Am I the only one for whom the paradox isn't intuitive? It's not clear to me why many distant dim stars should add up to a bright sky. It depends on how distant and how dense they are, doesn't it? Even assuming that the universe is infinite and eternal and approximately equally dense everywhere.
The embedded video describes the paradox by saying that the night sky "should be as bright as the sun". Imagine if that were the case. Then move yourself twice as close to the sun, making the sun four times brighter. Then the night sky is 1/4 as bright as the sun.
So clearly, distance and (lack of) density could make the night sky less bright, presumably to below the threshold of human perception. Right? Even aside from their explanations of distant light not having had time to reach us, and/or being red-shifted out of our visible range.
How does distance affect brightness? Distant stars are exactly as bright as close stars - however, the "brightness" is just spread over a greater area of space.
In particular, the perceived brightness of a star falls off according to the square of distance - you can work this out for yourself by comparing the surface area of a sphere of radius d, with the surface area of a sphere of radius 2d.
But how many stars are at that distance? If you assume uniform density, then the answer is exactly the opposite of what we found above! The number of stars at a distance of d is proportional to the square of the distance.
This means that the total amount of light perceived from stars at a distance d is exactly the same, irrespective of the value of d.
Then if the universe was also both eternal and infinite, then there would be an infinite amount of light reaching the earth!
Okay, if the universe were perfectly homogenous, i.e., uniformly dense at all scales, then this argument would be easy to buy.
If you allow density variation at some scales, like the difference in density between the interior of a star and interstellar space, then it changes a bit, right? If you're really close to a star, then obviously that star is brighter than the average brightness of the universe. Right?
If so, then the night sky wouldn't be "as bright as the sun" (like the video says), as observed from earth.
But would the night sky be uniformly bright? Doesn't it depend on the average density of the universe? I.e., if the average density gets low enough, then don't those small-scale density variations start to matter at some point?
It's generally hard to speculate on how things "would" be if the universe were markedly different than it how it actually is. Or rather, it's easy to speculate, but it's nigh-impossible to come up with one solution to the exclusion of others. I can come up with many hypothetical universes where the night sky would be uniformly bright, and many hypothetical universes where there would be substantial amounts of variation.
The general statement of the paradox is that the total amount of light coming from distant stars massively outweighs the light coming from a local star, so while the local star might create a slightly brighter patch of sky, that difference is small enough that even in its absence the sky would look "bright".
you're right that it's not going to work out exactly equal to the brightness of the sun. another way to see this is to imagine an alien who lives on a (undiscovered) planet incredibly close to the sun - the sun would appear much brighter to the alien who would, presumably, expect a correspondingly brighter sky everywhere else (which clearly makes no sense since looking in other directions the alien should agree with us).
but the effect of variations is most important when you have fewest stars (so the largest variation should be the sun, which seems reasonable). at large distances, with many stars, things will even out despite the fluctuations (for physically reasonable fluctuations).
to make the argument rigorous, you need to work out how bright things would be "on average".
another (more convincing?) way to understand the problem is to see that if we have an infinite, static universe, full of stars, all burning away, it should get hotter and hotter over time... (and if it's infinitely old, should be infinitely hot by now!). clearly something is wrong with that model.
Red shift. The universe is filled with photons. But as the universe expands, everything moving away from everything else, the human visible light moves into the infrared spectrum.
Unless I am mistaken, they both do. There are multiple kinds of red shift.
> "Redshifts are attributable to the Doppler effect, familiar in the changes in the apparent pitches of sirens and frequency of the sound waves emitted by speeding vehicles; an observed redshift due to the Doppler effect occurs whenever a light source moves away from an observer. Cosmological redshift is seen due to the expansion of the universe, and sufficiently distant light sources (generally more than a few million light years away) show redshift corresponding to the rate of increase of their distance from Earth. Finally, gravitational redshifts are a relativistic effect observed in electromagnetic radiation moving out of gravitational fields. Conversely, a decrease in wavelength is called blueshift and is generally seen when a light-emitting object moves toward an observer or when electromagnetic radiation moves into a gravitational field."
The increasing distance between stars due to expansion is not velocity as we traditionally think of it. Things that far away get red-shifted because at distances that large expansion becomes a factor, not because of how they are otherwise moving about. It's basically the general idea behind Hubble's Law.
Cosmological redshift isn't Doppler -- the mechanism is different. For cosmological redshift, light's wavelength changes because the space through which the light is moving is expanding, which stretches the waves. Doppler is often brought up in this context, but it has no role to play.
The reason is that the flux from any particular star goes as 1 / distance^2, but the number of stars observed in a patch of sky increases like the distance^2. The two cancel each other out.
An easier way of thinking of it is to think about looking along a single direction. No matter which direction you look, this ray will always be pointed towards the surface of a star.
The sun's brightness per area is constant with distance. If you move twice as close to the sun, the brightness per area is exactly the same as it is on Earth, it just covers four times as much of the sky.
If every sight line ended on a star, you'd expect the entire sky's brightness per area to be that of a star.
It reminded me of the 'paradox' that 1 + 0.5 + 0.25 + 0.125... is finite and not even very large. You could have an infinite universe with infinitely many stars and still end up with a certain percentage of the sky being dark.
Or maybe I'm mathematically wrong, but the above summation has broken any intuition for me that "the sum of infinitely many things must certainly surpass everything" :(
Oh, that's a nice explanation. I like to think that I am not adding something, just always going half the way to 2.0. Still, when this was introduced to me in school, I remember my head hurting a little. :)
I should correct myself that historically, the paradox didn't hinge on the universe being infinitely old, but on the speed of light being infinitely fast.
Yeah, you are right. It could be in frequencies we cannot observe with the naked eye, but eventually, we would have to tweak some other postulates, too. Let's start over and postulate a gigantic turtle that carries the world…
> Alternatively, most of the stars really far away could be covered in a Dyson sphere.
The principle of energy conservation dictates that all the energy inside the sphere gets out, in one form or another. So the existence of Dyson spheres, dust clouds, dark matter etc. only delays the appearance of the energy in the universe at large.
It's not usually noted, but Olber's paradox relies on a false assumption. The argument goes that the night sky is dark and therefore the universe must be finite in extent or duration or both. But the night sky isn't really dark. Olber was just looking at the wrong wavelength. If you look in microwave wavelengths, of course, you see the CMB. The fact that the CMB is out in microwave wavelengths rather than being somewhere where Olber could see it is strong evidence for an expanding universe.
Being right for the wrong reason can be even worse than being wrong. CMB is very relevant to the question of the color of the sky, it just happens to be pre-star material.
This is one of these 'unreadable on my tablet' articles, where sharing buttons cover the content (bad) and something disables pinch/zoom (inexcusable) for reasons I don't get.
FF's reading mode saved me, but is there any permanent workaround for problems like this? Addons?
I think it is completely absurd that tablet OS's would ever allow a website to disable zooming. It's like a usability nightmare. Permanent solutions... maybe email the websites that do it?
(Shrug) I just go to other websites and read something else. On the Internet, there really is something interesting to see in every possible direction you look.
The fundamental question here is, if you pick a random vector going outward from the earth, what us the probability of that vector intersecting a star? If it is near 100%, then you would expect a bright sky at night, and if you don't see one then you have a paradox.
Even if it is 100%, it would have to be multiplied by the probability of photons from that star making it past all the interferences like nebulae, Oort cloud, and Earth's atmosphere along that exact vector. That I think is a much lower percentage.
> Even if it is 100%, it would have to be multiplied by the probability of photons from that star making it past all the interferences like nebulae, Oort cloud, and Earth's atmosphere along that exact vector.
You're missing the point that, given enough time, all those objects would be heated up by stellar radiation to the temperature of the originating star.
Consider the temperature over time of a body that is energetically coupled to a star, however far away. Because the star's temperature is relatively constant (a property of fusion reactions), it is the receiving body's temperature that changes, according to this equation:
All the bodies exposed to a star's energy radiation follow the above law. And given enough time and barring any other effects, all of them reach the star's surface temperature. Which leads us to Olbers' Paradox -- given billions of years and copious energy sources, why didn't this happen?
The theory also assumes that objects in the Universe can only emit light. This isn't true: most matter in the Universe is dark (dust, planets, dark matter), and absorbs light.
We know that this is highly true at intragalactic scales -- the core of the Milky Way is completely obscured from Earth due to the dust between us and it. There's good reason to believe it's also true at intergalactic scales.
Other aspects of the paradox contribute, but I strongly suspect that various dark matter effects are stronger.
I think you're wrong here. Given an infinite amount of time and an infinite number of stars distributed evenly in an infinite universe, even the dust and planets will start to radiate[1].
The paradox hinges on the assumption that the universe is infinite in size with an even distribution of stars which have been radiating for eternity. So, it's only a paradox if you assume those things. Remember, this question was first asked in the 1600s.
Yes, true, but Olbers' Paradox was posed long before the Big Bang theory or the idea that the universe is expanding.
In a static universe such as Einstein proposed in 1916, eventually the entire universe would heat up to the temperature of its stars. This made Olbers' paradox an important reality-test, and reality failed the test.
It was only because of the Big Bang and universal expansion was Olbers' Paradox reconciled with observation.
Err, Einstein's static universe did not preclude the death of stars via exhaustion of their fuel. So, the entire universe would "heat up" to a uniform distribution (i.e. evolve according to the heat equation), with the future local heat being everywhere equal to the mean local heat at present. And, in general, the universe is overwhelmingly empty and cold.
I'm not sure what the mean energy of the universe is, or what the minimal energy required to coax an electron to jump around and create visible light is, but it could well be that the values are such that an entire universe homogeneously set to the mean local energy of our current universe would be nowhere energetic enough to cause the birth of (naked-human-eye-visible) photons. (note: it would also be important to know the relative amounts of energy dedicated to mass and motion)
In other words, given a perhaps dubious mixing of temporally diverse understandings of physics, the relevant homogeneously energetic universe would likely be nowhere energetic enough to cause light. Thus, perhaps we should be more surprised that everywhere we look isn't dark?
> Err, Einstein's static universe did not preclude the death of stars via exhaustion of their fuel.
Yes, by a process of radiating away massive amounts of energy.
> So, the entire universe would "heat up" to a uniform distribution (i.e. evolve according to the heat equation), with the future local heat being everywhere equal to the mean local heat at present.
No, not "at present" "At present" is the outcome of a combination of energy radiation and cosmological expansion leading to the present. Were it not for the factor of expansion, the universe would be much, much hotter than it is now.
> And, in general, the universe is overwhelmingly empty and cold.
Yes, it is -- because of cosmological expansion. Were this not the case, the universe's temperature would be equal to or or greater than it was at "recombination" time, i.e. when normal atoms formed and the universe first became transparent to radiation, at about 300,000 years and an average temperature of about 4000 kelvins.
> I'm not sure what the mean energy of the universe is ...
Don't you mean average temperature? One can speak of total energy, or average temperature, but "mean energy" doesn't make much sense.
> ... or what the minimal energy required to coax an electron to jump around and create visible light is ...
That's well-established. When the energy of an impinging photon is equal to that for a possible electron orbital transition, and ignoring for the moment a few other considerations, the electron will absorb the photon and move to a higher orbit. Conversely, if an electron should drop from its present orbit to a lower orbit, a photon will be emitted whose wavelength is proportional to the energy difference between the orbits.
> In other words, given a perhaps dubious mixing of temporally diverse understandings of physics ...
At any given time, there is one understanding of physics. It's obviously open to challenge as all scientific theories are, but each challenge must be accompanied by observational evidence. The point of science is not to have any number of theories, the point is to have one -- the one that best answers observation.
> the relevant homogeneously energetic universe would likely be nowhere energetic enough to cause light.
For a sufficiently comprehensive definition of "light" (meaning electromagnetic radiation), no, not possible. There will always be electromagnetic radiation, even for a universe at zero Kelvins, because of quantum effects.
> Thus, perhaps we should be more surprised that everywhere we look isn't dark?
Not in this universe, no -- not with stars converting mass into prodigious amounts of energy everywhere we look. Which leads, full circle, to Olbers' Paradox.
When I said "at present", I was operating in the context of your previous post, i.e. assuming a universe with static space-time geometry. In this context, the present empty coldness of the universe is relevant and the past crowded hotness is not. Certainly, when a full modern understanding of cosmology is brought into play, Olbers' paradox is quickly downgraded from paradoxical to merely non-intuitive.
As noted previously, I was mixing temporally diverse conceptions of physics. Obviously, at any point in time there is a physics representing the current scientific consensus. I meant that my construction of an argument using ideas sampled from non-contemporary points in the stream of evolving understandings of physics was potentially dubious. Or, metaphorically, I was mixing metaphors.
After I first put the focus on naked-human-eye-visible light, it was meant to be assumed that any use of the term "light", as opposed to, say, "electromagnetic radiation", was also intended to invoke the concept "naked-human-eye-visible light", and likewise for dark as the absence of "light".
I'm aware of the basic process underlying the emission/absorption of photons via orbital jumping. My precise point was that the incident energy required to invoke a jump of sufficient size to produce "light" may be greater than that which would be omnipresent in a homogeneously energetic universe with a space-time geometry equivalent to that of the universe in which we currently reside. Certainly, as you mentioned, the relative amounts of energy stored in mass versus motion would play an important role.
Anyhow, my entire line of argument was all just an exercise in Devil's advocacy, seeing as how satisfactory resolution of Olbers' paradox is readily available within our current best understanding of physical law.
> When I said "at present", I was operating in the context of your previous post, i.e. assuming a universe with static space-time geometry.
Yes, but for a static universe, we wouldn't have anything remotely like present temperatures, which is why Olbers' Paradox ultimately leads to universal expansion apart from any other issues.
> it was meant to be assumed that any use of the term "light", as opposed to, say, "electromagnetic radiation"
But they can't be opposed -- all light is electromagnetic radiation, and vice versa for a sufficiently large time frame. What was gamma rays at the time of the big Bang is now visible light. What was visible light at the time of the Big Bang is now microwaves. There's no reasonable way to talk about these issues without describing the electromagnetic field.
> seeing as how satisfactory resolution of Olbers' paradox is readily available within our current best understanding of physical law.
Yes, but not for a static universe, which was my point -- for a static universe, the assumption until 1929, Olbers' Paradox remained unresolved -- and without cosmological expansion, the issues are not "available within our current best understanding of physical law". Not remotely.
Paradoxes and assumptions aside, is it literally true that there is a star at the end of every vector you can draw from my eyeball into space? I understand it's true if you assume the universe is infinitely large, but we know that's not true, right?
My understanding is that it would be true but for the fact that the longer those vectors get, the farther back in time they reach, and thus eventually reach into a time when stars did not exist and thus you hit the CMB instead. The stars you would have seen are in space that has moved away from us faster than c.
My understanding is that the universe is believed to be literally infinite in the three spatial dimensions that are familiar to us, and that its mass is also believed to be infinite. It really blows the mind.
Disclaimer: I'm a programmer not a physicist. :-)
EDIT: I did a little more reading on this. Answers are all over the place. But from what I can make out of the most recent sources, it seems that modern models treat the universe "as if" it were infinite although there is no way to know whether it is or not.
There are very few patches of the sky where if you look you won't see (very many) stellar objects or galaxies. Astronomers know about them--they're great for calibration of instruments.
That said, Hubble took a many-day exposure of one of these ultra-deep regions, and this is what it saw:
Genuine question: at what age is Olber's Paradox explored in high school physics these days? (It was part of my A-level physics curriculum in the UK, age 17, circa 1981 ... I'm finding it rather odd that it was unfamiliar to this journalist!)
The physics courses I took (in both high-school and college) didn't generally deal with astronomy. Not sure how common that is. Instead they covered mostly "foundational" topics: general & special relativity, electricity & magnetism, mechanics, atomic structure, etc.
I think your experience is pretty typical. I had the same. I took what was technically considered a college-level physics course in high school, and we never really delved into astronomy. Only in college itself did the subject start to come up, and that's because I selected those classes.
I suspect this is because the US high school education system has a fairly standardized, one-size-fits-all curriculum. There are some allowances and exceptions, of course. But, for the most part, everyone is going to be covering roughly the same material. And astronomy isn't deemed as necessary, for the beginner, as some other rudiments of physics. College, on the other hand, offers more opportunity for individual choice in one's curriculum.
I had the same situation in college as well, though that could be because I went to a somewhat unusually set up science/math uni (hmc.edu), in which all majors had to take a science/math "common core". There were 3 required physics classes for non-physics majors, which were these, going pretty in-depth into physics but still not covering any astronomy: http://physics.hmc.edu/course/3/, http://physics.hmc.edu/course/46/, http://physics.hmc.edu/course/4/
Astrophysics is generally popular among students, but afaict it hasn't been included basically because the physicists consider the above three courses to be higher priority.
It wasn't taught in any of the physics classes I took in the US circa 1990. As a matter of fact, I hadn't heard about it (by name) until watching a Jim Al Khalili documentary from the BBC. I suspect that proper treatment of the subject would have offended those in the US that still believe in the firmament of heaven.
(I'm only partly joking. My high school biology class had a chapter on evolution. The teacher said "I have to teach this but I won't be testing you on it. Read the chapter and let yourselves out when the bell rings." He then left the room.)
I think that that "UK" makes quite a difference. In my experience, British education focuses more on historical and philosophical (aka 'impractical' :-)) knowledge than that of most other countries.
That experience is heavily colored by watching University Challenge and Mastermind, but I do not think that makes a difference when comparing the top levels (which, I guess, we are; those not in the top levels at A level physics will not remember hearing about Olbert's paradox)
Why unfortunately? They can hardly cover everything! And they certainly can't mention everything covered in the syllabus.
Typically it would be discussed in the context of cosmology; if they don't cover cosmology at all that's unfortunate, but not mentioning this very specific footnote to it would be understandable. And even if they do plan on covering it, I'd be a little surprised if it was listed on the syllabus.
My biggest problem with this explanation is that even if the star-filled universe were infinite that doesn't necessarily mean there would be a star at every point you look at in the sky.
Depending on the density of the stars in space, it's quite probable that as you zoom in farther and farther you see more and more distant stars, you also see space between those stars. It becomes a limit problem where the 'star density' of the sky (vectors from your viewpoint which will eventually hit a star) gets closer and closer to a specific percentage the further you extend your sphere of view (or magnification level) but will never exceed it, and won't ever go to 1.
Assuming that there's some small but non-zero chance of a randomly selected line intersecting with a star in a finite volume of space, it's pretty clear that for an infinite volume, the probability of hitting at least one star will approach 1. (So long as the density of stars is approximately constant, or at least has some lower bound.)
And since stars are not point like objects, a line does indeed have a non-infinitesimal chance of intersecting a star.
Although all of this is a bit different from arguing about the net brightness of light coming from distant stars.
If the sphere is expanding, then the result is the same -- a gradual decline in energy density per unit of volume. So the specific geometry of the universe is unrelated to Olbers' Paradox.
But there is strong evidence that the universe is geometrically flat at large scales, which in turn argues that it's infinite in size.
How does the apparent large-scale flatness of the universe make an argument for an infinite size? To explain, and just as a simplifying example, imagine that the universe is the surface of sphere. Now include the implications of the fact that we observe large-scale flatness.
Picture this -- imagine that the universe is the surface of a sphere, but the sphere's surface is perfectly flat. How large must the sphere's radius be for its surface to be perfectly flat? Think about how a sphere's surface is defined -- it's the unique surface that's equidistant from the center of the sphere, the surface that has a distance of R (R = radius).
To make both properties true -- to accommodate (a) that it is a sphere and (b) that its surface is perfectly flat, all you need to do is make the radius infinite.
In the case of the universe, with more dimensions, to achieve the measured large-scale flatness, all one need do is assume that the universe is infinite in size.
> if the speed is greater or equal to speed of light, how we can be sure that we won't see ourselves in telescope?
That doesn't follow. We can't see an object moving away at greater than C, so we also can't see ourselves.
There is one place where we might see the backs of our own heads -- while observing at the event horizon of a black hole, all practical considerations aside. At that location, the spacetime curvature is such that light emitted "horizontally" would curve around the horizon (and the black hole) and reappear 360 degree away -- for example, from the opposite direction of someone shining a laser beam "horizontally" along the horizon.
> I mean, even if the radius is infinite, because speed is increasing, we should see sun light returning to us over universe surface at some point
> not that long ago we didn't know that we live on a sphere
Actually, the ancient Greeks knew it was a sphere, and everyone knew by the Middle Ages. Surprisingly perhaps, given their other astronomical work, the Chinese were the last hangers on. The notion that we discovered it relatively recently seems to have been due to a propaganda campaign in the 19th Century.
There is actually a much better explanation than this. When you look at the nights sky you see a snapshot of the universe. The further back you look the more stuff there is, but while there more objects there proportionally dimmer.
Now, in an unaging and infinite universe with random stars everywhere you would get what amounts to unlimited light. But, our universe is finite and does age, so you get a finite amount of light from that fixed volume. As to how much light you end up seeing it's a function of:
A) Being close to our Galaxy the Milky Way with a large clump of stars inside it.
B) The average of all the galaxy's in the observable universe which relates to the average amount of matter in the universe which is not that high.
Thus, a fairly dim sky outside of the disk that is the milky way.
Dust does not resolve the paradox. Dust occludes by absorbing the light, which means that the dust would eventually heat up enough to glow itself. Dust can't reduce the amount of radiation and energy in the universe, just shift it in time or wavelength or direction.
That generation will not get to live on Earth at all, because by then the sun will have expanded and swallowed it. Even ignoring that humans as we know them will not exist at that point, this is surely a bigger problem than the lack of stars.
According to the redshift and mass measurements of distant galaxies, it seems like the universe is expanding faster than gravity would keep it together.
The future generation will not see most of the stars in the universe due to accelerated expansion in the universe. The distant galaxies will move faster and faster away from us until their light has red-shifted to be dimmer than the CMB. We will be alone with our Milky Way, may be with some others nearby in the super cluster.
Um is it just me or does the conclusion of the article not match the ultimate conclusion of the video?
In the last 15 seconds of the video they say that it's actually because once you get far enough away from earth, the stars are moving so fast away that they redshift to infrared.
The embedded video describes the paradox by saying that the night sky "should be as bright as the sun". Imagine if that were the case. Then move yourself twice as close to the sun, making the sun four times brighter. Then the night sky is 1/4 as bright as the sun.
So clearly, distance and (lack of) density could make the night sky less bright, presumably to below the threshold of human perception. Right? Even aside from their explanations of distant light not having had time to reach us, and/or being red-shifted out of our visible range.