
Sun Goes Down. Up Comes A Mystery - iProject
http://www.npr.org/blogs/krulwich/2012/10/10/162630285/sun-goes-down-up-comes-a-mystery
======
surrealize
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.

~~~
jbri
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!

~~~
surrealize
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?

~~~
jbri
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".

------
splat
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.

~~~
shardling
Ehh, the CMB doesn't come from stars, so bringing it up in this context is a
bit of a red herring.

~~~
Dylan16807
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.

------
darklajid
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?

~~~
pi18n
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?

~~~
CamperBob2
(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.

------
rcthompson
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.

~~~
chime
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.

~~~
lutusp
> 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:

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...](https://www.dropbox.com/s/bt63bt59t9q76th/newtons_cooling_law.png)

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?

------
dredmorbius
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.

~~~
drcube
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.

[1] <https://en.wikipedia.org/wiki/Black_body_radiation>

~~~
dredmorbius
The dust and planets will start to radiate ... at the blackbody rate.

On average, that's somewhere in the neighborhood of 3K.

~~~
lutusp
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.

~~~
psb217
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?

~~~
lutusp
> 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.

~~~
psb217
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.

~~~
lutusp
> 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.

------
lutusp
Another discussion of Olbers' Paradox (that predates Dark Energy):

<http://www.arachnoid.com/sky/>

------
erikpukinskis
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?

~~~
svachalek
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.

------
cstross
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!)

~~~
_delirium
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.

~~~
jonnathanson
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.

~~~
_delirium
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.

------
kfury
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.

~~~
shardling
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.

------
iscrewyou
Click the picture for The Milky Way from Mars. It's worth it.

------
dotborg

      *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*
    

not that long ago we didn't know that we live on a sphere

what if universe is a 4 dimensional sphere?

~~~
lutusp
> 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.

~~~
dotborg
the idea of universe size increasing speed now comes to my mind,

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

~~~
lutusp
> 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

No, not really.

------
wazoox
Interestingly, E. A. Poe provided one of the first explanation of Olbert's
paradox : <https://en.wikipedia.org/wiki/Eureka:_A_Prose_Poem>

------
Retric
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.

------
waynecochran
I always thought the sky was dark for the same reason we don't see the bright
center of the Milky Way at night: dust.

Space is mostly vacuum, but there is enough dust over the vast volumes to
occlude light.

~~~
T-hawk
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.

------
munyukim
I hope science is wrong this time, because if it's true a whole generation
will never enjoy the beauty of stars at night

~~~
danbruc
That conclusion is wrong - the expansion of the universe will not tear apart
galaxies because the stars are bound by gravity.

~~~
pi18n
According to the redshift and mass measurements of distant galaxies, it seems
like the universe is expanding faster than gravity would keep it together.

~~~
drcube
That's on an intergalactic scale. Theres no evidence that I know of that
galaxies or galactic clusters will be torn apart from cosmic expansion.

------
lelf
<http://en.wikipedia.org/wiki/Olbers_paradox>

------
tkahn6
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.

