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

http://www.amnh.org/education/resources/rfl/web/essaybooks/cosmic/cs_paradox.html

by fauria • 10 years ago

264 143 10 years ago

3pt141592• 10 years 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).

paulddraper10• 10 years 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.

3pt141592• 10 years 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.

mjn• 10 years 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

jdimov10• 10 years 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• 10 years ago

Stars fuse light elements it into heavier elements. Eventually all the lighter elements will be used up.

TranquilMarmot• 10 years ago

One of my favorite short stories about this is The Last Question by Isaac Asimov

http://multivax.com/last_question.html

pc862• 10 years 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?

mjevans• 10 years 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

Describes what I recall reading/hearing many years ago.

maskedinvader• 10 years 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.

VeilEm2• 10 years 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

ranko• 10 years 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.

platz2• 10 years 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?

paulddraper10• 10 years 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.

paulddraper10• 10 years ago

Yep. Currently, some galaxies are traveling away from us faster than light.

http://curious.astro.cornell.edu/about-us/104-the-universe/c...

joering22• 10 years ago

That blew my mind! So now it turns out Einstein was wrong??

We can't get particle to seriously travel faster than light and there is entire galaxy going faster??

snowwrestler• 10 years 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.

paulddraper10• 10 years ago

Yep, explained here: 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• 10 years 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.

Retric• 10 years ago

This assumes a minimum energy from each photon. If you could red-shift indefinitely you could end up with ex: 1 + 1/2 + 1/4 + 1/8 +... which sums to 2.

I believe the minimum energy of a photon is directly bound by the age of the universe, so if the universe was twice as old you could have photons at 1/2 the energy. You do get more light sources as you increase distance, but the inverse square law balances that. So Sum (1/n) from 1 to N which really slowly grows to infinity. As in 10^100 = 230.84

brc• 10 years ago

I thought this was the obvious answer.

The sky is not dark at night when you use the right telescope. So either the sky changes when you point a telescope at it, or the 'sky' as we see it, is just an artefact of what our primitive eyes and mammalian brain sees.

paulddraper10• 10 years 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• 10 years 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?

paulddraper10• 10 years ago

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

EGreg• 10 years 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.

paulddraper10• 10 years 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• 10 years 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

mixmastamyk• 10 years ago

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

cristianpascu• 10 years 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• 10 years 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_...

[2] http://www.compuphase.com/electronics/candela_lumen.htm

jackcarter• 10 years 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.

nostromo3• 10 years 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)

jwally2• 10 years 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.

tamana3• 10 years ago

No, infinity times infinitesimal is undefined, you have to define your infinities more carefully to get an answer.

typon2• 10 years 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...

pc862• 10 years ago

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

dang• 10 years ago

Thanks, fixed.

goodside7• 10 years 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.

kyberias2• 10 years 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.

goodside7• 10 years 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".

notalaser2• 10 years ago

Yes, it's still incorrect! The complete quote is:

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. There may be an infinite number of stars beyond that cosmic horizon but we can’t see them because their light has not yet arrived. And the observable part of the universe contains too few stars to fill up the sky with light.

(Emphasis mine because that's where the error is: 13 billion year-old light has traveled over a distance that is now much higher than than 13 billion light-years)

Potential ambiguity (in cases such as this one) is one of the reasons why using light-years for distances may not be a good idea.

(By the way, there are real astronomers arguing about this, too, e.g. http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html . So it's not just this nerd ranting on HN).

GRB 090423 (admittedly, not a star -- it's a gamma ray burst) happened approximately 13 billion years ago. This means that light traveled for 13 billion years to reach us -- but, by the time it got to us, GRB 090423 was no longer 13 billion light-years from us, because all that space got bigger! GRB 090423 "was" about 9.2 Gpc away from us by the time that light reached us, i.e. about 30 billion light-years.

If the light that hits us is 13 billion years old, that object (assuming it still exists) is a lot farther than 13 billion light-years from us now.

joering22• 10 years ago

No, its correct.

I lost a youtube video that explains Universe. Basically a universe observer is like an ant sitting on a big balloon that is constantly being pump with air. So while the balloon age might be 12 billion years old, the speed the air is pumped in it makes it grow and therefore objects "placed" far further than originally; hence 46B for an observer.

jerf2• 10 years ago

At the risk of going more-pedantic-than-thou, this entire thread of nitpicks (and indeed, most of the posts I see right now to this story in general) is(/are) mostly irrelevant. The argument is not particularly sensitive to the exact way in which the universe is not steady state, including redshifting all the light until we're not staring at the sun in every direction. Olber's Paradox disproves the Steady State hypothesis, it doesn't positively prove anything in particular. Popular treatments of Olber's Paradox are not obligated to come attached to a complete course in cosmology. I'm sure at least one of "Steven Soter and Neil deGrasse Tyson" are fully aware of all the issues raised in this entire HN page.

goodside7• 10 years ago

There are plenty of ways the Universe could be steady-state and still not have a white-hot sky. Suppose you have metric expansion as you do now, but new matter magically appears as a sparse, uniform cloud of particles throughout space to feed the creation of new stars and maintain the energy density we see today. Metric expansion guarantees that light is redshifted in proportion to distance, so the sky remains dark, even though the Universe is infinitely old and stable.

This model is wrong, obviously, but the reason has nothing to do with Olber's paradox.

Cyph0n4• 10 years ago

So we don't know the age of the universe then?

lutusp6• 10 years ago

We do know the age of the universe, to a reasonable certainty. The discussion above doesn't argue against our current estimate of the age of the universe -- it addresses other issues.

MAGZine2• 10 years ago

It sort of is nitpicking.

We haven't observed objects with redshifts that indicate distances larger than 13.some Gly away.

Yes, the physical objects are farther, but the point is moot. Those objects aren't the same as what we see today. They're totally different. We don't know what they look like today. Even low-mass stars have lived and died.

In summary, there is no way for us to see those 46.5 Gly objects other than wait 50 Gy (with our given technology)

goodside7• 10 years ago

Yes, it's true that the most distant galaxies we've observed are only around 13 Gly away, but the fact that number is so close to (speed_of_light * age_of_universe) is just a coincidence. We could, in principle, see light emitted from points in space that are currently 46.5 Gly away, but all such light was emitted long before any galaxies had formed. The OP wasn't mentioning that we can see to a maximum distance of ~13 Gly as an unrelated fact with its own cause, it was saying it was because the Universe is ~13 Gy old and that's how far light can travel in that time, which isn't true.

xenophonf4• 10 years ago

I assume you're talking about UDFy-38135539 (https://en.wikipedia.org/wiki/UDFy-38135539), with a redshift of z=8.6. It is not 13 Gly away, even though the light detected by Hubble's infrared camera was emitted about 13 billion years ago. Due to the metric expansion of space, the distance to that object is around 32 Gly (9710 Mpc according to http://www.bo.astro.it/~cappi/CosmoWidget.html).

ank_the_elder• 10 years ago

But how can something that is further away than the maximum travel distance allowed by the time elapsed since the big bang exist? Is there a non-locality of the time dimension that makes it so? Was the expansion rate of the universe faster than the speed of light? Or... what?

goodside7• 10 years ago

https://en.wikipedia.org/wiki/Metric_expansion_of_space

The short version: The distant object wasn't traveling through space, it sat stationary while more space came into existence in the gap between us and it, resulting in it being farther away. This happens everywhere, all the time -- it's what cosmologists are talking about when they say the Universe is "expanding". The laws that prohibit faster-than-light travel concern movement within space ("peculiar motion"), not the expansion of space itself.

xenophonf4• 10 years ago

This might help you understand:

"Misconceptions about the Big Bang" http://www.physics.uq.edu.au/download/tamarad/papers/SciAm_B...

grondilu3• 10 years 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.

nostromo3• 10 years 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.)

grondilu3• 10 years 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.

gusmd• 10 years 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• 10 years 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• 10 years ago

Space itself might be able to expand faster than the speed of light.

Lawtonfogle• 10 years 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• 10 years ago

This is an important concept to understand: https://en.wikipedia.org/wiki/Comoving_distance

vorotato• 10 years ago

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

amelius• 10 years ago

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

eutropia• 10 years 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• 10 years 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• 10 years 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• 10 years 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• 10 years 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

lutusp6• 10 years 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.

rdiddly6• 10 years 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• 10 years ago

Is was an amazing conceptual comment - thank you

gpsx• 10 years 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• 10 years 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".

rdiddly6• 10 years ago

BTW that's (4)(pi)(a gazillion light-years ^ 2) in case the point wasn't obvious!

lutusp6• 10 years ago

Your explanation is correct for individual stars, but it doesn't take universal expansion into account, which independently reduces the energy available from distant sources (apart from the 1/r^2 law). The reason? Same energy, more space, so a reduction in energy per unit of volume.

Also, setting aside the issue of expansion and redshift, if you imagine a sphere with a uniformly illuminated interior (imagine a surface composed of so many stars that counting them individually makes no sense) and an observation point at the center, if you increase the radius of the sphere, there's no change in the energy received at the center.

This idea works for an infinite plane as well, and is a bit easier to grasp. Imagine an infinite plane with a fixed optical brightness, and an observation point at some distance d. Now double the distance -- no change in received energy because the plane is infinite in extent.

pdonis6• 10 years ago

As the Earth's distance from a star increases, it subtends a decreasing angle in that star's "sky."

But the number of stars at a given distance increases as the distance increases, and this increase exactly cancels out the decrease in the amount of light from a given star that reaches the Earth. So your argument does not explain why the night sky is dark.

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.

Now do it the other way: draw a sphere around the Earth with some radius r. Calculate how many stars are on that sphere. The number increases as r^2; and, as you have shown, the amount of light reaching Earth from a given star decreases as r^2. So, as I said above, the increase in the number of stars exactly cancels out the decrease in the amount of light from each star that reaches the Earth; thus, the total starlight reaching Earth from a given radius r is a constant, independent of r.

rdiddly6• 10 years ago

There's no reason to believe the universe is infinite nor that stars are evenly distributed throughout its volume. So "the number of stars increases as r^2" is the part that doesn't hold and is causing the paradox.

cousin_it• 10 years ago

Nope.

A ball of radius R around Earth contains R^3 stars. The angular size of Earth as seen from each star is 1/R^2 or more. So the total light coming to Earth is proportional to R. As R goes to infinity, you get Olbers paradox.

If you insist on talking about trees, in an infinite forest of trees that are 800 miles apart and 1mm thick, you wouldn't see the sky.

rdiddly6• 10 years ago

Yup. The universe was declared infinite not because it is, but because it repeatedly defied our hubris. "If we can't find the end of it, it must be endless!" Kind of like "If she doesn't like me she must be a lesbian!"

gaur3• 10 years ago

Is this really not obvious to people? It's about subtended angles - simple geometry.

If the universe is infinite and filled uniformly with stars, the 1/r^2 falloff in the radiation captured from each star is cancelled by r^2 dependence on the number of stars at radius r. So as you integrate r from 0 to ∞, you accumulate an infinite amount of radiation.

Is this really not obvious to you? It's all about infinitesimals - simple calculus.

rdiddly6• 10 years ago

As with others here, your problems start with "if the universe is infinite."

jwally2• 10 years ago

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

kjell• 10 years ago

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.

dschiptsov• 10 years 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.

jonmccreery2• 10 years 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.

jonmccreery2• 10 years 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• 10 years 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• 10 years 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• 10 years ago

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

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

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