# Olbers' paradox: why is the night sky dark?

Started Nov 12, 2012 | Discussions thread
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Re: Olbers' paradox: why is the night sky dark?

trisd wrote:

Jonny Boyd wrote:

You're avoiding the question. I am claiming two things:

1. The brightness that we perceive is directly connected to the flux experienced by each photoreceptor i.e. photoreceptors experiencing a high flux will be bright, those with a low flux will be dim.
2. If each photorecptor experiences the same flux, then we will consequently perceive the sky to be of uniform brightness.

Do you dispute either of those and if so, on what basis?

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

- "Luminous flux is not used to compare brightness, as this is a subjective perception which varies according to the distance from the light source."

Then there is radiant flux which is not the same thing as luminous flux

given that I have repeatedly referred to irradiance in the past, which is the radiant flux density, it should be obvious that. i'm talking about radiant flux, not luminous flux.

and both refer to TOTAL EMITTED amount of light, rather than RECEIVED amount of light,

radiant flux or radiant power is the measure of the total power of electromagnetic radiation (including infraredultraviolet, and visible light). The power may be the total emitted from a source, or the total landing on a particular surface.

so you see brightness is not directly connected to either flux as much of it can be blocked in our paradox before reaching the sensor.

In my calculations I simply calculate the light coming from unobstructed stars, something which I only rcently reminded you oF, so your objection is wrong.

However, in order to not complicate this any further I will agree with what you said if you substitute word "flux" with "number of photons reaching sensor per unit area per unit time". The correct term to use would be "irradiance" (radiometry) or "illuminance" (photometry).

Funnily enough, I already told you that over a week ago and asked if you agreed. But as you so often do, you didn't bother to reply and kept talking about brightness instead.

Are you now agreed then that irradiance corresponds to brightness and that if the night sky could be shown to produce uniform irradiance on the human eye then that would be perceived as unifrom brightness and if there is not uniform irradiance then there is not unform brightness?

If you take the field of view covered by the stars in the first image and work out the angular flux, then do the same for the stars in the second image, you will get the same result Because each star in the second image covers a quarter of the field of view, but there are four times as many.

No, they do not cover any less of the field of view as they are all POINT sources.

Are they point sources in reality, or are they merely point sources because of the limited resolution of our eyes?

If it is because of the resolution of our eyes, then they still cover an area of the sky, even if we do not perceive the area directly. It is important therefore when you work out how many stars will be in an area of sky, that you remember the real area occupied.

Basically the amount of light for each field of view that ends on a star is the same.

The question is whether the two shell appear equally bright.

Do you see two equally bright shells on these two images?

I've answered that plenty of times already. Stop avoiding the issue About lines of sight – do you agree that every line of sight will end in a star?

What causes us to perceive brightness? The arrival of photons at our photodetectors. How do we quantify that? Luminance and flux.

Yes, amount of photons arrived at photo-detector per unit area per unit time defines brightness. However, you do not quantify that with either luminance or flux, but with received intensity, that is irradiance" in radiometry or "illuminance" in photometry.

irradiqnce is simply the density of radiant flux and I've told you before that it is the term we should be using, but you ignored that and kept hsing brightness. Since you're apparently happy with it now, we will use it hence forth.

You quoted from http://www.astro.cornell.edu/academics/courses/astro201/olbers_paradox.htm They use flux and luminance to quantify brightness. Are they wrong?

Not luminance just flux.

The luminance determines the flux.

And yes they are wrong, because total amount of light emitted, just like total amount of light received, is not a measure of perceived brightness by human eyes,

Irradiance is flux density, and you've already said that you agree that is a measure of brightness.

Eqch point in the sky will have a number of stars proportional the the square of the distance. Why can't you accept that? That's why they say 'but there are four times as many stars'

Each point? Ughh. No, no, no. Area, not point - AREA.

Good grief, you complain when I talk about area and then moments later you complain when I use point. Some consistncy would be nice.

Take a unit anglular area of sky That is equivalent to th field of view of a single photoreceptor. at a distance r there are n stars each producing sufficient light to produce an irradiance of b on the photoreceptor, resulting in a total for that photoreceptor of nb. Go to a distance 2r and you have 4n stars each producing light that gives an irradiance b/4, for a total of nb. Each of these groups of stars covers the same angular area and results in the same irradiance on a photoreceptor. So wherever you look in the sky, whatever star your line of sight ends in, will result in the same irradiance on your photoreceptors, resulting in uniform brightness.

"...if you look at a shell twice as far, each star is only a quarter as bright, but there are four times as many stars, so each shell is equally bright."

Do you think the two images correctly represent the above statement?

i've told you a million times, YES.

Do you think then those images above show two equally bright shells?

I've told you a million times, YES.

What part of 'the two effects should cancel' do you not understand? Nobody disputes the bit about fainter stars. The problem is everyone else then agrees with the second bit while you ignore it.

The "effect" that will cancel is TOTAL amount of light, but total amount of light is not the same thing as brightness perceived by human eyes

You can do exactly the same calculation for individual photoreceptors and you end up with every photoreceptor, whatever combination of stars they see, receiving the same irradiance.

Consider a number of photoreceptors that have various combinations of stars in their field of view:

1. 1 star at 1r, 4 stars at 2r, 16 stars at 4r
2. 9 stars at 3r, 25 stars at 5r, 36 stars at 6r
3. 1 star at 1r, 2 stars at 2r, 8 stars at 4r, 20 stars at 5r, 20 stars at 10r
4. 3 stars at 2r, 1 star at 4r, 2 stars at 3r, 28 stars at 6r, 12 stars at 8r, 100 stars at 10r

All these combinations will cover the same area of sky and will result in the same irradiance on a photoreceptor, so each photoreceptor will register the same brightness. Why does this work? Because the angle occupied by a star  decreases with the square of the distance, meaning that the brighness per unit angle remainds constance. So whatever combination of stars you use, you end up with the same perceived brightness. That's how simple Olbers' paradox is.

There are various things you failed to reply to my my previous posts. Do you accept now that infinite shells are involved in Olbers' paradox?

And do you now accept the validity of my calculations?

If you leave these questions unanswered, I will have to assume that the answer to each is yes, which means that at last you agree with the rest of the world that the inverse square law by itself does not deal with Olber's paradox.

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