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Brady Yoon
2004-Mar-24, 07:39 AM
I read an article on Olbers Paradox a while back, but I didn't understand it. Can someone give me an explanation or a link? Thanks.
Brady Yoon :-?

Wally
2004-Mar-24, 02:58 PM
Isn't that the one that says if the universe is infinite and has been around forever, then there should be no part of the night sky that is not taken up by starlight. i.e. the night sky would be as bright (???) as daytime.

Psi-less
2004-Mar-24, 03:13 PM
Yup, that's basically the one (why isn't the night sky uniformly as bright as the Sun's surface?). This was a nice link with an explanation of the paradox, some of the explanations against it (and why some of them are wrong) and a couple that are probably correct: http://tinyurl.com/36e7x I liked the guy's page--it put it in terms even I could understand! =D> I really need to take some classes one of these here days. #-o

Psi-less

Brady Yoon
2004-Mar-24, 08:06 PM
Thanks for the link, but it still doesn't make much sense.

We live inside a spherical shell of "Observable Universe" which has radius equal to the lifetime of the Universe. Objects more than about 13.7 thousand million years old (the latest figure) are too far away for their light ever to reach us
It said in the link that objects more than 13.7 billion years are too far away for light to reach us. But there are no objects older than 13.7 billion years old!! How could something be older than the universe itself? Shouldn't the explanation of the paradox be: There just isn't enough stars to light up the sky; 13.7 billion years worth of stars isn't enough?

Emspak
2004-Mar-24, 08:43 PM
You're confusing two issues: the size of the universe we can see and the actual age of the universe.

According to some theories about the Big Bang, (one known as "inflation") there was a short period when the universe may have been expanding faster than light. That would mean that any object on the other"side" of the universe (it's a multidimensional shape so the word "side" is a bit misleading) were too far away for the light to get to us by now.

That means that if you are an object 13.7 billion years old, your light may not reach us because the universe may be larger than 13.7 billion light years across. Since the universe is still expanding (albeit more slowly than light) it may be some time before we see it and the light "catches up" to where we are.

Even if the observable size -- that really means the furthest distace we can see backwards in time -- and the age of the universe match, you still would not be able to see some part of the universe because of that period when the expansion was faster than light.

Does this help?

Brady Yoon
2004-Mar-24, 10:04 PM
Yes, that helps. :D So the reason why my argument was wrong was because the universe is not expanding at the same rate as the velocity of light?

Brady Yoon
2004-Mar-24, 10:07 PM
But then this must mean that the universe has expanded faster than the speed of light right? And that's not possible..

skrap1r0n
2004-Mar-24, 10:26 PM
You're confusing two issues: the size of the universe we can see and the actual age of the universe.

According to some theories about the Big Bang, (one known as "inflation") there was a short period when the universe may have been expanding faster than light.

Hold the phones, isn't the universe still expanding at the speed of light? or is there a thoeretical barrier out there what stops all electromagnetic wavelengths?

Example: If the farthest star/galaxy out on the edge of the expanding bubble we call the universe emits light, and that star is 13.7 billion years old, then it stands to reason that radiation has travelled 13.7 billlion light years in all directions from that star, including past the "edge" of the universe.

Once it passes the edge, it increases the size of the universe by whatever distance it the electromagnetic radiation traveled in that time.

I think I may have sprained my brain on that one, hope it came across as I visualize it.

Brady Yoon
2004-Mar-24, 10:32 PM
Example: If the farthest star/galaxy out on the edge of the expanding bubble we call the universe emits light, and that star is 13.7 billion years old, then it stands to reason that radiation has travelled 13.7 billlion light years in all directions from that star, including past the "edge" of the universe.

Once it passes the edge, it increases the size of the universe by whatever distance it the electromagnetic radiation traveled in that time.

Ok, now I'm really confused. :( Does that mean that starlight creates more universe? Someone please help me!!!

skrap1r0n
2004-Mar-24, 10:41 PM
Ok, now I'm really confused. :( Does that mean that starlight creates more universe? Someone please help me!!!

Heh I am not an expert, it just makes sense that unless the outer edges of the universe are dampening electromagnetic radiation, then regardless of how far away the farthest body is away from the center, or how fast it's travelling, any radiation it emits will expand at the speed of light in all directions including outwards.

Just read that article BTW. I wonder if the fact that there is actualy so much radiation buzzing around, that the sin waves could cancel each other out. I have seen this accomplished with sound, where you can take a sound wave, modulate a second wave of the same frequency half a step off, and the conflicting sin waves cancel each other out.

Dark matter may be interrupting some of the light too <shrug>

Emspak
2004-Mar-24, 11:12 PM
The thing is the universe can expand faster than light because the speed of light limit only applies to material objects (photons are obviously not such, so they get to go at lightspeed).

Anyhow, according to inflation theory there was a period when space was expanding faster than light. This has no bearing on anything in space moving around. The universe has slowed down a lot since then, by the way, dropping to its sub-lightspeed expansion rate early in its history.

It is a little confusing. But think of this: Space itself gets bigger. Things get farther away from each other with time as a result. So something "standing still" .looks like it is moving away at whatever velocity that space is expanding at.

Picture a rubber band, and draw dots on it. When you stretch it, the dots get farther apart. You can travel along its length between the dots at whatever speed bu the speed you go between the dots at and the speed of the stretch are not necessarily related.

In three dimensions, the closest analogy is balloon: blow it up and if you paste little confetti bits to it they get farther apart. But they aren't moving.

Light, by the way, stretches out along with the universe, which is why it is red-shifted when we look at faraway galaxies -- they aren't shooting through space, they are sort of moving with it, though "moving" is a bit misleading here. Again, think of the rubber band, and draw a sinewave on it betwen the dots -- the wavelength increases as you stretch it
even though the dots are in the same place on the band.

Olbers' paradox demonstrates that the universe is finite and expanding -- if it weren't the microwave background radiation wouldn't be at that wavelength -- it would be gamma rays or something really high-energy. The stretching of space has taken the light we see when we look back in time and made its wavelength longer and longer. Eventually that background radiation will be the wavelength long wave radio and after that, really low-frequency radio emission.

Light doesn't go past the "edge" of the universe because it doesn't have one, any more than the surface of a sphere does. There is an "edge" in the sense of a horizon to what we can see, like there is an "edge" when I look out over the ocean. But a ship travelling over the ocean out of my view doesn't increase the ocean's size. I just can't see it because I am only about 1.8 meters tall and the curvature of the earth puts things out of view. New things can enter your horizon, however. If the rate of universal expansion were to get slower and slower, we would see more and more of the universe as the light "caught up" with us.

If you want to get really mathematical about it, the universe is an 11-dimensional shape which describes a curve like a hyperbola ("saddle shaped") in three dimensional space plus one of time. You can't go to the edge of the universe and look out someplace and see nothing because there is nothing to see and no edge to get to. It's like if you were a 2-dimensional person sliding around on the surface of a sphere-- no matter where you go you can't see the edge.

Nereid
2004-Mar-25, 02:33 AM
There's (almost) now a pragmatic answer to the paradox - we're taken a (small) representative (we hope) sample of lines of sight to the edge of the (observable) universe, and there are very few stars on them! (the lines of sight, that is).

Take a look at the Hubble UltraDeep Field (sorry, I don't have a link to hand); most of the image is 'blank', and it's 'deep' enough that it probably has detected high concentrations of early stars - a.k.a. proto-galaxies. Are there other stars at z ~>10, that are not captured in the image? Certainly! Stars closer than z = 10? Certainly squared!!

How much more of the 'blank space' in the image would they fill in, if we could take an ultra-ultra-deep piccie? Place your bets now! My bet is on maybe 5x, maybe 10x, but that'll still leave 'most' lines of sight to the edge of the observable universe *not* intersecting the surface of a star!

(Caveats apply)

Emspak
2004-Mar-25, 12:04 PM
Well, almost. As you look further away you lok further back in time, and when you see the cosmic microwave background you are actually looking at a time before stars existed.

If the Hubble were much larger and could see objects further away, you would actually see more proto galaxies, I would bet -- the firld would become more full but only because billions of years ago there wasn't as much universe to stuff things in.

Hubble has mapped a pretty big chunk of sky as it is. You can already see all the lines of sight in a given direction. In a finite universe it makes sense becuase you just run out of stars and you run out of universe. (It is finite in time as well as space).

John Kierein
2004-Mar-25, 02:01 PM
Well. I'm a believer in a static universe so I have to solve Olbers' paradox. In my universe the red shift is caused by the Compton effect.

The usual way to state Olbers' paradox is that if the universe is static, infinite and has a constant density of stars you should eventually hit a star wherever you look. I like to state it an even more difficult way, and that is to calculate the energy received from such a universe. The argument goes something like this:
The number of sources (Galaxies or stars) increases as the cube of the distance (volume of a sphere is 4/3 pi R^3) , but the energy received from these sources fall off only as the inverse square. Thus the energy received is infinite! If there are intervening stars in the way they would be vaporized and heated even above their radiating temperature. Luckily this is not observed so there's the paradox.

Adding a red shift to the problem doesn't solve it either. If the shift is Z=1 then the change in wavelength is 1 and the new wavelengths of the source are twice the wavelength originally radiated. This cuts the energy in half. So if you add the infinite series of energies from z + 1 to infinity you get 1/2 + 1/3 + 1/4 + 1/5 etc. which does not converge to a finite number.
Luckily, for a Compton effect red shift we deviate from Hubble's law at high red shifts and as the distance increases we get a higher red shift that produces a series which does converge. So I am able to solve Olbers' paradox for a static universe with a Compton effect red shift. This is provided the energy lost to the intervening medium is not immediately re-radiated. I believe it is not re-radiated because it is converted to mass as a result of special relativity. This is probably in the form of electron-positron pair formation or a similar process that I have proposed in several articles.
Thus, as old stars burn out, their energy is converted to new mass that can form new ones.

The big bang has a problem with Olbers' paradox, too. This is solved because stars moving away at high velocity are dimmer than stationary ones. This is due to the quantization of light into photons and the distance between photons gets greater as the speed of the source going away gets higher. So really fast moving objects are seen with fewer photons per second being received and they are less bright. If they could actually go the speed of light away from us they couldn't be seen at all! Maybe you could be hit by one photon of infinite wavelength; but that wouldn't be detectable because it would have zero energy and it would take an infinite amount of time for it to pass through you.

http://www.geocities.com/CapeCanaveral/9335/compton.html

Spaceman Spiff
2004-Mar-25, 03:06 PM
The big bang has a problem with Olbers' paradox, too. This is solved because stars moving away at high velocity are dimmer than stationary ones. This is due to the quantization of light into photons and the distance between photons gets greater as the speed of the source going away gets higher. So really fast moving objects are seen with fewer photons per second being received and they are less bright. If they could actually go the speed of light away from us they couldn't be seen at all! Maybe you could be hit by one photon of infinite wavelength; but that wouldn't be detectable because it would have zero energy and it would take an infinite amount of time for it to pass through you.

I won't comment on the universe that JK lives in, but I will comment on his disussion of what big bang cosmology says about Olbers' paradox. First, big bang cosmology has no problem with Olbers' paradox. In fact it is one of the many pieces of observational evidence (http://www.astro.ucla.edu/%7Ewright/cosmology_faq.html#BBevidence)for a universe that has been evolving in time. The paradox is not "solved" by the redshifting of starlight, although it plays a minor role. However, it does make a very important statement about the (observable) universe we live in:

the lookout limit is is FAR, FAR larger than the lookback limit for stars and galaxies.

The lookout limit is how far away (let's stick to a static universe for the moment for simplicity, to separate effects caused by expansion redshift) you have to look out in order that the integrated starlight equals the intensity of the Sun's photosphere hanging right over your head. The lookback limit is how far out we can see as limited by the length of time the phenomenon known as stars and galaxies has been around in this universe. Plagiarizing my own web page on the subject (http://homepages.wmich.edu/%7Ekorista/bigbang-darksky.html):


The lookout limit for stars in our universe is far too large in comparison to the distance light can travel over the time span that stars and galaxies have been around. In fact it's a factor of roughly 10 trillion too large! When averaged over the sky, starlight from all the stars in all the galaxies in the observable universe amounts to a feeble intensity of 1-ten trillionth the intensity of light from the Sun's surface. The sky is dark.

The effect of redshift upon the starlight in this universe is there, but it's a minor player.

On the other hand, redshift plays THE role in regards to another observed phenomenon, again lifting from my page:


But let us now go further. What do we see when we gaze out past the first and youngest stars and galaxies...[snip]We see the cosmic background radiation....[snip]This light comes to us from a time in the far distant past when a very smooth distribution of gas filled the universe; at that time the universe was much denser, much hotter, and just becoming transparent to the light within it. Conditions everywhere were then similar to standing on the inside of a star - nearly perfect thermal equilibrium...[snip]We see this same light today completely covering our sky, but mercifully redshifted by the expansion of space-time to a blackbody with a temperature of 2.725 K (-455 F), and so is emitted at very low intensity at microwave (millimeter) wavelengths. It's called the cosmic background radiation. The paradox of Olbers' paradox is that it isn't paradox after all. The sky is bright, not with starlight - but with light echoing the creation of the cosmos.

Emspak
2004-Mar-25, 03:30 PM
I think JK's universe (a static one) has one other problem: if you posit an infinitely aged universe, you have to find some mechanism for the old star matter he posits to become new stars -- and it has to turn back in to hydrogen.

Another issue is the existence of black holes, which get bigger with time as they eat up more mass. In an infinitely old universe of finite and static size, the holes would eat up all the available matter, then slowly dissipate via Hawking radiation into stray photons (gamma rays) and particles. There would be no way to form new stars because the resultant particles aren't hydrogen atoms -- more often they are much lighter bits of atoms like electrons or other short lived stuff.

To say nothing of the thermodynamic arrow of time -- that pretty much puts limits on how long a given universe can be around with a given amount of matter and energy in it.

Now one could posit an infinite static universe of infinite size but then you run into the getting hit with infinite energy problem.

Seems to me the evidence points to a finite universe, and a non-static one.

Nereid
2004-Mar-26, 12:12 AM
I say the horse has 36 teeth!

1) we know how many stars to expect in the faint, outer regions of nearby galaxies; the error bars are relatively small

2) ditto, for loose stars in nearby clusters (and super-clusters)

3) error bars are larger, but mid-distance galaxies and clusters are also moderately well characterised (probability of a big surprise non-zero, but still very small)

4) the largest remaining unknowns are the MLF for stars in the first billion years or so, and their distribution among proto-galaxies. The HUDF gives us something to work with to make some *observational* estimates (the theorists will have to get consistent with these data). What will the space density of stars be seen to be, between z = 1100 (the CMB) and z ~= 10?

5) So, imagine a 100m diameter super-Hubble space telescope, staring at a patch of sky 5' in diameter for 100 million seconds - what will the image look like? At some high level, we already know. From this we can say what the resolution to Olbers paradox is, to ~+/-50%.