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Olbers’ Paradox: Why Is the Sky Dark at Night? (2000)

264 points by fauria 11y ago

3pt14159 11y ago
Isn't the issue one of lumens? The light from a star is inversely quadratically related to its distance. Assuming a random distribution of stars across a ring or plate in 3D space we should expect the quadratically growing number of stars for the incremental space. The two cancel and it becomes a ratio of the average brightness of a star (bright) versus the density of stars in space (super sparse).
- paulddraper 11y ago
  Imagine an infinite series of nested hollow shells of equal thickness around Earth. The number of stars in each shell is quadratic relative to the radius. The brightness of each star is inversely quadratic relative to the radius of the shell. Thus, each shell has a constant total brightness, as perceived from Earth. An infinite number of these shells add up to infinite brightness.
  - 3pt14159 11y ago
    I'm not quite following. The light in each "shell" continues to dissipate in an inversely quadratic method from the shells distance from earth, no? It would help if I had this drawn out.
    - paulddraper 11y ago
      No, the total light in each spherical "shell" is the same as every other shell. Stars that are 20 light-years away are 4x dimmer than stars 10 light-years away. But there are 4x more stars 20 light-years away than 10 light-years away. As you go outward from Earth, the stars get dimmer and more numerous, but these balance each other, and the infinite sum is 1 + 1 + 1 + ... (This is no chance happening; regardless of the # of spatial dimensions the universe has, this relationship holds true.)
mjn 11y ago
I can recommend the book Darkness at Night by Edward Harrison [1] for a detailed look at the history of this paradox. An enjoyable read, and ties it in with several closely related historical debates in cosmology. [1] http://www.hup.harvard.edu/catalog.php?isbn=9780674192713 http://www.hup.harvard.edu/catalog.php?isbn=9780674192713
jdimov10 11y ago
I don't get the "running out of fuel" argument... If the universe (as assumed in the text) is infinitely old and infinitely large, why should there be any scarcity of nuclear fuel?
- randlet 11y ago
  Stars fuse light elements it into heavier elements. Eventually all the lighter elements will be used up.
  - TranquilMarmot 11y ago
    One of my favorite short stories about this is The Last Question by Isaac Asimov http://multivax.com/last_question.html http://multivax.com/last_question.html
  - pc86 11y ago
    I think they were saying if we're conceding infinite size and an infinite number of stars, why not an infinite amount of those lighter elements as well?
    - kyberias 11y ago
      Imagine an infinite space divided in infinite number of finite volumes each containing a finite number of "lighter elements". All the light elements form a star in their local volume and burn up all the light elements locally. The result: all the infinite number of finite volumes are void of the light elements. The infinite space is dark.
- mjevans 11y ago
  Most stars we see are burning Hydrogen, possibly helium, in a process of gravity well driven nuclear fusion. This fusion results in heavier atomic particles and some waste that we see as radiation (light, heat, various forms of EM energy). I am not an astrophysicist, nor am I an expert in the early universe, but I recall that the prevailing theories of our time are that somehow the universe came in to being with predominantly hydrogen atoms. These combine through fusion in what we call stars to form denser matter. This process continues until the result of combining the elements reaches a limit. I believe that iron happens to be that limit if I recall correctly. https://en.wikipedia.org/wiki/Iron_peak https://en.wikipedia.org/wiki/Iron_peak Describes what I recall reading/hearing many years ago.
maskedinvader 11y ago
isnt the answer that most of the stars are inside galaxies that are for the most part moving away from us and for that matter from each other (due to space itself expanding) with the speed of expansion or their apparent motion away from us proportional to their distance from us. This means most of the star light reaching us is red shifted (due to doppler effect of light) and since we humans cannot see this red shifted light, the night sky appears dark to us. anybody with a physics background can point out where I got this wrong, but I thought this is why the sky is dark.
VeilEm 11y ago
This didn't mention the expansion of space at all. The universe may be infinite in size but we'll never see the light of stars that exist so far from us that they are beyond the distance at which space expands faster than light can travel. That's why we have a dark sky and it will just get darker as more things we see now eventually expand beyond that barrier. One suggested end to the universe is the Big Rip in which all matter eventually separates in this way such that the distance between all matter is infinite: https://en.wikipedia.org/wiki/Big_Rip https://en.wikipedia.org/wiki/Big_Rip
- ranko 11y ago
  The expansion of the universe also leads to red shift of the light from (nearly) all the stars that we'd otherwise expect to see. This means that the frequency of their light is moved away from the range that our eyes can see.
- platz 11y ago
  My understanding of the expansion of space is that the expansion doesn't occur locally, but is only noticeable over large distances. is that incorrect?
  - paulddraper 11y ago
    It occurs everywhere, proportionally. The effect isn't great enough to notice unless you are looking at light-years. Also, gravity and electromagnetism increase at close proximity, so on less-than-cosmic scales, they overcome the minute amount of spatial expansion.
    - platz 11y ago
      therefore the statement " all matter eventually separates in this way" , strictly speaking, seems false since gravity and electromagnetism overcome expansion at local levels.
      - paulddraper 11y ago
snowwrestler 11y ago
There is one more complimentary answer, which is that the night sky is not as dark as it seems, but our eyes cannot see all the wavelengths of light that populate the night sky. If we could see deep into the infrared, we might see more faraway stars and galaxies, whose light has been red-shifted by the expansion of space. If we could see wavelengths in the single cm range, we might perceive a dim uniform glow in the night sky: the cosmic background radiation. If we could see radio waves we might see all sorts of light sources in the night sky.
- paulddraper 11y ago
  Yep, explained here: http://www.physics.org/facts/sand-dark.asp http://www.physics.org/facts/sand-dark.asp Of course, if there were an infinite amount of light (visible or not) reaching Earth, you'd be dead.
  - archgoon 11y ago
    Suppose that the Energy distribution for a certain amount of light (as seen by earth) was given by /- 1 if f < f0 E(f) = > \- 1/f^2 if f > f0 Then we would have light "at all frequencies" which could be said to be "an infiinite amount of light" but the total amount of energy would still be finite. Most of these explanations don't seem to first figure out whether if you had a uniform distribution of stars (at discrete points) in an infinite (Euclidean) space, if the amount of radiated energy seen at an arbitrary point would diverge if you summed over all available frequencies. If it doesn't, it seems like lack of sensitivity is the main issue here, and the cosmological arguments are simply additional reasons for why it doesn't happen.
    - wfn 11y ago
      Pity someone down-voted you. From what I take it, you were basically simply asking, "what if the 'infinite amount' at 'all frequencies' were reaching you in a non-uniform distribution of frequencies? - would the original arguments and premises still stand?"
  - Retric 11y ago
paulddraper 11y ago
This is a great explanation, up until the last part, which is slightly misguided. "So even if the universe were infinitely old as well as infinitely large, it would not contain enough fuel to keep the stars shining forever and to fill up all of space with starlight." If the universe were infinitely old, fuel was consumed, and fuel had finite density, then the sky would be completely dark. Because there would be no starts. The author is really just thinking "It would require infinite time to receive light from infinitely far away." Which is the relevant answer to the paradox.
mrdufrain 11y ago
Isn't it also the case that, because of the accelerated expansion of the universe, some stars are moving away from us at more than the speed of light, and their light will therefore never reach us?
- paulddraper 11y ago
  Yes, this is currently true, and will continue to be, unless we end in the Big Crunch.
EGreg 11y ago
Actually this was the argument that bothered Newton, but about gravity. In an infitely old but finitely large universe, why wouldn't gravity pull everything together? Unless in all directions gravity canceled out. Similarly, we can ask why the universe isn't filled with light. If the universe was infinitely old then indeed the light would eventually heat up all the matter and penetrate everywhere. But if it's expanding, then the light didn't have time to fill the space-time before it expanded further.
- paulddraper 11y ago
  In an infinitely large universe, the net force of cosmic gravity would be 0. Kind of like how an real number divides the number line into "same size" infinite intervals. Granted, entropy in the system would cause matter to clump into larger and larger bunches. But if the matter were perfectly arranged by an outside force (e.g. God) and didn't deteriorate, the universe could remain static.
  - Strilanc 11y ago
    Gravity actually acts kind of... weird... in an infinitely large uniform universe. You end up with gravity acting like a time-dependent position-independent scaling factor on position. Leonard Susskind goes over the derivation (for Newtonian gravity) in a Cosmology lecture available on youtube [1]. 1: https://youtu.be/ERjkSbdn6-4?t=53m50s https://youtu.be/ERjkSbdn6-4?t=53m50s
mixmastamyk 11y ago
Hmm, didn't seem to mention the Inverse-square law, which I was waiting patiently for.
cristianpascu 11y ago
Or the Universe is neither infinite or as old as it's assumed to be. Although there's strong evidence for it being as old as we (me included as a figure of speech) currently believe it, our belief is based on some fundamental assumptions that can only be strengthen but not proven. At least for the sake of honesty, one must be aware of the nature of this kind of opinions. Science is part of the larger discipline called epistemology, so all the rules valid there, are valid in science too.
DINKDINK 11y ago
>The entire sky would be about as bright, and as hot, as the surface of the Sun. Not so according to “The Inverse Square Law”.[1] If one measures the light flux through a hypothetical sphere drawn around a light source and then doubles that spheres size, the light density must decline or you've broken conservation of energy. [2] [1] http://bccp.berkeley.edu/o/Academy/workshop08/08%20PDFs/Inv_Square_Law.pdf http://bccp.berkeley.edu/o/Academy/workshop08/08%20PDFs/Inv_... [2] http://www.compuphase.com/electronics/candela_lumen.htm http://www.compuphase.com/electronics/candela_lumen.htm
- jackcarter 11y ago
  Yes, but as you look deeper into the night sky, you see more and more stars (proportional to the square of the distance). These two factors cancel exactly.
- nostromo 11y ago
  If you reduce the power of infinite stars, you still have infinite stars producing infinite light. x * infinity = infinity (so long as x > 0; even if x is infinitesimally small)
  - jwally 11y ago
    But you can't have infinite stars in your field of view since they'd get in each other's way; blocking radiation. Using the tree example from the article, you wouldn't see infinite trees, you'd only see the pieces that are directly in front of you.
  - tamana 11y ago
    No, infinity times infinitesimal is undefined, you have to define your infinities more carefully to get an answer.
- typon 11y ago
  Remember parallel plate capacitors from Electromagnetics class? They're infinite in size for a reason, to get around not having to worry about the inverse square law. An infinite amount of stars would produce an infinite amount of energy...
pc86 11y ago
Title fix: "Olbers'" not "Olber's," named after Heinrich Olbers. It is wrong in the linked article's title as well.
- dang 11y ago
  Thanks, fixed.
goodside 11y ago
"Astronomers have concluded that the universe began some 12 to 15 billion years ago. That means we can only see the part of it that lies within 12 to 15 billion light-years from us." This is false, because it ignores the metric expansion of spacetime. We can see radiation from objects that are now ~46.5 billion light-years from Earth. This isn't picking nits. The explanation given here makes it sound like the Universe is a Euclidean volume that got instantaneously filled with stars, at roughly their present density, and that this density is low enough that light from distant stars hasn't reached us yet. If this were true, it wouldn't only explain why the sky is dark now, but predict that it has always been dark. We know this is false: for the first 380,000 years after the Big Bang, the Universe was filled with hydrogen plasma and completely opaque to radiation, which we can still see in the form of CMBR. As spacetime expands, energy density decreases, space becomes less light-emitting and more transparent, and light already in transit becomes red-shifted. Our field of vision is still technically flooded with light, as it always has been, but by now the red-shift is so extreme that the light is in the radio spectrum.
- kyberias 11y ago
  > As spacetime expands, energy density decreases, space becomes less light-emitting and more transparent, and light already in transit becomes red-shifted. Our field of vision is still technically flooded with light, as it always has been, but by now the red-shift is so extreme that the light is in the radio spectrum. You talk about the radiation generated before 1M years in the universe. This article talked about the light from the existing stars in the universe.
  - goodside 11y ago
    The red shift applies to distant stars too. The important point is that even in the extreme scenario where all stars last forever and you wait an infinite amount of time for light to reach you, you will still never see a fully illuminated sky because the stars are receding much faster than the light propagates due to metric expansion. Saying the sky is dark because 1) the Universe is young or 2) stars are short-lived is just false. The Universe gets darker and darker as it expands, despite there being "more time for light to reach us".
grondilu 11y ago
I've always been puzzled by this paradox. More particularly, I'm baffled that apparently the mainstream explanation involves cosmological arguments such that the expansion of the Universe. Is it really that complicated? Take Hubble's deep field image, for instance. It was shot in a tiny area of the sky that looks completely black. But with enough exposure, Hubble found that it's actually full of galaxies. Can't I just conclude that if this part of the sky if completely black, it's not because space is expending, but just because our eyes are not sensitive enough? Olber's Paradox points out that wherever we look at, at some distance our line of sight will meet the surface of a star. But that does not mean that this point will register as a light for our eyes. Our eyes would have to be sensitive enough.
- nostromo 11y ago
  Imagine Hubble's deep field image again, but this time imagine you can see towards infinity (beyond the observable universe). If the universe is infinitely big (and old), then there would be so many stars in the image that there would be an infinite amount of light in the image. In this hypothetical universe, the Sun would actually be a dark spot in the sky -- because it would be blocking the infinite amount of light coming from an infinite amount of stars behind it. That's the paradox -- that we do not see that. No matter how sensitive our eyes are, we would be able to see infinite light. (Actually, our eyes would be melted... and all current forms of life impossible... but you get the picture.)
  - grondilu 11y ago
    But stars are getting fainter and fainter as they are further and further away. I get that there would be an infinite amount of them, but then it's an infinite times a zero. The limit is not obvious and I've never seen anyone discussing the actual maths of this. I don't know those maths, but it seems reasonable to me that since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density.
    - nostromo 11y ago
gusmd 11y ago
I'm missing something here and would so happy if someone explained to me. I am sorry if I'm making false assumptions as my knowledge on the subject is very limited. If the universe started from a single point in space and time (i.e., Big Bang), and no matter moves faster than the speed of light, how could ANY star be more distant from us than light could have traveled in the same time frame? (I'm assuming no matter is travelling at v > c/2, otherwise my argument would only be valid for things traveling in the same hemisphere of the expansion as Earth)
- Practicality 11y ago
  The matter isn't moving. Space is expanding, ie, space is being inserted in-between all bits of matter. Edit: To elaborate further: Since all the newly expanded space also expands, the distance to travel continuously increases as the light travels, to the point where over a certain distance the light never completes the journey. So, the net effect is that the two objects become further apart faster than c, even though neither of them are moving.
- hoorayimhelping 11y ago
  Space itself might be able to expand faster than the speed of light.
- Lawtonfogle 11y ago
  Expansion of space allows for the distance of two objects to increase such that it appears that one is moving away from the other at a speed greater than c/2. I think it is possible for this to even be greater than c because it is the expansion of space and not objects movement contributing to the increase in distance.
- joe5150 11y ago
  This is an important concept to understand: https://en.wikipedia.org/wiki/Comoving_distance https://en.wikipedia.org/wiki/Comoving_distance
vorotato 11y ago
what about all the light that doesn't hit us.
amelius 11y ago
An easy explanation is here: https://www.youtube.com/watch?v=gxJ4M7tyLRE https://www.youtube.com/watch?v=gxJ4M7tyLRE
eutropia 11y ago
I find it odd that so many people seem to have trouble accepting this explanation. Light travels at a finite speed, ergo anything far enough away(adjusted for expansion of space) is invisible, because we've only existed for a dozen billion years. If the universe were infinitely old, then we'd have something interesting to talk about.
jcoffland 11y ago
One answer to this problem is that the night sky isn't dark at all. It's just less bright than during the day. Hear me out. As a species that evolved on this planet under it's particular conditions we perceive day to be bright and night to be dark because of the particular range of light sensitivity of our eyes. Too often science leaves the human observer out of the equation. It lets us feel like gods presiding over our universe but is a big mistake. All that said it's not unreasonable to question why the night sky is not brighter than it is.
- alanwatts 11y ago
  >Too often science leaves the human observer out of the equation. It seems this problem may have come full circle with the Measurement Problem. But yes, human beings themselves emit light, however that light resonates on a frequency that our eyes have not evolved to see, so we invented infrared optics.
dantillberg 11y ago
A mathematical explanation would involve a comparison of the density of stars throughout the universe with the inverse-square drop-off in light intensity from each. If you assume for the sake of argument that all stars are as bright as the sun, and that stars have a uniform density throughout the universe (either a finite-but-huge or infinite universe, it makes little difference here), then you could solve for the mean intensity of light throughout, or in our case, "how bright the sky is at night." The article makes a classic (and really hard to escape! I've seen this sort of thing called a "paradox" on many occasions.) mistake of examining two infinite quantities (infinite stars, up to an infinite distance away) and assuming that they must cancel each other out, that infinity/infinity=1. But not all infinities are the same, and infinity/infinity can work out to 0, or to 0.1, or to pi, or to infinity (as in the case of "# real numbers"/"# integers"), or to anything else; you have to look at the details -- what kind of infinity is it? -- and figure out how they compare.
- jakobegger 11y ago
  The article makes no mistake, it just doesn't go into enough detail. To determine the amount of energy reaching us, we need to integrate over the energy density divided by the square of the distance over the whole 3d space. As any physicist can tell you, an integral over the whole space will diverge unless the kernel falls off faster than 1/r^2. This means that one of the following must be true a) either the universe is finite, ie. the density falls off b) we don't integrate over the whole space (we can't see far enough due to age of universe) Which is exactly the argument this article is making Edit: in other words, infinite or finite-but-huge is an important difference when integrating over constant density; the former integral will diverge, the latter will not
lutusp 11y ago
As is often the case, this explanation fails to take cosmological expansion into account. An expanding universe is a cooling one. The explanation is correct as far as it goes, but failing to take expansion into account either dates the explanation or fails to evaluate a factor that's a bit more complex than relying on the finite age of the universe.
rdiddly 11y ago
Subsequent edit: Assuming the universe is infinite, is where the problem begins. There is no reason to assume that. Original comment: Is this really not obvious to people? It's about subtended angles - simple geometry. As the Earth's distance from a star increases, it subtends a decreasing angle in that star's "sky." Assuming radiation does indeed proceed radially and in straight lines, at increasing distance the Earth is capable of catching a decreasing portion of that star's radiation. As the distance approaches infinity, the subtended angle approaches zero and the amount of light reaching us approaches zero. The star is just as bright, but most of its radiation goes somewhere else besides Earth. Imagine building a giant spherical shell around a star. Its radius equals the distance between earth and the star. It catches 100% of that star's radiated energy. Now paint the Earth on the inside of the shell, actual size. It looks, to someone standing on the surface of that star, like the real earth, i.e. a tiny dot. Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2). That's how much of that star's energy our planet catches. Assuming zero degradation across space. So imagine you're in a forest of trees the closest of which are 800 miles away from you. You'd see the goddamned sky just fine.
- samstave 11y ago
  Is was an amazing conceptual comment - thank you
- gpsx 11y ago
  You are correct in your geometry, but you forgot one thing. The earth receives a smaller portion of light for stars that further away, but the number of stars at that radius goes up by the exact same amount. So from any shell the amount of light we get is the same. If the shells go out to infinity, the light becomes infinite (well, according to the naive argument).
  - meric 11y ago
    The nearest star is the Sun. With a giant Sun nearest to Earth, it's impossible for the number of stars to go up proportionally as distance to Earth increases. There isn't 4 suns at 2 AU, and at 100000 light years wide, with 63000 AUs per light year, the milky way does't contain (63000 * 100000)^2 stars. There needs to be 4 billion times more stars in the milk way for there to be proportionally as many stars as in our solar system. You can fill the entire sky with AA battery torches and they won't be as bright as the one stuck right up to your eye. The night sky is dark, but it doesn't mean it isn't full of rays of lights heading our way. It's darker than the day sky due to the Sun being so close, yes, but the night sky is full of light, everywhere we look. It's only because the way our minds perceive relatives, we call the night sky "dark".
jwally 11y ago
Stab in the dark: Inverse Square Law + The number of stars in your field of vision can't be infinite.
kjell 11y ago
https://twitter.com/5point9billion https://twitter.com/5point9billion calls out the inverse: light traveling from earth out towards the nearest stars. It's a twitter bot that takes a twitter user's birthday, and tweets to them as their "light cone" expands across the universe.
deleted 11y ago
[deleted]
dschiptsov 11y ago
This is mere ray-tracing problem. What we call bright sky is reflections of Sun rays from particles in atmosphere. What we see is reflected light. When Sun is shadowed by Earth we see only light reflected by distant object, such as Moon. The darkness of the night sky is relative - some rays are here, but our visual system is conditioned for days (reflected light), not nights. The idea that everything should be filled with starts is just wrong. Rays from distant stars were deflected, blocked by particles, etc.
jonmccreery 11y ago
This looks like a question that actually looks like two questions; namely, 'is the universe infinite' (and as a side question, what is the actual dimensional and geometric configuration of the universe), and if the first question is true, 'why do we not observe an infinite flux of photons, or really any other type or radiation, bathing our chunk of the universe'. This one's easy. The first, foundational, assumtion is way easy to knock down, via all the accumulated evidence that we erupted from a singularity 13-some billion years ago. So.. no infinite time. But we could probably get by with, even with an infinite universe, if we just assume a universal speed, which is most definitely supported by current academic consensus. This is because of the concept of the light cone, which says that you can't be illuminated by things that lie outside your temporal and spacial vicinity, as defined by how long it takes light in a vacuum to reach you. That's a stronger statement than just how bright the sky is... it applies to any conceivable mechanism of information transfer, and it's universally supported by any experiments that we've tried (note: wormholes... possible, super crazy loop hole here... maybe an infinite universe has infinitely many wormholes to pump radiation into our light cone, so basicly multiverse, but we've already talked about the universe having an age). I see no paradox here, but then again the Big Bang and Special Relativity are pretty new as ideas and we all benefit from the shoulders of the giants we stand on. Edit: On further reflection, a truly infinite universe probably would park an infinite number of unstable wormholes on top of our neighborhood, but in that case the the fact that our sky is in fact dark just adds more evidence to the pile that we already have that it's not.
jonmccreery 11y ago
This looks like a question that actually looks like two questions; namely, 'is the universe finite' (and as a side question, what is the actual dimensional and geometric configuration of the universe), and if the first question is true, 'why do we not observe an infinite flux of photons, or really any other type or radiation, bathing our chunk of the universe'.
frogpelt 11y ago
If there are an infinite number of stars in an infinitely large universe that is infinitely old, how is the nuclear fuel finite? Help me here.
mnw21cam 11y ago
I am quite amazed that noone has pointed out that in terms of the cosmic microwave background, the sky is not black. The radiation that travels the furthest before hitting us is this background radiation. It only appears to be dim because it has been redshifted a huge amount due to the expansion of the universe since then. But yes - everywhere you look in the sky (unless there is something in the way), you are looking directly at the intense fire of the birth of our universe. Red-shifted until you can't even see it any more.
mrnobody4 11y ago
So should the earth heat up over time as more light reaches us or does the expansion of the universe negate that?

264 points by fauria 11y ago

Isn't the issue one of lumens? The light from a star is inversely quadratically related to its distance. Assuming a random distribution of stars across a ring or plate in 3D space we should expect the quadratically growing number of stars for the incremental space. The two cancel and it becomes a ratio of the average brightness of a star (bright) versus the density of stars in space (super sparse).

paulddraper 11y ago
Imagine an infinite series of nested hollow shells of equal thickness around Earth. The number of stars in each shell is quadratic relative to the radius. The brightness of each star is inversely quadratic relative to the radius of the shell. Thus, each shell has a constant total brightness, as perceived from Earth. An infinite number of these shells add up to infinite brightness.
- 3pt14159 11y ago
  I'm not quite following. The light in each "shell" continues to dissipate in an inversely quadratic method from the shells distance from earth, no? It would help if I had this drawn out.
  - paulddraper 11y ago
    No, the total light in each spherical "shell" is the same as every other shell. Stars that are 20 light-years away are 4x dimmer than stars 10 light-years away. But there are 4x more stars 20 light-years away than 10 light-years away. As you go outward from Earth, the stars get dimmer and more numerous, but these balance each other, and the infinite sum is 1 + 1 + 1 + ... (This is no chance happening; regardless of the # of spatial dimensions the universe has, this relationship holds true.)

mjn 11y ago

I can recommend the book Darkness at Night by Edward Harrison [1] for a detailed look at the history of this paradox. An enjoyable read, and ties it in with several closely related historical debates in cosmology. [1] http://www.hup.harvard.edu/catalog.php?isbn=9780674192713 http://www.hup.harvard.edu/catalog.php?isbn=9780674192713

jdimov10 11y ago

I don't get the "running out of fuel" argument... If the universe (as assumed in the text) is infinitely old and infinitely large, why should there be any scarcity of nuclear fuel?

randlet 11y ago
Stars fuse light elements it into heavier elements. Eventually all the lighter elements will be used up.
- TranquilMarmot 11y ago
  One of my favorite short stories about this is The Last Question by Isaac Asimov http://multivax.com/last_question.html http://multivax.com/last_question.html
- pc86 11y ago
  I think they were saying if we're conceding infinite size and an infinite number of stars, why not an infinite amount of those lighter elements as well?
  - kyberias 11y ago
    Imagine an infinite space divided in infinite number of finite volumes each containing a finite number of "lighter elements". All the light elements form a star in their local volume and burn up all the light elements locally. The result: all the infinite number of finite volumes are void of the light elements. The infinite space is dark.
mjevans 11y ago
Most stars we see are burning Hydrogen, possibly helium, in a process of gravity well driven nuclear fusion. This fusion results in heavier atomic particles and some waste that we see as radiation (light, heat, various forms of EM energy). I am not an astrophysicist, nor am I an expert in the early universe, but I recall that the prevailing theories of our time are that somehow the universe came in to being with predominantly hydrogen atoms. These combine through fusion in what we call stars to form denser matter. This process continues until the result of combining the elements reaches a limit. I believe that iron happens to be that limit if I recall correctly. https://en.wikipedia.org/wiki/Iron_peak https://en.wikipedia.org/wiki/Iron_peak Describes what I recall reading/hearing many years ago.

maskedinvader 11y ago

isnt the answer that most of the stars are inside galaxies that are for the most part moving away from us and for that matter from each other (due to space itself expanding) with the speed of expansion or their apparent motion away from us proportional to their distance from us. This means most of the star light reaching us is red shifted (due to doppler effect of light) and since we humans cannot see this red shifted light, the night sky appears dark to us. anybody with a physics background can point out where I got this wrong, but I thought this is why the sky is dark.

VeilEm 11y ago

This didn't mention the expansion of space at all. The universe may be infinite in size but we'll never see the light of stars that exist so far from us that they are beyond the distance at which space expands faster than light can travel. That's why we have a dark sky and it will just get darker as more things we see now eventually expand beyond that barrier. One suggested end to the universe is the Big Rip in which all matter eventually separates in this way such that the distance between all matter is infinite: https://en.wikipedia.org/wiki/Big_Rip https://en.wikipedia.org/wiki/Big_Rip

ranko 11y ago
The expansion of the universe also leads to red shift of the light from (nearly) all the stars that we'd otherwise expect to see. This means that the frequency of their light is moved away from the range that our eyes can see.
platz 11y ago
My understanding of the expansion of space is that the expansion doesn't occur locally, but is only noticeable over large distances. is that incorrect?
- paulddraper 11y ago
  It occurs everywhere, proportionally. The effect isn't great enough to notice unless you are looking at light-years. Also, gravity and electromagnetism increase at close proximity, so on less-than-cosmic scales, they overcome the minute amount of spatial expansion.
  - platz 11y ago
    therefore the statement " all matter eventually separates in this way" , strictly speaking, seems false since gravity and electromagnetism overcome expansion at local levels.
    - paulddraper 11y ago

snowwrestler 11y ago

There is one more complimentary answer, which is that the night sky is not as dark as it seems, but our eyes cannot see all the wavelengths of light that populate the night sky. If we could see deep into the infrared, we might see more faraway stars and galaxies, whose light has been red-shifted by the expansion of space. If we could see wavelengths in the single cm range, we might perceive a dim uniform glow in the night sky: the cosmic background radiation. If we could see radio waves we might see all sorts of light sources in the night sky.

paulddraper 11y ago
Yep, explained here: http://www.physics.org/facts/sand-dark.asp http://www.physics.org/facts/sand-dark.asp Of course, if there were an infinite amount of light (visible or not) reaching Earth, you'd be dead.
- archgoon 11y ago
  Suppose that the Energy distribution for a certain amount of light (as seen by earth) was given by /- 1 if f < f0 E(f) = > \- 1/f^2 if f > f0 Then we would have light "at all frequencies" which could be said to be "an infiinite amount of light" but the total amount of energy would still be finite. Most of these explanations don't seem to first figure out whether if you had a uniform distribution of stars (at discrete points) in an infinite (Euclidean) space, if the amount of radiated energy seen at an arbitrary point would diverge if you summed over all available frequencies. If it doesn't, it seems like lack of sensitivity is the main issue here, and the cosmological arguments are simply additional reasons for why it doesn't happen.
  - wfn 11y ago
    Pity someone down-voted you. From what I take it, you were basically simply asking, "what if the 'infinite amount' at 'all frequencies' were reaching you in a non-uniform distribution of frequencies? - would the original arguments and premises still stand?"
- Retric 11y ago

paulddraper 11y ago

This is a great explanation, up until the last part, which is slightly misguided. "So even if the universe were infinitely old as well as infinitely large, it would not contain enough fuel to keep the stars shining forever and to fill up all of space with starlight." If the universe were infinitely old, fuel was consumed, and fuel had finite density, then the sky would be completely dark. Because there would be no starts. The author is really just thinking "It would require infinite time to receive light from infinitely far away." Which is the relevant answer to the paradox.

mrdufrain 11y ago

Isn't it also the case that, because of the accelerated expansion of the universe, some stars are moving away from us at more than the speed of light, and their light will therefore never reach us?

paulddraper 11y ago
Yes, this is currently true, and will continue to be, unless we end in the Big Crunch.

EGreg 11y ago

Actually this was the argument that bothered Newton, but about gravity. In an infitely old but finitely large universe, why wouldn't gravity pull everything together? Unless in all directions gravity canceled out. Similarly, we can ask why the universe isn't filled with light. If the universe was infinitely old then indeed the light would eventually heat up all the matter and penetrate everywhere. But if it's expanding, then the light didn't have time to fill the space-time before it expanded further.

paulddraper 11y ago
In an infinitely large universe, the net force of cosmic gravity would be 0. Kind of like how an real number divides the number line into "same size" infinite intervals. Granted, entropy in the system would cause matter to clump into larger and larger bunches. But if the matter were perfectly arranged by an outside force (e.g. God) and didn't deteriorate, the universe could remain static.
- Strilanc 11y ago
  Gravity actually acts kind of... weird... in an infinitely large uniform universe. You end up with gravity acting like a time-dependent position-independent scaling factor on position. Leonard Susskind goes over the derivation (for Newtonian gravity) in a Cosmology lecture available on youtube [1]. 1: https://youtu.be/ERjkSbdn6-4?t=53m50s https://youtu.be/ERjkSbdn6-4?t=53m50s

mixmastamyk 11y ago

Hmm, didn't seem to mention the Inverse-square law, which I was waiting patiently for.

cristianpascu 11y ago

Or the Universe is neither infinite or as old as it's assumed to be. Although there's strong evidence for it being as old as we (me included as a figure of speech) currently believe it, our belief is based on some fundamental assumptions that can only be strengthen but not proven. At least for the sake of honesty, one must be aware of the nature of this kind of opinions. Science is part of the larger discipline called epistemology, so all the rules valid there, are valid in science too.

DINKDINK 11y ago

>The entire sky would be about as bright, and as hot, as the surface of the Sun. Not so according to “The Inverse Square Law”.[1] If one measures the light flux through a hypothetical sphere drawn around a light source and then doubles that spheres size, the light density must decline or you've broken conservation of energy. [2] [1] http://bccp.berkeley.edu/o/Academy/workshop08/08%20PDFs/Inv_Square_Law.pdf http://bccp.berkeley.edu/o/Academy/workshop08/08%20PDFs/Inv_... [2] http://www.compuphase.com/electronics/candela_lumen.htm http://www.compuphase.com/electronics/candela_lumen.htm

jackcarter 11y ago
Yes, but as you look deeper into the night sky, you see more and more stars (proportional to the square of the distance). These two factors cancel exactly.
nostromo 11y ago
If you reduce the power of infinite stars, you still have infinite stars producing infinite light. x * infinity = infinity (so long as x > 0; even if x is infinitesimally small)
- jwally 11y ago
  But you can't have infinite stars in your field of view since they'd get in each other's way; blocking radiation. Using the tree example from the article, you wouldn't see infinite trees, you'd only see the pieces that are directly in front of you.
- tamana 11y ago
  No, infinity times infinitesimal is undefined, you have to define your infinities more carefully to get an answer.
typon 11y ago
Remember parallel plate capacitors from Electromagnetics class? They're infinite in size for a reason, to get around not having to worry about the inverse square law. An infinite amount of stars would produce an infinite amount of energy...

pc86 11y ago

Title fix: "Olbers'" not "Olber's," named after Heinrich Olbers. It is wrong in the linked article's title as well.

dang 11y ago
Thanks, fixed.

goodside 11y ago

"Astronomers have concluded that the universe began some 12 to 15 billion years ago. That means we can only see the part of it that lies within 12 to 15 billion light-years from us." This is false, because it ignores the metric expansion of spacetime. We can see radiation from objects that are now ~46.5 billion light-years from Earth. This isn't picking nits. The explanation given here makes it sound like the Universe is a Euclidean volume that got instantaneously filled with stars, at roughly their present density, and that this density is low enough that light from distant stars hasn't reached us yet. If this were true, it wouldn't only explain why the sky is dark now, but predict that it has always been dark. We know this is false: for the first 380,000 years after the Big Bang, the Universe was filled with hydrogen plasma and completely opaque to radiation, which we can still see in the form of CMBR. As spacetime expands, energy density decreases, space becomes less light-emitting and more transparent, and light already in transit becomes red-shifted. Our field of vision is still technically flooded with light, as it always has been, but by now the red-shift is so extreme that the light is in the radio spectrum.

kyberias 11y ago
> As spacetime expands, energy density decreases, space becomes less light-emitting and more transparent, and light already in transit becomes red-shifted. Our field of vision is still technically flooded with light, as it always has been, but by now the red-shift is so extreme that the light is in the radio spectrum. You talk about the radiation generated before 1M years in the universe. This article talked about the light from the existing stars in the universe.
- goodside 11y ago
  The red shift applies to distant stars too. The important point is that even in the extreme scenario where all stars last forever and you wait an infinite amount of time for light to reach you, you will still never see a fully illuminated sky because the stars are receding much faster than the light propagates due to metric expansion. Saying the sky is dark because 1) the Universe is young or 2) stars are short-lived is just false. The Universe gets darker and darker as it expands, despite there being "more time for light to reach us".

grondilu 11y ago

I've always been puzzled by this paradox. More particularly, I'm baffled that apparently the mainstream explanation involves cosmological arguments such that the expansion of the Universe. Is it really that complicated? Take Hubble's deep field image, for instance. It was shot in a tiny area of the sky that looks completely black. But with enough exposure, Hubble found that it's actually full of galaxies. Can't I just conclude that if this part of the sky if completely black, it's not because space is expending, but just because our eyes are not sensitive enough? Olber's Paradox points out that wherever we look at, at some distance our line of sight will meet the surface of a star. But that does not mean that this point will register as a light for our eyes. Our eyes would have to be sensitive enough.

nostromo 11y ago
Imagine Hubble's deep field image again, but this time imagine you can see towards infinity (beyond the observable universe). If the universe is infinitely big (and old), then there would be so many stars in the image that there would be an infinite amount of light in the image. In this hypothetical universe, the Sun would actually be a dark spot in the sky -- because it would be blocking the infinite amount of light coming from an infinite amount of stars behind it. That's the paradox -- that we do not see that. No matter how sensitive our eyes are, we would be able to see infinite light. (Actually, our eyes would be melted... and all current forms of life impossible... but you get the picture.)
- grondilu 11y ago
  But stars are getting fainter and fainter as they are further and further away. I get that there would be an infinite amount of them, but then it's an infinite times a zero. The limit is not obvious and I've never seen anyone discussing the actual maths of this. I don't know those maths, but it seems reasonable to me that since the sky is indeed black, then it has to be that it's because the dimness of stars prevails over their number and/or density.
  - nostromo 11y ago

gusmd 11y ago

I'm missing something here and would so happy if someone explained to me. I am sorry if I'm making false assumptions as my knowledge on the subject is very limited. If the universe started from a single point in space and time (i.e., Big Bang), and no matter moves faster than the speed of light, how could ANY star be more distant from us than light could have traveled in the same time frame? (I'm assuming no matter is travelling at v > c/2, otherwise my argument would only be valid for things traveling in the same hemisphere of the expansion as Earth)

Practicality 11y ago
The matter isn't moving. Space is expanding, ie, space is being inserted in-between all bits of matter. Edit: To elaborate further: Since all the newly expanded space also expands, the distance to travel continuously increases as the light travels, to the point where over a certain distance the light never completes the journey. So, the net effect is that the two objects become further apart faster than c, even though neither of them are moving.
hoorayimhelping 11y ago
Space itself might be able to expand faster than the speed of light.
Lawtonfogle 11y ago
Expansion of space allows for the distance of two objects to increase such that it appears that one is moving away from the other at a speed greater than c/2. I think it is possible for this to even be greater than c because it is the expansion of space and not objects movement contributing to the increase in distance.
joe5150 11y ago
This is an important concept to understand: https://en.wikipedia.org/wiki/Comoving_distance https://en.wikipedia.org/wiki/Comoving_distance

vorotato 11y ago

what about all the light that doesn't hit us.

amelius 11y ago

An easy explanation is here: https://www.youtube.com/watch?v=gxJ4M7tyLRE https://www.youtube.com/watch?v=gxJ4M7tyLRE

eutropia 11y ago

I find it odd that so many people seem to have trouble accepting this explanation. Light travels at a finite speed, ergo anything far enough away(adjusted for expansion of space) is invisible, because we've only existed for a dozen billion years. If the universe were infinitely old, then we'd have something interesting to talk about.

jcoffland 11y ago

One answer to this problem is that the night sky isn't dark at all. It's just less bright than during the day. Hear me out. As a species that evolved on this planet under it's particular conditions we perceive day to be bright and night to be dark because of the particular range of light sensitivity of our eyes. Too often science leaves the human observer out of the equation. It lets us feel like gods presiding over our universe but is a big mistake. All that said it's not unreasonable to question why the night sky is not brighter than it is.

alanwatts 11y ago
>Too often science leaves the human observer out of the equation. It seems this problem may have come full circle with the Measurement Problem. But yes, human beings themselves emit light, however that light resonates on a frequency that our eyes have not evolved to see, so we invented infrared optics.

dantillberg 11y ago

A mathematical explanation would involve a comparison of the density of stars throughout the universe with the inverse-square drop-off in light intensity from each. If you assume for the sake of argument that all stars are as bright as the sun, and that stars have a uniform density throughout the universe (either a finite-but-huge or infinite universe, it makes little difference here), then you could solve for the mean intensity of light throughout, or in our case, "how bright the sky is at night." The article makes a classic (and really hard to escape! I've seen this sort of thing called a "paradox" on many occasions.) mistake of examining two infinite quantities (infinite stars, up to an infinite distance away) and assuming that they must cancel each other out, that infinity/infinity=1. But not all infinities are the same, and infinity/infinity can work out to 0, or to 0.1, or to pi, or to infinity (as in the case of "# real numbers"/"# integers"), or to anything else; you have to look at the details -- what kind of infinity is it? -- and figure out how they compare.

jakobegger 11y ago
The article makes no mistake, it just doesn't go into enough detail. To determine the amount of energy reaching us, we need to integrate over the energy density divided by the square of the distance over the whole 3d space. As any physicist can tell you, an integral over the whole space will diverge unless the kernel falls off faster than 1/r^2. This means that one of the following must be true a) either the universe is finite, ie. the density falls off b) we don't integrate over the whole space (we can't see far enough due to age of universe) Which is exactly the argument this article is making Edit: in other words, infinite or finite-but-huge is an important difference when integrating over constant density; the former integral will diverge, the latter will not

lutusp 11y ago

As is often the case, this explanation fails to take cosmological expansion into account. An expanding universe is a cooling one. The explanation is correct as far as it goes, but failing to take expansion into account either dates the explanation or fails to evaluate a factor that's a bit more complex than relying on the finite age of the universe.

rdiddly 11y ago

Subsequent edit: Assuming the universe is infinite, is where the problem begins. There is no reason to assume that. Original comment: Is this really not obvious to people? It's about subtended angles - simple geometry. As the Earth's distance from a star increases, it subtends a decreasing angle in that star's "sky." Assuming radiation does indeed proceed radially and in straight lines, at increasing distance the Earth is capable of catching a decreasing portion of that star's radiation. As the distance approaches infinity, the subtended angle approaches zero and the amount of light reaching us approaches zero. The star is just as bright, but most of its radiation goes somewhere else besides Earth. Imagine building a giant spherical shell around a star. Its radius equals the distance between earth and the star. It catches 100% of that star's radiated energy. Now paint the Earth on the inside of the shell, actual size. It looks, to someone standing on the surface of that star, like the real earth, i.e. a tiny dot. Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2). That's how much of that star's energy our planet catches. Assuming zero degradation across space. So imagine you're in a forest of trees the closest of which are 800 miles away from you. You'd see the goddamned sky just fine.

samstave 11y ago
Is was an amazing conceptual comment - thank you
gpsx 11y ago
You are correct in your geometry, but you forgot one thing. The earth receives a smaller portion of light for stars that further away, but the number of stars at that radius goes up by the exact same amount. So from any shell the amount of light we get is the same. If the shells go out to infinity, the light becomes infinite (well, according to the naive argument).
- meric 11y ago
  The nearest star is the Sun. With a giant Sun nearest to Earth, it's impossible for the number of stars to go up proportionally as distance to Earth increases. There isn't 4 suns at 2 AU, and at 100000 light years wide, with 63000 AUs per light year, the milky way does't contain (63000 * 100000)^2 stars. There needs to be 4 billion times more stars in the milk way for there to be proportionally as many stars as in our solar system. You can fill the entire sky with AA battery torches and they won't be as bright as the one stuck right up to your eye. The night sky is dark, but it doesn't mean it isn't full of rays of lights heading our way. It's darker than the day sky due to the Sun being so close, yes, but the night sky is full of light, everywhere we look. It's only because the way our minds perceive relatives, we call the night sky "dark".

jwally 11y ago

Stab in the dark: Inverse Square Law + The number of stars in your field of vision can't be infinite.

kjell 11y ago

https://twitter.com/5point9billion https://twitter.com/5point9billion calls out the inverse: light traveling from earth out towards the nearest stars. It's a twitter bot that takes a twitter user's birthday, and tweets to them as their "light cone" expands across the universe.

deleted 11y ago

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dschiptsov 11y ago

This is mere ray-tracing problem. What we call bright sky is reflections of Sun rays from particles in atmosphere. What we see is reflected light. When Sun is shadowed by Earth we see only light reflected by distant object, such as Moon. The darkness of the night sky is relative - some rays are here, but our visual system is conditioned for days (reflected light), not nights. The idea that everything should be filled with starts is just wrong. Rays from distant stars were deflected, blocked by particles, etc.

jonmccreery 11y ago

This looks like a question that actually looks like two questions; namely, 'is the universe infinite' (and as a side question, what is the actual dimensional and geometric configuration of the universe), and if the first question is true, 'why do we not observe an infinite flux of photons, or really any other type or radiation, bathing our chunk of the universe'. This one's easy. The first, foundational, assumtion is way easy to knock down, via all the accumulated evidence that we erupted from a singularity 13-some billion years ago. So.. no infinite time. But we could probably get by with, even with an infinite universe, if we just assume a universal speed, which is most definitely supported by current academic consensus. This is because of the concept of the light cone, which says that you can't be illuminated by things that lie outside your temporal and spacial vicinity, as defined by how long it takes light in a vacuum to reach you. That's a stronger statement than just how bright the sky is... it applies to any conceivable mechanism of information transfer, and it's universally supported by any experiments that we've tried (note: wormholes... possible, super crazy loop hole here... maybe an infinite universe has infinitely many wormholes to pump radiation into our light cone, so basicly multiverse, but we've already talked about the universe having an age). I see no paradox here, but then again the Big Bang and Special Relativity are pretty new as ideas and we all benefit from the shoulders of the giants we stand on. Edit: On further reflection, a truly infinite universe probably would park an infinite number of unstable wormholes on top of our neighborhood, but in that case the the fact that our sky is in fact dark just adds more evidence to the pile that we already have that it's not.

jonmccreery 11y ago

This looks like a question that actually looks like two questions; namely, 'is the universe finite' (and as a side question, what is the actual dimensional and geometric configuration of the universe), and if the first question is true, 'why do we not observe an infinite flux of photons, or really any other type or radiation, bathing our chunk of the universe'.

frogpelt 11y ago

If there are an infinite number of stars in an infinitely large universe that is infinitely old, how is the nuclear fuel finite? Help me here.

mnw21cam 11y ago

I am quite amazed that noone has pointed out that in terms of the cosmic microwave background, the sky is not black. The radiation that travels the furthest before hitting us is this background radiation. It only appears to be dim because it has been redshifted a huge amount due to the expansion of the universe since then. But yes - everywhere you look in the sky (unless there is something in the way), you are looking directly at the intense fire of the birth of our universe. Red-shifted until you can't even see it any more.

mrnobody4 11y ago

So should the earth heat up over time as more light reaches us or does the expansion of the universe negate that?