What Is Beyond The Observable Universe?

[marcus]

...When dealing with the universe, we consult general relativity, not special relativity. Look at Hubble's Law:

v = Hr (here v is the recession velocity of an object at a distance r, H is a constant).

From this expression (which is general relativistic, although approximate), we see that there is a point (r = c/H), at which distant objects are receding from us at greater than the speed of light. No contradiction here with SR: it's the space that is expanding -- all objects are at rest locally. And this is true for any expanding universe, not just inflation.

Powell I want to express support and appreciation. You've been giving Constantin the straight story about the standard cosmology model.
I'll add some detail (I hope it doesn't make things confusing to have extra detail. So far you and Dave have managed to be very clear.)

Constantin, you should understand what distance measure is used in the Hubble law
v = Hd.
A good way to think about it is to imagine freezing expansion right before you measure. So the distance doesn't change while you are measuring it.
You freeze at a certain moment, and measure by timing a light pulse or radio blip.* And then unfreeze so things are back to normal again.
Maybe we could call it "freeze-frame radar ranging".

The Hubble law applies to large distances like those separating independent clusters of galaxies and it says that a distance d, imagine it measured the way I described, expands at rate v = Hd.

The Hubble ratio H(t) changes over time, so I should specify a present moment t when we make the measurements and say v = H(t)d, but that too is a technicality. The standard cosmo model gives us past values of H as well as the present value.

Check this out:
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

To use it, put in .27 for matter density and .73 for cosmo constant, and 71 for present value of H(t). Then you can put in any redshift z and it will tell you the present (freeze) distance and the past (freeze) distance when the light was emitted and started traveling towards us. And it will tell the past value of H(t) when the light started its journey. And it will tell the distance expansion rates.

Personally I avoid saying "space itself expands". I say distances expand. I think of geometry as dynamic and geometry is about distances, angles, areas etc. I don't say "space" expands because I don't like to give the impression that it is a substance like rubber or bread-dough. I focus on geometry that rides on the material metaphor. But at this point, for Constantin and Powell and the rest of us, that technical distinction is not important. The main thing is picture Hubble law and picture the relevant distances.

Constantin, how about trying that calculator and getting distances for, say z = 1.4 and z = 1.7, and z = 1090. z=1090 is pretty close to the edge of the observable universe. The microwave background (CMB) comes in with redshift 1090 and it comes from the most distant matter we can see. Let us know if you have any trouble.

I keep the link to that calculator in my sig, to have it convenient, since it is very useful.

-----------------------------------footnote-----------------------------------------
*technically the CMB (the background of ancient light) helps in defining the moment when you freeze expansion.

 

[Constantin]

Recession velocities exceed the speed of light in all viable cosmological models for objects with redshifts greater than z ~ 1.5.
We routinely observe galaxies that have, and always have had, superluminal recession velocities.
The above is quoted from: http://arxiv.org/PS_cache/astro-ph/pdf/0310/0310808v2.pdf .

In my view, the light coming from the edge of the observable universe comes from a time when the age of the Universe was almost zero. And nothing can get further than that. So in this view nothing can ever get out of the observable universe.

The way I imagine the edge of the observable universe has similarities with a Milne universe, in that I imagine the objects near the edge as infinitely dense, either because of Lorentz contraction, or because we observe those objects as they were when the Universe was very young and dense.

That way we can already observe all the Universe, although it is infinite.

I must add that these ideas are very hard to imagine. This is not an easy subject.

 

[sylas]

Recession velocities exceed the speed of light in all viable cosmological models for objects with redshifts greater than z ~ 1.5.
We routinely observe galaxies that have, and always have had, superluminal recession velocities.
The above is quoted from: http://arxiv.org/PS_cache/astro-ph/pdf/0310/0310808v2.pdf .

In my view, the light coming from the edge of the observable universe comes from a time when the age of the Universe was almost zero. And nothing can get further than that. So in this view nothing can ever get out of the observable universe.

That doesn't follow. The observable universe is just that part of the universe which is sufficiently close that there's been enough time for the light to get from there to here. Nothing we see can be more distant than that; but plenty that we can't see may be more distant.

Think of it this way. The material from which we are made was emitting light 13.7 billion years ago, and that light will be seen now by alien astronomers who are formed from the stuff that WE now see with light that old (the cosmic background). So WE are at the edge of the observable universe for any astronomers who happen to be at the edge of our observable universe. And there's no extra density, or bound, or limit involved.

Furthermore, consider two regions, at opposite sides of the sky, which we can see with light coming in opposite directions since the origin of the universe. We only see those regions when they were very young, of course. Strictly, we see hot glowing gas with a redshift of about 1100; since then that gas has had 13.7 billion years to form into galaxies, just like out galaxy was formed from hot dense gas that long ago.

Both those regions are at the edge of our observable universe... and we are the edge of their observable universe as measured now. But those two regions at opposite sides of the sky are OUTSIDE the observable universe for each other.

Cheers -- sylas

 

[Calimero]

Check this out:
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

To use it, put in .27 for matter density and .73 for cosmo constant, and 71 for present value of H(t). Then you can put in any redshift z and it will tell you the present (freeze) distance and the past (freeze) distance when the light was emitted and started traveling towards us. And it will tell the past value of H(t) when the light started its journey. And it will tell the distance expansion rates.

Why at z=~2.5 'speed away from us now' becomes less then 'speed away from us then' ?

 

[Constantin]

Think of it this way. The material from which we are made was emitting light 13.7 billion years ago, and that light will be seen now by alien astronomers who are formed from the stuff that WE now see with light that old (the cosmic background). So WE are at the edge of the observable universe for any astronomers who happen to be at the edge of our observable universe. And there's no extra density, or bound, or limit involved.

There is extra density, that cosmic background represents the Universe as it was ~380,000 years after t=0 , as dense as it was then. And of course, not counting the technological limits we could see very close to t=0 . And if we could observe that cosmic background for a long enough period of time, like billions of years, we would see stars and galaxies forming out of it.

Furthermore, consider two regions, at opposite sides of the sky, which we can see with light coming in opposite directions since the origin of the universe. We only see those regions when they were very young, of course. Strictly, we see hot glowing gas with a redshift of about 1100; since then that gas has had 13.7 billion years to form into galaxies, just like out galaxy was formed from hot dense gas that long ago.

Both those regions are at the edge of our observable universe... and we are the edge of their observable universe as measured now. But those two regions at opposite sides of the sky are OUTSIDE the observable universe for each other.

That example can't be used. Two observers in those two regions can see the same Universe in a different way, because they're in a different frame of reference. In order for what observer A sees to have any meaning for observer B, observer A needs to send that information, presumably with the speed of light. Observer B would receive that information after a very long time, very many billions of years, and by then the way the Universe looks for observer B will match observer A's information well enough.

 

[marcus]

Why at z=~2.5 'speed away from us now' becomes less then 'speed away from us then' ?

This is a really perceptive question. You have been experimenting with the standard cosmo model (which is realized in this calculator in a concrete hands-on form.) It is so important to get hands-on numerical experience with the usual model of the universe! Thanks for the great question, Calimero!

Anyone interested in cosmology should do this, what you obviously have done.

Put successively z = 1, 2, 2.5, 3, 4, 1090* into the calculator and notice what happens to the "speed now", "speed then", and also the HUBBLE parameter, as z increases. These "speeds" should be thought of as the rate that the distance is increasing. (The distance used in the model here is the freeze-frame distance, and the recession rate is the rate that distance is increasing.)

The Hubble parameter gives the relation of distance to recession rate. For each distance it tells the rate at which that distance is growing. v = Hd

If H would not change, then since distance now is always bigger than distance then, we would have that recession rate now would always be bigger than recession rate then.

Indeed this is what happens for smaller redshift like z = 1 and 2, because over the fairly recent past the H has not changed very much.

But H has been much bigger in the past, and has been constantly decreasing during the whole history of expansion, and according to the model it will continue to decrease, but ever more slowly.

So this effect competes with what I said earlier. And if you go out to z = 2.5 it just balances. The two effects cancel!

* I added z = 1090 to the list of sample redshifts because 1090 is the redshift of the background of ancient light---the socalled CMB.

You, Calimero, probably know most of what I am saying but I hope some more newcomers will read this as well and be persuaded to try using the online model of the cosmos.

You should already be thinking of a followup question---how can H be always decreasing when we are told that expansion accelerates?---well, ask if you want that to be discussed. It's often good when one answer leads to a further question.

I assume you know what these numbers are. Anyone else reading this thread can guess:

  1      .78   .66      120.7
  2     1.24   1.17    201.1
  2.5   1.40   1.40    301.3
  3     1.53   1.62
  4     173    2.03
1090    3.3    56.7     1.3 million

 

[Calimero]

Thanks, I have to digest this. What you wrote is clear, but now I am puzzled with other stuff. I'll be back for more.

 

[Calimero]

You should already be thinking of a followup question---how can H be always decreasing when we are told that expansion accelerates?---well, ask if you want that to be discussed. It's often good when one answer leads to a further question.

Exactly. That is what I am puzzled about. If something is receding slower now then it was receding then, it means it is slowing down !? Furthermore it would appear that at z=2.5 there is some kind of 'boundary' where expansion from acceleration goes to deacceleration? But I am guessing that it is not the case.

 

[marcus]

Then you should get acquainted with the scale-factor a(t). This is the most basic quantity in the standard cosmos model.

Sometimes it is intuitively described as a dimensionless number which increases with time, and which keeps track of "the average distance between galaxies".

(It is always the "freeze-frame" distance we are talking about. any question about that? you freeze expansion at some moment t and then do radar ranging.)

Mathematically, a(t) is a factor which plugs into the Friedman metric. The standard model IS the time-evolution of the Friedman metric, a solution to the Einst. equation which provides the best fit to the data. We do not need to speak so technically. a(t) is a handle on the size of the world, it is a numerical handle on the average distance between galaxies.

The Friedman equations (look Wiki for "Friedmann equations") are the simple differential equations that govern the increase in a(t). That is really all that the standard model amounts to, in essence---modeling the growth of a(t).

Because it is dimensionless a(t) can be normalized so that, at the present time, it equals anything you want. It is usual to normalize it so that a(t) = 1 at the present time.

Now their are two easy hurdles, two easy low fences for you to get over.

YOU MUST UNDERSTAND THAT the wavelength expansion factor is 1+z
(a 50% increase in wavelength is expressed as z = 0.5 and therefore the wavelength now is 1.5 times the wavelength then)
and you must understand that 1+z = a(now)/a(then)

We measure that the light from some galaxy has z = 2.5, therefore the wavelength now is 3.5 times what it was when the light was emitted. And also the average distance between galaxies is now 3.5 times what it was when the light began its journey to us.

And YOU MUST UNDERSTAND WHY the Hubble parameter at any time t is equal to a certain fraction H(t) = a'(t)/a(t).
This is a sort of non-trivial interesting fact, nice to think about. The time derivative of a(t) divided by a(t) itself. The Hubble parameter H(t) is the time derivative of the scalefactor divided by the scalefactor itself, at any given instant in time.

The first people on Earth to discover interesting facts about the geometry of the world were the Ionians, and this is because the air on the Aegean coast of Anatolia is extremely clear and the outlines of the islands are very sharp. These facts about the scale factor and the Hubble ratio are essentially "Ionian" facts. heh heh That's just my private point of view. Carl Sagan said something like this.

 

[Calimero]

Ok, now I really have some work to do. But basically it would mean that nothing odd is happening to the scale factor, it is steadily increasing over time?

 

[marcus]

Ok, now I really have some work to do. But basically it would mean that nothing odd is happening to the scale factor, it is steadily increasing over time?

It is always increasing, but at first the increase slows because matter dominates over the effect of the cosmological constant (or "dark energy") and matter always slows the increase of a(t).

Saying that the cosmo constant is constant over time means the same thing as saying that the energy density of the "dark energy" is constant over time. Since it is a small density, it is at first dominated by the matter density. But as distances and volumes expand the matter density becomes small, and then the constant dark energy density becomes more important.

When you used the calculator you put .27 for matter and .73 for dark energy or cosmo constant.

So at first the increase in a(t) SLOWS and then after the cosmo constant term becomes dominant the increase in a(t) accelerates.

When they told you "expansion is accelerating" they were not talking about H(t). They were talking about a(t).

 

[marcus]

... a followup question---how can H be always decreasing when we are told that expansion accelerates?---well, ask if you want that to be discussed. It's often good when one answer leads to a further question.

I assume you know what these numbers are. Anyone else reading this thread can guess:

  1      .78   .66      120.7
  2     1.24   1.17    201.1
  2.5   1.40   1.40    301.3
  3     1.53   1.62
  4     173    2.03
1090    3.3    56.7     1.3 million

When they say expansion accelerates they are not talking about the recession of some particular galaxy, they are talking about the behavior of a(t). Focus on a(t). It is the most important quantity in the cosmo model.

When they say expansion accelerates they are not talking about H(t) either. H(t) is just a convenience because it relates nicely to observational data, the plots of the distance-redshift relation. H(t) is always decreasing.

Why? because H(t) = a'(t)/a(t) and the denominator of that fraction dominates. The growth in the denominator swamps any diddly changes that might be happening to the numerator.

One can imagine universes where H(t) does not decrease. Like the extreme case where there is no matter at all but only pure dark energy and a(t) increases exponentially. Then H(t) will be constant, so it will at least not decrease, then.

But in any universe at all like ours, H(t) will always be decreasing---only more and more slowly as time goes on, so that it kind of levels out.

Our model tells us what H(t) will level out to. What the asymptotic value is.

Take your time and assimilate this stuff. Ask more questions when you want to. I thought your first question was really good because it showed you had been playing around with the Cosmos Calculator.
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

 

[bapowell]

That example can't be used. Two observers in those two regions can see the same Universe in a different way, because they're in a different frame of reference. In order for what observer A sees to have any meaning for observer B, observer A needs to send that information, presumably with the speed of light. Observer B would receive that information after a very long time, very many billions of years, and by then the way the Universe looks for observer B will match observer A's information well enough.

You're missing sylas's point. He's merely suggesting that there may be more to the universe than what we can observe -- he's not setting up some elaborate experiment that requires two observers to communicate.

I think it's great that you are interested in these questions about the universe. However, many of your views expressed so far in this thread are not factually correct. Myself and the others in this thread have tried to offer more correct views of the way the universe actually behaves, not how it ought to behave. I think you could benefit from thinking deeply about some of the things we've mentioned, and perhaps modifying your views to incorporate them. Perhaps you should pick up a good popular science treatment of the subject, eg, the books by Weinberg, Guth, or Harrison.

 

[Phyisab****]

I voted other because... wait for it... we can't observe it.

 

[sylas]

There is extra density, that cosmic background represents the Universe as it was ~380,000 years after t=0 , as dense as it was then. And of course, not counting the technological limits we could see very close to t=0 . And if we could observe that cosmic background for a long enough period of time, like billions of years, we would see stars and galaxies forming out of it.

I agree with all of this.

We may be talking at cross purposes. Much of what you say is fine, but I have a problem sorting out what you could have meant by this:

Recession velocities exceed the speed of light in all viable cosmological models for objects with redshifts greater than z ~ 1.5.
We routinely observe galaxies that have, and always have had, superluminal recession velocities.
The above is quoted from: http://arxiv.org/PS_cache/astro-ph/pdf/0310/0310808v2.pdf .

In my view, the light coming from the edge of the observable universe comes from a time when the age of the Universe was almost zero. And nothing can get further than that. So in this view nothing can ever get out of the observable universe.

I think I misunderstood you previously, so forget my last post. I was simply saying that there's stuff outside the observable universe which is the same as stuff inside the observable universe, but I see you agree with this. My fault for missing your point.

But I still think you may be mistaken, so let me try again. Your reference, Davis and Lineweaver 2003, is very good, IMO. Have a look at their figure 1. Here it is: click to enbiggen.

The three diagrams in this figure are showing the same thing, but with different co-ordinates for the axes. The bottom diagram is the simplest, though the notions of co-moving distance and conformal time may be unfamiliar to many folks. The top diagram is the most intuitive for many readers, as it uses proper distance and proper time co-ordinates, which correspond to time and distance as we normally understand them.

What we usually mean by "observable universe" is everything within our present light cone. In a trivial sense, pretty much everything has "now" moved out of the observable universe, because the light leaving it "now" hasn't reached us yet. This only means that what we see at a distance is as things were in the past, and which is obvious.

But in an accelerating universe, something rather more strange can happen.

Figure 1 is showing the ΛCDM model, a flat universe with matter (0.3) and dark energy (0.7). In this case the expansion of the universe is accelerating, and will continue to accelerate. When this occurs you have an "event horizon", which is shown in the diagrams. This means everything which we can ever hope to observe now or at any time in the future. And look... in this case, all co-moving particle WILL eventually move past the event horizon!

What this means, in more practical terms, is that distant galaxies which are not gravitationally bound to us will eventually move out of the observable universe. What we can actually see, for such a galaxy, as time passes, is that the red shift of the galaxy will increase without limit. It is, in fact, red shifted to invisibility. We will never see the galaxy at any age beyond the age at which it crossed our event horizon. If we had the capacity to see infinitely redshifted signals, we would actually see the galaxy appear to be "frozen" in time, at the age at which it crosses the event horizon. We never ever see it older than that moment.

There is an intriguing implication of this for astronomers of the distant future!

The current models for the universe suggest that as time passes the universe will appear more and more "empty", as we see less and less of the universe, until at a time billions of years into the future astronomers will only ever be able to see a small number of galaxies that have become gravitationally bound with us. Our local group of galaxies. The rest of the sky will be dark, betraying no hint of the nature of the universe, or of the billions of galaxies which will have, by then, moved forever beyond any possibility of observation. It seems that such astronomers will have no available evidence to be able to identify the big bang, or dark energy, or expansion.

Cheers -- sylas

 

[Constantin]

I thank everyone for the replies.

This is the explanation that has helped me most:

What this means, in more practical terms, is that distant galaxies which are not gravitationally bound to us will eventually move out of the observable universe. What we can actually see, for such a galaxy, as time passes, is that the red shift of the galaxy will increase without limit. It is, in fact, red shifted to invisibility. We will never see the galaxy at any age beyond the age at which it crossed our event horizon. If we had the capacity to see infinitely redshifted signals, we would actually see the galaxy appear to be "frozen" in time, at the age at which it crosses the event horizon. We never ever see it older than that moment.

It explains the way objects can look while moving out of the observable universe, which is very hard to imagine without proper explanation. Naively one can imagine that they simply move out of sight and disappear, which is of course illogical.

 

[sylas]

It explains the way objects can look while moving out of the observable universe, which is very hard to imagine without proper explanation. Naively one can imagine that they simply move out of sight and disappear, which is of course illogical.

Thanks very much; I get a real buzz when something I've written manages to help like this.

You've hit the nail on the head about what is hard to imagine here; I also had a hard time figuring this one out, in another closely related situation. You have exactly the same thing occurring when a particle moves across the event horizon of a black hole!

For an outside observer, they can never see this occur. What they can see is a signal redshifted without limit, and (if you find a way to see an arbitrarily redshifted signal) this signal reveals the particle apparently frozen in time at the point of approaching the event horizon. The particle itself crosses the horizon just fine; but we can never see this occur, no matter how long we wait.

Cheers -- sylas

 

[Skolon]

You've hit the nail on the head about what is hard to imagine here; I also had a hard time figuring this one out, in another closely related situation. You have exactly the same thing occurring when a particle moves across the event horizon of a black hole!

For an outside observer, they can never see this occur. What they can see is a signal redshifted without limit, and (if you find a way to see an arbitrarily redshifted signal) this signal reveals the particle apparently frozen in time at the point of approaching the event horizon. The particle itself crosses the horizon just fine; but we can never see this occur, no matter how long we wait.

That mean we can study all history of a black hole after its born just observing more and more redshifted signals? Very interesting.

What this means, in more practical terms, is that distant galaxies which are not gravitationally bound to us will eventually move out of the observable universe. What we can actually see, for such a galaxy, as time passes, is that the red shift of the galaxy will increase without limit. It is, in fact, red shifted to invisibility. We will never see the galaxy at any age beyond the age at which it crossed our event horizon. If we had the capacity to see infinitely redshifted signals, we would actually see the galaxy appear to be "frozen" in time, at the age at which it crosses the event horizon. We never ever see it older than that moment.

There is an intriguing implication of this for astronomers of the distant future!

Why we don't observe that kind of "frozen" galaxies right now? I think right now must be a lot of galaxies beyond the current event horizon already. Or I'm wrong?

 

[Constantin]

The answers to Skolon's questions would be interesting.

Thing is very very few people can imagine these things properly: the way objects would look to an observer.
And you can look for an explanation on the internet for hours, days, weeks, but you won't find it. Or at least I didn't.

 

[Ich]

That mean we can study all history of a black hole after its born just observing more and more redshifted signals?

No. Redshift increases exponentially with time near the horizon, after a few seconds it is far in the millions. There is nothing to observe.

Why we don't observe that kind of "frozen" galaxies right now?

The universe is too young. The first galaxies have a redshift of about 8, which does not exactly qualify as "frozen", I think. If you wait for another ~50 billion years, their redshift will be ~280.
The CMB has a redshift of 1088. That's quite frozen.

 

[sylas]

That mean we can study all history of a black hole after its born just observing more and more redshifted signals? Very interesting.

I qualified my remarks to say IF we could actually see a signal redshifted arbitrarily far. But we can't.

If you think in terms of a classical wave, a red shifted signal is one in which the distance between successive wave crests becomes large. That is, wavelength increases as light is shifted into the infrared.

Light is also quantized... it is made up of photons. Another difference with a red shifted signal is that the distance between successive photons is increased... or in other words, you get less photons per unit time. As a signal is shifted arbitrarily far, in the limit there is an arbitrary distance between photons.

Another way of think about it. A particle crossing an event horizon emits only a finite number of photons before it has crossed the horizon. Hence there are only a finite number of photons available to an observer. There will be a last photon from an arbitrarily redshifted source, after which... nothing more, ever.

Why we don't observe that kind of "frozen" galaxies right now? I think right now must be a lot of galaxies beyond the current event horizon already. Or I'm wrong?

Well, yes, there are galaxies "now" beyond the event horizon, assuming a universe homogenous on large scales and a ΛCDM model. But have a look at the diagram from Davis and Lineweaver, attached above in message [post=2591939]post #135[/post]. and read off the implications.

We can only ever see matter before it crosses the event horizon. In the current epoch, the oldest light we see is the cosmic background radiation. The galaxies formed from that material, given a (0.3,0.7) ΛCDM model, crossed the event horizon long ago. But what we see now is still only material from which they were made, redshifted with about about z=1088. Time is not quite frozen, but in the signal we perceive it appears to run about 1089 times more slowly than reality. We don't even see it formed into galaxies yet.

Given enormous lengths of time and the capacity to see extreme redshift signal, it will eventually be possible to see it formed into galaxies. That material will have crossed our event horizon (from the diagram) about a billion years after the Big Bang; which is comparable to the age of the most distant actual galaxies we can now see.

What about galaxies we see with z=9? That's a little bit more redshifted that the best we've observed so far, but its close. We would be seeing light emitted when the scale factor was a=0.1, and there's a vertical line in the diagrams to help pinpoint those galaxies. So this is a convenient example.

The z=9 galaxy will have crossed the event horizon about 4 billion years after the Big Bang; and what we see now is from less than a billion years after the Big Bang. So in principle, there are still three billion more years of their history potentially visible to future astronomers.

Now... hold on to your hat and think on this. Consider material from a=0.001 (which is very close to what we see in the CMBR) and material from a=0.1 (which is very close to the most distant galaxies detected). When in the future would we be potentially able to observe that CMBR material developed into galaxies at the same epoch as we now observe in the most distant galaxies? You can read that off the diagram; it will be hundreds of billions of years into the future.

I have not done the actual calculations for myself. Sometime I might try it, for fun.

Cheers -- sylas

 

[Calimero]

And YOU MUST UNDERSTAND WHY the Hubble parameter at any time t is equal to a certain fraction H(t) = a'(t)/a(t).
This is a sort of non-trivial interesting fact, nice to think about. The time derivative of a(t) divided by a(t) itself. The Hubble parameter H(t) is the time derivative of the scalefactor divided by the scalefactor itself, at any given instant in time.

I have two questions:

1. Is there any significance in fact that when we divide speed of light wit current H(t) we get 13.6 GLY?

2. How can we see something that is now and ever was (at least when light ventured towards us) receding from us faster then light?

 

[sylas]

1. Is there any significance in fact that when we divide speed of light wit current H(t) we get 13.6 GLY?

No. Current indications are that it is simply a co-incidence.

2. How can we see something that is now and ever was (at least when light ventured towards us) receding from us faster then light?

Because as the photon crosses space, it eventually moves into regions where co-moving observers are receding at less than the speed of light. The "proper distance" from us to a photon emitted from such a galaxy makes a kind of pear shape. Initially, when the photon is emitted, the proper distance from us to the photon is actually increasing. That is, the direction of motion of the photon is towards us, but the distance between us and the photon is increasing, at first, because of how the universe expands.

You can reasonably speak of a "recession velocity" for the approaching photon. Locally, the photon moves at c. But the rate of change of proper distance from us to the photon is another matter. Initially, it is receding; but as it crosses space it recedes more and more slowly. Eventually, it moves into a region where the co-moving recession velocity is equal to the speed of light. At that point, the "recession velocity" of the photon is zero. But the recession velocity continues to fall, so that the photon from this point actually starts to become closer to us.

Eventually, the photon comes into our own local region of space, and it is now approaching at the speed of light.

Cheers -- sylas

 

[marcus]

...2. How can we see something that is now and ever was (at least when light ventured towards us) receding from us faster then light?

Because as the photon crosses space, it eventually moves into regions where co-moving observers are receding at less than the speed of light. The "proper distance" from us to a photon emitted from such a galaxy makes a kind of pear shape. Initially, when the photon is emitted, the proper distance from us to the photon is actually increasing. That is, the direction of motion of the photon is towards us, but the distance between us and the photon is increasing, at first, because of how the universe expands.

You can reasonably speak of a "recession velocity" for the approaching photon. Locally, the photon moves at c. But the rate of change of proper distance from us to the photon is another matter. Initially, it is receding; but as it crosses space it recedes more and more slowly. Eventually, it moves into a region where the co-moving recession velocity is equal to the speed of light. At that point, the "recession velocity" of the photon is zero. But the recession velocity continues to fall, so that the photon from this point actually starts to become closer to us.

Eventually, the photon comes into our own local region of space, and it is now approaching at the speed of light.

Calimero, I agree with everything Sylas said here. He gave you a good answer. But left out an important reason why this happens. It has to do with H(t) decreasing.
In the past it has decreased very rapidly. H(t) used to be like 1.3 million (when the background was emitted) and is now only 71. A huge decrease. Playing with the calculator let's you track this decrease.

You showed that you know how to get the HUBBLE RADIUS c/H. Good, so when H was decreasing rapidly then c/H was increasing rapidly.

But notice this distance divides space into two regions: Anything outside that radius is receding faster than c and anything inside is receding slower than c.

So if a photon is aimed at us, it may at first be swept back by expansion of distance as long as it is outside the c/H radius. But if it hangs in there and keeps trying to reach us, then eventually it may happen that c/H reaches out and takes it in.

Once it is inside the region of slower than c recession then its own speed dominates and it will gradually reduce its distance to us. It will gradually get closer.

The key thing is that in the past the c/H radius has extended out very very fast.

This is the basic reason we can see a lot of stuff which, when it originally emitted the light, was receding several times faster than c.

You can see this happening graphically in an animation. Google "wright balloon model"

The wiggly things (cartoon photons) travel a fixed speed like 1 millimeter per second. The whirly things are galaxies

 

[Calimero]

Marcus and Sylas, thank you both.
So what is now receding at, say, 2 C will need much more time to reach to us (light from it) then it would need earlier in the history?
And what is 'proper distance' ? Distance measured if we freeze expansion, and then measure? Also, what is proper time?

 

[sylas]

And what is 'proper distance' ? Distance measured if we freeze expansion, and then measure? Also, what is proper time?

Proper time is simply time as measured by a conventional clock that is at rest with the Hubble flow. That is, there's no additional peculiar motions to worry about. You can also think of it as the time measured by co-moving clocks.

Your description of proper distance is fine. Another way to think of it... imagine all of space filled with co-moving observers equipped with conventional clocks and rulers. The proper distance between two co-moving observers at a designated proper time instant would be the instantaneous sum of distances given by all the co-moving rulers.

And thanks Marcus for adding the point about H changing over time!

 

[marcus]

So what is now receding at, say, 2 C will need much more time to reach to us (light from it) then it would need earlier in the history?
...

Indeed infinitely more, will never get there. Good intuition. Abs. on target!

In fact even 25% greater than c and the galaxy cannot send us a message that will reach us.
This is because H(t) is decreasing so much slower now than in the past. So the distance c/H is reaching out so much more slowly now.

The distance limit as of now is about 15 Gly. Somewhere between 15 and 16 as I recall.

If a galaxy is within that range, we could send a light signal to it today that would reach it eventually. And some event occurred there today, an explosion say, we would eventually see it. Even though the distance to the galaxy is increasing faster than c.

But if it is beyond that range today, say more than 16 Gly in "now" freezeframe distance, we can as of today send no signal that will get there. But of course there is plenty of information already on its way, we can look forward to watching her for a long long time. Just nothing she does from now on will ever reach us.

As a very very rough estimate (Sylas may be able to refine this) the breakpoint is redshift z = 1.6
You can refer to Morgan's cosmos calculator and see what that corresponds to in distance terms. It corresponds to distance just slightly less than 15 Gly, and a recession rate of around 1.1 c.

I haven't checked this but I think its roughly right.

It used to be that H was decreasing so fast that material could be receding at 3 c or faster and emit light and it would reach us. Now if a galaxy or other material is receding at even 1.15 c or so, it can't reach us
but if it is receding 1.05 c it can emit light that will still eventually reach us.
And borderline is around 1.1.

I'm overstating the precision because I want to talk concrete examples, but I don't actually know the breakpoint (and it depends on cosmo parameters like 0.73 and 0.27 and 71 which are themselves uncertain!)

I have to go do something realworld. Can't finish this post. Sylas mentioned something extremely interesting--observers at rest with respect to the expansion process itself.

In practical terms that means at rest with respect to the ancient light. the background. that means no doppler hotspot in any direction, when you measure the microwave sky temperature. Absolutely an all important concept.
The concept of a network of observers at rest is what the ideas of NOW and then rest on, the idea of being able to specify a moment when you freeze expansion in order to define the freeze distance. The time "t" that is really there in the Hubble law v = H t. That time depends on the concept of being at rest with respect to background, or with respect to the expansion process. It is so important, so basic. It is the "t" in the basic Friedman equations model that all cosmology rests on, and the "t" of the scalefactor a(t).

Have to go move the car, however, because tomorrow is street cleaning. Don't want to get a ticket.

 

[E=mc^84]

We may not be able to observe it at the moment but we need to make the assumption something is there. We have never seen life outside our planet but we assume it exists and create ways to seek out and prove it. A similar thing should be done in cosmology. We should be making insturments that can help us study the beyond.



Yes it maybe irrevelent and these other universes may contian different laws of Nature. However like alien life, I do think we will be able to learn about it in the future. We shouldn't give up. No one has ever seen a quark (correct me if I'm wrong) but we assume the microverse goes further.

If we had a spaceship that can do this, what do you think it will run into at the ends of the universe? Will the spaceship keep going or is it constricted to this universe only? What do you think?

What if we can observe it indirectly lke we do with black holes?

 

[Calimero]

In fact even 25% greater than c and the galaxy cannot send us a message that will reach us.
This is because H(t) is decreasing so much slower now than in the past. So the distance c/H is reaching out so much more slowly now.

The distance limit as of now is about 15 Gly. Somewhere between 15 and 16 as I recall.

If a galaxy is within that range, we could send a light signal to it today that would reach it eventually. And some event occurred there today, an explosion say, we would eventually see it. Even though the distance to the galaxy is increasing faster than c.

But if it is beyond that range today, say more than 16 Gly in "now" freezeframe distance, we can as of today send no signal that will get there. But of course there is plenty of information already on its way, we can look forward to watching her for a long long time. Just nothing she does from now on will ever reach us.

As a very very rough estimate (Sylas may be able to refine this) the breakpoint is redshift z = 1.6
You can refer to Morgan's cosmos calculator and see what that corresponds to in distance terms. It corresponds to distance just slightly less than 15 Gly, and a recession rate of around 1.1 c.

I haven't checked this but I think its roughly right.

It used to be that H was decreasing so fast that material could be receding at 3 c or faster and emit light and it would reach us. Now if a galaxy or other material is receding at even 1.15 c or so, it can't reach us
but if it is receding 1.05 c it can emit light that will still eventually reach us.
And borderline is around 1.1.

I'm overstating the precision because I want to talk concrete examples, but I don't actually know the breakpoint (and it depends on cosmo parameters like 0.73 and 0.27 and 71 which are themselves uncertain!)

That numbers are just about right according to calculator. Does it mean that it tends to even at C at some distant future?

Let me ask you another question about calculator. I obviously lack math behind it, but for any redshift (z), you can put any value for H(t) above ~35 and speed away is not affected, just the distance is changing proportionally. Why is that? Can you even "go trough time" with changing just H(t), or you must change Omega too?

 

[Chronos]

So how are we able to observe the CMB at z ~ 1090? I perceive an ATM reply.