe 2 but accelerate expansion so that in 3 minutes the universe is expanding at light speed. At six minutes the universe is expanding at 10x lightspeed. They say you will have something like universe 2 where you will be able to see a bunch of particles in each light bubble for a little while. You ask if it will ever look like universe 4 and they say no, you will always be able to see photons from the flash. You agree with them as long as you stand outside the universe and watch it rapidly expand into a bunch of light bubbles. But you are adamant that when you step into a light bubble, there will come a time when all the other particles and their photons will disappear. Chaos reigns.

 

[mfb]

Ah, there is the misconception. The universe does not have a center, and as it is not a ball in space it is not possible to describe expansion with a speed.
No light ever "crossed the entire universe" and that concept does not even make sense. Similarly, we don't know how large the universe is in total, but it is certainly much larger than the observable universe (maybe infinite), and it probably does not have an "edge" at all.

 

[Ken G]

After you let go you see this glowing fog expand around you. You sit in the center in human form and pretend to be as stupid as a human. One of the hardest things you do. Nothing much happens for a while but after an hour you notice a phase change and the fog disappears. In its place are a bunch of hot particles glowing white. The phase change is accompanied by a release of energy which appears as a flash of cosmic rays. These travel across the 2 kilometer diameter universe in almost an instant because lightspeed is a billion kilometers an hour. Roughly. And then the flash is gone.

The issue is not how fast you make the expansion, because to be like our model, your universe needs to be infinite in size (that's part of the cosmological principle in a flat universe)-- so there is always some distance away from you that is moving away at great speed. Also, there will always be sufficient distances such that you will continue to see the "flash" of recombination-- it never ends, it just gets weaker in intensity and redder in color, forever (or until you get to that last photon if you are using a discrete emission model in an accelerating expansion, but again that has nothing to do with the source that was moving away from you at c at the time of emission, there's nothing special about that distance).