Sun Goes Down. Up Comes A Mystery
npr.org
npr.org
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.
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.
(Incidentally, when thinking about these sorts of problems, it helps to distinguish flux from specific intensity: http://en.wikipedia.org/wiki/Specific_radiative_intensity)
Basically, the fact that the sky is dark tells us that at least one of the above assumptions is wrong.
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.
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!
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?
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".
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.
> "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.
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" :(
1 + 0.1 + 0.01 + 0.001 + 0.0001 +...
clearly, after any number of terms have gone by, you're still not at two (though of course, once they all have, you are).
If every sight line ended on a star, you'd expect the entire sky's brightness per area to be that of a star.
FF's reading mode saved me, but is there any permanent workaround for problems like this? Addons?
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:
q = (e^(-t/k) - 1)*(a - b) + a
Where:
t = time
k = energy transfer factor
q = temperature at time t
a = temperature at time 0
b = temperature of source
The above expresses Newton's Law of Cooling:
https://www.dropbox.com/s/bt63bt59t9q76th/newtons_cooling_la...
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?
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.
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.
On average, that's somewhere in the neighborhood of 3K.
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.
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?
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.
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.
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.
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.
That said, Hubble took a many-day exposure of one of these ultra-deep regions, and this is what it saw:
To the best of my knowledge, and in general, it isn't.
> I'm finding it rather odd that it was unfamiliar to this journalist!
It wasn't. It was unfamiliar to his daughter. He posted it because he's aware that the public is generally unaware of it, not that he is.
Most people, even the best students (I was one of those), did not.
Disgusting, isn't it?
(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 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.
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.
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.
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)
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.
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.
*A few billion years after that, you'll be standing on a hill looking up on a clear night, and the sky will be close to pitch black*
what if universe is a 4 dimensional sphere?
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?
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
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
No, not really.
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.
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.
Space is mostly vacuum, but there is enough dust over the vast volumes to occlude light.
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.