Can you expand on this? What starts can't you see when, and why is that?

well I dunno their names obviously Im assuming its because they are too far away. There are only like 5-10K stars visible to the human eye on the whole planet, am I just incorrectly assuming that not all of the other 299,999,999,995 are in the cloud of the milky way?

http://en.wikipedia.org/wiki/Olbers_paradox

I read and understand (well obviously not, but I think do) the part about the shells X distance away, and each shell has the same output of light, and since there are infinity many shells, then infinitely intense light hits us. But why isnt most of that light just blocked by other stars? Like if some point in the night sky, the first star is say 50 billion light years away, then arent all the other stars behind that star just blocked from my view, so I only see the photons from that 50 billion light year away star, which is only going to be a photon every I dunno how long, but long enough that it just doesnt appear to me? So I dont see any light from that point? And if all the points next to it are from stars similarly far or farther away, that point isnt drowned out by the light from the points next to it? Is it because that star would then absorb so much light from all the stars behind it that it heats up and becomes more visible to me? Is that how it actually would work?

I mean I know im obviously wrong, because people much smarter than me say I am, I just have never understood why.

I like how Edgar Allen Poe offered one of the early explanations.

Darkness there and nothing more.
Deep into that darkness peering, long I stood there wondering, fearing,
Doubting, dreaming dreams no mortal ever dared to dream before.

Consider a grid of stars with side a=1 unit and see how much intensity you receive from all of them. To simplify things and avoid the problem of your sight being blocked by other stars (until we devise a mathematical procedure to be thorough about it) consider first only contributions from stars that belong in the planes 1 unit above and 1 unit below. Consider now a unit of area in the origin of the grid and calculate the intensity received by all the stars belonging to the 2 planes above and below. Photons from these stars arrive at you always unobstructed from other stars.

That sum is not exactly the one i will offer next but its probably of similar order of magnitude;

That sum (because intensity goes like 1/distance^2 (times proper angular factors that have to do with the orientation of the surface) is like double sum Sum(1/(n^2+m^2+1),{n,m from 1 to infinity)). This sum can be connected in estimates with 2d integral of 1/(x^2+y^2)dxdy that goes like log(M)where M is the distance of the most distant star which if you then take to infinity diverges.

(because in reality the stars are not points but have each a radius eventually the above integration/sum will start having problems with overestimating certain distant stars. This correction is not going to be radically important in establishing darkness though because the distance between stars vs their radius is huge ratio (like ~ 10^8). The overall result will be still a very bright sky as the intensity now compares well with the intensity at the surface of a typical star (which is massively more dramatic than the sky we look up during day, basically its a burning your eyes event). Plus we have only used the 2 planes and we have an infinity of more planes higher.

Basically until you can follow better accurate calculations imagine that every solid angle however small you select in the sky to look will be sending you a large number of photons because no matter how small the angle eventually it will be hitting the surface of a star (or many stars added up to fill it) and receiving all photons from that direction in that small cone from all the stars that sent it that way. So everywhere you look no matter how small the solid angle as long as its finite you get photons at huge rates, not a few thousands per second as probably is the case for a look in the night sky without moon, but way more than trillions of trillions per second. Notice that in a finite grid this is not necessarily the case, there will be small enough solid angles that no star exists in that direction (the sky would be dark in that small solid angle direction).

Additionally of course in an infinite system that has a start we (eventually given enough time) have problems with even those stars that obstruct the photons from others behind them still receiving a lot of radiation, more than they produce on their own locally and eventually heating up a lot beyond fusion leading potentially to explosive situations.

Ok, let's pick star S to be the one you're staring at, 50 billion light years away. It's not very bright as it's far away. If there's another star T in the same line of sight more than 50 billion light years away, then you wouldn't see T because it'd be blocked.

But if there's a star R twice as far away as S, but just to the left of it, then it will add a little brightness there. You wouldn't notice R individually, necessarily, as S is brighter, but it does add to the brightness of that area. Imagine looking out towards the sun and someone shining a flashlight in your face at the same time. You might not notice the flashlight since it only adds a little brightness relative to the sun, but it is contributing. The sun doesn't drown out the light of the flashlight by eliminating the flashlight's light.

And if we have infinitely many stars, then even though S and R aren't very bright, there will be more (infinitely more!) stars all around them adding to the brightness to the point that it's actually visible to you.

Even with an infinite number of stars, only a finite number of them will transmit photons that hit us tho, correct? Because there is only so much room in the night sky, so eventually its filled, and the infinity of other stars are all blocked.

but I think this is where im going wrong, my mental image of this is pretty bad and since I think its finite Im just grossly underestimating how many stars that really is, and how much light that actually is (im assuming thats the forumula masque talked about that im too math dumb to understand). So in my head its like looking at a screen of pixels all the size of a dot I see in the sky, and if 1 of those dots is too far away to be seen, then I think its blocked and thats that, but the angles and distances are such that my non existant understanding of the math and how big the numbers really are, just confuses me into thinking the way I have been. Really each of those "pixels" could contain a number of stars so large that even if they were super far away still combine to generate enough light that it would be very bright.

am I sorta there?

Why worry about an infinite number of stars? The night sky will never fill up where we are. Near the middle of the galaxy might be a different story. Or when Andromeda collides with us, but you'll have been dead about 4 billion years by then.

Ok Alobar i will try a lengthy description without any math really, only several examples to visualize what is happening. You can understand the math too if you put some effort into it and i could suggest proper astrophysics books that discuss the topic more extensively if interested. The true calculation for the real universe (that is not very bright) is not at all a trivial thing by the way. It would have been very bright if it were different (ie infinite or big enough and dense enough and old enough). But it isnt and so we are left with one more reason to enhance the big bang theory plausibility.

Just think of it like this; Every solid angle you consider, like say pick a direction and draw a tiny cone around it with its apex/vertex at your eye, eventually meets the surface of a star in an infinite system of near uniform star distribution (i used the grid example that is only an approximation of the real star distribution which is more random and less organized like that, but it allows to put numbers to what is going on and recognize why local light intensity gets real large eventually without more serious math).

Now either the tiny solid angle cone when extended far directly meets some star surface eventually or you can break the cone into subcones where each one eventually meets a star completely or partially. You may need many of them if the cone is not very small (ie 10^-12 steradian etc) because stars are very far away and their size is not obvious with the naked eye as it would be for say a satellite like moon even if it were 100 times further way than it is now. The stars are in fact millions, billions etc of times farther away from us than the sun is. But if you selected a small enough solid angle eventually you could fill it with one star on occasion and in any case eventually with many stars if needed because they are not points, they are spheres, and they have angular size eventually. Every piece left without a star will be filled eventually by a more distant star until nothing is left dark ie there is no direction left inside that tiny angle cone unable to receive photons from some far place (in the grid example you can understand that this is the case ie that you will eventually hit a star anyway because any general direction ie a vector in 3D, is described by the sum of 3 vertical vectors, one in each axis, and in real life you can always find a vector using integer units in all 3 axes - that is a vector that ends in a grid point or so close to it that it hits a star surface - that approximates as much as you want any given direction you pick in the sky, much like the rational approximation of real numbers thing to any given precision needed). So in the end all this cone has the property that it has no dark pieces anywhere inside it. All the hemisphere of course in the sky you see is made of billions of such cones added up. If you imagine it as pixels then no pixels in that small cone would be dark (say a distance of 1 m from your eyes projected in some fictitious sphere). So with no dark pixels what is left? All lines inside that cone terminate in some star surface. What is left if all directions terminate in some stellar surface that emits photons? Just pure bright light, these photons coming at you! It has to be that billions of photons are coming at you from all directions with no dark spot left and at rates similar to the rates emitted by these stars' surfaces.

So not only its not dark but it has to be at least as bright as if the star was just outside (instead of being a collection of many different little pieces of surfaces all very very far but who add up to 4Pi steradians) and you were looking at its surface up close (imagine how impossible this is as we cant even look the sun with our eyes for even a brief fraction of the second before it gets unpleasant, plus its a bad idea for safety reasons).

The surface of the sun behaves as say a hot liquid metal furnace that has temperature of 5500K, not very far from the light of a bulb. So imagine if all your room was filled with light bulbs and you were unable to see anything else only bright bulbs no walls behind them because they are so many that they cover the background. Try to look at your room's bulb and see that you cant keep your eyes at it for more than 1 second anyway because its very bright. So imagine how bright it would be if all areas of your vision field were filled with bulbs and you had no refuge to take your eyes away by looking at the ground or a wall because everywhere you looked there would be more bulbs. What a blinding nightmare!!! This is how bright, and even more, the sky would look if the universe was uniform and infinite and had no recent start.

In the room example the bulb is a big object and is close. But if i had a huge stadium filled with bulbs randomly placed every ~1m you would soon fill all the sky with bulbs (like the cone example) in any direction you picked. You would be impossible to find a part of the sky that doesnt have photons coming from some bulb. And as a result the sky would feel as if it was all a giant bulb and you were looking at it from eg 1 m distance! Also notice in a room that you have one bulb close to you and another many meters away, you still recognize both bulbs as blinding bright when you focus on them, even if the second one is so much farther away that it has say 1/4 the effective angular area (so imagine many of them added together, the brightness per solid angle remains the same even if they individually appear smaller and contribute less intensity in your current position, the accumulation of all of them to fill the view still leaves a huge bulb effectively even if most of them are so far away. Try it in your home and you will see what i mean, then imagine adding hundreds of bulbs in your house and imagine what happens, when at some point you no longer can see the walls/furniture etc behind them, it no longer matters how far they are, all that matters is that they leave no gaps, they become one "body" in the cross section sense, if their number increases with the square of the distance you will get the described net effect if they are either infinite or at least very many to fill the viewpoint gaps one time).

Try to imagine the star equivalent using bulbs like that in your room at night and you will recognize how inevitable it becomes that all the sky becomes a giant bulb! Same with a star. All the sky becomes the surface of a star. (about >100 mil watts per m^2 kind of intensity, the sun as total power is 10^26W but it has a huge surface r=700000km this all is emitted from).

I will try to give you one more example to visualize better why the sky is effectively filled by stars with no void in the background if the system is infinite or if the system is dense enough and the stars are of significant radius each.

Imagine there were at the same time 10 different parties for little kids going on in some apartment complex near your home and they all used colorful balloons. After the parties ended instead of deflating the balloons or breaking them they all brought the balloons in your home and in fact placed all of them in your room, hundreds of them . You came later in your room and saw a room full with balloons. There were so many that you couldnt even see the walls of your room, it was balloons everywhere. This is what is meant above by saying the sky appears to have no void/dark spot. It is easy to see this in a finite example with balloons because they are closely packed and big. But imagine we increased your room by a factor or 2 per side and we kept adding balloons in there in order to keep them now farther away from each other but still plenty of them (imagine a gravity free system that the balloons stay at fixed points without anything holding them there). You would still be unable to see walls if we had enough balloons even if they are now less densely packed. In fact we could make your room be an entire building and assuming we added enough balloons we could make the avg distance from each other 5m, even less densely packed and still you woudlnt be able to see the walls if you were placed at the center. So imagine this process expanding the room adding balloons, even increasing the distance between them up to a point and you still wouldn't be able to see the walls. Because there are so many of them and the effective cross section they create is essentially 4Pi (the full solid angle around you). I could in fact make their distance 100m from each other and added billions of balloons and you still wouldn't be able to see behind them (imagine when a set of balloons is released in group, you dont really see anything behind them ,their total effective cross section covers the background for a while as they are rising to the sky say, same with a huge group of birds or insects flying that are packed so close they cover the sky behind them)

The case with the stars is the same thing really only the distances involved are billions of times larger. You look anywhere and you see stars with no end and they eventually cover all the sky leaving no voids if the system is either big enough and dense enough or infinite at whatever density and infinite in age or at least old enough.


Additionally do not let yourself think that a photon emitted 1 meter away from you is any different from the same energy photon emitted 1 bil light years away (in a static universe). The 2 photons are identical in energy and you cant tell by them alone, if you are in front of them as they hit your eye, whether they were emitted 1 m in front of you or billions of light years away. The photons themselves do not know the difference anyway as they have no sense of travel time. What diminishes with the distance is the intensity of light (number of photons per sec per m^2 say) not the energy of individual photons. If you still add up all the diminished intensities by the huge or infinite even number of stars you still recreate a very big overall intensity.

So as long as we have established that we see photons coming from all directions around us, many of them per second and per small solid angle considered , the end result is to have trillions and trillions of photons per second arriving at our eyes from all directions added together. This is if the system is dense enough and big enough or better yet infinite. If the system is not infinite and its not dense enough and it has a small age then clearly the stars do not cover all the sky, they leave voids , the total cross section they create is not 4*Pi (in steradians) and the resulting light intensity is not impressive enough to leave the impression of the night sky that is mostly dark.

To try to be thorough with the math all you need is to look at either the argument they offered with the spherical shells or the paper i linked that does a proper calculation for our true universe where of course he gets a finite result but one that is not as bright as the infinite case, far from it.

The fact is the real sky is still filled with many stars that we cant see (telescopes do, thats why you zoom and zoom and still see more stars for a while). We do get photons from them but they come one by one every few seconds or hours because their effective cross section doesnt cover the sky, very far from it (unlike the grid case) , so you never form a picture of them in your brain because its not a dense system and you see dark instead as the dominant state. The total intensity is of some respectable value but still very low, thousands of times lower than even an early morning sky 45 min before sunrise.

If you look at the long exposure picture i posted on another recent astronomy thread you will see how after a few hours the accumulation of all this light illuminates a completely dark background. So you know its thousands of times less than even a small flash light and it is there even if our eyes cant see it to respect it (it needs long exposure to be appreciated).

I think so. There's just one thing in there that I want to clarify: what do you mean by a star being blocked if it's "too far away to be seen"?

I don't know if anyone understands him, or actually reads through more than 10% of each of his posts.

Try also this video

alright guys, I think I understand it now, thanks a bunch!

poor wording on my part, I meant that in my limited view of the situation that some star that was too far away to be detected by the eye, was blocking all those other further stars behind it, as if i twas somehow taking up the same amount of space in the sky as the star thats close enough to be seen. Thats prolly not worded well either. I prolly cant really word it well cuz its sort of the confusing way I was looking at it before, which was obviously part of my problem.