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Thread: Olbers paradox, a possible solution.

  1. #1 Olbers paradox, a possible solution. 
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    I thought a discussion on Olbers parodox deserves a thread of it's own.

    I have considered Olbers paradox and wondered whether I might shed some light where there is now darkness. :wink:

    At first I thought maybe dust, rocks dead planets, cold stars, discarded alien space trash and amino acid molecules could account for the dark sky but decided these might only make the sky 'less bright' rather than 'dark'.

    Next I considered whether light might reduce in frequency with age but good old Quantum theory says not.

    I have now considered a third possibility which I believe would account for an infinite universe or universes and yet leave a dark sky.

    Suppose we are in space and I shine a flashlight at you, close up, then from 10 miles then 100 then 1000. Now you don't see it getting dimmer it just becomes a finer point of light. Let's say for arguments sake that at a range of 1 Metre the light falling on a 1 metre square (from my flashlight) is 1 million photons per second. At two metres range the number of photons per square metre will fall to around 250k/square metre. Increasing the distance will eventually reduce this photon count to less that 1 photon/sq metre per second at which point if your eyes could detect single photons you may just see the light flash briefly every few hours or so.

    Now multiply this up to an infinite universe, most of the stars(or other universes) will be at such a distance that their individual photons may never hit your eyes.

    Please note I am considering Olbers Paradox not debating whether the universe is steady state, cyclic, or from a Big Bang.

    Incidentally, taking an average size star, given a figure for mass loss (by way of photon emmision) and the density of stars that we see in the visible universe it ought to be possible to program some computer to calculate whether this hypothesis might hold light(ok water then).

    Wadja fink?


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  3. #2  
    Universal Mind John Galt's Avatar
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    The point is that in an infite universe every direction you look towards, every tiny little point, is a source of photons coming straight at you. Everywhere you look there are nothing but stars. That is the whole point of Olber's paradox.


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    I would debate further, if at some distant point there is a star in your direct vision it may very well be far enough away for the radial distribution of photons to be so dispersed that none of them come anywhere near the earth even IF the whole sky is a background of stars. Olber's paradox comes from the late 17th century? he may not have realised that a star emits a finite number of photons.
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    No matter what your cosmology is, we appear to be in the expansion phase of a big bang. As for Olbers’ paradox and our big bang, the answer is easy. Light travels at a finite speed, stars have a finite life, the universe is expanding so galaxies are moving away from us, and the average distance from us of the stars that would form a complete canopy of star light day and night, according to Jespersen and Fitz-Randolph, in their book, “Looking at the Invisible Universe”, 1990 Macmillan Publishing, turns out to be 100 billion trillion light years.

    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.

    As we look out into space, we are looking back in time in the sense that the light we see took time to reach us and so was emitted by the star sometime in the past. If a star is 10 billion light years away from us, not only will it be very dim, and not only may it have burned out by now, the light we see was emitted 10 billion years ago, and if you figure in the expansion of the universe, that light may not have even reached us yet. If the light hasn’t reached us yet, it can be thought of as a spear of light 10 billion light years long heading toward us at the speed of light. Yikes, I’m getting out of the way.
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    Quote Originally Posted by bogie
    No matter what your cosmology is, we appear to be in the expansion phase of a big bang. As for Olbers’ paradox and our big bang, the answer is easy. Light travels at a finite speed, stars have a finite life, the universe is expanding so galaxies are moving away from us, and the average distance from us of the stars that would form a complete canopy of star light day and night, according to Jespersen and Fitz-Randolph, in their book, “Looking at the Invisible Universe”, 1990 Macmillan Publishing, turns out to be 100 billion trillion light years.

    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.

    As we look out into space, we are looking back in time in the sense that the light we see took time to reach us and so was emitted by the star sometime in the past. If a star is 10 billion light years away from us, not only will it be very dim, and not only may it have burned out by now, the light we see was emitted 10 billion years ago, and if you figure in the expansion of the universe, that light may not have even reached us yet. If the light hasn’t reached us yet, it can be thought of as a spear of light 10 billion light years long heading toward us at the speed of light. Yikes, I’m getting out of the way.
    Um bogie, the fact that stars have a finite life and light has a finite transit speed does not solve olbers paradox. The distance is also not a factor (just do the math, the light received is distance independant), metric stretching also does not help - the killer is finite time, allow infinite time and olber bites your arse.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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    Quote Originally Posted by river_rat
    Um bogie, the fact that stars have a finite life and light has a finite transit speed does not solve Olbers' paradox. The distance is also not a factor (just do the math, the light received is distance independent), metric stretching also does not help - the killer is finite time, allow infinite time and Olbers’ bites your arse.
    I don't think so River_Rat. You must be making some assumption that I am not making.

    I assume that the universe is infinite.

    I assume we are in a big bang expansion that is about 13.7 billion years old.

    I assume that there is dark space surrounding our expanding big bang that is a trillion light years across, i.e. 500 billion light years of darkness in all directions after you pass the 13.7 billion light years since our big bang lit up.

    I also assume that the universe is made up of big bangs and crunches, and that they are separated by a minimum of 20 trillion light years.

    So with these simple assumptions we can say some things for sure.

    One thing is that our observable universe does not light up the night sky.

    Another thing is that with infinite time, and with our universe expanding during that time, there will never be more light arriving here from within our expanding universe because as new stars form, old stars burn out, and the old stars are moving away and getting dimmer.

    Now let's consider the greater universe as an additional light source. Sorry, no light reaches us from those other big bangs for at least ten trillion light years. So let's say we wait for ten trillion light years to see the first dim flicker of light from the nearest big bang, and Oops, our big bang has burned out and we are gone, and there is no more light coming from our big bang.

    What are you assuming that differs from my assumptions?
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    when you look into a night sky you are limited, when a land based telescope looks out it has limitations and even the Hubble has many limitations. each progressively further however. the same would hold true if you observed the flash light with help, it could appear as though 10 foot away but be a miles and the light as bright.

    to simplify a very long explanation, with perfect equipment, with nothing to distort (atmosphere, debris, other light or time) and the only thing between you and your equipment and the very furthest spiral galaxy in the universe would appear as the milky way. this could be 15-70 or 1000 trillion light years out.

    of course none of this is possible or likely to ever be. because of distortions i like to question just how far some of those dots are and suggest the 13.7 figure and some may be brighter objects appearing as others from much further away. in fact i would suggest if some one were
    using Hubble to look back at us, we would be the dot we and if turned the other direction away from earth, there would be another dot -x- number
    of light years away and so on...
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    Quote Originally Posted by jackson33
    ... the very furthest spiral galaxy in the universe would appear as the milky way. this could be 15-70 or 1000 trillion light years out.
    Here's why I don't agree. According to the most popular theory of the universe, what we see is what we get. By back tracking from the observed distant visable objects, and using the redshift data that define the rate of expansion of the big bang universe, our expanding big bang has only existed for 13.7 billion years, so nothing connected to our big bang could be farther away that that.

    You estimate of up to 1000 trillion light years takes us out beyond our expanding big bang. I'm glad to go there because I think that place exists, but it is outside our big bang.

    Now remember, stars only burn and give off light for about 10 billion years. If there is a place beyond our big bang, it would be quite a lot further away and quite a lot dimmer than any stars we now see even with our best equipment.

    But if there is such a place called the greater universe, then I assume our big bang would have come from a big crunch that accumulated from the greater universe. A big crunch would take about ten trillion years to accumulate and would create an essentially empty arena in space of about a trillion light years across with the crunch in the center.

    When the crunch becomes a bang, it would take a half a trillion years to fill the arena. We are only 13.7 billion years into that 500 billion years so there is a large dark arena out beyond us before we even get to what ever exists out there beyond our arena.

    There are no galaxies or stars in the dark arena except what comes from our expanding big bang. Those big bang stars don't light up the night and can't under any circumstances make the night as bright as day.

    If you could imagine some galaxies out beyond our arena they would be trillions of light years away. They are probably ordinary stars and galaxies that burn for 10 billion years and they are spread out like the galaxies in our big bang are spread out, there is no complete canopy of stars no matter how far out you go that could burn long enough to cause a visible beam of the dimmest possible light to reach us.

    of course none of this is possible or likely to ever be. because of distortions i like to question just how far some of those dots are and suggest the 13.7 figure and some may be brighter objects appearing as others from much further away. in fact i would suggest if some one were
    using Hubble to look back at us, we would be the dot we and if turned the other direction away from earth, there would be another dot -x- number
    of light years away and so on...
    If I read you correctly you are saying that you can go to the edge of where we see light coming, and then look out further from there and see more stars buring that will send light that eventually reaches us. I don't think so because of the arena of dark sky, and because of the trillions of light years you would have to go to just see the nearest big bang. And that nearest big bang in total would not be as bright as our dimmest stars.

    The greater universe, with big bangs separated by trillions of years of dark arenas could never even become visible from here I bet.
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    bogie; all you say is based on BB. there are other versions by nearly the same number of scholars that feel there was no BB and things have pretty much been there forever. they might suggest the BB suggests a beginning and infer and end, not in BB theory and that if there were no beginning there would be no end. just a procreation system, which you can see in the images Hubble gives us at regular intervals.

    i used the "word" time for a reason. it would be the last element to the perfect view from any location. time can distort, though in my opinion light itself is not subject to time, only our concept and ways to observe limit the results.

    with the BB, you might try to answer why all we see is so identical in each direction. this infers the bang itself had to happen so far away, that what we see is in our limits and the central point well out of sight.
    makes no sense. w/o BB, the distortions etc., stand.

    star's on average, probably do only last so many years on average. for the sake of discussion, lets say 10 billion years. in that ten billion years
    another formed. like people if zero plus gain, was imposed. another few
    million in a galaxy died and were replaced as well. at any point in the life span of a galaxy the total gain would be determined on absorption of other
    systems, small dwarfs, no doubt. now for ages of galaxy, we have no idea how old they could be. if stars die, form or even eaten up by giant stars, turned "black holes", the cycle in a continuous mode and disregarding the BB, the age of a galaxy with no star over 10 billion yo, could be in the millions of billion age group or even beyond imagination. i will remind you however, science feels sol, or sun is at least 5 billion yo and considered very young; that giant stars 25 times that of ours and those thought to be black hole potentials and near centers of galaxy are only 13.7 yo. this is not consistent with nature and they may reach there limit or maturity, well before demise and live or exist much more than 30 or 50 billions years.

    past poker time, but if i missed an answer, let me know and ill try again. or if you question one i really want to hear back.
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    I don't think so River_Rat. You must be making some assumption that I am not making. Nope, not making any more assumptions - let me explain.

    I assume that the universe is infinite. in space and time? It can be infinite in space and not in time, or infinite in time and not in space - olbers comes from allowing infinite time for a suffiently large universe. Seeing that your "big" universe is infinite in both time and space olbers rears its head.

    I assume we are in a big bang expansion that is about 13.7 billion years old. Okay, but lets treat our universe as a point in your large universe - infact lets treat every universe as a star (that has a huge light output!)

    I assume that there is dark space surrounding our expanding big bang that is a trillion light years across, i.e. 500 billion light years of darkness in all directions after you pass the 13.7 billion light years since our big bang lit up. - Just like normal space, large stretches of emptiness between "stars". So we have nothing new yet.

    I also assume that the universe is made up of big bangs and crunches, and that they are separated by a minimum of 20 trillion light years. - So each "star" is far apart, but once again 20 trillion years means nothing in an infinite past background.

    So with these simple assumptions we can say some things for sure. You can say very little without doing the actual math but anyway, lets just assume it can be demonstrated.

    One thing is that our observable universe does not light up the night sky. - Okay, thats the standard response to olbers, finite past etc.

    Another thing is that with infinite time, and with our universe expanding during that time, there will never be more light arriving here from within our expanding universe because as new stars form, old stars burn out, and the old stars are moving away and getting dimmer. - for infinite past to make sense, the number of stars needs to be non-decreasing (else you would have no stars no matter how slow the decrease is) so lets be generous and say that stars are at equilibrium. Stars moving away doesnt help, if the star is 15 million light years away and is moving at 99% the speed of light relative to us the light still only takes 15 million years to get to us. So you can take a snap shot of the universe right now relative to an observer on earth and ignore expansions and other metric effects (to first order anyway). The total light reaching earth is distance indepedant, moving the star further away may make the light dimmer but that is compensated by there being more stars now in a sphere of that size - so we still receive the same amount of light. It is just a function of the number of stars really.

    Now let's consider the greater universe as an additional light source. Sorry, no light reaches us from those other big bangs for at least ten trillion light years. So let's say we wait for ten trillion light years to see the first dim flicker of light from the nearest big bang, and Oops, our big bang has burned out and we are gone, and there is no more light coming from our big bang. - Now this is where olbers bites your bum. As each universe can be treated as a point source (a star) all you have done is reintroduce an infinite number of "stars" in an infinite universe. Now as we have an infinite amount of time for this light to reach us (as we have an infinite past for the point where we find our universe in this snap shot) and since the amount of light we receive from any shell of "stars" is independant of the radius of that shell we would observe an infinite amount of light and the sky would be infinitely bright. So your model has jusst reintroduced the monster.

    Do you understand the problem now? Your bigger universe is just a model for the old cosmological models that suffered from olber's paradox and thus also suffer from it. Replace universe with "star" and bam.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  12. #11  
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    Quote Originally Posted by jackson33
    bogie; all you say is based on BB. there are other versions by nearly the same number of scholars that feel there was no BB and things have pretty much been there forever. they might suggest the BB suggests a beginning and infer and end, not in BB theory and that if there were no beginning there would be no end. just a procreation system, which you can see in the images Hubble gives us at regular intervals.

    i used the "word" time for a reason. it would be the last element to the perfect view from any location. time can distort, though in my opinion light itself is not subject to time, only our concept and ways to observe limit the results.

    with the BB, you might try to answer why all we see is so identical in each direction. this infers the bang itself had to happen so far away, that what we see is in our limits and the central point well out of sight.
    makes no sense. w/o BB, the distortions etc., stand.

    star's on average, probably do only last so many years on average. for the sake of discussion, lets say 10 billion years. in that ten billion years
    another formed. like people if zero plus gain, was imposed. another few
    million in a galaxy died and were replaced as well. at any point in the life span of a galaxy the total gain would be determined on absorption of other
    systems, small dwarfs, no doubt. now for ages of galaxy, we have no idea how old they could be. if stars die, form or even eaten up by giant stars, turned "black holes", the cycle in a continuous mode and disregarding the BB, the age of a galaxy with no star over 10 billion yo, could be in the millions of billion age group or even beyond imagination. i will remind you however, science feels sol, or sun is at least 5 billion yo and considered very young; that giant stars 25 times that of ours and those thought to be black hole potentials and near centers of galaxy are only 13.7 yo. this is not consistent with nature and they may reach there limit or maturity, well before demise and live or exist much more than 30 or 50 billions years.

    past poker time, but if i missed an answer, let me know and ill try again. or if you question one i really want to hear back.
    Important matters first. Poker time for me has been significantly impaired by the recent law passed by Congress. My game, Party Poker closed for USA customers and I have had to move to Poker Stars. I like to play for pennies and maybe a dollar tourney once in awhile just to relax.

    You mentioned my post being based on BBT, and I can only say that I must acknowledge the observations that lead to BBT, while at the same time my bias is toward a universe that has always existed and is infinite in space and content. The content is matter and energy that, in total, has always existed.

    Matter and energy go through a cycle starting from the hot dense energy released by a big bang, and ending up in the cold dead matter that is the result of the matter/energy cycle. All of the matter condenses out of the high energy density of young big bang space, goes through the expansion during which all of the star and galaxy formation takes place, and after all of the stars have followed the expansion out into the greater universe, they die a quiet death and become the cold dead matter that then starts the cycle again by being accumulated into a big crunch.

    You obviously understand the universe from the perspective of an alternative cosmology that I see as similar to the quasi-steady state. This may surprise you but so do I. Let me explain. To me, if the universe has always existed, and contains matter and energy throughout it, then it is the nature of that matter and energy to find a balance or equilibrium between the matter content and the energy content on a large scale.

    The greater universe doesn’t collapse from gravity because after a small portion collapses into a big crunch, the crunch becomes a big bang. Since there would be infinite matter/energy, the crunches would be occurring all throughout the universe, and as they mature, bangs would be occurring all throughout the universe. Here we are on the expansion phase of a big bang that came from one of those big crunches.

    The light in the universe comes from electromagnetic radiation that is emitted by matter. Only a narrow band of this electromagnetic radiation is in the form of visible light. Because the matter and energy in the greater universe are in equilibrium, only a portion of the energy available is actually in the form of matter. And because stars and galaxies form from existing matter and energy, there is only a portion of the available matter actually emitting visible light.

    The question is, is there enough light generated in the grand universe to light up the night sky. The obvious answer is no, because the night sky is dark. From the fact that the night sky is dark, you have to conclude one of two things. Either there isn’t enough light generated, or the universe isn’t infinite.

    Since I conclude that the universe is infinite, I must conclude that there isn’t enough light generated.

    This is logical to me because the light comes from only a small portion of the matter/energy. I think that the balance between matter and energy in the universe does not provide enough matter at any given time to form enough stars to light up the entire universe.

    When a star burns out, the space around it goes dark. The darkness expands as the light recedes. Since there is only a brief phase of a big bang expansion that is characterized by star formation, when that period is over, that big bang goes dark and the darkness expands as the light recedes.

    If this lighting up and burning out takes place over 500 billion years, by the time the expansion reaches the original volume of space from which the crunch formed, the entire arena is turned off like a light bulb as the last person leaves the room. There is a light sphere expanding into the greater universe that is 500 billion light years thick, and that light sphere is followed by a darkness that lasts forever.

    The next nearest big bang starts out twenty trillion light years away and also sends out a light sphere 500 billion years thick, follow by darkness.

    These two light spheres move toward each other through the nineteen trillion years of darkness between them. When light spheres meet they pass by each other but everything remains dark until the light spheres reach the cold dead matter from the respective old dead bang expansions. By then the light is so disbursed, that its temperature must be in the vicinity of one degree Kelvin, hardly hot enough to be measured, let along hot enough to make the excellent black bodies of dead matter burn like stars.
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  13. #12  
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    Quote Originally Posted by river_rat
    I don't think so River_Rat. You must be making some assumption that I am not making. Nope, not making any more assumptions - let me explain.

    I assume that the universe is infinite. in space and time? It can be infinite in space and not in time, or infinite in time and not in space - olbers comes from allowing infinite time for a suffiently large universe. Seeing that your "big" universe is infinite in both time and space olbers rears its head.

    I assume we are in a big bang expansion that is about 13.7 billion years old. Okay, but lets treat our universe as a point in your large universe - infact lets treat every universe as a star (that has a huge light output!)

    I assume that there is dark space surrounding our expanding big bang that is a trillion light years across, i.e. 500 billion light years of darkness in all directions after you pass the 13.7 billion light years since our big bang lit up. - Just like normal space, large stretches of emptiness between "stars". So we have nothing new yet.

    I also assume that the universe is made up of big bangs and crunches, and that they are separated by a minimum of 20 trillion light years. - So each "star" is far apart, but once again 20 trillion years means nothing in an infinite past background.

    So with these simple assumptions we can say some things for sure. You can say very little without doing the actual math but anyway, lets just assume it can be demonstrated.

    One thing is that our observable universe does not light up the night sky. - Okay, thats the standard response to olbers, finite past etc.

    Another thing is that with infinite time, and with our universe expanding during that time, there will never be more light arriving here from within our expanding universe because as new stars form, old stars burn out, and the old stars are moving away and getting dimmer. - for infinite past to make sense, the number of stars needs to be non-decreasing (else you would have no stars no matter how slow the decrease is) so lets be generous and say that stars are at equilibrium. Stars moving away doesnt help, if the star is 15 million light years away and is moving at 99% the speed of light relative to us the light still only takes 15 million years to get to us. So you can take a snap shot of the universe right now relative to an observer on earth and ignore expansions and other metric effects (to first order anyway). The total light reaching earth is distance indepedant, moving the star further away may make the light dimmer but that is compensated by there being more stars now in a sphere of that size - so we still receive the same amount of light. It is just a function of the number of stars really.

    Now let's consider the greater universe as an additional light source. Sorry, no light reaches us from those other big bangs for at least ten trillion light years. So let's say we wait for ten trillion light years to see the first dim flicker of light from the nearest big bang, and Oops, our big bang has burned out and we are gone, and there is no more light coming from our big bang. - Now this is where olbers bites your bum. As each universe can be treated as a point source (a star) all you have done is reintroduce an infinite number of "stars" in an infinite universe. Now as we have an infinite amount of time for this light to reach us (as we have an infinite past for the point where we find our universe in this snap shot) and since the amount of light we receive from any shell of "stars" is independant of the radius of that shell we would observe an infinite amount of light and the sky would be infinitely bright. So your model has jusst reintroduced the monster.

    Do you understand the problem now? Your bigger universe is just a model for the old cosmological models that suffered from olber's paradox and thus also suffer from it. Replace universe with "star" and bam.
    In my reply to Jackson I provide additional information about my thinking that applies to the points made in your post as well. You can see that we don't agree and you can read why in my post to Jackson.
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  14. #13  
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    Quote Originally Posted by bogie
    Quote Originally Posted by jackson33
    bogie; all you say is based on BB. there are other versions by nearly the same number of scholars that feel there was no BB and things have pretty much been there forever. they might suggest the BB suggests a beginning and infer and end, not in BB theory and that if there were no beginning there would be no end. just a procreation system, which you can see in the images Hubble gives us at regular intervals.

    i used the "word" time for a reason. it would be the last element to the perfect view from any location. time can distort, though in my opinion light itself is not subject to time, only our concept and ways to observe limit the results.

    with the BB, you might try to answer why all we see is so identical in each direction. this infers the bang itself had to happen so far away, that what we see is in our limits and the central point well out of sight.
    makes no sense. w/o BB, the distortions etc., stand.

    star's on average, probably do only last so many years on average. for the sake of discussion, lets say 10 billion years. in that ten billion years
    another formed. like people if zero plus gain, was imposed. another few
    million in a galaxy died and were replaced as well. at any point in the life span of a galaxy the total gain would be determined on absorption of other
    systems, small dwarfs, no doubt. now for ages of galaxy, we have no idea how old they could be. if stars die, form or even eaten up by giant stars, turned "black holes", the cycle in a continuous mode and disregarding the BB, the age of a galaxy with no star over 10 billion yo, could be in the millions of billion age group or even beyond imagination. i will remind you however, science feels sol, or sun is at least 5 billion yo and considered very young; that giant stars 25 times that of ours and those thought to be black hole potentials and near centers of galaxy are only 13.7 yo. this is not consistent with nature and they may reach there limit or maturity, well before demise and live or exist much more than 30 or 50 billions years.

    past poker time, but if i missed an answer, let me know and ill try again. or if you question one i really want to hear back.
    Important matters first. Poker time for me has been significantly impaired by the recent law passed by Congress. My game, Party Poker closed for USA customers and I have had to move to Poker Stars. I like to play for pennies and maybe a dollar tourney once in awhile just to relax.

    PLAYING -PLAY MONEY- AT PARTY AS THEY TRY TO WORK SOMETHING OUT. PREFER OMAHA AND BEST SITE FOR THAT GAME. ALSO PLAY TO RELAX AFTER PLAYING IN STOCKS ALL DAY.

    You mentioned my post being based on BBT, and I can only say that I must acknowledge the observations that lead to BBT, while at the same time my bias is toward a universe that has always existed and is infinite in space and content. The content is matter and energy that, in total, has always existed.

    SORRY, I GET LAMBASTED SO OFTEN, JUST THOUGHT YOU WERE COMING FROM THE BB, CAMP. WE SEEM TO HAVE SIMILAR OPINIONS ON THIS.

    Matter and energy go through a cycle starting from the hot dense energy released by a big bang, and ending up in the cold dead matter that is the result of the matter/energy cycle. All of the matter condenses out of the high energy density of young big bang space, goes through the expansion during which all of the star and galaxy formation takes place, and after all of the stars have followed the expansion out into the greater universe, they die a quiet death and become the cold dead matter that then starts the cycle again by being accumulated into a big crunch.

    You obviously understand the universe from the perspective of an alternative cosmology that I see as similar to the quasi-steady state. This may surprise you but so do I. Let me explain. To me, if the universe has always existed, and contains matter and energy throughout it, then it is the nature of that matter and energy to find a balance or equilibrium between the matter content and the energy content on a large scale.

    THINK YOU ARE NEAR PERFECT IN YOUR PREMISE, IN MY OPINION.

    The greater universe doesn’t collapse from gravity because after a small portion collapses into a big crunch, the crunch becomes a big bang. Since there would be infinite matter/energy, the crunches would be occurring all throughout the universe, and as they mature, bangs would be occurring all throughout the universe. Here we are on the expansion phase of a big bang that came from one of those big crunches.

    YOU PHRASE IT A LITTLE DIFFERENT. I AM TRYING TO FIGURE IN BLACK HOLES AND THE POSSIBILITY THESE UNITS PRODUCE THE DEBRIS THAT FORM THE MATERIAL FOR THAT VIEW OF FORMATION. AT THE MOMENT I FEEL IT IS LIKELY SOME NEW SYSTEMS FORM NEAR THERE ORIGINAL GALAXY AND RE-ENTER...SO TO SPEAK.

    The light in the universe comes from electromagnetic radiation that is emitted by matter. Only a narrow band of this electromagnetic radiation is in the form of visible light. Because the matter and energy in the greater universe are in equilibrium, only a portion of the energy available is actually in the form of matter. And because stars and galaxies form from existing matter and energy, there is only a portion of the available matter actually emitting visible light.

    YOU PUT THIS VERY WELL. FROM GAMMA RAY TO RADIO WAVES WE SEE ONLY A PORTION. SINCE THESE ARE REGISTRABLE, YOU MIGHT CONSIDER WHAT IS NOT REGISTERED. PUT ANOTHER WAY, THERE COULD BE ADDITIONAL ITEMS ON THE "ELECTROMAGNETIC SCALE" ABOVE OR BELOW, WE ARE NOT AWARE OF.

    The question is, is there enough light generated in the grand universe to light up the night sky. The obvious answer is no, because the night sky is dark. From the fact that the night sky is dark, you have to conclude one of two things. Either there isn’t enough light generated, or the universe isn’t infinite.

    OK, YES THERE IS ENOUGH ACTUAL LIGHT TO LIGHT UP OUR NIGHT SKY AS WE PERCEIVE LIGHT. SIT IN A DARK ROOM FOR AN HOUR AND TURN ON THE DIMMEST OF LIGHT, YOUR VISION IS VERY HIGH, YOU SEE MOST ALL YOU WOULD IN DAYLIGHT. THIS IS PERCEPTION AND YOU HAVE ALTERED THE NORMAL CONCEPT. NOW, WHAT WE SEE IN THE SKY IS
    THE RESULT OF MUCH MORE THAN LIGHT AND I SUGGEST THE DARKNESS YOU SEE IS NOT THAT FAR AWAY AND DISTURBED BY THE LIGHT THAT FLOWS THROUGH AND THAT THIS DARKNESS MAY BE THE RESULT OF PERCEPTION. I'D RATHER NOT GO THERE NOW, BUT DARKNESS ITSELF MAY BE AN ELEMENT (NOT NECESSARILY ABSENCE OF LIGHT) AND JUST NOT UNDERSTOOD.

    I ALSO NEED TO ADD; WITH REFERENCE TO THE THREAD, WE ARE USING EQUIPMENT TO OBSERVE LIGHT FROM DISTANT PLACES AND THAT LIGHT WAS GENERATED BILLIONS OF YEARS AGO AND STILL GETS THROUGH.


    Since I conclude that the universe is infinite, I must conclude that there isn’t enough light generated.

    ANSWERED ABOVE. ASSUME THERE IS NO LIGHT WHAT SO EVER, WHAT WOULD YOU SEE IF YOU LOOKED INTO THE NIGHT SKY. IF THIS WERE POSSIBLE, I WOULD GUESS, NOT WHAT YOU DO SEE AS DARKNESS, NOW.

    This is logical to me because the light comes from only a small portion of the matter/energy. I think that the balance between matter and energy in the universe does not provide enough matter at any given time to form enough stars to light up the entire universe.

    AGREE, BUT THE SAME DARKNESS APPEARS BETWEEN SOLAR SYSTEMS IN A GALAXY, THAT APPEARS IN DEEP SPACE. THIS WOULD ACCOUNT OR JUSTIFY LIGHT SLIPPING THROUGH DARKNESS.

    When a star burns out, the space around it goes dark. The darkness expands as the light recedes. Since there is only a brief phase of a big bang expansion that is characterized by star formation, when that period is over, that big bang goes dark and the darkness expands as the light recedes.

    YES, WHEN THE LAST OF THAT KNOWN ENERGY REACHES YOUR EYE, THE LIGHT IS GONE FROM YOUR SIGHT.

    If this lighting up and burning out takes place over 500 billion years, by the time the expansion reaches the original volume of space from which the crunch formed, the entire arena is turned off like a light bulb as the last person leaves the room. There is a light sphere expanding into the greater universe that is 500 billion light years thick, and that light sphere is followed by a darkness that lasts forever.

    IN MY MIND, THE UNIVERSE HAS BEEN, WHAT IT IS NOW FOR WELL OVER ANY FIGURE YOU DREAM UP. THE TOTAL MATTER, IF ATOMS COULD BE COUNTED WOULD BE THE SAME NOW AS BACK TO THAT FIGURE, ONLY AS DIFFERENT FORMATIONS AS ONE CEASES AND A NEW ONES GENERATED. THAT IN THIS PATTERN, IF THERE WERE NO BEGINNING, THEN A NEED TO EXPLAIN AN END WOULD NOT BE REQUIRED. WHAT WE PERCEIVE AS LIGHT MAY BE UNIQUE ONLY TO US AND TO OTHER LIFE, MAY EVEN BE DARKNESS.

    The next nearest big bang starts out twenty trillion light years away and also sends out a light sphere 500 billion years thick, follow by darkness.

    These two light spheres move toward each other through the nineteen trillion years of darkness between them. When light spheres meet they pass by each other but everything remains dark until the light spheres reach the cold dead matter from the respective old dead bang expansions. By then the light is so disbursed, that its temperature must be in the vicinity of one degree Kelvin, hardly hot enough to be measured, let along hot enough to make the excellent black bodies of dead matter burn like stars.
    ...........................
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    I was under the assumption that the generally accepted solution to the "dark night sky" in an infinitely expanding Universe is the finite speed at which light travels. So all the light does not bombard the Earth all at once and therefore the night sky is not as bright as the sun.

    Just throwing that out there. Ultimately, I am ignorant in this matter.
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    Quote Originally Posted by Kosta
    I was under the assumption that the generally accepted solution to the "dark night sky" in an infinitely expanding Universe is the finite speed at which light travels. So all the light does not bombard the Earth all at once and therefore the night sky is not as bright as the sun.

    Just throwing that out there. Ultimately, I am ignorant in this matter.
    i hardly think the universe is expanding, so earth will not be bombarded with light. if the light of what has not escaped our view, reached earth, it would be more than enough to light up the night sky, beyond our suns ability. frankly, i doubt the universe is expanding at all.

    the electromagnetic field mentioned above, of which the vision of light is part of, includes many other wave lengths that are continuously bombarding us and with out any apparent results and this includes light
    waves from our sun, though this intensity (no reference to vision) has
    energy that affects us.

    i have suggested, our vision of a night sky, is what we observe and is probably not that far away, certainly its not the out limits of the universe. that what we see as stars etc. is light that penetrates this apparent view. much the way as we view daylight; we look into the day sky and see blue, which is actually part of this field and gives us that vision. (if it were at a lower wave length it could be red and at sunset, sometime is as, curvatures and atmospheric conditions change the waves and our vision).
    everything we see at night is of course there in daylight, but our vision is obscured and my point is, at night it is obscured for other reasons. keep in mind we can see the moons reflection in daylight as it penetrates the cause that stars don't.

    ignorant, is not a bad word. we are all; i am passing on some thoughts and most of it is opinion, to explain part of an over view of something much larger. perception.
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    Sorry Jackson33,

    I think you'll find the evidence is the universe IS expanding, at present it is a finite size and hence the night sky is generally dark. If the universe is NOT expanding then it's doing a good job of fooling us into thinking it is.
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    Quote Originally Posted by jackson33
    Quote Originally Posted by Kosta
    I was under the assumption that the generally accepted solution to the "dark night sky" in an infinitely expanding Universe is the finite speed at which light travels. So all the light does not bombard the Earth all at once and therefore the night sky is not as bright as the sun.

    Just throwing that out there. Ultimately, I am ignorant in this matter.
    i hardly think the universe is expanding, so earth will not be bombarded with light. if the light of what has not escaped our view, reached earth, it would be more than enough to light up the night sky, beyond our suns ability. frankly, i doubt the universe is expanding at all.

    the electromagnetic field mentioned above, of which the vision of light is part of, includes many other wave lengths that are continuously bombarding us and with out any apparent results and this includes light
    waves from our sun, though this intensity (no reference to vision) has
    energy that affects us.

    i have suggested, our vision of a night sky, is what we observe and is probably not that far away, certainly its not the out limits of the universe. that what we see as stars etc. is light that penetrates this apparent view. much the way as we view daylight; we look into the day sky and see blue, which is actually part of this field and gives us that vision. (if it were at a lower wave length it could be red and at sunset, sometime is as, curvatures and atmospheric conditions change the waves and our vision).
    everything we see at night is of course there in daylight, but our vision is obscured and my point is, at night it is obscured for other reasons. keep in mind we can see the moons reflection in daylight as it penetrates the cause that stars don't.

    ignorant, is not a bad word. we are all; i am passing on some thoughts and most of it is opinion, to explain part of an over view of something much larger. perception.
    What your saying sounds interesting, but I'm having trouble understanding the concept.


    Additionally, I was under the assumption that accepting the theory of General Relativity and its 'cosmological constant' necessitated an Expanding Universe. I also believe that Edwin Hubble observed that distant galaxies are moving away from the earth (the father the faster). These seem to be firm supporters for an expanding universe.
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    Quote Originally Posted by Kosta
    I was under the assumption that the generally accepted solution to the "dark night sky" in an infinitely expanding Universe is the finite speed at which light travels. So all the light does not bombard the Earth all at once and therefore the night sky is not as bright as the sun.

    Just throwing that out there. Ultimately, I am ignorant in this matter.
    You are correct according to what I understand also. In our Big Bang expanding universe, as you get a look further and further out into space, i.e. back in time, you come to a time that there were no stars or galaxies. This situation defeats Olbers’ using the finite time argument.

    As we expand and because the speed of light is finite, the expansion slows the progress of light toward us (causing the red shift). Even if there were stars and galaxies beyond what we observe, and even if their light was heading toward us, it is thought that at some point the expansion would reach the speed of light and become an effective horizon beyond which no light could ever reach us. This situation defeats Olbers’ using the finite speed of light argument.

    But that is BBT, not quasi-crunch/bang-steady state which I call the ISU, the Infinite Spongy Universe idea.

    The reason for River_rat, Jackson33, and my extended discussion is that I have concluded that the universe is infinite in space, time, and content. This position can lead people to want to reconsider Olbers' Paradox in a different setting (different from Big Bang Theory).

    The old version of steady state theory, pre-1920 (or up to mid 1900’s even), pictured stars and galaxies everywhere, evenly distributed, and in a delicate balance due to gravity (Newtonian). Olbers' Paradox from the early 1800’s was introduced to advance the idea that the universe was not infinite in size or that it had a fairly recent beginning. Then came big bang theory with the beginning as a singularity from which space-time was created. And then came my quasi-crunch/bang-steady state idea that says the universe always existed but is characterized by crunch bangs here and there, now and then, forever throughout the infinite greater universe.

    The new quasi-crunch/bang-steady state idea has crunch bangs occurring throughout the entire greater universe, but the matter/energy balance, a natural equilibrium, does not allocate enough energy to matter to enable enough light to be generated to light up the night sky, as I mentioned in previous posts. It is worth pointing out that visible light is only a small portion of the energy emitted by matter throughout the electromagnetic spectrum.

    Those like Rat and others conclude that in any infinite universe, with infinite time, there is nothing to keep the stars and galaxies form burning endlessly (being replace by new ones when the old ones burn out), and that if you go far enough out into space, you will have to run into a buring star whose light will fill a point in the sky, and so all points in the sky would have such a point of light, and the sky would be as bright as the sun in all directions at all times.

    I dissagree because stars have a finite life, as do big bangs themselves. The balance between energy and matter includes a matter-enegy cycle. That life cycle runs from big bang where energy is released, and runs through a period of abundant matter formation from the high energy density of early big bang space, progresses to matter forming stars and galaxies, and eventually the expansion has disbursed the new matter throughout the greater universe, where upon that old cold matter is caught up in some new big crunch somewhere else and the cycle continues.

    I conclude that Big bangs are so far apart that they can light up and then burn out long before their point of light reaches the nearest possible observer outside that particular crunch bang. Oh sure, that dim point of light may travel through space and reach the nearest crunch/bang neighbor, but but the time it gets there its source will have burned out and the spear of light will end before another spear of light sets out to replace it, leaving extended dark periods, and a dark night sky.

    Don't get too wrapped up in the ISU idea unless you have doubts about the singularity that serves as the beginning of everything, space, time, energy, and matter emanating from an infinitely dense, zero volume singularity. And if you are wavering at all, then wonder about how that singularity also contained the internal negative pressure to push that tiny hot energy ball exponentially at speeds greater than the speed of light in the first picoseconds after the big bang in order to explain that our observable universe is causally connected to the big bang.
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    i will not say the universe is not expanding. first of all the universe to me, is much, much larger than most will consider. then almost all agree BB or SS or any other rational opinion of the universe, will agree nothing new is produced, as to the total. no little factories out there producing new atoms to produce new matter. this to me indicates the lack of need to, expand.
    people involved in expansion all seem to have BB in their minds and that the need to expand is written into the theory, in fact or implied.

    yes, Edwin Hubble, using a land telescope in 1929, did offer a paper on the expansion. he used red and blue shifts to see through closer systems and determined this. as i understand it, this is an assumption; that since the galaxy are scattered, further apart at out distances they must be the advance systems into an unknown and therefore expanding. the problem is he was seeing 6-9 billion light years out and his namesake telescope in orbit detects the same thing but now, its 13-14 b/l/y out and whats 6-9 appears constant, but the sparsity is 14 b/l/y. this was followed up by COBE, another system in orbit. the next version of Hubble will no doubt go out 16-18 b/l/y and see what we now see at 13.7. no has one determined which direction or how fast anything is moving, only that everything does seem to move and at reasonably fast speeds. even our solar system movement around the milky ways core, each 250 million years is an educated guess.
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    Quote Originally Posted by jackson33
    I hardly think the universe is expanding, so earth will not be bombarded with light. if the light of what has not escaped our view, reached earth, it would be more than enough to light up the night sky, beyond our suns ability. Frankly, I doubt the universe is expanding at all.
    Let's say it is not expanding, do you think it is finite in extent or infinite in extent?

    the electromagnetic field mentioned above, of which the vision of light is part of, includes many other wave lengths that are continuously bombarding us and with out any apparent results and this includes light
    waves from our sun, though this intensity (no reference to vision) has
    energy that affects us.

    I have suggested, our vision of a night sky, is what we observe and is probably not that far away, certainly it’s not the out limits of the universe. That what we see as stars etc. is light that penetrates this apparent view. Much the way as we view daylight; we look into the day sky and see blue, which is actually part of this field and gives us that vision. (If it were at a lower wave length it could be red and at sunset, sometime is as, curvatures and atmospheric conditions change the waves and our vision).
    Everything we see at night is of course there in daylight, but our vision is obscured and my point is, at night it is obscured for other reasons. Keep in mind we can see the moons reflection in daylight as it penetrates the cause that stars don't..
    Yes, I agree that we are immersed in electromagnetic radiation across the full spectrum from radio and microwave, visible light, and ultraviolet, X-rays, Gamma Rays and who knows what else. Technically all of this radiation is referred to as "light" as distinguished from visible light. I would agree that the night sky is lighted up like the daytime sky if you are talking about the full spectrum of electromagnetic radiation. However, Olbers was only talking about visible light.[quote]
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    Quote Originally Posted by Megabrain
    Sorry Jackson33,

    I think you'll find the evidence is the universe IS expanding, at present it is a finite size and hence the night sky is generally dark. If the universe is NOT expanding then it's doing a good job of fooling us into thinking it is.
    here we go again; i am not saying the universe is or is not expanding. i do and will contest the theory that requires a need to expand and the reasons used to explain an expansion. there would seem to be no need to expand, but if an outer galaxy say 3-4 or 1000 trillion light years out drifts to far, its not going to vaporize. to me its a simple cellular comparison and as the electrons of lead cell (about 100), rotate around its nucleus, they have no desire or need to exit. there is thought to be a membrane around a cell, but there is no indication one or more of the electrons orbit at that point or distance from the nucleus and so on.

    yes, its dark up there at night and all that we do see, is there all day and we don't see it. now why can't you take that explanation and extend it to what is seen at night. it just seems such a simple idea, that we and our visual observations are limited to what our systems (eyes-brain-understanding) are capable of and that what is not seen, in daylight, is only explained by what we see at night.


    bogie; think this answers one of your questions and gets to the brunt of the other. i don't know, of course but i would think Newton had no idea what gravity was or was not, on the moon. but for his time and ours, his observations seem correct. the same for Olber, and i am not convinced
    our observation, at night, of a star or galaxy is a correct one. with equipment (telescopic lens or telescope) we know what we see is not all there is and as this equipment develops, what is seen now, may be the tip of something beyond our expectations.
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    Quote Originally Posted by bogie
    I would agree that the night sky is lighted up like the daytime sky if you are talking about the full spectrum of electromagnetic radiation. However, Olbers was only talking about visible light.
    If I could just interject here, the night sky is most definitely not lit lit up with EM radiation like the daytime sky is, and here's why...

    The energy from EM waves at the earth's surface when the sun is directly overhead is around 1060Watts per SQ Metre (from the sun). The total extrasolar EM radiation getting to the earths surface (at night) is a figure I cannot find, however I can say it is less than 1 billionth of a watt/per metre cos that's about how much 'man made' radiation there is in my area which varies as things around here get truned on/off.

    Second if it was of the same order as daytime radiation we would not need bloody great dish antenna 200feet wide with liquid nitrogen cooled RF pre-amplifiers to detect it, you'd be able to hang a coathanger out of the window!
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    Quote Originally Posted by Megabrain
    Quote Originally Posted by bogie
    I would agree that the night sky is lighted up like the daytime sky if you are talking about the full spectrum of electromagnetic radiation. However, Olbers was only talking about visible light.
    If I could just interject here, the night sky is most definitely not lit lit up with EM radiation like the daytime sky is, and here's why...

    The energy from EM waves at the earth's surface when the sun is directly overhead is around 1060Watts per SQ Metre (from the sun). The total extrasolar EM radiation getting to the earths surface (at night) is a figure I cannot find, however I can say it is less than 1 billionth of a watt/per metre cos that's about how much 'man made' radiation there is in my area which varies as things around here get truned on/off.

    Second if it was of the same order as daytime radiation we would not need bloody great dish antenna 200feet wide with liquid nitrogen cooled RF pre-amplifiers to detect it, you'd be able to hang a coathanger out of the window!
    You point out some good facts about the amount of radiation hitting the earth during the day vs. at night. I certainly agree with the order of magnitude in the day being large multiples of the radiation at night, simply because of the huge radiation from all across the electromagnetic spectrum from the sun.

    Now let me back peddle a little.

    Light vs. visible light.

    If we are talking just visible light there is no argument about the day being lighted and the night relatively dark with only moon shine and a smattering of stars giving us light.

    My reference to the sky being lighted up like the day time sky was careless enthusiasm. I wanted to acknowledge to Jackson that if you consider the technical definition of light being any electromagnetic radiation, then certainly we are getting radiated at night by a full spectrum of wavelengths.
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    Quote Originally Posted by bogie
    My reference to the sky being lighted up like the day time sky was careless enthusiasm. I wanted to acknowledge to Jackson that if you consider the technical definition of light being any electromagnetic radiation, then certainly we are getting radiated at night by a full spectrum of wavelengths.
    I'm afraid not even by a whole spectrum at night. The EM spectrum starts at just above zero hertz, and continues to a theoretical maximum of around 10^43 Hertz. Huge chunks of this never get through to us I'm afraid, the area that does also has holes in it, some radio frequencies are 'quiet' and no known cosmic sources have yet been found to radiate within. Mind you, in order to make the above statement I choose to ignore the doppler shift effect as it merely moves visible light up or down the spectrum and therefore 'appears' as a different frequency.
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    Quote Originally Posted by Megabrain
    Quote Originally Posted by bogie
    My reference to the sky being lighted up like the day time sky was careless enthusiasm. I wanted to acknowledge to Jackson that if you consider the technical definition of light being any electromagnetic radiation, then certainly we are getting radiated at night by a full spectrum of wavelengths.
    I'm afraid not even by a whole spectrum at night. The EM spectrum starts at just above zero hertz, and continues to a theoretical maximum of around 10^43 Hertz. Huge chunks of this never get through to us I'm afraid, the area that does also has holes in it, some radio frequencies are 'quiet' and no known cosmic sources have yet been found to radiate within. Mind you, in order to make the above statement I choose to ignore the doppler shift effect as it merely moves visible light up or down the spectrum and therefore 'appears' as a different frequency.
    . . . . . . . . . Well everybody knows that, lol.

    No, just kidding. Thanks for the info.
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  27. #26 A geometrical observation 
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    It is reasonable to suppose that the further a star is from the earth the dimmer it must appear until, one might suppose, a star of a fixed absolute magnitude m is invisible to an observer on earth when it is located outside a circle of a given radius R, depending only upon m. One might give an informal geometrical proof of this as follows. A star S under consideration is R light years from earth. The surface area of the sphere of radius R centered at S is X = 4 (pi) RR light years. The total amount of light reaching the earth from S must be approximately proportional to the ratio (pi)rr /X, where r is the radius of the earth. Clearly this ratio approaches zero as R tends toward an arbitrarily large number. Thus, in an infinite universe, there could be an infinite number of stars of absolute magnitude less than or equal to m in the universe and the sky would, nevertheless, be quite dark at night.
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    It is reasonable to suppose that the further a star is from the earth the dimmer it must appear until, one might suppose, a star of a fixed absolute magnitude m is invisible to an observer on earth when it is located outside a circle of a given radius R, depending only upon m.
    in an infinite universe, there could be an infinite number of stars of absolute magnitude less than or equal to m in the universe and the sky would, nevertheless, be quite dark at night.
    in an infinite universe with an infinite number of stars you only need one photon from each star, in an infinite length of time, to reach your detector for the sky to appear light.
    Sometimes it is better not knowing than having an answer that may be wrong.
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  29. #28 Continuation of a geometric demonstration... 
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    When a star S is sufficiently far away from planet E, there is a probability p that at least one photon from S will reach the surface of E. For great enough distances, p may be less than that 1 and over greater and greater distances will approach zero. This is all that needs to be proved, ie, that the sky should probably be dark.
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    It also occurs to me that the number of photons in the universe at time t is countable, because the union of a countable number of countable sets is countable. Thus, since three dimensional Cartesian space is an uncountable set, there must be points in space from which no stars whatever are visible.
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    No, because the number of stars per unit area increase with distance at the same rate that the amount of light from those stars falls of. So, the net effect is that the amount of light is constant.

    There is nothing wrong with Olber's logic. He just didn't know that the universe is expanding and of finite age. Therefore there is no paradox to solve.
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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    Quote Originally Posted by Peter Mancevice View Post
    It also occurs to me that the number of photons in the universe at time t is countable
    Unless the universe is infinite, of course.
    Without wishing to overstate my case, everything in the observable universe definitely has its origins in Northamptonshire -- Alan Moore
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    The universe may be infinite but only contains a finite number of stars, the fact that we can see as many as we can suggests that the universe is still youngish.
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    The Olber's Paradox is no more a paradox than escape velocity is a paradox. If an object is traveling away from Earth at escape velocity, then it will continually be traveling slower and slower, and yet it will keep moving forever. It seems like a paradox until you break out the math and see that the rate at which it slows is less than the rate at which the slowing is decreasing (kind of a mouthful to say.)

    Olber's Paradox has the same issue. The rate at which the number of stars in view grows as you look further and further into space is less than the rate at which those stars become dimmer and dimmer.
    Some clocks are only right twice a day, but they are still right when they are right.
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    Also there is strong evidence that the density of stars is "tapered". Each level of structure has proportionally less star density than the last. The solar system has more matter per cubic meter than the Milky Way. The Milky Way has on average more matter per cubic meter than the cluster of which it is part. The cluster has more matter per cubic meter than the super cluster it is part of.................... etc.

    There's increasingly more empty space between the objects the higher up you go.

    At the largest structure level, the overall density of matter would be so very near to zero that you might round it to zero.


    (And want to point out that my previous post is really just a rephrasing of the OP's idea, just a bit more mathematical.)
    Some clocks are only right twice a day, but they are still right when they are right.
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