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humbleteleskop
2014-May-29, 09:36 PM
Hello,

What the title says. I'll use instructions from Wikipedia: - "To show this, we divide the universe into a series of concentric shells, 1 light year thick. Thus, a certain number of stars will be in the shell 1,000,000,000 to 1,000,000,001 light years away. If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell between 2,000,000,000 to 2,000,000,001 light years away. However, the second shell is twice as far away, so each star in it would appear four times dimmer than the first shell. Thus the total light received from the second shell is the same as the total light received from the first shell."
http://en.wikipedia.org/wiki/Olbers%27_paradox


If we start with 10 bright stars in the first shell, then there should be 40 stars 4 times less bright in the second shell, like this:

http://upload.wikimedia.org/wikipedia/commons/0/0b/Stars7.jpg

...so the total amount of light received from both shells is the same.

Right?

Jens
2014-May-29, 11:22 PM
I'm not sure if the 4 is correct (I think it may be 4 x pi, but the effect is the same and yes, I think your understanding is correct.

humbleteleskop
2014-May-30, 12:09 AM
I'm not sure if the 4 is correct (I think it may be 4 x pi, but the effect is the same and yes, I think your understanding is correct.

The paradox says: - "...there would be four times as many stars in a second shell... the second shell is twice as far away, so each star in it would appear four times dimmer"

The problem is we are supposed to get completely white image, but our image is getting darker.

ShinAce
2014-May-30, 12:27 AM
4*pi usually means 360 degrees but in 3D.
2*pi is the angle you measure for the circumference of a circle(measuring from inside the circle), while 4*pi is like the surface area of a soccer ball, but as an angle.

But yes, that is the correct idea behind Olber's paradox. Twice as far away, there are 4 times as many stars, but each one only appears to output 1/4 as much power. Keep simulating starfields for more and more slices of space and then add them up. From basic programming, we can see if we have X pixels with a 'brightness' between 0 and 255. Once every pixel gets to 255, the screen is pure white. Let's say that each slice gets a total value of 1024 divided up among all the stars in that frame. If we add 1024 each frame, it's only a matter of time before we exceed 255 in every pixel. So basically, if the average star surface is 5000K, why isn't the whole sky at 5000K?

Be careful how you measure brightness and you mean by dimmer. Intensity is the easiest way to do it.

humbleteleskop
2014-May-30, 03:39 PM
From basic programming, we can see if we have X pixels with a 'brightness' between 0 and 255. Once every pixel gets to 255, the screen is pure white. Let's say that each slice gets a total value of 1024 divided up among all the stars in that frame. If we add 1024 each frame, it's only a matter of time before we exceed 255 in every pixel.

That's what I thought, but it raised two questions I couldn't answer.

1.) How could Olbers arrive to his conclusion without ever considering anything like that?

2.) Consider little patches in the paradox sky equivalent to Hubble eXtreme Deep Field. When we look at it with our naked eyes we see nothing but black. The light coming from there is so faint the Hubble telescope needed exposure time of almost a month to obtain this image:

http://upload.wikimedia.org/wikipedia/commons/thumb/2/22/Hubble_Extreme_Deep_Field_%28full_resolution%29.pn g/300px-Hubble_Extreme_Deep_Field_%28full_resolution%29.pn g

- "The exposure time was two million seconds, or approximately 23 days. The faintest galaxies are one ten-billionth the brightness of what the human eye can see."
http://en.wikipedia.org/wiki/Hubble_Extreme_Deep_Field

...so wouldn't such patches in the paradox sky appear completely black just the same as they actually are in the real world to the naked eye?

Extrasolar
2014-May-31, 10:28 PM
Twice as far as each previous shell, there are only 4 times the number of stars if you adjusted for the thickness of the shell. In reality, if the thickness of the shell remains constant, the volume will not scale to 4x. The volume of a sphere is given by V=\frac{4}{3}\pi r^{3}. The volume of the shell of a 3 LY outer radius, 2 LY inner radius shell is only 2.71 times more volume than a shell with an outer radius of 2 LY and an inner radius of 1 LY.

humbleteleskop
2014-Jun-01, 01:40 AM
Not sure if my previous post got lost or is still waiting on approval.


Twice as far as each previous shell, there are only 4 times the number of stars if you adjusted for the thickness of the shell. In reality, if the thickness of the shell remains constant, the volume will not scale to 4x. The volume of a sphere is given by V=\frac{4}{3}\pi r^{3}. The volume of the shell of a 3 LY outer radius, 2 LY inner radius shell is only 2.71 times more volume than a shell with an outer radius of 2 LY and an inner radius of 1 LY.

Having infinite number of shells would that make any difference?

cjameshuff
2014-Jun-01, 02:30 AM
The paradox says: - "...there would be four times as many stars in a second shell... the second shell is twice as far away, so each star in it would appear four times dimmer"

The problem is we are supposed to get completely white image, but our image is getting darker.

How are you expecting to get a completely white image? If you are looking at individual slices, the brightness of each slice should be constant. Double the radius, and you get 4 times as many stars with 1/4th the brightness = identical brightness. How are you doing the simulation? How are you calculating the brightness? How are you representing the slices?



Twice as far as each previous shell, there are only 4 times the number of stars if you adjusted for the thickness of the shell. In reality, if the thickness of the shell remains constant, the volume will not scale to 4x. The volume of a sphere is given by V=\frac{4}{3}\pi r^{3}. The volume of the shell of a 3 LY outer radius, 2 LY inner radius shell is only 2.71 times more volume than a shell with an outer radius of 2 LY and an inner radius of 1 LY.

That's a red herring. The shell thickness is assumed to be small in comparison to the radius, and any finite thickness is going to become small as radius increases.

Jeff Root
2014-Jun-01, 02:48 AM
Extrasolar,

You don't need to adjust for the thickness, you need to make
the outer shell twice the radius of the inner shell. You didn't
do that.

I think ... If your inner shell is between 1 LY radius and 2 LY
radius, then the outer shell needs to be between 2.5 LY radius
and 3.5 LY radius.

Though that gives a much closer result, it still isn't exact, so I
suspect the geometric mean is needed to define the center of
the thickness of a shell, not the arithmetic mean. Maybe if I
get ambitious I can work that out. But I hope you'll do it first.

-- Jeff, in Minneapolis

Extrasolar
2014-Jun-01, 05:57 PM
How are you expecting to get a completely white image? If you are looking at individual slices, the brightness of each slice should be constant. Double the radius, and you get 4 times as many stars with 1/4th the brightness = identical brightness. How are you doing the simulation? How are you calculating the brightness? How are you representing the slices?




That's a red herring. The shell thickness is assumed to be small in comparison to the radius, and any finite thickness is going to become small as radius increases.

You're saying that this equation doesn't depend on the volume of the shell? The scenario is a pretty exact equation that does not equal the stated result. I think it is fundamental to the question.


Extrasolar,

You don't need to adjust for the thickness, you need to make
the outer shell twice the radius of the inner shell. You didn't
do that.

I think ... If your inner shell is between 1 LY radius and 2 LY
radius, then the outer shell needs to be between 2.5 LY radius
and 3.5 LY radius.

Though that gives a much closer result, it still isn't exact, so I
suspect the geometric mean is needed to define the center of
the thickness of a shell, not the arithmetic mean. Maybe if I
get ambitious I can work that out. But I hope you'll do it first.

-- Jeff, in Minneapolis

That doesn't work either. Any comparison of shells should be equal to 4x the volume of the previous shell, and that's what I was attempting to do. If you are going to keep to a strict 1 LY thick shell and simply move the radius, you're altering exactly 2 parameters of the equation just as I did. So no, you don't need to adjust for thickness, you just need to move the radius of the shells to 2.5413814 LY and 3.5413814 LY, or you can adjust the thickness of the shell so that the next shell starts where the previous shell ends. Both answers lead to 4x the volume of the 1-2 LY shell.

It would be interesting if the equation was done correctly, but I don't think this is much of a paradox at all. The space doesn't scale in the stated way, so either would the magnitude of the stars contained in that space.

Jeff Root
2014-Jun-01, 06:26 PM
Extrasolar,

I misunderstood what you were demonstrating. I got the impression
that you wanted to compare two shells of equal thickness where the
outer shell has twice the radius of the inner shell, but now I see you
were comparing the volume of successive shells of equal thickness.

-- Jeff, in Minneapolis

cjameshuff
2014-Jun-01, 06:56 PM
You're saying that this equation doesn't depend on the volume of the shell? The scenario is a pretty exact equation that does not equal the stated result. I think it is fundamental to the question.

No, you're getting hung up on an approximation error that has nothing to do with the question. You are using thick slices with small radii while using an approximation that requires the shells be thin in relation to their radii. Of course it doesn't work, the answer is don't do that.

In the limit, you're looking at the derivative of the volume of a sphere. Volume is 4/3*pi*r^3, so that's 4*pi*r^2...the area of the sphere, exactly canceling the inverse squared law for stars on that sphere, meaning that under the assumptions of Olber's paradox, the contribution of starlight is independent of distance of the stars being considered. The total contribution out to distance r is thus directly proportional to r. When you extend r out to infinity, you encounter a bit of a problem.

This assumes stars are continuous and breaks down for the smallest radii where there are only a few discrete stars or where lumpiness in distribution such as galaxies is significant, but considering that it works for the entire rest of the universe, that's not a particularly big issue.

Extrasolar
2014-Jun-01, 07:09 PM
Oh, you're right, I wasn't looking at this correctly. Sorry about that! A shell at 2,000,000 - 2,000,001 shell is 4x the volume of a 1,000,000 - 1,000,001 LY shell.

caveman1917
2014-Jun-01, 08:36 PM
This assumes stars are continuous and breaks down for the smallest radii where there are only a few discrete stars or where lumpiness in distribution such as galaxies is significant, but considering that it works for the entire rest of the universe, that's not a particularly big issue.

It's not even an issue at all, you're not forced to start at a small radius, you can start at any radius as large as you want and simply ignore anything smaller. It still gets you infinity no matter where you start.

Ken G
2014-Jun-02, 01:43 AM
It's actually not even the worst of the situation to say that Olbers' paradox is that the whole sky should be as bright as a star if the universe is infinitely full of stars and is infinitely old, because in fact that really says the whole sky should be arbitrarily bright. Two paths of reasoning lead to that. One is, if there is no net transport of light out of a box because the surrounding boxes are just the same, then since there are no sinks for the light (stars and dust are in radiative equilibrium), the light energy in the box must build up without limit over infinite time. Also, one can simply note that stars convert mass energy into light energy, so if there are always sources of new stars (which requires an eternal source of mass, as is required for an infinitely old universe), then there is always a source of light, and there will be infinite light after infinite time.

All of this really makes me wonder why astronomers in Newton's day seemed to feel that the universe should be infinitely large and infinitely old. It really just can't make sense. Sure, it meant they didn't need any new physics to explain the origin of a universe, but they still needed new physics to understand what could happen to all that light that stars are making. Perhaps Einstein's solution was to say it was infinitely old but there was infinite space beyond the stars for the light to escape into, with a cosmological constant to explain why the stars didn't all fall together. Since astronomers tended to think of the universe as infinitely old, they must have thought along those lines, or else their view just made no sense. It has always seemed odd to me that it took Hubble's observation for people to imagine that the universe must have a finite age, surely someone must have come to that realization just from the action of stars themselves. But I guess the stars were not that well understood either, even in the days of Einstein's cosmology. Astronomy has been playing catch-up to physics for a long time, but now it seems that worm has turned, with dark matter and dark energy.

baskerbosse
2014-Jun-02, 03:53 AM
I'm no mathematician or cosmologist so I'm probably missing something glaringly obvious here..

-But here goes;
Is it not possible to have an infinite number of stars distributed across the sky without them necessarily filling up the entire sky?

With a fractal distribution you could fit an infinity of stars in the sky and still have it mostly black, couldn't you?

Jeff Root
2014-Jun-02, 05:35 AM
I have never understood that fractal distribution claim.
Why would a fractal distribution make any difference?

You'll probably need to explain what you mean by "fractal"
in order to answer that question.

I hope humbledesktop returns and tells us whether any of
this is helpful to answering the original question, because
I'm not sure exactly what the question was.

-- Jeff, in Minneapolis

humbleteleskop
2014-Jun-02, 08:32 AM
Hoya!? I posted two messages in the meantime and was informed each time it will be waiting for approval.

antoniseb
2014-Jun-02, 09:59 AM
Hoya!? I posted two messages in the meantime and was informed each time it will be waiting for approval.
New members' posts go into a moderation queue to help prevent spam. Unfortunately for you you posted on a weekend with few moderators looking at this section.
Thanks for joining, hopefully this early experience won't turn you away.

Jeff Root
2014-Jun-02, 11:34 AM
humbleteleskop,

Now that your third post has gone up, with the Hubble image,
I have a better idea of what you're after.

Consider that the vast majority of lines of sight to the galaxies
in that image go straight through the galaxies without hitting a
star. Almost all the area of each individual galaxy is very dark.
The limited resolution of the image means each galaxy looks
like it is just about solid light, even if it is dim. If there were
enough stars in the sky, scattered about randomly, every line
of sight would end on a star, and the whole sky would be as
bright as the surfaces of those stars.

The big lesson for me is how few and far-between stars are,
relative to the enormous spaces between them.

-- Jeff, in Minneapolis

caveman1917
2014-Jun-02, 01:32 PM
I'm no mathematician or cosmologist so I'm probably missing something glaringly obvious here..

-But here goes;
Is it not possible to have an infinite number of stars distributed across the sky without them necessarily filling up the entire sky?

With a fractal distribution you could fit an infinity of stars in the sky and still have it mostly black, couldn't you?

Strictly speaking you don't need a fractal distribution for that, the number of stars in the sky will be countably infinite yet the number of points on a sphere are uncountably infinite so most (as in the full measure) of the sky will still be black. However this is just a mathematical curiosity (though still an interesting one i believe) since neither are stars really points with zero surface area nor can any detector resolve an image up to points of zero area.

IsaacKuo
2014-Jun-02, 02:28 PM
All of this really makes me wonder why astronomers in Newton's day seemed to feel that the universe should be infinitely large and infinitely old. It really just can't make sense. Sure, it meant they didn't need any new physics to explain the origin of a universe, but they still needed new physics to understand what could happen to all that light that stars are making.
Seeing as scientists of Newton's day didn't have a scientific grasp of what light even was, the requirement of "new physics" to explain all that light wouldn't exactly be a shocker.

In particular, Newton himself didn't have a grasp on the concept of kinetic energy (he thought of momentum as the fundamental notion of "oomph" contained in moving matter), much less the concept of conservation of energy. So your intuitive problem of an infinitely cooking universe oven probably wouldn't have even occurred to him.

Ken G
2014-Jun-02, 07:37 PM
With a fractal distribution you could fit an infinity of stars in the sky and still have it mostly black, couldn't you?
Yes, and that is an important point to make-- Olbers' paradox assumes a homogeneous distribution of stars. You could even have a distribution which fell off with distance fast enough, still have an infinity of stars, and not get Olbers' problematic result.

Ken G
2014-Jun-02, 07:41 PM
Seeing as scientists of Newton's day didn't have a scientific grasp of what light even was, the requirement of "new physics" to explain all that light wouldn't exactly be a shocker.
Yes, in Newton's time it was not as surprising as in, say, Einstein's day. But you're right it's easy to forget all the other things people didn't know, like squat about stellar evolution or nuclear fusion in stars.


In particular, Newton himself didn't have a grasp on the concept of kinetic energy (he thought of momentum as the fundamental notion of "oomph" contained in moving matter), much less the concept of conservation of energy. So your intuitive problem of an infinitely cooking universe oven probably wouldn't have even occurred to him.It might surprise us all the things that could have occurred to Newton that we don't know about! Surely when he imagined an infinite, static, and infinitely old universe, he must have asked "but what happens to all the light that stars emit"? He must have considered some version of Olbers' paradox, because he would have known that light intensity falls off like an inverse square law, and that's all you need. (Indeed, he felt that the infinite gravity must cancel out from all directions, but he could not have thought light would do the same.) He must have thought there was some way to "get rid" of light, but I have no idea what process he was imagining for doing that. Maybe he thought something absorbs it, the absence of a concept of conservation of energy might have been very key, you make a good point there. But even that would require some concept of an interstellar medium, which was not a common idea in Newton's day.

ShinAce
2014-Jun-02, 11:15 PM
...so wouldn't such patches in the paradox sky appear completely black just the same as they actually are in the real world to the naked eye?

That's an easy one. We don't live in the infinite extent and infinite age universe of Olber's paradox. Therefore, the paradox simply does not exist.

We live in a universe of finite age, which expands continuously, but keeps changing its rate of expansion.

baskerbosse
2014-Jun-03, 01:41 AM
Yes, and that is an important point to make-- Olbers' paradox assumes a homogeneous distribution of stars. You could even have a distribution which fell off with distance fast enough, still have an infinity of stars, and not get Olbers' problematic result.

Thanks,
I guess that's what I was asking, because I didn't quite get why there is a paradox here.
As caveman1917 pointed out, fractal distribution is not required.
(That's just how I came to think of it originally because in fractals you can have mostly empty areas that when zoomed reveals infinite complexity)

Also, fewer photons would arrive at increased distance. As a star approaches infinite distance, wouldn't it also approach infinite improbability that you would get hit by a photon from it?


-Cheers,
Peter

baskerbosse
2014-Jun-03, 02:22 AM
Strictly speaking you don't need a fractal distribution for that, the number of stars in the sky will be countably infinite yet the number of points on a sphere are uncountably infinite so most (as in the full measure) of the sky will still be black. However this is just a mathematical curiosity (though still an interesting one i believe) since neither are stars really points with zero surface area nor can any detector resolve an image up to points of zero area.

Very interesting. Mathematically, can't you have an uncountably infinite number of stars provided they are of different sizes approaching infinitely small? Still without complete coverage?

Quick thought experiment in 1D:
Say that for each kilometer, you have one piece of meter length string, ten pieces of centimeter strings, hundred pieces of micrometer strings and so on to infinity.
Then spread them randomly along the kilometer line. I would think it's pretty clear it would be mostly not-line along that kilometer?
Especially if they are detected by means of a particle release rate that are proportional to their size (photons)


thanks,
Peter

caveman1917
2014-Jun-03, 02:48 AM
Very interesting. Mathematically, can't you have an uncountably infinite number of stars provided they are of different sizes approaching infinitely small? Still without complete coverage?

Quick thought experiment in 1D:
Say that for each kilometer, you have one piece of meter length string, ten pieces of centimeter strings, hundred pieces of micrometer strings and so on to infinity.
Then spread them randomly along the kilometer line. I would think it's pretty clear it would be mostly not-line along that kilometer?
Especially if they are detected by means of a particle release rate that are proportional to their size (photons)


thanks,
Peter

That's all still countable. Countably infinite means that there are an infinite number of objects but you can go "one, two, three, ..." without missing any, uncountable means you can't do that.

cjameshuff
2014-Jun-03, 03:43 AM
Also, fewer photons would arrive at increased distance. As a star approaches infinite distance, wouldn't it also approach infinite improbability that you would get hit by a photon from it?

Two problems: first, the number of stars increases with distance, exactly countering the decrease in rate of photons received from individual stars. Second, the total contributions of all stars out to infinite distance would still be infinite.

humbleteleskop
2014-Jun-03, 05:17 PM
New members' posts go into a moderation queue to help prevent spam. Unfortunately for you you posted on a weekend with few moderators looking at this section.
Thanks for joining, hopefully this early experience won't turn you away.

It's because the first two posts went online in a matter of hours, so when nothing happened for more than a day I thought they got lost.

humbleteleskop
2014-Jun-04, 03:48 AM
How are you expecting to get a completely white image?


Images of the first two shells are only separated for comparison. After some number of these shell layers are combined together they should eventually make the image uniformly bright. I believe that's the conclusion of the paradox.



If you are looking at individual slices, the brightness of each slice should be constant. Double the radius, and you get 4 times as many stars with 1/4th the brightness = identical brightness. How are you doing the simulation? How are you calculating the brightness? How are you representing the slices?


I'm not sure how to calculate brightness, there are quite a few definitions to choose from, like: radiant flux, radiant intensity, radiance, irradiance, radiosity... I think "radiance": power per unit solid angle per unit projected area?

I have no idea how to do "simulation" except to keep drawing shells and see what happens, but it didn't seem the image was getting much brighter. After only several shells the color of stars dropped drastically and I was adding almost completely black layers that were only going to get even darker.

Jeff Root
2014-Jun-04, 11:14 AM
I don't know whether the questions cjameshuff asked were
questions he wanted you to post answers to, or just to think
about. The answers to those questions are important factors
in you working out the answer to your question.

What you are doing *is* a simulation, even if you are going
at it a bit haphazardly.

Rather than looking at images in the hope that your computer
monitor and your eyes will tell you if the light adds up the way
it is asserted to do, look at the numbers in your simulation.
Each pixel in your bitmap image is represented by an integer
from zero to 255. Zero represents complete darkness and 255
represents saturation of that pixel. This simulation has the
problem that you only have 255 different brightness levels,
and you want to keep dividing forever. When you pass the
minimum positive value of 1, what do you do? Keep using
a value of 1 from then on, or stop adding any more beyond
that point, or what? (The best answer is to analyze the
problem mathematically rather than using a simulation, but
you've already seen the math and don't quite get it, so the
simulation is to help you understand the math.)

Trying to judge the brightness of the pixels by eye makes
the problem much worse, since the pixel values represent
very roughly a linear range, while neither the monitor nor
your eyes work at all linearly. A range of only 255 values
is pretty useless for this particular purpose. Some tricky
programming could undoubtedly improve that greatly, but
I don't see a simple way to do it offhand. You are trying
to stuff an essentially infinite range of brightnesses into
just 255 values.

So don't do it by looking at the pictures, do it by looking
at the numbers, and use floating-point numbers rather than
the very limited set of 255 values that your monitor uses.

If you are familiar with matrix arithmetic, you will know what
I mean: Add together the values of corresponding pixels in
each frame of your simulation.

The more pixels (matrix elements) in your simulation, the
longer it will be before stars always appear in every pixel,
adding to the total value for that pixel.

-- Jeff, in Minneapolis

cjameshuff
2014-Jun-04, 09:30 PM
Images of the first two shells are only separated for comparison. After some number of these shell layers are combined together they should eventually make the image uniformly bright. I believe that's the conclusion of the paradox.

The total brightness will increase in direct proportion to the number of images stacked, provided that the pixels are of infinite range and precision. Typical image formats actually only support values in the range 0 to 255, so the brightest possible pixel value can only be halved 7 times and still give a value larger than the dimmest possible non-black pixel value. In addition, an image computed this way will only approach uniform brightness if it has infinite resolution and the brightness of the stars is determined by their size, which certainly isn't the case here. It wasn't clear whether you were using some standard graphics library, custom image code that works around these issues, or if the images were only representations of the simulation results.

Generating images and adding them together is an extremely poor way of approaching the problem. You have the number of stars and the brightness of each star, the total brightness of each slice is simply N*B. Since N is proportional to r^2 and B to 1/r^2, you can just reuse the value of one slice for all the others, they're all the same. Efficiently summing up the contribution from a given number of slices is left as an exercise for the reader.

You can also avoid the need for infinite resolution by computing the brightness of be the patch of sky covered by each pixel. The computation will be identical for each pixel, so you can do it once and reuse it for all the other pixels. The result will obviously be the expected uniform image.



I'm not sure how to calculate brightness, there are quite a few definitions to choose from, like: radiant flux, radiant intensity, radiance, irradiance, radiosity... I think "radiance": power per unit solid angle per unit projected area?

"Total power received from the star" works fine.

IsaacKuo
2014-Jun-04, 11:12 PM
As I originally learned Olber's paradox, each point in the sky was only supposed to be the brightness of a star's surface--rather than infinite. This was because of the intuitive assumption that light from behind a star would be blocked by it. Without sophisticated concepts of thermodynamics and conservation of energy, this intuitive idea seems reasonable enough.

However, this take on Olber's paradox assumes that the blocked light either magically disappears, or somehow the absorption of light is assumed to be baked into the ultimate brightness of a star already.

You need to apply some non-trivial reasoning with conservation of energy and thermodynamics to see the the absorption of blocked starlight is ultimately canceled out by the re-emission of the absorbed energy. So, you do indeed end up with the conclusion that the sky should be infinitely bright, but it's not as simplified as presented in this thread.

(Note that there's a non-obvious question of where the stars get all this infinite energy. Fusion only provides a limited amount of energy, so even an infinitely old homogeneous universe wouldn't be infinitely bright.)

baskerbosse
2014-Jun-05, 01:18 AM
Two problems: first, the number of stars increases with distance, exactly countering the decrease in rate of photons received from individual stars. Second, the total contributions of all stars out to infinite distance would still be infinite.

Ok,

Thanks for that.
I just didn't have enough math knowledge to see why that would be the case.

I thought you could have a distribution with an infinite number of progressively smaller contributions that still add up to a finite luminosity, in the same way as you could fit an infinite number of progressively smaller lengths into a finite length.
But that is me completely ignoring the 3D geometry with infinites and infinitesimals distribution that I don't know how to calculate for this problem.

Thanks for clearing that up, now I have yet another thing on my to-do study list.. :-)

Cheers!
Peter

Jeff Root
2014-Jun-05, 01:56 AM
I believe the original version of Olbers' paradox assumed a
constant light flux coming from a constant number of stars,
and did not forsee that the flux would naturally increase
over time. The brightness of the sky being equal to the
brightness of the emitting surfaces is the basic geometric
inference from all lines of sight ending on a star.

The buildup over time of light flying around the Universe,
giving the sky infinite brightness, would be a refinement
that one might not get to if one stops at the obvious
conflict with observation of the more basic analysis.

-- Jeff, in Minneapolis

cjameshuff
2014-Jun-05, 03:31 AM
I thought you could have a distribution with an infinite number of progressively smaller contributions that still add up to a finite luminosity, in the same way as you could fit an infinite number of progressively smaller lengths into a finite length.

You can, but the contributions aren't progressively smaller in this case. Just having a decreasing function isn't enough for the integral to converge, and you certainly won't get convergence with a constant function.

humbleteleskop
2014-Jun-05, 05:12 AM
I don't know whether the questions cjameshuff asked were
questions he wanted you to post answers to, or just to think
about. The answers to those questions are important factors
in you working out the answer to your question.

What you are doing *is* a simulation, even if you are going
at it a bit haphazardly.


Like watching a film negative getting hit by photons in slow-motion? That would be sweet, but just animated gif should be good enough for me, something like the image from Wikipedia Olbers' paradox article, which is what made me fiddle with this in the first place:

http://upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Olber%27s_Paradox_-_All_Points.gif/300px-Olber%27s_Paradox_-_All_Points.gif

This is doesn't look right, look at all those oranges falling from the sky! All the stars are the same color-brightness, there are no any dim, dimmer, and very dim stars like I was getting and as they are described in the article. They faked it. I hope I (we) can do it better.




Rather than looking at images in the hope that your computer
monitor and your eyes will tell you if the light adds up the way
it is asserted to do, look at the numbers in your simulation.
Each pixel in your bitmap image is represented by an integer
from zero to 255. Zero represents complete darkness and 255
represents saturation of that pixel. This simulation has the
problem that you only have 255 different brightness levels,
and you want to keep dividing forever. When you pass the
minimum positive value of 1, what do you do? Keep using
a value of 1 from then on, or stop adding any more beyond
that point, or what?


I wouldn't know where to even begin with that method. Image size, pixel size, aperture size, exposure time, pixel sensitivity... I'm afraid that's too ambitious for me. I need some super-simplification of that, doesn't have to be accurate, just to get some sense of what is going on. And of course it should be better and more realistic than that Wikipedia image above.

humbleteleskop
2014-Jun-05, 05:55 AM
That's an easy one. We don't live in the infinite extent and infinite age universe of Olber's paradox.

But stars in Hubble Deep Field are not too far away, their light did have enough time to reach us, we have photos of them. So also, whatever light from those stars red-shifted there is apparently still plenty left in the visible spectrum. Hubble telescope just needed to gaze at that patch of sky for 23 days, because intensity of light coming from all the way there is low due to inverse-square law. So why would not such patch of sky, like Hubble Deep Field, be completely black to the naked human eye in Olbers' paradox universe too?

humbleteleskop
2014-Jun-05, 07:05 AM
The total brightness will increase in direct proportion to the number of images stacked, provided that the pixels are of infinite range and precision. Typical image formats actually only support values in the range 0 to 255, so the brightest possible pixel value can only be halved 7 times and still give a value larger than the dimmest possible non-black pixel value. In addition, an image computed this way will only approach uniform brightness if it has infinite resolution and the brightness of the stars is determined by their size, which certainly isn't the case here. It wasn't clear whether you were using some standard graphics library, custom image code that works around these issues, or if the images were only representations of the simulation results.


Just plain pixel sized points, which are blurred a bit due to resizing.



Generating images and adding them together is an extremely poor way of approaching the problem. You have the number of stars and the brightness of each star, the total brightness of each slice is simply N*B. Since N is proportional to r^2 and B to 1/r^2, you can just reuse the value of one slice for all the others, they're all the same. Efficiently summing up the contribution from a given number of slices is left as an exercise for the reader.


I'm not aware of any better way that I could do myself. Where do I even start if I wanted to make an actual simulation? Is there some magic software so easy to use I could learn it in a day or two? I've played a little bit around Blender 3D modeler, no way I want to learn anything like that.



You can also avoid the need for infinite resolution by computing the brightness of be the patch of sky covered by each pixel. The computation will be identical for each pixel, so you can do it once and reuse it for all the other pixels. The result will obviously be the expected uniform image.

I think 3oox3oo pixels resolution should be enough for some sketch to start with. I would like to make it much more illustrative than just uniform blending. To show what is going on and how it is happening, more realistic, as if we are watching in slow-motion how the image is getting formed.




"Total power received from the star" works fine.

Unfortunately I'm not that much familiar with neither math nor physics. I can use equations, but I don't really know any unless I look them up in Wikipedia. How do I get how much energy per second would fall on a single pixel in Olbers' paradox universe? What equations should I be looking for?

Jeff Root
2014-Jun-05, 10:21 AM
humbleteleskop,

I misread your username and typed it incorrectly in earlier
posts. My apologies.

What you want to do here is exactly the same kind of thing
I like to do, apparently for the same reasons, using the same
methods. Doppelganger!


It occurred to me that there is an extremely crucial point
which you may not be familiar with: The intensity of the light
from a uniformly illuminated or light-emiting surface -- such
as the "surface" of a star -- does not vary with distance.
Move twice as far from the surface, and it will still appear
just as intensely bright.

If the surface has a limited area -- say, one square meter --
when you move twice as far from the surface, it will subtend
only half the angle, and a quarter the solid angle. So it looks
a quarter as large, and only a quarter as much light reaches
you from that one square meter. The reduction of the light
reaching you is due entirely to the reduction in the apparent
size (solid angle) of the surface. The intensity or density of
the light is unchanged. It looks just as intensely bright from
twice as far away, but the rate at which light from the whole
surface reaches you is reduced to 1/4 of what it was.

If instead the surface does not have a limited area, but goes
on forever, an infinite wall in front of you, then moving twice
as far away reduces the solid angle of each square meter of
the wall to 1/4 of what it was, but 3 more square meters of
the surrounding area of the wall fill in that part of your field
of view. You are looking at 4 square meters of illuminated
wall, where each square meter is giving you 1/4 as much light
as before. Each bit of the wall looks just as bright as it did
when you were closer to it.

It is the same thing with stars, except for the very important
difference that stars have such small angular size, and such
small solid angles, that they appear to be points rather than
areas. Thus instead of looking smaller but unchangingly bright
as you move away from them, they look dimmer. Their angular
size is already as small as it can get, so the reduction in the
light reaching you is interpreted as a reduction in brightness.

Simulating that with pixels on a screen has limits. You can do
it, but you run up against the limits pretty quickly and have to
deal with them somehow.



Like watching a film negative getting hit by photons in slow-
motion? That would be sweet, but just animated gif should be
good enough for me, something like the image from Wikipedia
Olbers' paradox article, which is what made me fiddle with this
in the first place:
Somehow I missed seeing that GIF animation before.



This is doesn't look right, look at all those oranges falling from
the sky!
I wonder why they were made to look that way.

Edit to add: I looked more closely at the biggest "orange", and
I see that it is a very realistic-looking image of a small star with
granules, spots, and flares, which isn't immediately obvious at
such a small size.



All the stars are the same color-brightness, there are no any
dim, dimmer, and very dim stars like I was getting and as they
are described in the article. They faked it. I hope I (we) can do
it better.
I think that is not a problem, but I can understand wanting a
more realistic range of brightnesses. We need to think about
whether it is important enough to include in your illustration.




Rather than looking at images in the hope that your computer
monitor and your eyes will tell you if the light adds up the way
it is asserted to do, look at the numbers in your simulation.
Each pixel in your bitmap image is represented by an integer
from zero to 255. Zero represents complete darkness and 255
represents saturation of that pixel. This simulation has the
problem that you only have 255 different brightness levels,
and you want to keep dividing forever. When you pass the
minimum positive value of 1, what do you do? Keep using
a value of 1 from then on, or stop adding any more beyond
that point, or what?
I wouldn't know where to even begin with that method. Image
size, pixel size, aperture size, exposure time, pixel sensitivity...
I'm afraid that's too ambitious for me. I need some super-
simplification of that, doesn't have to be accurate, just to get
some sense of what is going on. And of course it should be
better and more realistic than that Wikipedia image above.
Could you list what you would like the illustration to show,
and what you feel are critically-important shortcomings of
the Wikipedia animation? Everything you can think of.
The existing animation looks adequate to me, though
obviously far from optimal. I want a better idea of what
improvements you hope to make, and what features you
can do without.

-- Jeff, in Minneapolis
.

Jeff Root
2014-Jun-05, 10:36 AM
But stars in Hubble Deep Field are not too far away, their
light did have enough time to reach us, we have photos of
them.
HST can't see the individual stars. All it sees is a fog of
light from the billions of stars in each galaxy.



So also, whatever light from those stars red-shifted there
is apparently still plenty left in the visible spectrum. Hubble
telescope just needed to gaze at that patch of sky for 23 days,
because intensity of light coming from all the way there is low
due to inverse-square law. So why would not such patch of sky,
like Hubble Deep Field, be completely black to the naked
human eye in Olbers' paradox universe too?
What I explained in my post just above about how the
intensity or surface brightness of the light doesn't change
with distance, combined with what I said in post #20 about
lines of sight passing through galaxies, should answer that
question. If you could see the galaxies in the Hubble Deep
Field with unlimited resolution, you would see that each
individual galaxy is almost entirely black or very dark space,
with billions of intensely bright but extremely tiny stars
scattered about. With the limited resolution of HST, all we
see is a handful of pixels which have been illuminated by
those billions of stars. It takes HST such a long time to
register their light because the vast majority of the area of
each galaxy is dark, with no star along that line of sight.
Only a very, very few lines of sight land on a star in the
galaxy compared to the vast number of lines of sight which
pass right through the galaxy to the space beyond it.

-- Jeff, in Minneapolis

Jeff Root
2014-Jun-05, 11:06 AM
Just plain pixel sized points, which are blurred a bit due to
resizing.
I noticed that the "stars" in your original post were blurred
but almost exactly identical. Each covers roughly 25 pixels,
with some scattered light pixels around them. I said the
brightness values of pixels range from 0 to 255. The values
of pixels in the central parts of your dots generally differ by
only one step in a few of the pixels, so I wondered how that
came about.

The best you can do, I think, is begin with stars that have
the maximum value of 255. I can't tell if that is what you
did. If so, resizing dimmed them considerably.



I'm not aware of any better way that I could do myself. Where
do I even start if I wanted to make an actual simulation? Is
there some magic software so easy to use I could learn it in
a day or two? I've played a little bit around Blender 3D modeler,
no way I want to learn anything like that.
I'm a decade or two behind most people. I'm still doing it
the same way you are. (I finally got a broadband Internet
connection two weeks ago.)



I think 3oox3oo pixels resolution should be enough for some
sketch to start with. I would like to make it much more illustrative
than just uniform blending.
You need to spell out in some detail what you mean by this.
Exactly what do you want? How do you envision your result
being different from "uniform blending"?

-- Jeff, in Minneapolis

cjameshuff
2014-Jun-05, 10:50 PM
This is doesn't look right, look at all those oranges falling from the sky! All the stars are the same color-brightness, there are no any dim, dimmer, and very dim stars like I was getting and as they are described in the article. They faked it. I hope I (we) can do it better.

As Jeff said, the surface brightness remaining the same is accurate. The progression depiction likely isn't, but that's a limitation of the finite resolution.



I wouldn't know where to even begin with that method. Image size, pixel size, aperture size, exposure time, pixel sensitivity... I'm afraid that's too ambitious for me. I need some super-simplification of that, doesn't have to be accurate, just to get some sense of what is going on. And of course it should be better and more realistic than that Wikipedia image above.

None of those are necessary, most aren't even relevant. I detailed how to do the simulation in my previous response.



I'm not aware of any better way that I could do myself. Where do I even start if I wanted to make an actual simulation? Is there some magic software so easy to use I could learn it in a day or two? I've played a little bit around Blender 3D modeler, no way I want to learn anything like that.

I just detailed how to do it. Was there something specific you had a problem with? You haven't even given any details of how you're trying to do it, just a couple images that have some unstated relationship to your efforts. This makes it a bit difficult to advise you, beyond pointing out the problems with your apparent approach.

And no, Blender won't help. A 3D modeling tool is completely unsuited for this.



I think 3oox3oo pixels resolution should be enough for some sketch to start with. I would like to make it much more illustrative than just uniform blending. To show what is going on and how it is happening, more realistic, as if we are watching in slow-motion how the image is getting formed.

There's just not much you can do in terms of realism with the limitations of resolution and color depth of general purpose code and tools for dealing with images. They just aren't intended for this kind of thing.



Unfortunately I'm not that much familiar with neither math nor physics. I can use equations, but I don't really know any unless I look them up in Wikipedia. How do I get how much energy per second would fall on a single pixel in Olbers' paradox universe? What equations should I be looking for?

It doesn't matter. Use units of "power received from the stars in one shell". The result is infinite power no matter what number you use.

humbleteleskop
2014-Jun-05, 11:27 PM
If the surface has a limited area -- say, one square meter --
when you move twice as far from the surface, it will subtend
only half the angle, and a quarter the solid angle. So it looks
a quarter as large, and only a quarter as much light reaches
you from that one square meter. The reduction of the light
reaching you is due entirely to the reduction in the apparent
size (solid angle) of the surface. The intensity or density of
the light is unchanged. It looks just as intensely bright from
twice as far away, but the rate at which light from the whole
surface reaches you is reduced to 1/4 of what it was.


Due to finite resolution there is a point in distance where stars project on an area smaller than a single pixel. Pixel color-brightness will depend on the amount of energy received and its sensitivity or 'film speed'. Pixels would not get instantly bright unless the amount of energy received is infinite.




I think that is not a problem, but I can understand wanting a
more realistic range of brightnesses. We need to think about
whether it is important enough to include in your illustration.

Could you list what you would like the illustration to show,
and what you feel are critically-important shortcomings of
the Wikipedia animation? Everything you can think of.
The existing animation looks adequate to me, though
obviously far from optimal. I want a better idea of what
improvements you hope to make, and what features you
can do without.


Unlike Wikipedia animation I'd like to start with stars no larger than 3-4 pixels. Those oranges they have are far too large, also far too orange. I'd rather use greyscale black and white than any particular color.

humbleteleskop
2014-Jun-06, 01:06 AM
None of those are necessary, most aren't even relevant.


I think I know that much about photography. Image brightness will depend on aperture size, exposure time and film speed. Those are the most important, how can they not be relevant?



I just detailed how to do it. Was there something specific you had a problem with? You haven't even given any details of how you're trying to do it, just a couple images that have some unstated relationship to your efforts. This makes it a bit difficult to advise you, beyond pointing out the problems with your apparent approach.

The problem is I don't think all the pixels should be getting equally bright at every point in time.




It doesn't matter. Use units of "power received from the stars in one shell". The result is infinite power no matter what number you use.

I don't see the paradox concludes the sky would be infinitely bright. Just bright, perhaps as bright as an average star.

baskerbosse
2014-Jun-06, 02:26 AM
This is doesn't look right, look at all those oranges falling from the sky! All the stars are the same color-brightness, there are no any dim, dimmer, and very dim stars like I was getting and as they are described in the article. They faked it. I hope I (we) can do it better.


Yes, that looks terrible. Does not look real at all..
Obviously stars are organised in galaxies, galaxy clusters, superclusters, large scale structure and who knows what above that..

This looks more like the insides of an infinite star cluster or something..

Should be possible to improve on.. :-)

Jeff Root
2014-Jun-06, 08:58 AM
baskerbosse,

The paradox was defined long before it became known that
stars are organized into galaxies. Galaxies aren't relevant
to the presentation of the paradox. The animation is accurate
in that regard.

-- Jeff, in Minneapolis

Jeff Root
2014-Jun-06, 11:17 AM
Due to finite resolution there is a point in distance where
stars project on an area smaller than a single pixel.
I'm not sure whether this is a potential source of confusion
or not, but you might want to be careful in distinguishng
between pixels in a camera, pixels in an image, theoretical
or actual image resolution, and imaging by other kinds of
detectors such as eyes and photography. The use of pixels
to describe what happens to light is a recent development.
You are concerned with pixels because the images you want
to make will be composed of pixels, and because images
of the sky that you see are often composed of pixels, but
pixels do not figure into Olbers' paradox.


Except for a very few cases where a telescope or an array
of telescopes is set up to give extreme resolution, zooming
in for a closeup of a single extraordinarily large and nearby
star, no star other than the Sun can be resolved to anything
but a point. So, in effect, *every* star in the night sky
projects onto an area smaller than a single pixel.



Pixel color-brightness will depend on the amount of energy
received and its sensitivity or 'film speed'. Pixels would not
get instantly bright unless the amount of energy received
is infinite.
Here you are using the term "pixel" to refer to an imaging
device. I think that -- ignoring a bunch of nitpicks -- I agree
with what you're saying here as uncontroversial.



Unlike Wikipedia animation I'd like to start with stars no
larger than 3-4 pixels.
Can you explain why?

If you could get perfect (ideal) focusing of starlight on a
real (non-ideal) detector array (with resolution limited by
pixel size rather than optics), every star would fit in a
single pixel, with room to spare. Of course, when you
display such an image with 1 pixel in the imager being
represented by 1 pixel on a computer screen, the stars
will be really tiny and hard to see. That would be one
good reason for using more pixels per star.



Those oranges they have are far too large, also far too
orange.
Far too large for what? They are far too large to be a
realistic view from any real place, even inside a globular
cluster, but so what? This is an illustration of Olbers'
paradox, not of the real sky. The large sizes of the first
stars clearly shows the progressive increase in distance
and resulting reduction in visible surface area which are
essential characteristics of the paradox. I'd say it is a
feature, not a bug.

Far too orange for what? Like the deliberately large
diameters, I think the color was chosen to illustrate more
clearly what is happening. You can see that the surface
brightness does not change as stars get farther away.
That is another essential feature of the paradox.



I'd rather use greyscale black and white than any particular
color.
That's what I generally do. I'm not sure if it is because I'm
trying to be as minimal as possible, or for the aesthetics.
I think your objections to the Wikipedia animation are
primarily about the aesthetics, and I tend to agree.
At that scale, the flare on the bottom of the star image
unfortunately makes it look like a deformed orange.

-- Jeff, in Minneapolis

cjameshuff
2014-Jun-06, 11:31 AM
I think I know that much about photography. Image brightness will depend on aperture size, exposure time and film speed. Those are the most important, how can they not be relevant?

Olber's paradox has nothing to do with photography.



I don't see the paradox concludes the sky would be infinitely bright. Just bright, perhaps as bright as an average star.

Add up an infinite number of shells, all having equal brightness, and the result certainly is infinite.

Jeff Root
2014-Jun-06, 11:48 AM
I think I know that much about photography. Image
brightness will depend on aperture size, exposure time
and film speed. Those are the most important, how can
they not be relevant?
What shows up in photographs, CCD images, or human
eyes isn't part of Olbers' paradox. The paradox and its
resolution do not depend on how the starlight is observed.



The problem is I don't think all the pixels should be
getting equally bright at every point in time.
The explanation cjameshuff gave appears to be
intended to describe what happens, while you want to
*illustrate* what happens. Quite different goals.



I don't see the paradox concludes the sky would be infinitely
bright. Just bright, perhaps as bright as an average star.
A first-order analysis of what is going on shows that every
line of sight would end on the surface of a star or other
object. But consider further and one realizes that the light
from all those stars never goes away. It just keeps being
added to constantly and forever. So after infinite time,
the brightness of the entire sky will become infinite. If the
Universe is infinitely old, then the sky would always have
been infinitely bright!

-- Jeff, in Minneapolis

Jeff Root
2014-Jun-06, 11:57 AM
Add up an infinite number of shells, all having equal
brightness, and the result certainly is infinite.
That would only happen if the Universe is infinitely old
(which is implied by light coming from infinitely far away)
and the light which lands on a star contributes to the
temperature of that star, increasing its light intensity.
Such that every star becomes infinitely bright. Except
that since the Universe is taken to be infinitely old,
every star would *always* have been infinitely bright!

-- Jeff, in Minneapolis

humbleteleskop
2014-Jun-06, 02:45 PM
Olber's paradox has nothing to do with photography.


It's a hypothetical universe in which I want to bring my hypothetical camera and snap a photo of the sky. Shouldn't we be able to reproduce how this image would look like at any point in time during the exposure interval? That's what I want to do, but I can't just keep drawing new shells to infinity to see what will happen eventually. I need some faster method that can collectively calculate hundreds or thousands of shells at once for a single frame in gif animation sequence.




Add up an infinite number of shells, all having equal brightness, and the result certainly is infinite.

Wouldn't closer stars eventually occlude all the further away stars?

Extrasolar
2014-Jun-06, 03:46 PM
I just wanted to add something in referrence to the limited resolution of using 256 values, instead of the actual range of floating point numbers that you would get from a calculation. You can use the 256 values to represent the floating point numbers without the complication of affecting the next time step in your calculation by convulving the results of a time step to from 0 to 255. For example, if you need to represent values between 3000 and 10000 with 256 grey values, you can find the range of the values (7000) and divide 255 by the range. This would give you a decimal to multiply by in the next calculation of the time step (255/7000=0.03642857 (d) ). To get the color value, you have to subtract the minimum of the range from the current value and then multiply by the decimal. Any number between the range would be calculated by finding [value-3000]*d and then round it or find the integer value of that number. Now, the lowest value in the range will be represented by a color value of 0 and the highest value will represented by a color value of 255. A value of 6535 would be 129 if you round up or 128 if you simply use the integer value.

Then, you could manually set the range and see what happens to the image. This will allow you to adjust brightness and contrast of the produced image since using only 256 values destroys the fine resolution. If you need more info, I'd be glad to be more specific as I've created software that uses this method.

Also, since the frequency of light declines with the distance of the source thanks to expansion, then how is this considered a paradox at all? Obviously, I am the one missing something here, but just wondering what exactly. You can add an infinite amount of energy to a microwave frequency and it might fry you, but it wouldn't effect the brightness in the optical range at all.

Jeff Root
2014-Jun-06, 06:53 PM
since the frequency of light declines with the distance of the
source thanks to expansion, then how is this considered a
paradox at all?
The paradox was first defined more than two hundred years
before the Doppler effect was described, and more than
three hundred years before the discovery that the Universe
is expanding. The cosmic expansion is the resolution of the
paradox.

-- Jeff, in Minneapolis

cjameshuff
2014-Jun-06, 09:30 PM
It's a hypothetical universe in which I want to bring my hypothetical camera and snap a photo of the sky. Shouldn't we be able to reproduce how this image would look like at any point in time during the exposure interval? That's what I want to do, but I can't just keep drawing new shells to infinity to see what will happen eventually. I need some faster method that can collectively calculate hundreds or thousands of shells at once for a single frame in gif animation sequence.

Your question implies you think the camera will expose nearer sources before later sources. This isn't so. Given a camera that doesn't vaporize under the conditions, the film/sensor would be instantly and uniformly fully exposed by the infinitely bright sky.

Now you can depict the contribution of stars going out to an increasingly large distance, but this isn't a simulation of any real effect, and if done by drawing stars on images it quickly runs into the problems already described with limited range and resolution. These can be mitigated by use of floating point or other image representations, but typical image processing software isn't going to do the job.



Wouldn't closer stars eventually occlude all the further away stars?

Only by absorbing the light they occlude, which will make them hotter. The same goes for all the other stars in the sky. In the end, you're constantly adding energy into a closed system, and after an infinite amount of time, the energy density is infinite.

At best, assuming an infinitely old, infinitely large universe with a finite energy content, you have a bunch of burned out stars at equilibrium with each other. If they're still hot enough to glow, so is every other star, and the sky is some finite brightness higher than it had when the stars were still burning.



The paradox was first defined more than two hundred years
before the Doppler effect was described, and more than
three hundred years before the discovery that the Universe
is expanding. The cosmic expansion is the resolution of the
paradox.

The expansion and the finite age it implies, to be precise. Olber's paradox is a demonstration that the universe is not static and infinite in age and extent.

humbleteleskop
2014-Jun-07, 12:33 AM
What shows up in photographs, CCD images, or human
eyes isn't part of Olbers' paradox. The paradox and its
resolution do not depend on how the starlight is observed.


What is "brightness" if not a property of perceived of color?




A first-order analysis of what is going on shows that every
line of sight would end on the surface of a star or other
object. But consider further and one realizes that the light
from all those stars never goes away. It just keeps being
added to constantly and forever. So after infinite time,
the brightness of the entire sky will become infinite. If the
Universe is infinitely old, then the sky would always have
been infinitely bright!


Every line of sight landing on a surface of a star doesn't mean the same or infinite amount of energy is received from every star. Hubble Deep Field is completely black to the human eye no matter if you are looking directly at those stars or with the corner of your eye.

cjameshuff
2014-Jun-07, 01:01 AM
What is "brightness" if not a property of perceived of color?

Emitted power. As far as Olber's paradox is concerned, perception is irrelevant.



Every line of sight landing on a surface of a star doesn't mean the same or infinite amount of energy is received from every star. Hubble Deep Field is completely black to the human eye no matter if you are looking directly at those stars or with the corner of your eye.

The Hubble Deep Field does not contain an infinite number of stars, is of a view within an expanding universe of finite age, etc. You seem to be missing the point of Olber's paradox, which is that the assumptions it is based on must be flawed. It wouldn't be a paradox if it matched what we actually observed.

Jeff Root
2014-Jun-07, 02:02 AM
What is "brightness" if not a property of perceived of color?
A property of the color.



Every line of sight landing on a surface of a star doesn't
mean the same or infinite amount of energy is received
from every star.
It does, after an infinite amount of time has passed during
which the light which hits a star or other body is absorbed,
increasing the temperature of the star or other body so that
it is the same as all the other stars and other bodies.

As far as I know, that wasn't realized until some decades
after Olbers was done with it.



Hubble Deep Field is completely black to the human eye no
matter if you are looking directly at those stars or with the
corner of your eye.
Yes. So?

-- Jeff, in Minneapolis

humbleteleskop
2014-Jun-07, 05:34 AM
Your question implies you think the camera will expose nearer sources before later sources. This isn't so. Given a camera that doesn't vaporize under the conditions, the film/sensor would be instantly and uniformly fully exposed by the infinitely bright sky.


You are the only one I see to have said that. I don't see Wikipedia says anything about infinite brightness, and I don't remember any other article on the internet mentions anything about any infinity other than infinite universe and infinite number of stars.



Only by absorbing the light they occlude, which will make them hotter. The same goes for all the other stars in the sky. In the end, you're constantly adding energy into a closed system, and after an infinite amount of time, the energy density is infinite.


I don't see anything like that was considered in the paradox. Where do you get your information from?

humbleteleskop
2014-Jun-07, 06:28 AM
A property of the color.


The color as seen by the eye. You are talking about emitted or reflected light, this is about received and perceived light. Infrared sensitive eye could say our night sky is brightly red, given sufficient exposure time. Would it be wrong, or are we to take that for truth despite we see otherwise?



It does, after an infinite amount of time has passed during
which the light which hits a star or other body is absorbed,
increasing the temperature of the star or other body so that
it is the same as all the other stars and other bodies.

Absorption is not part of the paradox, just one of proposed explanations that came later on.




Yes. So?


The rate at which energy is received from Hubble Deep Field stars would be just as week if they were in Olbers' paradox universe. Ok? So those stars by themselves would be just as invisible to the human eye as they are in the real universe. What then? Even weaker sources of energy behind those stars would somehow be able to change the rate at which we receive energy from the stars in the path between us?

humbleteleskop
2014-Jun-07, 07:34 AM
Emitted power.


Received power. Does there exist "brightness" without some 'sensor', an "observer", something to perceive/evaluate this photon power incident on its sensor's surface?



As far as Olber's paradox is concerned, perception is irrelevant.


Brightness is a quality of perceived color. Olbers' paradox is about brightness. Therefore, Olbers' paradox is about perception.




The Hubble Deep Field does not contain an infinite number of stars, is of a view within an expanding universe of finite age, etc. You seem to be missing the point of Olber's paradox, which is that the assumptions it is based on must be flawed. It wouldn't be a paradox if it matched what we actually observed.

What if the conclusion is flawed instead?

Jeff Root
2014-Jun-07, 11:16 AM
The color as seen by the eye. You are talking about
emitted or reflected light, this is about received and
perceived light.
Olbers' paradox is about light from stars, but it says
nothing about how that light is observed.



Infrared sensitive eye could say our night sky is brightly
red, given sufficient exposure time. Would it be wrong, or
are we to take that for truth despite we see otherwise?
There is no conflict. If Olbers' paradox had been formed
to describe infrared light instead of or in addition to the
portion of the spectrum that we can see, it would have
been very similar, or identical.




It does, after an infinite amount of time has passed during
which the light which hits a star or other body is absorbed,
increasing the temperature of the star or other body so that
it is the same as all the other stars and other bodies.
Absorption is not part of the paradox, just one of proposed
explanations that came later on.
Olbers and earlier definers of the paradox did not realize
that the light which comes from one star and eventually hits
another star would heat the second star, eventually bringing
all stars to the same temperature. They also didn't realize
that after infinite time -- the infinitely-old Universe they were
assuming -- every star would have absorbed an infinite amount
of light from other stars and thus would have been heated to
infinite temperature, and thus glowing infinitely brightly.

You are right that absorption is not part of the paradox that
Olbers and others of his time defined, but a later addition,
required by physical laws discovered after Olbers' time.
It is an extension of Olbers' paradox.



The rate at which energy is received from Hubble Deep Field
stars would be just as weak if they were in Olbers' paradox
universe. Ok?
Yes. Agreed.



So those stars by themselves would be just as invisible to
the human eye as they are in the real universe.
Those stars are also individually invisible to the Hubble
Space Telescope. The reason HST can see them despite
their being so far away is that there are so many of them
in a relatively small area, HST is able to see the general
fog of light from the collection. HST would not be able
to detect any one of the stars in those galaxies if it was
alone in the sky. A single star at that distance doesn't
give off enough light for HST to detect. The human eye
works the same way, except that having a much smaller
aperture and far less ability to integrate exposure over
time, it requires a far greater intensity of light to detect
that any light is there.



What then? Even weaker sources of energy behind those
stars would somehow be able to change the rate at which
we receive energy from the stars in the path between us?
No, the even weaker sources of energy beyond the galaxies
that HST sees would add to the total fog of light, increasing
the rate at which light from that direction reaches Earth,
and making that patch of sky look brighter.

Again: Those galaxies are almost completely empty space.
Almost none of the surface area of any of those galaxies is
the surface of a star. Look at one particular galaxy. Maybe
one part in a trillion of the galaxy's visible area is the surface
of a star. The rest is looking straight through the galaxy to
the dark space beyond it. The Universe assumed by Olbers'
paradox fills in that area with stars *completely*. A trillion
times as much light coming from the same area. That would
be about as bright as the surface of the Sun, and it would
probably look just like an ordinary star to the naked eye.

-- Jeff, in Minneapolis

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humbleteleskop
2014-Jun-07, 05:36 PM
Olbers' paradox is about light from stars, but it says
nothing about how that light is observed.


If you don't observe the sky, how can you tell what color it is?




No, the even weaker sources of energy beyond the galaxies
that HST sees would add to the total fog of light, increasing
the rate at which light from that direction reaches Earth,
and making that patch of sky look brighter.


Closer stars ought to completely occlude further away stars at some point. So the supply of "background" light for the hypothetical Hubble Deep Field in the paradox universe would be limited and likely insignificant.

Jeff Root
2014-Jun-07, 06:15 PM
Olbers' paradox is about light from stars, but it says
nothing about how that light is observed.
If you don't observe the sky, how can you tell what color it is?
That question doesn't have anything to do with Olbers' paradox
or with figuring out how to illustrate Olbers' paradox. It is a
philosophical question in the area of epistemology.

Olbers' paradox says what it says, and it doesn't say anything
about how the starlight is observed. You can't change that.




No, the even weaker sources of energy beyond the galaxies
that HST sees would add to the total fog of light, increasing
the rate at which light from that direction reaches Earth,
and making that patch of sky look brighter.
Closer stars ought to completely occlude further away stars
at some point.
Yes, when the sky (or this patch of sky) is completely packed
solid with stars, then more distant stars will be completely
occluded. Obviously. And obviously not before then. As it is,
doubling the number of stars, or increasing the number by an
order of magnitude, or two or three orders of magnitude, will
mean hardly any stars will be occluded at all. Almost all of
the area of the galaxies is empty space, not the surface of a
star or other body. That's why they are so dark.



So the supply of "background" light for the hypothetical
Hubble Deep Field in the paradox universe would be limited
and likely insignificant.
You can say that, but it is completely wrong.

-- Jeff, in Minneapolis

humbleteleskop
2014-Jun-07, 07:17 PM
Olbers' paradox says what it says, and it doesn't say anything
about how the starlight is observed. You can't change that.


How do you measure brightness in the real world, and how do you measure it in the paradox? The same method must be valid in both the real world and hypothetical scenarios. If you want to know the color of the sky, you must observe, it doesn't matter whether "light detector", an eye, or a camera, is real or imaginary.




You can say that, but it is completely wrong.


If it is indeed wrong, I really shouldn't be able to say it so it holds true, or partially true. I think it can either be true or false, nothing else or in between.