View Full Version : Large scale relativity question

wiggy

2011-Jun-26, 06:05 AM

Just trying to think this through, so please correct me.

One side of the universe is moving away from us at close to the speed of light.

The other side of the universe is moving away from us at close to the speed of light.

If a star on one edge of the universe emits two photons and things can not move apart at two times the speed of light, does one photon reach us at the same time (after the same number of periods) as it reaches the other side of the universe.

Or

Is relativity only localised to a few light years?

Or

Is one side of the universe beyond the event horizon of the other?

Jeff Root

2011-Jun-26, 07:15 AM

Is one side of the universe beyond the event horizon of the other?

That is correct. A galaxy that we see close to our horizon in the

east is beyond the horizon of a galaxy that we see close to our

horizon in the west. Very much like seeing things on the surface

of the Earth, which of course is the reason for the term "horizon".

Because of the acceleration of the expansion, photons which leave

our galaxy today -- or which left a galaxy near our "eastern" horizon

billions of years ago -- will never reach a galaxy near our "western"

horizon. Without the acceleration, they would get there eventually,

but it could take a very long time.

-- Jeff, in Minneapolis

wiggy

2011-Jun-26, 08:14 AM

So that means that the opposite sides of the universe are moving apart at greater than the speed of light?

Shaula

2011-Jun-26, 08:27 AM

Th relativistic limit is that information cannot be transferred faster than the speed of light. Objects causally disconnected by an event horizon can be moving apart arbitrarily fast as a consequence of metric expansion.

BTW when you say universe you mean observable universe, right? We have no evidence that the universe has an edge.

wiggy

2011-Jun-26, 11:04 AM

Err... my gut feeling here is that the observable universe should actually be shrinking.

The edge should be constantly dropping over the horizon.

Is that correct?

If so, the size of the universe beyond the horizon is

a/ unknown

b/ estimated to be slightly bigger than what we can see.

c/ possibly orders of magnitude greater than what we can see.

Shaula

2011-Jun-26, 12:31 PM

The observable universe is just a limit on the region of space that we can potentially see. Acceleration of expansion means that when you compare very large time scales the portion of the universe that at the later observer's time constitutes the observable universe is represented by a smaller and smaller region in the past observer's universe. If that makes sense! That is not the same as a shrinking observable universe.

caveman1917

2011-Jun-26, 12:32 PM

It also might help to remember that the speed of light limit is a local limit. A galaxy can have a recessional velocity well over c, yet still have its light arrive at us, so still be causally connected.

It's also important to distinguish between different surfaces in cosmology, the edge of the observable universe is not the event horizon, and so on.

caveman1917

2011-Jun-26, 12:34 PM

The observable universe is just a limit on the region of space that we can potentially see. Acceleration of expansion means that when you compare very large time scales the portion of the universe that at the later observer's time constitutes the observable universe is represented by a smaller and smaller region in the past observer's universe. If that makes sense! That is not the same as a shrinking observable universe.

We might be having a bit of a misunderstanding about terms, i thought the observable universe is the region that can be seen at any given time. The event horizon is the maximum extent of the observable universe, that we can potentially ever see.

caveman1917

2011-Jun-26, 12:37 PM

You can think of it this way. The observable universe expands, and catches up with the light of galaxies that aren't in it yet. As the expansion accelerates however, this will turn around and galaxies will be moving away quicker than the edge of the observable universe can catch up with the light they emit. So while the observable universe grows in size, it will contain less and less galaxies.

Shaula

2011-Jun-26, 12:44 PM

We might be having a bit of a misunderstanding about terms, i thought the observable universe is the region that can be seen at any given time. The event horizon is the maximum extent of the observable universe, that we can potentially ever see.

Yeah, bad wording on my part. I meant that the observable universe was a term only really valid for a given time. Hence why I was trying to relate it to an area of a previous universe and explain how that was changing with time. The horizon is, as you said, the point beyond which we can never see.

Perikles

2011-Jun-26, 12:56 PM

You can think of it this way. The observable universe expands, and catches up with the light of galaxies that aren't in it yet. As the expansion accelerates however, this will turn around and galaxies will be moving away quicker than the edge of the observable universe can catch up with the light they emit. So while the observable universe grows in size, it will contain less and less galaxies.I had to read this a dozen times, and am still not sure I understand it. Am I to understand that we have not yet reached this point in time when the observable universe contains fewer and fewer galaxies? If the expansion increases further, would there be a point in time when we can't actually see any galaxies at all? (If yes, then I suppose our solar system will have long gone anyway by that time)

caveman1917

2011-Jun-26, 02:47 PM

I had to read this a dozen times, and am still not sure I understand it. Am I to understand that we have not yet reached this point in time when the observable universe contains fewer and fewer galaxies? If the expansion increases further, would there be a point in time when we can't actually see any galaxies at all? (If yes, then I suppose our solar system will have long gone anyway by that time)

There are a couple of factors at play here, and it's easy to mess them up (so don't just take my word on all this :)).

The observable universe is all galaxies whose light has had time to reach us, from the beginning of the universe. This is limited at about 60 billion light years comoving distance, in other words stuff more than 60 billion light years away from us can never be seen by us. Currently we are not at that ultimate limit yet. So in that sense we have not yet seen everything we will ever be able to observe, i think we've seen about half of it yet at this time. So the number of galaxies will continue to increase for a while, and will technically remain at that max amount forever (1).

However there's another quirk in all this, because we define the observable universe to be that region for light that has had time from the start of the universe. So while we may have seen a galaxy when it was young, it doesn't mean we will continue to see it 'grow old', even though we keep counting it as 'in the observable universe'. So we define yet another boundary, which is the limit for light that is emitted now will ever reach us. This boundary lies at about 16 billion light years at the moment, and is shrinking. So in this sense galaxies pass 'out of view' as they pass this boundary (or more strictly, as this boundary shrinks over them) (2).

The question of how many galaxies are visible at any given time depends on the ratio of those two (1 to 2). It's the interplay between those two processes that determines what we see at any given time. I think (though i haven't done the math on this, and have learned not to try to do any math on a hangover sunday :)) the ratio is such that we see more and more galaxies for a while until the observable universe reaches the 'ultimate limit' (at ~60 billion light years), after which we start seeing less and less of them. However note that they are not the same galaxies, some move out of view while others move in view all the time.

In any case, given enough time in the far away future, all we will be able to see is the local gravitationally bound group, which is the Virgo supercluster.

Also, all of this depends on assuming that our current cosmological constant model is correct of course.

Perikles

2011-Jun-26, 03:54 PM

Very interesting - many thanks for the explanation. Does this second boundary ("So we define yet another boundary, which is the limit for light that is emitted now will ever reach us. This boundary lies at about 16 billion light years at the moment, and is shrinking.") have an accepted name? Consistent terminology here seems vital.

caveman1917

2011-Jun-26, 04:33 PM

Very interesting - many thanks for the explanation. Does this second boundary ("So we define yet another boundary, which is the limit for light that is emitted now will ever reach us. This boundary lies at about 16 billion light years at the moment, and is shrinking.") have an accepted name? Consistent terminology here seems vital.

It's also called a cosmological event horizon. It's principally the same thing as the 'maximum extent of the observable universe'. In order to get to this, we consider some time t. For the first event horizon, we set t=now, see from where light emitted at that time can get to us in the infinite future, and get the 16 billion light year figure. For the maximum extent horizon, we set t=0 and get the 60 billion light year figure. They're essentially the same thing. You could think of the cosmological event horizon as starting out at 60 billion light years at the start of the universe, and continuously shrinking over time, now being at 16 billion light years. In due time it will be as small as you want. But since our local supercluster is gravitationally bound, the parts of it won't 'disappear', so all that will be left for us to see is our local supercluster.

The reason we use the t=0 (60 billion light year) figure for the observable universe, is because everything outside is causally disconnected from us. However, not everything inside will remain causally connected to us. The 'observable universe' is not everything we see, it is everything we see and have seen in the past, but not necessarily see anymore right now.

Perikles

2011-Jun-26, 05:34 PM

Many thanks again - I'll need to sleep on that, but the definitions are extremely useful. (I hope I haven't highjacked somebody else's thread.)

caveman1917

2011-Jun-27, 02:17 AM

As was to be expected, i of course messed up in my previous post (perhaps i should change the "no math on a hangover day" to include "no explaining stuff on a no-math day" :)).

Let me start over.

Define the particle horizon to be the furthest we can see at any given time.

Define the cosmological event horizon to be the furthest point where light emitted at any given time will ever reach us in the future.

Define the limit horizon to be the maximum extent of the particle horizon, in other words that part of the universe that will ever be or has been visible.

Define the observable universe to be the region of the universe that can be seen at any given time.

In terms of comoving distance the following will hold at any time

particle horizon + cosmological event horizon = limit horizon. (1)

c \int_0^{t_0}\frac{\mathrm{d}t'}{a(t')} + c \int_{t_0}^{\infty}\frac{\mathrm{d}t'}{a(t')} = c \int_0^{\infty}\frac{\mathrm{d}t'}{a(t')}

Equation 1 is the key to the entire thing :)

Right now the cosmological event horizon is at 16 billion light years. So light that is emitted now at 16 billion light years away will still (barely) reach us, however this also means that the 'first light' that was emitted from far-away galaxies that is now coming in at 16 billion light years from us will also reach us, though not yet. There are still 'new galaxies' waiting to be seen by us as long as the cosmological event horizon > 0 (since their 'first light' could be inside the cosmological event horizon, and thus to be seen in the future by us). In other words, the galaxies that are between the particle horizon and the limit horizon all have their 'first light' within the cosmological event horizon.

The observable universe will first expand with the particle horizon, until it hits the limit horizon (or alternatively, until the cosmological event horizon equals 0). After which it will start to shrink again until it hits 0 again (not exactly 0 since our local supercluster is gravitationally bound, and thus not as a whole comoving with the hubble flow).

A mental picture might be this.

Consider a point, and a shell 62 billion light years in radius around that point. At the moment the universe starts, a 'pulse' is given off by the point towards the shell (this is the particle horizon/observable universe) and another 'pulse' is given off by the shell inwards towards the central point (this is the cosmological event horizon). By the time the first pulse hits the shell, the latter pulse hits the central point. The first pulse will then be reflected off the shell, back inwards towards the central point. This first pulse is how the observable universe behaves.

This only works in comoving distance, which is not the intuitive proper distance, the two are related by the scale factor.

In essence, comoving distance is saying that everything at rest with the hubble flow always remains at the same distance from eachother.

Perikles

2011-Jun-27, 10:30 AM

Thanks yet again! A lot to ponder over. I think I'll give cosmology a miss on Sundays as well.

caveman1917

2011-Jun-27, 01:22 PM

The observable universe will first expand with the particle horizon, until it hits the limit horizon (or alternatively, until the cosmological event horizon equals 0). After which it will start to shrink again until it hits 0 again (not exactly 0 since our local supercluster is gravitationally bound, and thus not as a whole comoving with the hubble flow).

The first pulse will then be reflected off the shell, back inwards towards the central point. This first pulse is how the observable universe behaves.

This last bit might not be completely correct, about what happens to the observable universe after the particle horizon reached its maximum extent.

It seems that we can consider the cosmological event horizon as the "last picture of the universe" that we will ever see, since at the moment the cosmological event horizon reaches 0 there will be no more light reaching us anymore. One could think of it like this, it starts out at the ultimate edge of the observable universe containing a picture of the furthest galaxies when they were most young. As this shell comes towards us, the light of intermediate galaxies is added to it, at the age they have when the shell passes them.

So at the moment that shell of light reaches us, it contains an entire 'picture' of the universe, with the closest galaxies being older and further galaxies increasingly younger. This by itself doesn't seem all that surprising, and in fact we could do this for every 'shell of light' that reaches us before the event horizon and thus contains a picture of the universe.

However this gives a surprising result. At the time the particle horizon reaches the "limit horizon", what we see goes immediately completely black. One moment we see a picture of the entire universe, the next moment we see nothing at all, rather than having further galaxies fade out of view before closer ones. As if someone suddenly "pulls the plug out of the universe" rather than having a smooth retreat of the observable universe. The math seems to say this, but the result is quite counterintuitive. I'll have to think about (and research) this a little more, but that's for another time :)

caveman1917

2011-Jun-27, 04:15 PM

The reasoning in the post above is by itself correct, but the problem of galaxies disappearing from view has more to do with the redshift. Further galaxies will be redshifted more (at any given time), and a galaxy disappears whenever the wavelength of its light gets larger than the observable universe. Since further galaxies will reach this wavelength earlier, they will disappear earlier. Thus giving us the "smooth retraction" of the observable universe.

WayneFrancis

2011-Jun-27, 04:34 PM

Just trying to think this through, so please correct me.

One side of the universe is moving away from us at close to the speed of light.

The other side of the universe is moving away from us at close to the speed of light.

If a star on one edge of the universe emits two photons and things can not move apart at two times the speed of light, does one photon reach us at the same time (after the same number of periods) as it reaches the other side of the universe.

Or

Is relativity only localised to a few light years?

Or

Is one side of the universe beyond the event horizon of the other?

Good questions.

One side of the universe is moving away from us at close to the speed of light.

Actually the edge of the observable universe is receding from us at a speed much greater then c but I won't get into that and will stick with the normal z value translation of

http://latex.codecogs.com/gif.latex?\tiny%20\inline%20\dpi{300}%20z%20=%20\f rac{\Delta\lambda%20}{\lambda}%20=%20\sqrt{\frac{1 +\frac{v}{c}}{1-\frac{v}{c}}-1}

If a star on one edge of the universe emits two photons and things can not move apart at two times the speed of light, does one photon reach us at the same time (after the same number of periods) as it reaches the other side of the universe.

Actually things can move apart at speeds > c. No information may be transmitted faster then c. Points in space can recede from each other at any speed, do to cosmic expansion.

Is one side of the universe beyond the event horizon of the other?

Yes, the stuff we see on one side of our universe is outside of the observable universe of a point on the other side of the universe. CMBR that is passing us now will never reach the point in space where the CMBR on the opposite side of us was emitted from unless expansion some how slows down.

WayneFrancis

2011-Jun-27, 04:40 PM

The observable universe is just a limit on the region of space that we can potentially see. Acceleration of expansion means that when you compare very large time scales the portion of the universe that at the later observer's time constitutes the observable universe is represented by a smaller and smaller region in the past observer's universe. If that makes sense! That is not the same as a shrinking observable universe.

Let me see if I can put that is different words. While the size of the visible universe grows over time the amount of stuff in it gets less. So the energy density of the visible universe is shrinking but this is different then hubble volume shrinking. The Hubble volume grows...just the amount of stuff in our Hubble volume decreases.

Ken G

2011-Jun-29, 06:53 PM

Define the particle horizon to be the furthest we can see at any given time.

Define the cosmological event horizon to be the furthest point where light emitted at any given time will ever reach us in the future.

Define the limit horizon to be the maximum extent of the particle horizon, in other words that part of the universe that will ever be or has been visible.

Define the observable universe to be the region of the universe that can be seen at any given time.

In terms of comoving distance the following will hold at any time

particle horizon + cosmological event horizon = limit horizon. (1)

c \int_0^{t_0}\frac{\mathrm{d}t'}{a(t')} + c \int_{t_0}^{\infty}\frac{\mathrm{d}t'}{a(t')} = c \int_0^{\infty}\frac{\mathrm{d}t'}{a(t')}

Yes, these are important integrals. Note we can interpret them as choosing our distance coordinate to be comoving-frame distances at the current age of the universe, and then imagining that none of those distances ever change, either back in time or forward in time (they're just a coordinate, after all). Then the integrals above can be interpreted as saying that the coordinate speed of light is falling with the age of the universe. The first integral gives the largest distance at which any aliens in space can see our galaxy at this age, and the second integral gives the distance that the light now emitted from our galaxy will ever travel in the rest of the infinitude of time. That both of these distances are not infinite is an important aspect of the accelerating Big Bang. It also tells us that if the first integral is larger than the second (as must be true, you said the second integral is 16 billion LY and I believe the first is something like 40 billion LY), then there are aliens out there right now that can see our galaxy, but will never see the light our galaxy is now emitting. This implies our galaxy will "blink out" for them at some future time.

To see this, let's take some alien at 30 billion LY (in the coordinate distance we are using). Right now (at age 13.7 billion years), they can see our galaxy (as it was a very long time ago, let's not worry about the actual age of our galaxy), because that first integral is larger than 30 billion LY. But at some past to, the first integral was 30 billion LY, and that's when those aliens first saw us (assuming they've been around the whole time). Also, there was some other time, call it t1, when the second integral was 30 billion LY, and that's the last time light emitted by our galaxy will ever be seen by those aliens. That light will reach them in a finite time, so after that we will have "blinked out" for those aliens.

At the distance where t1 = to, we will eventually blink out for those aliens, a very long time from now. The same holds for galaxies that far from us, we will eventually not see them. At larger distances still, the "blink out" age gets earlier. You use the second integral to find the time when we emit the last light they will see, and then figure out how long it takes that light to reach them to see when we blink out.

caveman1917

2011-Jun-30, 02:11 PM

Yes, these are important integrals. Note we can interpret them as choosing our distance coordinate to be comoving-frame distances at the current age of the universe, and then imagining that none of those distances ever change, either back in time or forward in time (they're just a coordinate, after all). Then the integrals above can be interpreted as saying that the coordinate speed of light is falling with the age of the universe. The first integral gives the largest distance at which any aliens in space can see our galaxy at this age, and the second integral gives the distance that the light now emitted from our galaxy will ever travel in the rest of the infinitude of time. That both of these distances are not infinite is an important aspect of the accelerating Big Bang. It also tells us that if the first integral is larger than the second (as must be true, you said the second integral is 16 billion LY and I believe the first is something like 40 billion LY), then there are aliens out there right now that can see our galaxy, but will never see the light our galaxy is now emitting. This implies our galaxy will "blink out" for them at some future time.

To see this, let's take some alien at 30 billion LY (in the coordinate distance we are using). Right now (at age 13.7 billion years), they can see our galaxy (as it was a very long time ago, let's not worry about the actual age of our galaxy), because that first integral is larger than 30 billion LY. But at some past to, the first integral was 30 billion LY, and that's when those aliens first saw us (assuming they've been around the whole time). Also, there was some other time, call it t1, when the second integral was 30 billion LY, and that's the last time light emitted by our galaxy will ever be seen by those aliens. That light will reach them in a finite time, so after that we will have "blinked out" for those aliens.

At the distance where t1 = to, we will eventually blink out for those aliens, a very long time from now. The same holds for galaxies that far from us, we will eventually not see them. At larger distances still, the "blink out" age gets earlier. You use the second integral to find the time when we emit the last light they will see, and then figure out how long it takes that light to reach them to see when we blink out.

Thanks for the clarification. The problem i encountered was however one step deeper in the reasoning.

Let's do everything from our vantage point. Suppose there are two alien galaxies, A and B, where A is nearer to us than B Since both integrals are finite, there will be some last photon from either galaxy after which we receive nothing. Let's call these photons pA and pB respectively. It will also be true that pA is 'younger' than pB, the image it conveys pictures a younger galaxy for pA than for pB.

Let's look at the emittance of pA. When pA is emitted, there will also be a photon from B passing by A (this is assuming B is visible to A at the time pA is emitted, this assumption might be the fault in the reasoning though, but it looks ok). Since nothing else coming from A will reach us after pA, this means that pB is just passing by A at the time pA is emitted. So pA and pB travel "together" towards us. Since they are traveling together, there will be no differential effects on their arrival time at us. So pA and pB will arrive simultaneously. We will see both galaxies "blink out" at the same time, even though galaxy B will "look older" than A at that time.

Now since we didn't assume anything else about A and B other than that A is nearer, we can extrapolate this to the entire visible universe. This seems to suggest that the entire visible universe will "blink out" at the same time, rather than us loosing sight of the further galaxies first. It is true that the last we see of the further galaxies will be "older" light, but the "last light" of all of them arrives at the same time. So at one moment we see an "entire picture" of the universe, and the next moment we see nothing at all. This seems very strange.

Ken G

2011-Jun-30, 03:25 PM

Suppose there are two alien galaxies, A and B, where A is nearer to us than B Since both integrals are finite, there will be some last photon from either galaxy after which we receive nothing. Let's call these photons pA and pB respectively. It will also be true that pA is 'younger' than pB, the image it conveys pictures a younger galaxy for pA than for pB.I would have said pA conveys an older galaxy, but this is not really your issue. It might be easier to think about the light we send out, because our relationship with these galaxies is symmetric. Your second integral on the LHS tells us the range of the photons our galaxy emits at various to. We have distance to A, dA, and distance to B, dB, with dA<dB. This means the time we emit photon pA, call it tA, is later than the time we emit photon pB, i.e., tA > tB. Thus, pA is of an older version of our galaxy than is pB (where note I've reversed the meaning of pA, it's the last photon we emit that A gets, but this is a symmetric issue if all the galaxies are the same).

Let's look at the emittance of pA. When pA is emitted, there will also be a photon from B passing by A (this is assuming B is visible to A at the time pA is emitted, this assumption might be the fault in the reasoning though, but it looks ok). Since nothing else coming from A will reach us after pA, this means that pB is just passing by A at the time pA is emitted. So pA and pB travel "together" towards us. Since they are traveling together, there will be no differential effects on their arrival time at us. So pA and pB will arrive simultaneously. We will see both galaxies "blink out" at the same time, even though galaxy B will "look older" than A at that time.Yes, that is an interesting point (though galaxy B will look younger, but this is not your issue). I was wondering this before, it comes down to the question of at what age do we receive the last photons, rather than what age do we emit them. I wondered if maybe that age was infinite, but I figured it probably wasn't because people do talk about galaxies "blinking out". But your argument seems pretty bulletproof to me, yet we know the whole universe does not blink out at some time, so the only possible resolution is that everything blinks out at a time of infinity, i.e., things don't actually blink out at all, even in an accelerating universe.

So why do people talk about things blinking out? I don't know, but perhaps you are correct that they are actually talking about the dimming and Doppler shifting of the light. If you take into account the quantum nature of light, there is some expected time for the "last photon", such that you cannot use your argument that every time A emits a photon there is a photon from B going by. That's the classical limit of a continuous radiation field, with arbitrarily low intensity and arbitrary redshift, rather than quantized radiation that passes by discretely. Still, those kinds of considerations must only come up for extremely weak and highly redshifted galaxies-- more than likely, "blinking out" is a more practical issue of when our telescopes simply can no longer detect those galaxies, which happens well before we get to the "last quantum".

caveman1917

2011-Jun-30, 04:39 PM

I would have said pA conveys an older galaxy, but this is not really your issue {...} (though galaxy B will look younger, but this is not your issue).

Yes indeed :)

I was thinking of "older" in the sense that the photon existed for a longer time, but that indeed means it will convey a younger galaxy, my mistake.

caveman1917

2011-Jun-30, 04:52 PM

So why do people talk about things blinking out? I don't know, but perhaps you are correct that they are actually talking about the dimming and Doppler shifting of the light. If you take into account the quantum nature of light, there is some expected time for the "last photon", such that you cannot use your argument that every time A emits a photon there is a photon from B going by. That's the classical limit of a continuous radiation field, with arbitrarily low intensity and arbitrary redshift, rather than quantized radiation that passes by discretely. Still, those kinds of considerations must only come up for extremely weak and highly redshifted galaxies-- more than likely, "blinking out" is a more practical issue of when our telescopes simply can no longer detect those galaxies, which happens well before we get to the "last quantum".

After thinking about it some more, the resolution might indeed be with the redshift.

Let's assume two different scenarios, a simply expanding universe A and an accelerating expanding universe B.

The particle horizon of A has no limit, it will expand indefinitely. So the extent of the observable universe has no limit. This means that there will never be a time when the wavelength of a galaxy's light will be and always remains larger than the observable universe (we can just wait a bit for the observable universe to grow large enough). Though there is the issue here of which grows the fastest, the wavelength or the observable universe.

On the other hand, for B this is not true, since the "limit horizon integral" is finite. So at some point the wavelength of a galaxy's light will be larger than the observable universe, and will always remain that way.

It might just be that people are actually talking about the issue that in an accelerating universe, galaxies will go "undetectable in principle" (lambda > observable universe), where they won't in a simply expanding universe. So there might in fact never be any "last light" to hit us technically speaking (at least in a classical point of view), it's just that in one case the light that keeps hitting us becomes principally undetectable, but in the other case it doesn't.

The language of "blinking out" might be the confusing factor here, rather than "slowly redshifting out of detectability, even to the point of not being detectable in principle anymore".

Ken G

2011-Jul-01, 02:54 AM

So at some point the wavelength of a galaxy's light will be larger than the observable universe, and will always remain that way.

That can't quite be true either though, because the wavelength when emitted by the star is a tiny fraction of the observable universe, and as the universe expands, so will the wavelength, but it will never expand faster than the universe. So I really am hard pressed to see any fundamental difference between an accelerating universe and just a regular expanding one in terms of the "blinking out" of any galaxies. In both cases, galaxies get farther and redder, and at some point our instruments will not be sensitive enough to see them any more. It's true that for an accelerating universe, all the light emitted in a finite time before the "last light" from the galaxy is spread over an infinite time on Earth, but by then we won't be seeing that universe any more anyway. So I don't get that "blinking out" in an accelerating universe, it doesn't seem very important.

caveman1917

2011-Jul-01, 10:26 PM

That can't quite be true either though, because the wavelength when emitted by the star is a tiny fraction of the observable universe, and as the universe expands, so will the wavelength, but it will never expand faster than the universe. So I really am hard pressed to see any fundamental difference between an accelerating universe and just a regular expanding one in terms of the "blinking out" of any galaxies. In both cases, galaxies get farther and redder, and at some point our instruments will not be sensitive enough to see them any more. It's true that for an accelerating universe, all the light emitted in a finite time before the "last light" from the galaxy is spread over an infinite time on Earth, but by then we won't be seeing that universe any more anyway. So I don't get that "blinking out" in an accelerating universe, it doesn't seem very important.

I got it :)

We've been looking at the wrong integral.

Let's suppose, best case, we have a detector that's as large as the observable universe. The effective length of that detector at any given time however will be given by the cosmological event horizon (2nd integral), since whenever we want to do a measurement at t0, we can only get results back (even waiting an infinite time for them) from the part of the detector within the cosmological event horizon at t0.

This integral will grow smaller with increasing t, which in terms of comoving distance means that the size grows slower than the universe/scale factor, so galaxies will redshift out of detectability (even in principle!). The wavelength will expand faster than the effective length of the detector.

The reasoning in my previous post is correct, but i was wrong in that the "detectability in principle" is given by the 2nd integral (cosmological event horizon), not the 3rd (observable universe).

The important difference between simply expanding and accelerating is that the 2nd integral gets smaller (in comoving coordinates), where in the other case it is infinite.

Though i suppose we could still say it's because the observable universe has a finite limit, since that implies (by the equation) a shrinking cosmological event horizon.

Ken G

2011-Jul-02, 05:11 AM

The wavelength will expand faster than the effective length of the detector.That is true, but it cannot be what is meant by the claim that in an accelerating universe, galaxies "blink out." For that claim, they must mean this happens for the telescopes we actually have, and they cannot mean that galaxies blink out when there is not enough time left in creation for us to read out our telescope CCD. I'm tempted to conclude the whole "blinking out" argument is actually a mistake-- what is actually meant is that we will never see a given galaxy older than the to that associates by that second integral with the distance to that galaxy. But saying we'll never see a galaxy older than some age does not mean our telescopes will cease to see that galaxy-- it just means that galaxy will appear to freeze in time as it gets more and more redshifted. I suspect that is really what is meant when people talk about the key difference of an accelerating universe-- all related to that second integral being finite.

caveman1917

2011-Jul-02, 02:11 PM

That is true, but it cannot be what is meant by the claim that in an accelerating universe, galaxies "blink out." For that claim, they must mean this happens for the telescopes we actually have, and they cannot mean that galaxies blink out when there is not enough time left in creation for us to read out our telescope CCD.

I think you might have misunderstood the gist of the argument. It's not so much about the time left to read out our telescopes, but about what length they should have.

As i understand it, for someone to be able detect light at a certain wavelength, a detector is needed with a length at least as great as that wavelength (i may be wrong in this, it's just one of those factoids stuck in my mind, could you comment wether this is actually true as it's the basis of my argument?).

So what needs to be compared is wavelength vs length of detector.

But saying we'll never see a galaxy older than some age does not mean our telescopes will cease to see that galaxy-- it just means that galaxy will appear to freeze in time as it gets more and more redshifted.

But if the galaxy redshifts faster than the length of our "best possible in principle" detector increases, this means that at some finite time the galaxy will "blink out" for us, even in principle.

For a simply expanding universe, the length of our "best possible in principle" detector is infinite, thus nothing will "blink out".

In practical terms, i agree that the actual telescopes we have will stop seeing galaxies long before that (in both cases). But i have trouble imagining that all the fuss is about something practical, rather than something that's theoretically true in principle.

Ken G

2011-Jul-03, 06:18 PM

I think you might have misunderstood the gist of the argument. It's not so much about the time left to read out our telescopes, but about what length they should have.

As i understand it, for someone to be able detect light at a certain wavelength, a detector is needed with a length at least as great as that wavelength (i may be wrong in this, it's just one of those factoids stuck in my mind, could you comment wether this is actually true as it's the basis of my argument?).

So what needs to be compared is wavelength vs length of detector.

Sure, but that's not a practical limit. A galaxy emits plenty of UV light at, say, 1000 Angstroms, and we can detect, in principle, light at radio wavelengths of meters. So we can detect a redshift of a million, if the intensity would be bright enough--- but it wouldn't be, that is the practical problem. Still, to claim the galaxies are "blinking out", it would have to mean no light at all, not just practically undetectable light, so that's what I don't think is actually correct. I think they just mean we won't practically be able to see them any more.

But if the galaxy redshifts faster than the length of our "best possible in principle" detector increases, this means that at some finite time the galaxy will "blink out" for us, even in principle.Yes, but no one expects intelligent beings to be around any more by then-- that can't be what people mean about blinking out in an accelerating universe. It has to be something that would happen in just a few more tens of billion years at most, to make much sense.

But i have trouble imagining that all the fuss is about something practical, rather than something that's theoretically true in principle.I feel the opposite way-- it has to be something we can imagine actually happening to human (or alien) astronomers, with real telescopes that we can actually imagine building, or it's just more science fiction. And in that sense, it doesn't seem to be any more true in an accelerating universe than in a non-accelerating expansion. What is true, though, in an accelerating but not non-accelerating universes, is that we will never be able to see a certain distant galaxy at an older age than the limit given by that second integral.

caveman1917

2011-Jul-03, 07:07 PM

Yes, but no one expects intelligent beings to be around any more by then-- that can't be what people mean about blinking out in an accelerating universe. It has to be something that would happen in just a few more tens of billion years at most, to make much sense.

I did a quick google search and it came up with this (http://www.worldscinet.com/ijmpd/17/1703n04/free-access/S0218271808012449.pdf) (pdf). It seems that the timeframe is not all that long into the future, since the expansion goes approximately exponential.

There also seems to be a recent article on the universe today site (here (http://www.universetoday.com/87043/cosmology-in-the-year-1-trillion/)) touching on these issues. While it doesn't give much specifics, it seems the timeline under consideration is around 1 trillion years after the big bang, another factor of 100 or so from now.

caveman1917

2011-Jul-03, 08:08 PM

Another paper, which gets more to the core issue (see section 2), that came up is this (http://iopscience.iop.org/0004-637X/531/1/22/pdf/0004-637X_531_1_22.pdf) (pdf). The authors specifically note that technically it will take an infinite time before an observer loses causal contact with distant galaxies, but that the galaxies will redshift out of detectability (ie wavelength greater than observable universe). They calculate that everything outside our local group will be out of detectability in a little under 2 trillion years (about the lifetime of the longest living main sequence stars).

Ken G

2011-Jul-04, 02:23 PM

OK, that ices it, we were right-- there really is no fundamental causal differences in the accelerating scenario (as your "last photon" gedanken proved), but the accelerating universe is able to make things happen so much more quickly that losing practical contact with the rest of the universe can happen in something like the main-sequence lifetime of stars that might conceivably host life. One important difference for the accelerating scenario though is that the light our galaxy is emitting now will never reach the more distant alien astronomers that could be out there.

caveman1917

2011-Jul-05, 09:03 PM

Another thought on all this.

there really is no fundamental causal differences in the accelerating scenario

Technically you're saying that there's no fundamental differences as far as light cones go, and that's correct. But let's retrace one step for a moment, and consider what the concept of "causality" actually means.

The best as i can express it is: two events are in a causal relation when the information embodied in the first event 'can make a difference' to the second event. (1)

We know that GR only works when the energy density of spacetime is finite. In an accelerating universe we know that the cosmological event horizon at any given time is also finite, in other words the volume of space accessible to some point in that space is always finite. From this we can see that the total energy avaiilable to some point in space is always finite, this is a theoretical limit. The energy might be huge, but it is finite (as opposed to a non-accelerating universe where it is in principle infinite if we are willing to wait an infinite time to collect it).

Now let's suppose we want to send a bit of information to a distant galaxy (before we are outside of their cosmological horizon). We can send a photon (or gravitational wave if you will - or anything you can imagine really), but since the energy available is finite, so has the frequency some theoretical upper limit.

Since we sent it before we are out of their cosmological horizon, we know that it will arrive at some finite time for them (the light cone thing). However it is very possible that by the time it arrives, it is redshifted out of detectability in principle for them (the wavelength will have become larger than their cosmological event horizon at the time they receive it).

So although, speaking in terms of light cones, this is a causal relation, it is not consistent with the meaning of causality (1).

Perhaps the question we should ask ourselves is not "is the difference between the accelerating and non-accelerating scenario practical or causal-theoretical?", but "is our standard treatment of causality by the use of light cones sufficient when we are talking about accelerating universes"?

Ken G

2011-Jul-05, 11:04 PM

I see what you mean, but there is actually an even more fundamental causal difference that I wasn't considering. I just meant that the causal relation between two galaxies was never interrupted (except by practical issues related to how extreme exponential drops can be, which is what you are talking about) by the expansion, but that kind of "causal connection" is between the galaxies, not between ourselves at this moment and any other galaxies. So I guess we should count it as a different type of causal connection if a signal we send out now could, at least in principle (notwithstanding the absurd energy that would be needed, so it would be impractical as you say), be detected by some other given galaxy in the future of the universe. When that second integral is finite, then there are galaxies that would never get our signal, and we would never get theirs, if they were sent out at the present cosmological age. That's a kind of fundamental causal difference, though it's not so much about galaxies "blinking out" as it is about some received story we were getting from that galaxy never reaching its conclusion. It's reminiscent of a signal sent by someone falling into a black hole, their transmission gets in...ter.......rup................

caveman1917

2011-Jul-05, 11:32 PM

I see what you mean, but there is actually an even more fundamental causal difference that I wasn't considering. I just meant that the causal relation between two galaxies was never interrupted (except by practical issues related to how extreme exponential drops can be, which is what you are talking about) by the expansion, but that kind of "causal connection" is between the galaxies, not between ourselves at this moment and any other galaxies. So I guess we should count it as a different type of causal connection if a signal we send out now could, at least in principle (notwithstanding the absurd energy that would be needed, so it would be impractical as you say) , be detected by some other given galaxy in the future of the universe.

It's not so much that the energy is absurd, but that it is unreachable even in principle. The energy available is finite and limited, yet the energy required grows without bound.

When that second integral is finite, then there are galaxies that would never get our signal, and we would never get theirs, if they were sent out at the present cosmological age. That's a kind of fundamental causal difference, though it's not so much about galaxies "blinking out" as it is about some received story we were getting from that galaxy never reaching its conclusion.

Yes, but even before that there will be galaxies that "get" our signal, but don't actually "get" our signal in any meaningful physical way, even in principle.

It's reminiscent of a signal sent by someone falling into a black hole, their transmission gets in...ter.......rup................

I suppose we could consider it a mapping of the interval ]0,1[ to the positive reals ]0,+inf[. Where the first interval is the cosmological time for the emitter and the latter is for the receiver. When the emitter reaches 1, it has gone past the cosmological event horizon of the receiver, the effect you are talking about.

What i am trying to say however is that a signal that is emitted well before 1, will not, even in principle, be able to be detected by the receiver, because

1. The emitting frequency has a finite upper limit

2. The receiving galaxy has a finite lower limit frequency for what it could in principle detect.

3. The ratio of f0 to f1 grows without bound even well before the emitter gets to his t=1.

Because of 3, either 1 or 2 has to give at some time, well before the time (t=1) that you are talking about.

So an event could be within our current past light cone, yet not be in causal contact to us (in any physically meaningful way of "causal contact").

This again seems way too strange to be true, yet i cannot see fault in the argument (which of course doesn't mean there isn't one).

In order to remain within causal contact until 1 (where your effect sets in), the emitting galaxy would need infinite energy or the receiving galaxy must be able to detect arbitrarily large wavelengths. Both of those are precluded in an accelerating universe (though not in a non-accelerating one).

It's not just impractical, there seems to be a theoretical limit here (other than the one you referred to, and happening before the one you referred to).

All the assumptions that went into the reasoning are theoretical ones, i have nowhere assumed any actual value for the energy or anything else, just that it is finite, which is a direct result of the applicability of GR and the fact that the universe is accelerating.

Ken G

2011-Jul-06, 12:32 AM

What i am trying to say however is that a signal that is emitted well before 1, will not, even in principle, be able to be detected by the receiver, because

1. The emitting frequency has a finite upper limit

2. The receiving galaxy has a finite lower limit frequency for what it could in principle detect.

3. The ratio of f0 to f1 grows without bound even well before the emitter gets to his t=1.

Right, but we could frame it a different way. If I wanted to send the message "we are here" to an arbitrary galaxy, and the universe were not accelerating, I could calculate what frequency I'll need, given their detecting limitations, and the power I'd need in that frequency, and partake in a little sci fi adventure to generate it. In practice, this would quickly be ridiculous, but we can imagine doing it in principle. However, for an accelerating universe, there are galaxies I simply could never get that message to in an infinite time, even with unlimited resources of power and frequency. We both see what each other are saying here, it's just that what you are talking about is a practical limitation that only gets (a lot) worse in an accelerating universe, but I'm talking about an in-principle limit that only exists in an accelerating universe. Using only the practical issues, all galaxies eventually "blink out", whether the universe is accelerating or not-- it just happens much sooner in the accelerated case. So if people have the practical limit in mind, I think it is not really correct to try to make this some kind of fundamental difference between accelerating and non-accelerating universes.

Because of 3, either 1 or 2 has to give at some time, well before the time (t=1) that you are talking about.Maybe not all that much before-- I haven't worked it out, but it might be that you would only get in a few more words in going from the practical to the in-principle limits to the message we could get across.

So an event could be within our current past light cone, yet not be in causal contact to us (in any physically meaningful way of "causal contact").

This again seems way too strange to be true, yet i cannot see fault in the argument (which of course doesn't mean there isn't one).

That doesn't seem strange to me-- it would seem stranger if there could really be meaningful causal contact across distances of trillions of LY. We thought the 1/r^2 falloff would make it hard for us to see very far, but that was before we knew about supernovae and black holes, but it seems when you go really far, it's not the 1/r^2 you have to worry about, it's the accelerating expansion. But you'd still have to worry about that in a regular expansion-- the acceleration just makes it much worse, but not fundamentally different.

caveman1917

2011-Jul-06, 01:27 AM

However, for an accelerating universe, there are galaxies I simply could never get that message to in an infinite time, even with unlimited resources of power and frequency. We both see what each other are saying here, it's just that what you are talking about is a practical limitation that only gets (a lot) worse in an accelerating universe, but I'm talking about an in-principle limit that only exists in an accelerating universe.

As far as i can tell i'm also talking about an in-principle limit that only exists in an accelerating universe, but a different and somewhat earlier one than you.

Let's cut up the history of an accelerating universe in phases.

The last phase is the one you are talking about that is indeed an in-principle limit (ie t>=1 for emitter and associated loss of causal contact henceforth).

The first phase is the one you think i am talking about, and is indeed there, the practical limitation.

What i'm talking about is that there is a middle phase of non-zero length.

I think the reason you don't have this middle phase is because you assume "even with unlimited resources of power and frequency". It is this assumption that doesn't hold in an accelerating universe because

1. If GR applies the energy density of the universe is finite.

2. If the universe is accelerating (not if it isn't) the accessible volume (the 3rd integral, on the RHS) is finite.

If we let go of the qualifier "even with unlimited resources" (which we are forced to do in an accelerating universe), the middle phase appears. In which an event can be in the past light cone of another event, yet be causally disconnected from it. This is in-principle and only exists in an accelerating universe because 1&2 are in-principle and 2 only exists in an accelerating universe.

The dividing line between practical and in-principle comes earlier than the last phase because we have no choice but to abandon the "even with unlimited resources" assumption, on purely theoretical grounds. It's not practical because "no practical human/alien can gather the required energy", the energy just isn't there irrespective of practical considerations.

caveman1917

2011-Jul-06, 01:50 AM

This is of course assuming that a photon with wavelength larger than the cosmological event horizon is undetectable in-principle, in the sense that it is cannot participate in any physical process going on.

When i was talking about "we could emit nothing with higher frequency" or "we can detect nothing with lower frequency", i meant it in the general "there is no physical process that can do this" not so much the practical "we" can't do it.

That assumption could be the problem though.

Ken G

2011-Jul-06, 04:13 AM

As far as i can tell i'm also talking about an in-principle limit that only exists in an accelerating universe, but a different and somewhat earlier one than you.Why isn't that also true in a non-accelerating universe but infinitely expanding universe? Eventually, any galaxy is arbitrarily redshifted, so will meet with the limit you describe.

2. If the universe is accelerating (not if it isn't) the accessible volume (the 3rd integral, on the RHS) is finite.If we want to get a message to a distant galaxy, sent now, we only have access to the first integral, not the third, worth of energy. The first integral is finite even for a non-accelerated expansion. So given any technology, there will always be some distant galaxy that cannot get our message, even for a non-accelerated expansion. If the limitation we face there is practical, rather than causal, in nature, then all that changes is the distance to that galaxy that we cannot reach.

If we let go of the qualifier "even with unlimited resources" (which we are forced to do in an accelerating universe), the middle phase appears.Given the finiteness of the first integral, your middle phase always appears. If in the accelerated case, you calculate a distance to a galaxy that we cannot reach with the available energy and technology, I can convert that into an equivalent (but much larger) distance in the non-accelerated case that will amount to the same redshift. But if you give me a distance that exceeds that second integral, I can find no such parallel in the non-accelerated case.

Spoons

2011-Jul-06, 07:43 AM

Apologies for wading into the conversation so late and looking to turn the clock backwards somewhat but from what I was reading in this conversation, in considering the last bit of light we receive from the distant galaxies, would the resulting view end up not being similar to what happens when something falls into a black hole, in that the vision of what is seen would ultimately be effectively something like a "freeze frame" which fades through the redshift? (Based on the idea that at some point the speed at which the distance between any distant source increases due to expansion would be equal to the speed of light, so tending towards that time for any given object the light would be increasingly red-shifted until it fades from all practical detectable view)

I thought I saw Ken stating something like this on the previous page (or maybe it was caveman?) but I just wanted to check that my understanding is correct, since you've both been fleshing out the logic on the fly, as it were, throughout the thread.

(I appreciate that some of this will likely go at least a bit beyond what my current knowledge allows me to fully comprehend (you might say, beyond my ken - no caveman jokes at this point though) and that you may have already covered this, just checking if in bland laymens terms my understand is somewhere close to correct? If so then that would remove the scenario of something being fully visible at one point and then bang - gone, which I think caveman referred to earlier.)

Ken G

2011-Jul-06, 07:43 PM

Apologies for wading into the conversation so late and looking to turn the clock backwards somewhat but from what I was reading in this conversation, in considering the last bit of light we receive from the distant galaxies, would the resulting view end up not being similar to what happens when something falls into a black hole, in that the vision of what is seen would ultimately be effectively something like a "freeze frame" which fades through the redshift? Yes, I think that is a very analogous situation indeed. For a given source strength, there will be a time that we receive the "last photon" from that source. But the same holds in a non-accelerated expansion, it just takes a lot longer. I used to think this "blinking out" effect was a fundamental difference between accelerated and non-accelerated expansions, but as a result of this thread, I now believe that there is no such fundamental difference, it's just that acceleration makes it happen so much sooner that it becomes a practical possibility to consider in the main-sequence lifetime of low-mass stars.

caveman1917

2011-Jul-06, 08:41 PM

Why isn't that also true in a non-accelerating universe but infinitely expanding universe?

In a non-accelerating universe the receiver can at all times detect arbitrarily long wavelength (2nd integral is infinite), which is the same as saying that required energy for the emitter is almost zero.

I intend "the receiver can detect" as "any physical process can be influenced by", not "someone with some given telescope can detect".

In a non-accelerating universe:

1. The available energy grows without bound (3rd integral), though finite at any given time (1st integral)

2. The required energy is almost zero and doesn't grow.

In an accelerating universe:

1. The available energy also grows, but not without bound (3rd integral), and is also finite at any given time (1st integral)

2. The required energy grows without bound (2nd integral goes towards zero).

The middle phase comes in when the required energy gets larger than the available energy, and it signals the loss of causal contact.

This never happens in a non-accelerating universe, but does happen at a finite time in an accelerating universe. This time is earlier than the last phase.

Ken G

2011-Jul-06, 09:58 PM

In a non-accelerating universe the receiver can at all times detect arbitrarily long wavelength (2nd integral is infinite), which is the same as saying that required energy for the emitter is almost zero.But in addition to the wavelength issues, there is also the "last photon" issue-- we must imagine that whatever "causes" are out there, they must be communicated to us with quanta, and so for any given event, if we associate with it some rate of quanta generated by the event, at some distance we should expect that no quanta from that event will ever reach us in the rest of time-- even for nonaccelerated expansion. Events with larger quanta rates associated with them could affect us from farther away, but there's always a limit to where we don't expect an effect from that event.

caveman1917

2011-Jul-06, 10:18 PM

The longer we wait, the lower the wavelength we can detect

I see, you're looking at the 1st integral to find the maximum wavelength that can be detected, and thus you find no difference between accelerating and non-accelerating other than the rate at which it grows.

That's also what i thought at first, but actually it is, perhaps counterintuitively, the 2nd integral that's the deciding one on this.

Please see post 28 (http://www.bautforum.com/showthread.php/117144-Large-scale-relativity-question?p=1908110#post1908110).

You're right that we will need to wait to have fully resolved the signal ("get the results back"), yet in a non-accelerating universe there will be some finite time when we did resolve it, so we can't speak of a causal disconnection. However in an accelerating universe the 2nd integral is finite and shrinking, there will never be a time when we finally have resolved the signal, so we can speak of a causal disconnect.

Please note that the assumption of a "detector as large as the entire universe and able to detect arbitrarily small amplitude" is the same as "can be detected in principle". Once you start introducing practical constraints on this hypothetical detector, you will indeed reach those limits earlier and in different ways, but those are considerations of the first phase, not the middle one.

Ken G

2011-Jul-07, 05:07 AM

Please note that the assumption of a "detector as large as the entire universe and able to detect arbitrarily small amplitude" is the same as "can be detected in principle". Once you start introducing practical constraints on this hypothetical detector, you will indeed reach those limits earlier and in different ways, but those are considerations of the first phase, not the middle one.I'm not convinced that the range of the second integral is a meaningful way to talk about the maximum size of a detector we could use. It's true this is the maximum size of an apparatus that we could ever get a signal from, but to be a detector, the apparatus must itself get the signal it is detecting, and then relay it to us. If we are trying to detect a signal that a galaxy at distance D emits at time to, we first have to wait for that signal to reach the whole detector, at some later time t1. But by t1, the second integral goes from t1 to infinity, not to to infinity. But your argument still goes through-- because the second integral is infinite for the non-accelerating case, we don't mind the extra wait, we'll still get the signal.

So I guess the difference is, if all we want to know is if we are likely to receive influences directly from some past event, we can analyze the quanta it emits and ask if we'll get any, if the event will impose its influence on us. For suitably distant events, that will not happen, whether the universe accelerates or not. But your point is that if instead of taking a passive stance and letting the event affect us or not, we can take an active stance, build some huge device that effectively amplifies the signal or gathers its influence over a huge region, and then pointedly sends us back that influence. In that case, distant events can affect us when they would not have done so had we not expressly built a way for their influence to be focused on us. If that is what we mean by "in principle", then I think you are right.

caveman1917

2011-Jul-07, 08:10 PM

If that is what we mean by "in principle", then I think you are right.

I was approaching the "in principle" thing in the same vain you did for defining the third phase. You said that the third phase (in-principle loss of causal contact) started when the emitter couldn't manage to send the signal over "even with unlimited resources and frequency". In that same sense i considered it a loss of causal contact when the receiving side couldn't manage to detect the signal "even with unlimited resources", in other words "even with an infinitely large and infinitely sensitive detector".

But i suppose the concept of "in-principle" is not so easily defined anyway. However both seem reasonable since any actual physical process must be strictly more constrained than either "an emitter with unlimited resources" or a "detector with unlimited resources".

Ken G

2011-Jul-08, 01:10 AM

I certainly think we have gained a lot of understanding of the differences between expanding and accelerating models, by starting with your approach of "following the last detectable photon" as it progresses toward us through the intervening sources, and considering the finite vs. infinite nature of that all-important second integral in your post #16.

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