How can the Observable Universe be a closed system?

[Cerenkov]

TL;DR Summary

https://www.physicsforums.com/threads/is-the-universe-a-closed-system.620503/

https://www.physicsforums.com/threads/is-the-universe-a-closed-system.620503/

Hello.

I was looking back at this thread from 2012 and, to be honest, I'm a bit confused.

Quoting Drakkith...
To our knowledge it is. At minimum you could count the observable universe as a closed system because anything outside it will not have had time to affect you locally due to the finite speed of light.

Ok, I understand what he's saying here, but my confusion concerns a process which I naively thought happened in the 'opposite' direction. I had thought that with the expansion of space carrying galaxies away at faster and faster velocities they would effectively 'leave' the observable universe. With this loss of matter and energy from the observable universe I had naively assumed that the observable universe could not be considered to be a closed system.

In a closed system I had thought that nothing could pass across the boundary. Since the observable universe is just a visual horizon and not a true boundary I'm currently confused as to why (and how) the observable universe can be considered a closed system.

Clearly I'm mistaken about something and I hope somebody can help me out here.

Thank you.

Cerenkov.

 

[Bandersnatch]

Ok, I understand what he's saying here, but my confusion concerns a process which I naively thought happened in the 'opposite' direction. I had thought that with the expansion of space carrying galaxies away at faster and faster velocities they would effectively 'leave' the observable universe. With this loss of matter and energy from the observable universe I had naively assumed that the observable universe could not be considered to be a closed system.

This is a misconception. Galaxies never leave the observable universe (although some of them will end up virtually undetectable due to practical reasons).
There's always more light from ever further away that is reaching any observer. The observable universe always grows to encompass areas further and further away.
While galaxies are crossing the event horizon at any given moment, it merely means that a certain portion of their history won't be available to be observed - but their past history, i.e. light from before crossing the event horizon, will always keep coming. E.g. a spot that has only become observable yesterday as CMBR will remain observable forever, and over time keep evolving to some proto-galaxy, but we'll never see it evolve past a certain point.

With that being said, I don't quite get how one could treat the observable universe as a closed system, since every moment there is more and more 'stuff' in it. Heck, the horizon problem in the big bang model hinges on just that - different parts in the sky used to all be causally disconnected, but appear like they used to be a single connected system.

 

[Cerenkov]

Many thanks for this Bandersnatch.

I reckoned that I was going awry somewhere and now you've helped me see where.

So, these galaxies that are crossing the event horizon - their past will always be visible to us. That's understood. But let's say that a certain galaxy crosses that threshold today, we won't be able to see any of the light it emits tomorrow or any other time in the future? Is that right? Only light from yesterday and any time previous to that?

As regards the observable universe being classified as a closed system, I really don't want to pit you against Drakkith on this one. I simply cited what he said about this in July 2012 and used his comments as a basis for this thread.

I'm still scratching my head over this and really don't know what to think.

Do you have any suggestions?

Thanks again,

Cerenkov.

 

[anorlunda]

ping @Drakkith

 

[Drakkith]

ping @Drakkith

The quote from me in the first post was from 9 years ago when I had much less knowledge about cosmology. I don't know why I claimed that the observable universe could be considered a closed system, and I'd just ignore what I said unless someone else here with much more knowledge on the subject verifies it.

 

[Cerenkov]

Ah, thank you Drakkith.

You know how it is. This forum presents a list of threads with the same or similar topics, going back chronologically. The status of the observable universe re open and closed systems is of interest to me and so I clicked on a 2012 thread, finding your post.

The rest, as they say, is history.

Thanks again,

Cerenkov.

 

[Halc]

So, these galaxies that are crossing the event horizon - their past will always be visible to us. That's understood. But let's say that a certain galaxy crosses that threshold today, we won't be able to see any of the light it emits tomorrow or any other time in the future? Is that right? Only light from yesterday and any time previous to that?

As regards the observable universe being classified as a closed system, I really don't want to pit you against Drakkith on this one. I simply cited what he said about this in July 2012 and used his comments as a basis for this thread.

No, it isn't a closed system since matter is continuously coming into what is our visible universe.

There's a commonly used picture that might help with some of the concepts, from cosmic horizons:

They're all the same picture, but in different coordinate systems.
The first one uses proper distance. The event horizon is the orange line, and galaxies (the black dotted lines) are continuously passing out of this event horizon, and hence we can no longer see them beyond this event, even given infinite time. This is as you describe above. The event horizon does not define the visible universe.

The red line is our past light cone. The only events we can see now are ones on that red line. Not anything inside or outside it.

The visible universe is bounded by the green dotted line, the particle horizon. It is currently 46 BLY in radius, and you'll notice that galaxies are passing into (not out of) this boundary, which means things not visible to us before become visible over time.

The bottom graph (the only one with time going to infinity) shows that the size of the visible universe will eventually settle on a comoving (not proper) distance of about 62 BLY, which is about 2.4 times the current amount of matter currently within our visible universe. So there is a finite amount of material that will ever have a causal effect on us even given infinite time.

 

[kimbyd]

I think the closest to this that is actually used is periodic boundary conditions. With periodic boundary conditions, you consider a finite region where if you move in any direction you eventually come back to where you started.

This system is "closed" in that it's finite and nothing can enter or leave. But it also doesn't have a boundary that can be crossed in the first place. This model is generally not considered to be real in any sense. If your system happens to be very uniform on large scales, you can model it pretty well with just a finite chunk of the system.

And because our universe is indeed very uniform on large scales, periodic boundary conditions can be very useful.

All of this is to say that because our universe is quite uniform, many times it acts as if it were a closed system in the periodic boundary conditions sense. Basically, if stuff leaves a large enough chunk of our universe, just as much stuff is likely to enter.

 

[Cerenkov]

My thanks to Halc and kimbyd.



Buuuut...

Halc, I can read a HR diagram well enough, but could you please assist me in understanding of the Proper Distance diagram properly? Thanks in advance.

The central, vertical axis ( 0 zero ) represents where we are, with increments of 20, 40 and 60 giga lightyears of proper distance going along the lower ( X ? ) axis and Time in 5 giga year increments going up the left side ( Y ? ) or axis.

So why are the left-hand proper distance increments in negative values of -20, -40 and -60 giga lightyears?

Could you also please explain the significance of the Scalefactor on the right and the values 1, 3 and 10 along the top? (Which, unlike the proper distance values, don't become negative on the left side.)

Lastly, I seem to see a contradiction. Ok, there isn't one. But please bear with me.

You say that the observable universe, 'isn't a closed system since matter is continuously coming into what is our visible universe.'

and...
' you'll notice that galaxies are passing into (not out of) this boundary, which means things not visible to us before become visible over time.'

But how can this be if...
'...galaxies (the black dotted lines) are continuously passing out of this event horizon, and hence we can no longer see them beyond this event, even given infinite time.'

?

Could you please help resolve this by explaining how galaxies are continuously exiting the event horizon, yet also passing into this boundary? That makes it sound like a two-way flow of matter and energy.

Clearly my understanding of these boundaries needs some work.

Thank you.

Cerenkov.

 

[Ibix]

Halc, I can read a HR diagram well enough, but could you please assist me in understanding of the Proper Distance diagram properly? Thanks in advance.

It's from Davis and Lineweaver's paper, which has a lot of explanation.

 

[Halc]

I can read a HR diagram well enough, but could you please assist me in understanding of the Proper Distance diagram properly? Thanks in advance.

The central, vertical axis ( 0 zero ) represents where we are, with increments of 20, 40 and 60 giga lightyears of proper distance going along the lower ( X ? ) axis and Time in 5 giga year increments going up the left side ( Y ? ) or axis.

The vertical y-axis is time (of one sort or another) in all of them, yes. We're at spatial location X=0. The right side of each is scalefactor, which is a non-linear function of time. The bottom picture does not show linear time, and it would still have been nice if they had labeled actual time on it, but scalefactor is still there, and that translates to time, even if not directly.

So why are the left-hand proper distance increments in negative values of -20, -40 and -60 giga lightyears?

Only one dimension of space is shown. Positive location in one direction is negative distance in the other, else we'd not be at relative location zero. All is relative to 'here'. Many of the similar charts I've seen only bother to plot one side, but I think this mirror format allowed them more space to label different things.

Could you also please explain the significance of the Scalefactor on the right and the values 1, 3 and 10 along the top? (Which, unlike the proper distance values, don't become negative on the left side.)

Scalefactor is current 1 by definition, and scales the expansion of the universe over time. If you take the proper distance in the top picture and divide it by scalefactor, you get the middle picture. It's the relationship between proper distance and comoving distance. With comoving distance, all galaxies are nearly stationary and move on vertical lines, as seen on the lower two pictures both of which use comoving distance.
A nice graph of scalefactor appears on the wiki deSitter space page:

The commonly accepted curve is the magenta line, which meets the X axis about 13.7 billion years ago, which is how the age of the universe is determined. The other scalefactor lines are different models, each of which gives different ages (and eventual fates) of the universe.

The numbers on the top of each picture is redshift numbers. They label the redshift of each of the black dotted worldlines, so they don't correspond to the x-axis in the top picture.
They should have labeled that. So the CMB is just inside the dashed green line, and has a redshift of about 1100. Gn-Z11 is the furthest known galaxy which has a redshift of about 11, which gives it a current distance of 32 billion LY, even though the light we see from it was emitted from a proper distance far closer than that (like around 3 BLY) which is where the dotted line labeled 10 crosses the red light-cone line.

It is counter-intuitive that the light we see from the furthest galaxy was emitted at a proper distance from here considerably less than light from a much closer galaxy with a redshift of say 2, which comes from about 5.5 BLY away, the maximum of the 'bulge' of the red light cone line.

You say that the observable universe, 'isn't a closed system since matter is continuously coming into what is our visible universe.'
and...
' you'll notice that galaxies are passing into (not out of) this boundary, which means things not visible to us before become visible over time.'

Yes, the black dotted lines in all three pictures continuously cross over the green line, bringing new matter in.

But how can this be if...
'...galaxies (the black dotted lines) are continuously passing out of this event horizon, and hence we can no longer see them beyond this event, even given infinite time.'

The event horizon (orange) doesn't define the visible universe. The particle horizon (green) does.

Could you please help resolve this by explaining how galaxies are continuously exiting the event horizon, yet also passing into this boundary?

Nothing can cross into our side of the event horizon. It would not be an event horizon if it could. Similarly, nothing can cross back out of the event horizon of a black hole once it passes beyond it.
For similar reasons, nothing can exit our visible universe, crossing from inside to outside the green dashed line.

 

[Cerenkov]

It's from Davis and Lineweaver's paper, which has a lot of explanation.

Thanks Ibix.

I've bookmarked the PDF so that I can go back to it at my leisure to digest it properly.

 

[Cerenkov]

Many thanks Halc.

That's a very informative reply, pitched right at a level I can grasp.

I'll make it my business to do some further reading on the observable universe's event horizon and particle horizon so that I can better understand the difference between the two.

On another front, I now see that I had things reversed. It seemed to me that galaxies would be leaving the observable universe because the expansion of space would carry them away at superluminal speeds. I've taken on board that nothing can move through space faster than light, but space itself can stretch or expand at any speed.

But from the replies I've received I can now see that isn't the case. I still don't quite understand why the opposite is true. But that's probably because I'm using a mental comparison between a particle horizon that can only expand at light speed and space itself which can expand very much faster. In my naïve understanding the latter should exceed the former, causing galaxies to leave the observable universe.

Is there any point in you trying to explain why to me in a Basic-level thread or is the reason why to complex for me to grasp?

I'm happy to read and have a go, but some of this seems very counterintuitive to me.

Anyway, thank again.

Cerenkov.

 

[Halc]

On another front, I now see that I had things reversed. It seemed to me that galaxies would be leaving the observable universe because the expansion of space would carry them away at superluminal speeds. I've taken on board that nothing can move through space faster than light, but space itself can stretch or expand at any speed.

I'd not have described it that way exactly, but it's reasonable. In an inertial coordinate system, nothing can locally move at superluminal speeds. Distant galaxies are not local, and none of the pictures I posted use inertial (Minkowski) coordinate systems. It is quite common for things to move at faster than light in other coordinate systems.

But from the replies I've received I can now see that isn't the case. I still don't quite understand why the opposite is true.

If something could leave our observable universe, then something incoming could leave the observable universe of a really distant thing and affect us, which should not be possible from anything outside the observable universe. So it makes sense that nothing can leave it. It expands at the rate of the local speed of light of a hypothetical photon emitted from 'here' at the time of the big bang. Nothing can move faster than that photon, so nothing can overtake it and leave our visible universe.

But that's probably because I'm using a mental comparison between a particle horizon that can only expand at light speed and space itself which can expand very much faster.

The particle horizon is growing at a proper rate far greater than c, as would a photon emitted from here at the big bang.

In my naïve understanding the latter should exceed the former, causing galaxies to leave the observable universe.

You seem to imagine galaxies outrunning light that originated by us, which obviously isn't happening, else we'd not be able to see light from them. But speed of light is locally c, not relative to the emitting thing.

 

[PeterDonis]

It is quite common for things to move at faster than light in other coordinate systems.

More precisely, it is common for things to have coordinate speeds that are greater than $c$ in other coordinate systems; but in those coordinate systems, light itself will also have a coordinate speed greater than $c$. Nothing will ever have a coordinate speed faster than the coordinate speed of light at the same location.

 

[PeterDonis]

If something could leave our observable universe, then something incoming could leave the observable universe of a really distant thing and affect us, which should not be possible from anything outside the observable universe.

This is circular logic: basically you are arguing that something can't leave our observable universe because something can't leave the observable universe of a really distant thing. That argument proves nothing.

The correct way to approach this is to carefully define what we mean by "leave our observable universe" and "enter our observable universe". We will find that there are two different ways we need to define "observable universe" to make sense of these terms.

The worldlines of distant galaxies can leave the region of spacetime from which we can ever receive light signals. The boundary of that region of spacetime is the event horizon, and the diagrams you posted earlier make it obvious that the worldlines of objects can cross the event horizon. We can still see those objects; we just can't see any portion of their worldlines at or after the point where they cross the event horizon. @Bandersnatch explained this in post #2. So in that sense, objects can leave our observable universe, and in fact all objects to which we are not gravitationally bound will eventually do so.

However, the size of the region of spacetime from which we have received light signals up to now is always increasing; that is obvious too from the diagrams you posted, where the "light cone" is the boundary of the region of spacetime from which we have received light signals up to now, and that region is smaller than the region bounded by the event horizon. As we move up our worldline from "now" into the future, the "light cone" region will expand--which means it will contain the worldlines of objects whose worldlines it does not contain now. So no objects ever leave our observable universe in this sense; once a portion of some object's worldline is inside our "light cone" region, there will always be a portion (an increasing portion) of that object's worldline inside our "light cone" region. And new objects can enter our observable universe this way--our "light cone" region can expand to cover a portion of worldlines it didn't cover at all before.

What cannot happen is for the portion of some object's worldline that enters our observable universe ("light cone" region) to be after the portion of that object's worldline that is inside some really distant thing's observable universe ("event horizon" region). That is because worldlines of distant objects always enter our "light cone" region at time $t = 0$--the bottom of the diagram--but they always leave the "event horizon" region of some observer towards the top of the diagram. So in that sense, it is true that an object can't leave one observable universe and then enter another; it doesn't work that way.

 

[Halc]

This is circular logic: basically you are arguing that something can't leave our observable universe because something can't leave the observable universe of a really distant thing. That argument proves nothing.

No, I'm saying that if something can leave our observable universe (OU), then by definition the OU must be larger than the abstract line we've drawn. Otherwise, by broken symmetry, the distant thing's OU would be a different size than ours.

You can see it clearly in the 3rd picture where light speed is a 45 degree angle at all times, and the particle horizon goes off at that angle and thus cannot be crossed from inside to outside by anything. Light worldlines are curves in the upper two pictures, making it harder to see this property.

The correct way to approach this is to carefully define what we mean by "leave our observable universe" and "enter our observable universe". We will find that there are two different ways we need to define "observable universe" to make sense of these terms.

There's more than that, but only one correct definition, which is something like "relative to event X, the observable universe is the set of all matter that can ever have had a causal effect on event X". X is typically 'here and now'.
Feel free to kibitz my definition. I made it up, but it seems to be how cosmologists use the term when they say it currently has a radius of about 46 BLY.

The worldlines of distant galaxies can leave the region of spacetime from which we can ever receive light signals. The boundary of that region of spacetime is the event horizon, and the diagrams you posted earlier make it obvious that the worldlines of objects can cross the event horizon. We can still see those objects; we just can't see any portion of their worldlines at or after the point where they cross the event horizon.

I've never seen 'observable universe' refer to the event horizon (I stand corrected if Bandersnatch does so), which currently has a radius about a third of the 46 BLY radius of the OU. The Hubble distance is another 10% closer than that. Both are on the pictures (orange and purple respectively). I suppose there are those that use it that way, but it's not the distance you get when you google it.

Bandersnatch explained this in post #2. So in that sense, objects can leave our observable universe, and in fact all objects to which we are not gravitationally bound will eventually do so.

However, the size of the region of spacetime from which we have received light signals up to now is always increasing; that is obvious too from the diagrams you posted, where the "light cone" is the boundary of the region of spacetime from which we have received light signals up to now, and that region is smaller than the region bounded by the event horizon.;

Yes, this is limited to a proper distance of about 5.6 BLY. I doubt you'll find references to an observable universe of only that radius, but in theory, the universe could just stop there (fall off the edge of the simulation so to speak) and we'd have no way of knowing it.

As we move up our worldline from "now" into the future, the "light cone" region will expand--which means it will contain the worldlines of objects whose worldlines it does not contain now. So no objects ever leave our observable universe in this sense; once a portion of some object's worldline is inside our "light cone" region, there will always be a portion (an increasing portion) of that object's worldline inside our "light cone" region. And new objects can enter our observable universe this way--our "light cone" region can expand to cover a portion of worldlines it didn't cover at all before.

Agree to all, except calling it the OU. If I google 'size of observable universe' it says 93 BLY, which is a diameter, not a radius, and refers to the current distance between the two particle horizon lines.

What cannot happen is for the portion of some object's worldline that enters our observable universe ("light cone" region) to be after the portion of that object's worldline that is inside some really distant thing's observable universe ("event horizon" region). That is because worldlines of distant objects always enter our "light cone" region at time $t = 0$--the bottom of the diagram--but they always leave the "event horizon" region of some observer towards the top of the diagram. So in that sense, it is true that an object can't leave one observable universe and then enter another; it doesn't work that way.

It actually seems more like a semantic mistake to say an object enters our OU, but rather our OU expands to include objects (initial portions of worldlines) that were not included at earlier times. The object didn't move it, the 'in line' moved.

I agree that in comoving coordinates (either of the lower two pictures) the light cone defines the OU better than the particle horizon. I use the particle horizon only because it has a current proper distance of the 46 BLY we want, but it is the 46 BLY comoving distance of our light cone at t=big-bang that defines the size of the OU. But observing the universe has nothing to do with outgoing signals, and the particle horizon is an outgoing thing, and is how other observers might be able to observe our beginnings.

 

[PeterDonis]

I'm saying that if something can leave our observable universe (OU), then by definition the OU must be larger than the abstract line we've drawn. Otherwise, by broken symmetry, the distant thing's OU would be a different size than ours.

I have no idea what you are saying here.

the particle horizon

Is not what defines the observable universe. See further comments below.

only one correct definition, which is something like "relative to event X, the observable universe is the set of all matter that can ever have had a causal effect on event X". X is typically 'here and now'.

So this would be the set of worldlines that have any portion inside the "light cone" region on the diagram. Yes, for this sense of "observable universe", objects can't leave it because once a portion of a worldline is inside our "light cone" region, a portion of that worldline will always be inside our "light cone" region at any future time, since the "light cone" region always gets larger (and its limiting region as time goes to future infinity is the "event horizon" region).

I understand this, but I don't understand how what you said in the first quote I gave from you in this post, or the previous argument of yours that I said was circular in a previous post, is saying what I am saying in the above paragraph.

I made it up, but it seems to be how cosmologists use the term when they say it currently has a radius of about 46 BLY.

What cosmologists mean when they say the "observable universe" currently has a radius of about 46 GLy is that that is the distance from us "now" of the furthest comoving worldline that has some portion inside the "light cone" region on the diagrams. However, cosmologists are notorious, particularly in communications with non-cosmologists and the public, for loose usage of terminology. This statement by cosmologists does not really tell you anything useful about what we can observe. For example, it gives no hint that we can only see a portion of the worldline of any distant object that is in our observable universe--we can't see the portion that is outside the "light cone" region, and we will never, even in the infinite future, be able to see the portion that is outside the "event horizon" region.

Also, to get back to the original subject of this thread, from the standpoint of a "closed system", the observable universe is certainly not one. Even if objects can't leave it (which they can't if we adopt your preferred definition), they can enter it, and are continually doing so as we move into the future and our "light cone" region of spacetime covers portions of more worldlines (and note that this is true regardless of which definition we adopt, your preferred one or mine--but see below for a further comment on that).

It actually seems more like a semantic mistake to say an object enters our OU, but rather our OU expands to include objects (initial portions of worldlines) that were not included at earlier times. The object didn't move it, the 'in line' moved.

You can look at it this way, but the obvious question to ask if you do is, who the heck cares about the observable universe on this definition? If it's just some abstract line that's moving, and nothing about the objects is affected, what's the point?

Focusing on the "light cone" region, however, emphasizes that what is happening is that new objects are now able to causally influence us. True, it's just the initial portions of the worldlines of those objects, not those objects "now", because of the finite speed of light. But it's still a matter of new causal influences. You could say it's the new causal influences that are "entering" our observable universe rather than new objects, but that seems like, to use your terminology, a semantic mistake; the causal influences come from the objects.

I agree that in comoving coordinates (either of the lower two pictures) the light cone defines the OU better than the particle horizon.

No. The particle horizon does not define the OU at all. The light cone does. The strictly correct technical definition is, as I said above, the furthest comoving worldline that has any portion inside our past light cone "now". It so happens that the particle horizon crosses that same worldline "now", because of symmetry: the particle horizon is outgoing light rays from our origin event, and the light cone is ingoing light rays to our event "now". But the particle horizon still has nothing to do with the definition of the OU.

Note that this has nothing to do with any choice of coordinates; the "light cone" region of spacetime, and which worldlines have a portion in it "now", is independent of any choice of coordinates. It's just much harder to see on the "proper distance" diagram because the scale factor goes to zero at the bottom of the diagram, so all of the worldlines appear to "radiate" from the same initial point as ours does, and you can't really tell which ones are inside the "light cone" and which aren't. One of the great advantages of conformal diagrams is that they make aspects of causal structure like this much clearer.

 

[Bandersnatch]

Honestly, guys. This is the most quibbling (the quibbliest?) exchange I've seen in a while. You seem to broadly agree on everything (and I with you both!) apart from some rather inconsequential wording.

 

[Vanadium 50]

most quibbling (the quibbliest?)

Quibbleriffic!

 

[Cerenkov]

Hey guys!

I've just liked what Bandersnatch said and laughed at Vanadium50's input.

But I'm also feeling somewhat guilty too. As I stated earlier on, I didn't want to pit Drakkith against Bandersnatch and now I don't want for the same to happen between Halc and PeterDonis.

I feel a little bit like a dwarf causing trouble between two titans. (Metaphor, of course.)

Cerenkov.

 

[Drakkith]

I didn't want to pit Drakkith against Bandersnatch

You didn't. And good thing, too. I can take @Bandersnatch in a fight!
But seriously, asking questions is rarely a bad thing. Don't feel bad because two people got into a discussion over some details.

 

[Bandersnatch]

I can take @Bandersnatch in a fight!

Them's fightin' words! <runs away and hides>

 

[Cerenkov]

Ok, so nobody's (seriously) pitting anyone against anyone else.

But the exchange between Halc and PeterDonis, though fascinating, hasn't really helped me understand the movement of galaxies across the boundary of the OU - at my Basic level.

So Yes, Drakkith, I'm still asking questions.

Right now, I still don't understand how to reconcile the movement of galaxies into the OU's light cone with what I've read (in popular science books) about space being able to expand at any speed.

In my naivety I still see the speed of the latter outpacing the speed of the former and nothing I've read in this thread (that I can understand) has explained why this isn't the case.

Nobody and nothing's at fault here except my understanding - I accept that.

But rather than just accept what's been written here because experts have said it, I'd really like to try and understand why on terms that I can grapple with.

Any ideas as to what happens next?

Thanks,

Cerenkov.

 

[PeterDonis]

I still don't understand how to reconcile the movement of galaxies into the OU's light cone with what I've read (in popular science books) about space being able to expand at any speed.

Look at the bottom diagram in post #7. As we, here on Earth, move up our worldline from "now", the top of our "light cone" moves up at well (approaching the "event horizon" as $t \rightarrow \infty$). That means that the bottom of our "light cone" moves outward at both ends, and includes new worldlines. But it includes the initial portions of those worldlines--i.e., the parts at the beginning of the universe. In other words, as I said in post #18, new objects are now able to causally influence us--they "come into view" because more time has elapsed--but we are seeing them as they were near the beginning of the universe, because that is the only part of their worldlines that has had time to send light signals to us.

Also, what I have just described has nothing to do with "space expanding". It's a simple matter of more distant objects coming into view and being able to send us light signals as more time elapses. There is no "race" going on between the universe expanding and objects coming into our observable universe; the part of those objects' worldlines that is coming into view is at the beginning of the universe, not "now", and the fact that space is expanding "now" doesn't change what already happened back at the beginning of the universe.

 

[Bandersnatch]

Right now, I still don't understand how to reconcile the movement of galaxies into the OU's light cone with what I've read (in popular science books) about space being able to expand at any speed.

This is a counter-intuitive result of regular expansion. Visit Wikipedia page on 'ant on a rubber rope'. It aims to explain how in (non-accelerating) expanding space the recession velocity is not a barrier to signals, no matter how much it exceeds the signal speed. There's a helpful animation and a mathematical treatment.

 

[Cerenkov]

Hi Bandersnatch.

I've checked out that Wiki page and the animation.

https://en.wikipedia.org/wiki/Ant_o...,the principles of the puzzle remain the same.

But there's still a problem.

The ant is going in the same direction as the stretching of the rope. Which is not the scenario I was referring to. If the ant represents a galaxy receding from us (we are located at 0, on the left hand end of the rope) then its light will be traveling from right to left. Which means that the light must fight against the rapid extension of the rope to the right. The result of this being that its light never reaches us at 0. Space (the rope) is extending too rapidly.

Even if the ant (galaxy) were going from right to left, its speed is less than that of the extension of the rope. Which would yield the same result. The expansion of space still causes receding galaxies to disappear from our OU.

Can you help?

Thanks.

Cerenkov.

 

[Cerenkov]

Thank you PeterDonis.

With your help I can now 'read' the meaning of the diagram more clearly.

As our light cone moves upwards over time it must inevitably increase in size, allowing us to view a greater and greater volume of space.

Within this volume are galaxies that weren't visible to us, but now are.

So, this answers my core question about the OU being a closed system.

It cannot be, because new matter is entering our OU all the time.

Thank you very much for your help.

Cerenkov.

 

[Bandersnatch]

The ant is the signal (light). The ends of the rope are the emitting galaxy (left, where the ant starts its journey) and the observer (right). The animation has the rope anchored at its left end, but it could have been anchored at its rightmost, and the result would have been the same - much as it doesn't matter if we think of outgoing or incoming signals (i.e. the situation is symmetrical, which is the reason the particle horizon on the graphs has the same extent as the base of the past light cone).
The ends of the rope recede from each other at recession velocities higher than the local speed of the ant. Yet, the ant makes it from the source to the receiver. So, given enough time, and with non-accelerating expansion of the rope, the observer will receive ants from arbitrarily far away.

 

[Halc]

So, given enough time, and with non-accelerating expansion of the rope, the observer will receive ants from arbitrarily far away.

I want to underscore the importance of this statement, especially the non-accelerating part.
Given a rope with the far end moving away at some arbitrarily high speed, the slow ant, despite at first getting further away from the near end of the rope, will eventually get there no matter how long the rope is or the magnitude of the constant speed at which it is pulled.

On the other hand, if the end of the rope is accelerating away from the near end (not moving at uniform speed), then there is a point on the rope beyond which the ant will never reach. Such is the case with our universe, and without the accelerated expansion, there would be no event horizon beyond which light cannot reach us.

 

[Cerenkov]

Thank you Bandersnatch and Halc.

I get it now.

There's just one last item that I'd like some help with please.

Both of you and PeterDonis have been at pains to emphasize that the diagrams employ non-accelerating expansion.

But in 1998 those two supernova teams discovered that the universe's expansion is accelerating.

How would this change things?

Thanks again,

Cerenkov.

 

[PeterDonis]

Both of you and PeterDonis have been at pains to emphasize that the diagrams employ non-accelerating expansion.

Where did we say that? It's not correct. The diagrams @Halc posted are for our actual universe, in which, as you note, the expansion is accelerating (more precisely, it has been accelerating since a few billion years ago).

 

[PeterDonis]

This is a counter-intuitive result of regular expansion. Visit Wikipedia page on 'ant on a rubber rope'. It aims to explain how in (non-accelerating) expanding space the recession velocity is not a barrier to signals, no matter how much it exceeds the signal speed.

Unfortunately, the "ant on a rubber rope" analogy is useless in our actual universe, in which the expansion is accelerating (or, more precisely, has been since a few billion years ago).

Furthermore, that analogy is not necessary to explain why new objects are continually entering our observable universe. The latter does not just happen with non-accelerating expansion. It happens with accelerating expansion as well. The only difference with accelerating expansion is that there is an event horizon, which imposes an upper limit on how many objects will ultimately be inside our OU; but that limit is approached asymptotically, so new objects are always entering our OU, just fewer per unit proper time as we move into the future.

 

[Bandersnatch]

Unfortunately, the "ant on a rubber rope" analogy is useless in our actual universe, in which the expansion is accelerating

It's not meant to be an analogy for our universe. Nobody claimed that. If anything, it's an analogy for a Milne universe (and de Sitter, and Einstein-de Sitter, if we vary the stretching). Much like those simple models, it's a pedagogical tool for helping understand certain properties of expansion. As such, I find it far from useless.

 

[Cerenkov]

Where did we say that? It's not correct. The diagrams @Halc posted are for our actual universe, in which, as you note, the expansion is accelerating (more precisely, it has been accelerating since a few billion years ago).

I'm sorry Peter. My bad. I didn't know that the diagrams factored in accelerating expansion.