Inverse square law explains Olbers' paradox?

[humbleteleskop]

One other thing...

Hubble telescope gazed at those galaxies for 23 days to obtain this photo. At the beginning it was all dark and eventually got brighter, right? It didn't grow larger, the actual color got brighter. Doesn't that mean "apparent brightness" and inverse-square law is actually about color brightness and not the size, in this case at least?

 

[Bandersnatch]

Why in the world is it not called "apparent size" then?

Because size is the reason behind brightness difference. You can't resolve most stars as anything bigger than just a point, so all you can measure is the brightness. You call it apparent brightness, because brightness is what you measure. The brightness is what it is, because the size is what it is. It makes little sense to call it apparent size, as size is something you do not observe, even if it directly influences brightness.

Is it in any way becoming clearer now?

Wait a second, are you saying this is wrong:

No. We're talking about Olber's paradox, remember? The whole sky packed with stars with no empty spaces left between them, so that it looks like one big surface of the sun on the firmanent.

 

[russ_watters]

Yes, I am aware of that and I agree. What I don't agree with is when they say "dimmer" that they actually mean "smaller". Here is why:

http://en.wikipedia.org/wiki/Apparent_brightness

Is "apparent brightness" about differences in size or color brightness?

I don't know what "color brightness" is, but the article doesn't provide the details relevant to the question, so it is better to use a source that does. However in this case i don't think it really matters which assumption you pick. The one thing you may not do, however, is use both at the same time, which appears to be what you want to do. So please answer clearly:

Do you recognize that geometrically an object that is twice as far away covers 1/4 as much area in your field of view?

 

[russ_watters]

Are you kidding me?!? What's next, "wet" actually means "tall"? I can't possibly be the only one who thinks "brightness" is something that describes color. So many articles about it and no one cares to point at that semantic nonsense. Why in the world is it not called "apparent size" then? Unbelievable!

You win, I lose. Rrrrhh!

Because it isn't just size, it is size AND surface brightness.

 

[russ_watters]

Wait a second, are you saying this is wrong:

http://www.astronomynotes.com/starprop/s3.htm

No, it isn't wrong, you are wrong. Repeating it over and over again isn't going to change that.

Please go back and reread the first page of the thread. You are making the same wrong claims as you made before and chasing your tail. You should already know the things that you are saying are wrong.

 

[russ_watters]

One other thing...

Hubble telescope gazed at those galaxies for 23 days to obtain this photo. At the beginning it was all dark and eventually got brighter, right? It didn't grow larger, the actual color got brighter. Doesn't that mean "apparent brightness" and inverse-square law is actually about color brightness and not the size, in this case at least?

No, this has nothing whatsoever to do with photographic exposure time. You are just adding to your confusion by searching for other ways around this. Focus on the specific cases at hand.

 

[Drakkith]

But if we look at very distant star which appears very dim due to inverse-square law, and if we have enough resolution so no other star adds up its brightness to this star we are looking at, then shouldn't we see it as dim as it is?

You are still thinking of stars as point sources and are ignoring what we've said about surface brightness. As I explained earlier, a 1 arcsecond x 1 arcsecond section of the Sun is exactly the same brightness whether you're at 1 au or 2 au. In other words, if you were to measure number of photons emitted from this 1x1 arcsecond square, it would be equal in both cases. You need to forget everything else in this thread until you understand why this is so.

 

[humbleteleskop]

No, this has nothing whatsoever to do with photographic exposure time.

What do you believe was the purpose for 23 days exposure time?

 

[russ_watters]

What do you believe was the purpose for 23 days exposure time?

It makes the image bright enough to see. But again, this has nothing to do with Olbers paradox, since the HDF was not completely filled with star.

Now please: if a star's surface brightness is dropped to 1/4 and size is dropped to 1/4, how much less light is received?

 

[humbleteleskop]

You are still thinking of stars as point sources and are ignoring what we've said about surface brightness.

- "Generally a source of light can be considered a point source if the resolution of the imaging instrument is too low to resolve its apparent size. Examples: Light from a distant star seen through a small telescope"
http://en.wikipedia.org/wiki/Point_source

Where do you get your information from?

As I explained earlier, a 1 arcsecond x 1 arcsecond section of the Sun is exactly the same brightness whether you're at 1 au or 2 au. In other words, if you were to measure number of photons emitted from this 1x1 arcsecond square, it would be equal in both cases.

Photons emitted have nothing do with the distance it's measured from. Brightness, which is a function of photons received, does vary with the distance. For example, apparent brightness of the Sun as seen from Venus is -27.4, as seen from Jupiter is -23, and as seen from Neptune is -19.3.

http://en.wikipedia.org/wiki/Apparent_brightness

 

[russ_watters]

- "Generally a source of light can be considered a point source if the resolution of the imaging instrument is too low to resolve its apparent size. Examples: Light from a distant star seen through a small telescope"
http://en.wikipedia.org/wiki/Point_source

"If". For Olber's paradox, they are not considered point sources.

Again, if you want to make up your own different thought experiment that is different from Olber's paradox by using point sources, that's fine, but you have to recognize it is different and analyze accordingly...which we've already done and explained that it does not provide the result you desire.

 

[Drakkith]

- "Generally a source of light can be considered a point source if the resolution of the imaging instrument is too low to resolve its apparent size. Examples: Light from a distant star seen through a small telescope"
http://en.wikipedia.org/wiki/Point_source

Where do you get your information from?

The key phrase here is "can be considered". This means that real light sources are NOT point sources. We can "consider" real light sources to be point sources because we have limitations to our optics, and until the object's apparent size is larger than its airy disk we generraly don't have to worry about it, allowing us to simplify certain models and calculations. However, Olber's paradox is one of those situations where considering stars to be point sources will NOT help you understand.

Photons emitted have nothing do with the distance it's measured from.

Okay, change "emitted" to "received".

Brightness, which is a function of photons received, does vary with the distance. For example, apparent brightness of the Sun as seen from Venus is -27.4, as seen from Jupiter is -23, and as seen from Neptune is -19.3.

http://en.wikipedia.org/wiki/Apparent_brightness

That's measuring the brightness of the Sun as a whole as seen from those planets. A small 1x1 arcsecond section of the Sun has the same brightness at every planet. And by that I mean the number of photons received from this section will be the same. But since the Sun shrinks in apparent size as you move further away, there are fewer and fewer 1x1 arcsecond squares, so total brightness does go down.

 

[humbleteleskop]

It makes the image bright enough to see. But again, this has nothing to do with Olbers paradox, since the HDF was not completely filled with star.

I didn't say it has anything to do with Olbers' paradox. I said it has to do with apparent brightness and inverse-square law, and I pointed out how nothing grew in size, but only increased in brightness.

Now please: if a star's surface brightness is dropped to 1/4 and size is dropped to 1/4, how much less light is received?

I guess 8 times less, who knows. I thought the lesson you wanted to teach me was that amount of light received would be equal in either case.

Do you recognize that geometrically an object that is twice as far away covers 1/4 as much area in your field of view?

Yes. And it would have the same apparent brightness if it was at that same distance but 4 times bigger and with 4 times less of surface luminosity.

 

[humbleteleskop]

The key phrase here is "can be considered". This means that real light sources are NOT point sources. We can "consider" real light sources to be point sources because we have limitations to our optics, and until the object's apparent size is larger than its airy disk we generraly don't have to worry about it, allowing us to simplify certain models and calculations. However, Olber's paradox is one of those situations where considering stars to be point sources will NOT help you understand.

I disagree. If the size can not be resolved and the distance is increased it can not get any smaller only its color can get dimmer.

That's measuring the brightness of the Sun as a whole as seen from those planets. A small 1x1 arcsecond section of the Sun has the same brightness at every planet. And by that I mean the number of photons received from this section will be the same. But since the Sun shrinks in apparent size as you move further away, there are fewer and fewer 1x1 arcsecond squares, so total brightness does go down.

That arc-second will not correspond to the same surface area if the distance is increased, but larger area, so yes. I guess that example is supposed to represent a "wall of stars" relating to Olbers' paradox, but it's misleading as those stars are not in the same plane perpendicular to the line of sight.

 

[humbleteleskop]

"If". For Olber's paradox, they are not considered point sources.

Again, if you want to make up your own different thought experiment that is different from Olber's paradox by using point sources, that's fine, but you have to recognize it is different and analyze accordingly...which we've already done and explained that it does not provide the result you desire.

As Boris the Animal would say: let's agree to disagree.

 

[Vanadium 50]

I disagree. If the size can not be resolved and the distance is increased it can not get any smaller only its color can get dimmer.

Well that's just plumb wrong. The angular size of an object is what it is, independent of whether or not we can resolve an object of this size or not.

 

[russ_watters]

Separate post because of how important this is:

I guess 8 times less, who knows. I thought the lesson you wanted to teach me was that amount of light received would be equal in either case.

This raises a bunch of big, red flags:

1. I gave you the answer (in bold, no less!), so the fact that you answered wrong means you aren't trying hard enough. Our help here is not free: it comes with the requirement that you make an effort to learn what we are trying to teach you.

2. Who knows? Everyone who is posting in this thread and making a claim must know. That includes you: you can't claim to explain a principle in science if you can't do even the simplest calculations that describe it.

3. You didn't just guess wrong, you were doubly wrong: You contradicted your own claim (4x brightness reduction) with your wrong answer. You need to grasp that the math does not support your claim and listen to us when we explain why. Which makes:

4. You don't even recognize your own scenario when it is recited back to you! You need to organize your thoughts better: again, you need to try harder here.

 

[russ_watters]

I didn't say it has anything to do with Olbers' paradox. I said it has to do with apparent brightness and inverse-square law, and I pointed out how nothing grew in size, but only increased in brightness.

This is your thread on how the inverse square law relates to Olbers' paradox. If it doesn't relate to Olbers' paradox, then it isn't relevant to the thread and we shouldn't be discussing it.

Yes. [twice as far away = 1/4 the size]

So how can you claim that if you have 1/4 the size and 1/4 the surface intensity, you get 1/4 the total brightness? ...or, for that matter, 1/8th the total brightness (your two claims). It should be obvious to you that you are contradicting yourself.

As Boris the Animal would say: let's agree to disagree.

That's really not an option here. This is a pretty simple issue and there is a straightforward right and wrong answer. You can choose to be wrong if you want, but we won't indulge your insistence that your wrong answer is right for much longer.

 

[humbleteleskop]

Well that's just plumb wrong. The angular size of an object is what it is, independent of whether or not we can resolve an object of this size or not.

I was of course referring to apparent size. Let me try again. If the angular diameter of a star can not be resolved and the distance from the star is increased, then its apparent size can not get any smaller, only its apparent color can get dimmer. True?

 

[Vanadium 50]

False.

Let me say it again: The angular size of an object is what it is, independent of whether or not we can resolve an object of this size or not. The size of an object is not determined by our ability to measure.

This thread has gone on quite a while, largely because you post one incorrect statement after another. Are you really asking a question? Or are you trying to promote a position.

 

[Drakkith]

I was of course referring to apparent size. Let me try again. If the angular diameter of a star can not be resolved and the distance from the star is increased, then its apparent size can not get any smaller, only its apparent color can get dimmer. True?

Apparent size/angular diameter does not depend on our ability to resolve an object. Consider that the resolving power of an optical system is highly variable. Very small diameter telescopes have MUCH less resolving power than very large telescopes. Resolving power has nothing to do with apparent size/angular diameter, as the latter is purely a function of object size and distance. This is why it helps to look at the paradox using hypothetical "perfect" optical systems that can resolve whatever object we want to talk about. We can ignore what doesn't apply to the paradox.

That arc-second will not correspond to the same surface area if the distance is increased, but larger area, so yes. I guess that example is supposed to represent a "wall of stars" relating to Olbers' paradox, but it's misleading as those stars are not in the same plane perpendicular to the line of sight.

It doesn't matter if it's in the same plane or not, the light still comes out the same. That's what we've been trying to get you to understand. It's not misleading, it's the way it works.

 

[humbleteleskop]

Let me say it again: The angular size of an object is what it is, independent of whether or not we can resolve an object of this size or not. The size of an object is not determined by our ability to measure.

Apparent size/angular diameter does not depend on our ability to resolve an object. Consider that the resolving power of an optical system is highly variable.

"In astronomy the sizes of objects in the sky are often given in terms of their angular diameter as seen from Earth, rather than their actual sizes."
http://en.wikipedia.org/wiki/Angular_size


"Mathematically an object may be considered a point source if its angular size is much smaller than the resolving power of the telescope."
http://en.wikipedia.org/wiki/Point_source

 

[Bandersnatch]

Look, if your detector has got a very low resolution, less than 0.5 degree in the case of the picture with the Sun you've posted, it won't be able to tell how big the source of light is. It would record the same brightness whether it's a 0.5 degree diametre stellar disc of X brightness, or a point source of the same brightness. But it's actual physical size, as well as the resultant angular size on the sky remains the same.

Is that what you can't understand? It's hard to guess when you just post a bunch of wiki quotes, that all agree with everything that has been said, without pointing out the problem you've got with understanding them.


I agree with others, you need to show a bit of good will here. This is not a debate, so it's not about winning or losing an imaginary argument. You either learn or you don't.

 

[Drakkith]

I'm done. The OP has shown a clear unwillingness to actually consider what has been said and learn. Requesting this thread be closed, as the question of whether the inverse-square law explains Olber's paradox has been hammered to death repeatedly.

 

[humbleteleskop]

Resolving power has nothing to do with apparent size/angular diameter, as the latter is purely a function of object size and distance.

Mathematically an object may be considered a point source if its angular size is much smaller than the resolving power of the telescope. Ok? So what happens to apparent brightness of an object which you can not resolve and you move away to a point that is twice your current distance? Can its apparent size get any smaller? Or will its color instead get four times dimmer? Or what?

It doesn't matter if it's in the same plane or not, the light still comes out the same.

http://en.wikipedia.org/wiki/Apparent_brightness

Haven't we agreed just in our previous exchange that apparent brightness varies with distance?

So if apparent brightness varies with distance, how can possibly the amount of light received be the same from objects in the same plane perpendicular to the line of sight and from those which are not?

 

[Drakkith]

If you're willing to listen and not just link random wikipedia articles I'll help explain it to you. If something doesn't make sense, ASK for more detail on it, don't just find something that you think supports your understanding.

 

[Bandersnatch]

So if apparent brightness varies with distance, how can possibly the amount of light received be the same from objects in the same plane perpendicular to the line of sight and from those which are not?

We were talking about Olber's paradox, weren't we? It says there ought to be more stars farther away to compensate for the reduced brightness of each single star.

 

[humbleteleskop]

Look, if your detector has got a very low resolution, less than 0.5 degree in the case of the picture with the Sun you've posted, it won't be able to tell how big the source of light is. It would record the same brightness whether it's a 0.5 degree diametre stellar disc of X brightness, or a point source of the same brightness. But it's actual physical size, as well as the resultant angular size on the sky remains the same.

I don't think I said anything contrary to that. Please note Wikipedia does not define a point source in regards to low resolution sensor or blind people, it explicitly mentions telescope, so I suppose that has some relevance in which case it would render your example in relation to it invalid.

Is that what you can't understand? It's hard to guess when you just post a bunch of wiki quotes, that all agree with everything that has been said, without pointing out the problem you've got with understanding them.

I'm asking a question. I can't tell you what I understand or not unless we establish correct answer first.

QUESTION: What happens to apparent brightness of a star which is thousand million light years away, which apparent size you can not resolve with a telescope and you move away to a point that is twice your current distance? Can its apparent size get any smaller? Or will its color instead get four times dimmer? Or what?

 

[Bandersnatch]

Both. It's angular size will get smaller, which will result in less light reaching the detector.

 

[humbleteleskop]

Both. It's angular size will get smaller, which will result in less light reaching the detector.

How do you measure the difference in angular size if it is smaller than the resolving power of the telescope?

 

[Bandersnatch]

You don't. At that point you can only measure the total brightness of the area.

 

[humbleteleskop]

If you're willing to listen and not just link random wikipedia articles I'll help explain it to you. If something doesn't make sense, ASK for more detail on it, don't just find something that you think supports your understanding.

Please do explain. If apparent brightness varies with distance, how can possibly the amount of light received be the same from objects in the same plane perpendicular to the line of sight and from those which are not?

 

[Bandersnatch]

If apparent brightness varies with distance, how can possibly the amount of light received be the same from objects in the same plane perpendicular to the line of sight and from those which are not?

It's not true for individual stars. It's true for light coming from any area of the sky in Olber's paradox, as the stars fill the sky completely. Once again, it's not about individual stars - it's about the total contribution of all visible stars to the brightness of the sky.

 

[humbleteleskop]

You don't. At that point you can only measure the total brightness of the area.

Houston, we have an agreement.

We were talking about Olber's paradox, weren't we?

Does answer depend on it? We are talking about facts of reality, they should hold true in our hypothetical scenarios just like in the real world.

It says there ought to be more stars farther away to compensate for the reduced brightness of each single star.

It says total intensity received from each shell is the same, and we all agree. It does not mention any other kind of compensation or pixel saturation related to individual stars as suggested earlier on, but that doesn't bother me. Is that what you are referring to?

 

[Bandersnatch]

Does answer depend on it? We are talking about facts of reality, they should hold true in our hypothetical scenarios just like in the real world.

Answers you get depend on the setup you start with. The sky looks different if you start with an eternal, infinite universe, and different when you start with a finite one.

Yes, the physics is the same here and there, but the initial conditions are also improtant.

During this overly long discussion, there has been talk about both the physics of what makes stars less bright, and the end result of having infinitely many shells of equal brightness. I believe you've had them mixed at least once, which seems to be the source of the confusion.

It says total intensity received from each shell is the same, and we all agree. It does not mention any other kind of compensation or pixel saturation related to individual stars as suggested earlier on, but that doesn't bother me. Is that what you are referring to?

It also says there's an infinite number of shells. Which leads to pixel saturation.