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



## tris_d (Nov 12, 2012)

Olbers' paradox - Wikipedia, the free encyclopedia

I think treatment  originally used to discard inverse square law as the  solution to this question was not  set up correctly. I  would like to  confirm my findings, but people working in Astronomy and Cosmology field are  not receptive to even discuss it as it seems that would somehow   contradict mainstream theory, which is what brings me here. So this is  what I think about it, please let me know if you see any mistakes:


The original treatment ignores sensor surface area, that is some  2-dimensional  image receiving this light, like a photo or human eyes,  and by ignoring  that they get result as if the image has only one  pixel. So instead of  to "see" many dots, some bright some less bright,  they practically sum  all the received intensity in only one pixel and  thus result wrongly  indicates the sky would be bright. They also ignore  exposure time. The  rate of incoming photons is proportional to  distance, due to inverse  square law, which I find is well documented  and accepted fact, and just by looking at that makes it clear to me  inverse square law explains it all.

Let me explain with an example (all the stars are the same). Two  stars at distance r  would impact photo-plate with intensity I, and  eight stars at double the  distance will also impact photo-plate with  the same intensity I. That's  what they are saying, and that's fine.  However, what they are not  considering is that two closer stars will  produce two dots each with  brightens proportional to I/2, but eight further stars will  produce eight dots each with  brightness proportional to I/8.







There is difference between two bright dots and eight less bright dots, and there is difference between two dots on 10x10 resolution   image and 1x1 resolution image. So when they ignore this sensor surface   area they practically work with 1x1 resolution image where all the   intensity gets summed up at one pixel, and all they see is   "bright sky". To summarize I draw this conclusion: at infinite distance   there will be infinite number of stars and if we had infinite  resolution  they would produce infinite number of dots, but the  brightness of each  dot would be I/infinity, which is pretty much  nothing but black.


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## fjrabon (Nov 12, 2012)

If you want this to be taken seriously you need much more than back of the envelope 'logic'. Individual photons traveling from a far distance aren't less bright. Why the light traveling froma distance is less bright is because the photons have dispersed and few of them are hitting 'the sensor'. The problem with your logic is that when you have infinite light sources, you will still have an infinite steam of a very small number of photons hitting the sensor. Each photon will be as bright as a photon is, which would mean white sky. Your treatment basically assumes that the inverse square law derives from light being dimmed at the photon level by distance, which isn't true.


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## tris_d (Nov 12, 2012)

fjrabon said:


> If you want this to be taken seriously you need much more than back of the envelope 'logic'. Individual photons traveling from a far distance aren't less bright. Why the light traveling froma distance is less bright is because the photons have dispersed and few of them are hitting 'the sensor'. The problem with your logic is that when you have infinite light sources, you will still have an infinite steam of a very small number of photons hitting the sensor. Each photon will be as bright as a photon is, which would mean white sky. Your treatment basically assumes that the inverse square law derives from light being dimmed at the photon level by distance, which isn't true.



As you said photons get dispersed, so the amount of photons impacting image per surface area per unit time is less coming from more distant stars. It is this amount of photons and the time of exposure that will determine the brightness imprinted on the image, and that amount of photons is proportional to 1/r^2, correct? So, based on that I made these four pictures where exposure time is the same and the stars are the same, only distance doubles:






Now, this series of pictures is either true or false representation of how inverse square law influences image brightness relative to distance. And if you think it is incorrect, then please point out why, where is the mistake? How do you think it should look like?


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## fjrabon (Nov 12, 2012)

the problem is that if ANY number of photons are reaching the viewer from the source, the fact that there are infinite source stars would equal pure brightness.  Think about it this way, the photons aren't going anywhere when the inverse square law takes effect, they're just getting more dispersed, however, as they become more dispersed, their dispersion fields begin to overlap with nearby stars in the visual frame, which would then cause areas of overlap to brighten.  That's what your pictures don't take into account.  In your pictures, none of the 'stars' points of emission ever start to overlap, and thus total brightness only gets dimmer.  But, when you have an infinite number of point light surfaces, the inverse square law no longer holds, because then you no longer have a point surface of light, but a flat plane.  The inverse square law applies to point sources of light only.  The fact that every star is immediately adjacent to another in the visual plane means that the sky should act like a complete plane of light that completely envelops the universe.

And additionally, the fact that the universe is expanding has been confirmed pretty heavily, and is sufficient to explain olber's paradox anyway, since we now know the universe isn't in fact static.


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## tris_d (Nov 12, 2012)

fjrabon said:


> the problem is that if ANY number of photons are reaching the viewer from the source, the fact that there are infinite source stars would equal pure brightness.  Think about it this way, the photons aren't going anywhere when the inverse square law takes effect, they're just getting more dispersed, however, as they become more dispersed, their dispersion fields begin to overlap with nearby stars in the visual frame, which would then cause areas of overlap to brighten.  That's what your pictures don't take into account.  In your pictures, none of the 'stars' points of emission ever start to overlap, and thus total brightness only gets dimmer.  But, when you have an infinite number of point light surfaces, the inverse square law no longer holds, because then you no longer have a point surface of light, but a flat plane.  The inverse square law applies to point sources of light only.  The fact that every star is immediately adjacent to another in the visual plane means that the sky should act like a complete plane of light that completely envelops the universe.
> 
> And additionally, the fact that the universe is expanding has been confirmed pretty heavily, and is sufficient to explain olber's paradox anyway, since we now know the universe isn't in fact static.



I would like to confirm the basics first, so please forget about infinity for the moment. In my example there is only 30 stars in the whole universe, and if you prefer let it be 30 light bulbs in a dark room. The question is whether the series of four pictures I posted above is correct representation of how inverse square law influences image brightness relative to distance. Can you confirm? Or even better, can you point me to some actual photos taken of the same light bulb with the same exposure time at double, triple and quadruple distance, or something among those lines?


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## fjrabon (Nov 12, 2012)

tris_d said:


> fjrabon said:
> 
> 
> > the problem is that if ANY number of photons are reaching the viewer from the source, the fact that there are infinite source stars would equal pure brightness.  Think about it this way, the photons aren't going anywhere when the inverse square law takes effect, they're just getting more dispersed, however, as they become more dispersed, their dispersion fields begin to overlap with nearby stars in the visual frame, which would then cause areas of overlap to brighten.  That's what your pictures don't take into account.  In your pictures, none of the 'stars' points of emission ever start to overlap, and thus total brightness only gets dimmer.  But, when you have an infinite number of point light surfaces, the inverse square law no longer holds, because then you no longer have a point surface of light, but a flat plane.  The inverse square law applies to point sources of light only.  The fact that every star is immediately adjacent to another in the visual plane means that the sky should act like a complete plane of light that completely envelops the universe.
> ...



I have no idea what you're asking.  My point is that when two stars are close by, and their light overlaps, you get a brightening effect.  This can be seen with all sorts of pairs of stars that are close, and to the human eye look like one bright star, brighter than either individual would be.  That's what your examples above aren't taking into account, since none of your 'stars' overlap.  Once you start getting overlap on a large scale, you no longer have point sources of light.  The inverse square law ONLY APPLIES FOR POINT SOURCES of light, and thus, if any of the stars in the universe are close enough in the visual 2-D plane to overlap, you can no longer use your method of reasoning.


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## fjrabon (Nov 12, 2012)

look at the following picture:

bokeh-photography-9.jpg

notice how the areas where the bokeh overlaps are brighter?  That's the piece of this puzzle that you're missing.


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## Buckster (Nov 12, 2012)

As previously mentioned, the fact that we don't live in a static universe is the biggest factor/key to the answer.

Stars are born and die at different intervals and at different distances from Earth, requiring different amount of time for the photons to reach Earth. In other words, they turn on and turn off, so there's not a steady stream of photons from any part of the sky, let alone from all parts of the sky all at once and forever.

Also, as the universe expands, many stars (and more as the universe expands) are beyond the event horizon, so they will never be seen from Earth because they (the ones beyond the event horizon) are, in fact, moving away from Earth at faster than the speed of light (relatively), and as the expansion of the universe accelerates, that is more of a factor every day.

In addition, not all of 'empty' space is empty to allow the photons to make it to Earth unimpeded.  There is a lot of dark matter and dust out there that blocks a lot of photons along the way.  Photons zipping too near a black hole get sucked in and never make it to us either, and it turns out there are a lot more black holes out there than first thought as well.

Because of those factors, every possible part of the night sky is not populated with an observable star from our point of view and, in fact, most of it isn't.

Eventually, because of the expansion of the universe, especially because that expansion is accelerating, an observer anywhere in it will see no stars at all, because they will ALL be beyond the event horizon, no matter where in the universe the observer is.

Lawrence Krauss has a very interesting lecture that dives into this as a part of it here:






Jump to about the 49 minute mark of the video for the punchline, but I DO recommend watching the whole thing to best understand how he gets to that point.


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## amolitor (Nov 12, 2012)

There's no problem at all having an infinite universe with an infinite number of stars scattered around randomly in it, and NONETHELESS having whatever fraction of sight lines you like fail to terminate on the surface of a star. As always when dealing with infinities the details are quite subtle. This is loosely waved at in the "Fractal star distribution" section of the wikipedia article.

This is separate from the issues raised above, but still important.


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## tris_d (Nov 12, 2012)

fjrabon said:


> I have no idea what you're asking.



I'm asking about the basics first. -- There are two light bulbs in a dark room. Closer one (bottom-left) is 5 meters away, and further one (top-right) is 10 meters away from the camera. The exposure time and aperture size is such that when you take that photo and open it in Photoshop pixel brightness of the closer bulb is equal to 99. The question is, what would be the pixel brightness of the further light bulb?







I set it up in Photoshop for pixels of the further (top-right) bulb to have brightness 99/4 (~25). Is that correct, is that approximately how the photo would actually look like?


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## TCampbell (Nov 12, 2012)

You might have more fun posting this question on an astronomy forum.

The inverse square law (which photographers know well), says that if the amount of light emitted from a source remains the same and only the distance is changed, then the amount of light arriving at a subject will change based based on the inverse of the square of the change in distance.

In other words.... if I have a light bulb located 10' away and now I move that light bulb 14' away (it's distance has changed by 1.4x the original distance) then the amount of light hitting me will be cut in half because 1.4 squared is 2.  The inverse of 2 is 1/2.  If instead of moving the light farther away, I bring it closer (so I change it from 10' to 7' or .7x) then the amount of light will double because .7 squared is 1/2.  The inverse of 1/2 is 2.  (Yes, I did round off the math to keep it simple.)

In your example, you double the distance... and that will cut the amount of light to the inverse square of 2... or 1/4. 

Keep in mind that we can't assume all stars emit uniform brightness levels.  Only certain classes of stars can be used as "standard candles".  Those stars don't actually put out the same amount of brightness either... rather there's a correlation that lines up quite neatly on a graph when you graph the period of variability compared to the amount of light the star emits.  Which means if you know the period of variability for the cepheid you can make an accurate assumption about the amount of light being emitted -- not that all cepheids emit the same amount of light.

If your 30 "stars" or 30 light bulbs were known to be exactly the same brightness, then yes... the inverse square law would work and you could measure the distance of each bulb based on how bright that individual bulb appears to be.  This assumes the air in your "room" is clear.  

If we ignore the "infinite universe" assumption and the "steady state" assumption we should still get to apply this theory not to the whole sky... but at least to some limited areas of sky.  The center of the Milky Way galaxy is incredibly dense with stars.  This means that if we look to the center of the galaxy what we should see (based on this theory) is a large white blotch of sky.  Instead, what we really see is an awful lot of dust and we can't actually see the center of our galaxy in visible light at all.  Astronomers have to use IR to peer into the center.

The area of space in which we live has a star density of roughly 1 star for every 5 cubic light years of space.  In a globular cluster (globulars are VERY old) the density can be much much higher.  A typical globular has a star density which as about 60,000 times more dense than the area of space we live in.  So while the nearest star (Proxima Centauri) is 4.2 light years away, imagine having about 60,000 stars in the the roughly "cube" shaped area of space between our Sun and Proxima Centauri.  And yet... even if we DID live inside such a cluster, the amount of light from all those stars during the night time would only provide the amount of light comparable to a room with a few candles in it.  It wouldn't be particularly bright.

We do see "energy" everywhere... we've got the "cosmic microwave background radiation" which seems to be "everywhere".  But that's not visible light.

My other major hobby is astronomy.


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## tris_d (Nov 12, 2012)

TCampbell said:


> In your example, you double the distance... and that will cut the amount of light to the inverse square of 2... or 1/4.
> 
> If your 30 "stars" or 30 light bulbs were known to be exactly the same brightness, then yes... the inverse square law would work and you could measure the distance of each bulb based on how bright that individual bulb appears to be.  This assumes the air in your "room" is clear.



The light bulbs are the same, further one is at double the distance. And so I take it you confirm my image representing such two light bulbs is correct and the further light bulb would indeed appear dark gray. Ok? -- Now, before I get into argument about stars and the universe, I would like to clear this conclusion a bit more. Consider the photo below, those lights do not seem to shift their brightens to more darker shades with the distance like on my picture, they actually seem to keep their brightness and only shrink in size. Is this because the pixels get over exposed, and if we change exposure time we would actually see those lights do indeed become dimmer (darker shades) as my image would suggets?


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## spacefuzz (Nov 12, 2012)

Reading stuff about light cones may help you as well better understand how the photons get dispersed after they leave the star. 

Nice explanations Fjrabon.


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## christop (Nov 12, 2012)

tris_d said:


> fjrabon said:
> 
> 
> > I have no idea what you're asking.
> ...



No, that's not right. The far object appears to have one fourth of the area of the near object, so the sensor receives one fourth as much light from it than from the near object. The two objects appear to be the same brightness because the ratio of light being received by the sensor from the object to the apparent size of the object is constant regardless of distance (ignoring the normally negligible light loss due to contaminants in the air etc).

If what you are saying were true, mountains would look black far away, or blindingly bright up close. That is obviously not the case.

Besides, this part of the experiment is easy enough to test by yourself. Use fixed settings in your camera and take several shots of a constantly-lit object or light source, varying only the distance between your camera and subject. It would probably be best to move the camera rather than the subject to avoid inadvertently changing the lighting conditions.


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## fjrabon (Nov 12, 2012)

Furthermore, another error in your explanation is that you made your 'stars' both dimmer and smaller, essentially doubling your problem. The reason the inverse square law works is because of the 'smaller' effect. The light doesn't actually get dimmer itself. If you take a picture of two lights, and you cut out a piece of the picture that just covers the actual light itself, the two will appear equally bright on their surface. The inverse square law is saying that the intensity of the light from that point source that falls on a particular point in space is inversely proportional to the distance, not that the light itself seems brighter or  darker on its surface from the vantage point of a distant observer. 

Now, a star can get so far away that we have difficulty seeing it, not because its dim, but because its really small. But it is still adding some amount of light. And since the intensity of light is additive (ie if star x is 2 brightness and star y is 1 brightness, together they provide 3 light on the subject) any infinitesimally small amount if light, summed over infinity is still infinity.


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## tris_d (Nov 12, 2012)

christop said:


> No, that's not right. The far object appears to have one fourth of the area of the near object, so the sensor receives one fourth as much light from it than from the near object. The two objects appear to be the same brightness because the ratio of light being received by the sensor from the object to the apparent size of the object is constant regardless of distance (ignoring the normally negligible light loss due to contaminants in the air etc).
> 
> If what you are saying were true, mountains would look black far away,  or blindingly bright up close. That is obviously not the case.



I'm not saying anything, yet. That was a question. -- I don't think inverse square law is about apparent size, but about drop of intensity, like this:








Also, TCampbell seems to have agreed that my picture is basically correct. So what now, which is it? 

I do not want to talk about stars until we sort out the basics first.




> Besides, this part of the experiment is easy enough to test by yourself. Use fixed settings in your camera and take several shots of a constantly-lit object or light source, varying only the distance between your camera and subject. It would probably be best to move the camera rather than the subject to avoid inadvertently changing the lighting conditions.



I would, but I'm not photographer, I do not have a camera where I can set exposure time and aperture size manually. Could you perhaps snap such photo for us?


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## amolitor (Nov 12, 2012)

I think that you have the inverse square law right arithmetically, but I think you have the wrong pictures.

When the stars are twice as far away, they appear 1/4 as bright. You can represent this as a circle the SAME SIZE and 1/4 the brightness, OR as a circle of the SAME brightness with 1/4 the area (1/2 the diameter). You are shrinking the diameters of the circles, and simultaneously dimming them. This is wrong.

In reality, stars are pretty much points. The "image" of a star on any sensor is much much much much smaller than a pixel, or whatever the smallest sensor element it, so we represent it as a single pixel of suitable brightness. In reality, however, a star that is farther away appears less bright because the almost infinitesimal image circle is smaller, not because the brightness of the interior of the circle is any less (assuming that there's nothing in the way).

Olber's paradox hasn't been an issue for quite a while, so I am a little puzzled as to your interest in solving it.


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## fjrabon (Nov 12, 2012)

Yes, if your primary question is 'are my images a correct representation of what happens to stars as they get further away' the answer is no. You can make them smaller, or dimmer as a representation, but not both simultaneously.


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## tris_d (Nov 12, 2012)

fjrabon said:


> Yes, if your primary question is 'are my images a correct representation of what happens to stars as they get further away' the answer is no. You can make them smaller, or dimmer as a representation, but not both simultaneously.



I'm talking about photographing two light bulbs simultaneously, not "making" anything up. It is important the first bulb does not over expose the pixels, so that we can observe the difference in brightness compared to the further light bulb, if any. -- So you say both light bulbs would produce pixels of equal brightness, like this:







That does look more "natural", but I don't think that's how inverse square law is supposed to work. Intensity is supposed to drop with the distance, like on the picture below, and until we have an actual photograph to prove it one way or the other I'd like to wait and see what TCampbell and other people will say.


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## christop (Nov 12, 2012)

tris_d said:


> christop said:
> 
> 
> > Besides, this part of the experiment is easy enough to test by yourself. Use fixed settings in your camera and take several shots of a constantly-lit object or light source, varying only the distance between your camera and subject. It would probably be best to move the camera rather than the subject to avoid inadvertently changing the lighting conditions.
> ...



Well, in that case you can do the experiment without a camera. You can do this physically or as a thought experiment based on past experience. Look at an object (say, a ball) at 1 meter from your eye (about an arm's length away). Then throw it to 50 meters (about 164 feet) away. Does it look 2500 times less bright (or 2500 times dimmer, basically black) when it's far away? The same concept applies to stars.

I also think it's a bit... peculiar that you're on a photography forum but you're not a photographer (not that there's anything wrong with that). And while this question is vaguely related to photography, it would better suited to an astronomy forum.


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## Buckster (Nov 12, 2012)

christop said:


> tris_d said:
> 
> 
> > christop said:
> ...


Or a physics forum.


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## amolitor (Nov 12, 2012)

tris_d said:


> fjrabon said:
> 
> 
> > Yes, if your primary question is 'are my images a correct representation of what happens to stars as they get further away' the answer is no. You can make them smaller, or dimmer as a representation, but not both simultaneously.
> ...



Intensity does drop, but because the light-emitting circle is smaller not because it's dimmer. The picture here is correct.

We don't need even to look at a picture. The correct exposure for any sunlit object is (roughly) given by the sunny-16 rule. This applies to an apple six inches from the lens, as well as to the moon.

This isn't a thing we're voting on, it's physics. It doesn't care what your opinion, or what TCampbell's opinion is.


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## tris_d (Nov 12, 2012)

amolitor said:


> I think that you have the inverse square law right arithmetically, but I think you have the wrong pictures.
> 
> When the stars are twice as far away, they appear 1/4 as bright. You can represent this as a circle the SAME SIZE and 1/4 the brightness, OR as a circle of the SAME brightness with 1/4 the area (1/2 the diameter). You are shrinking the diameters of the circles, and simultaneously dimming them. This is wrong.
> 
> ...



Are you saying as long as they are bigger than one pixel they will keep the brightness and shrink in apparent size, but when they get smaller than one pixel they will start turning to darker shades with the distance?


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## amolitor (Nov 12, 2012)

christop said:


> I also think it's a bit... peculiar that you're on a photography forum but you're not a photographer (not that there's anything wrong with that). And while this question is vaguely related to photography, it would better suited to an astronomy forum.



Oh, I think the OP made it pretty clear that this has been tried out in science forums, and been told to buzz off and go learn some basic stuff.


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## amolitor (Nov 12, 2012)

tris_d said:


> Are you saying as long as they are bigger than one pixel they will keep the brightness and shrink in apparent size, but when they get smaller than one pixel they will start turning to darker shades with the distance?



Um. When you're dealing with a real sensor, that is in fact what will happen. If you were, for instance, to fly away from the sun, taking photographs of the sun at some specific exposure, the pixel values within the circle of the sun would remain more or less constant (the sun boils around a bit, there might be junk/dust/gas in the way etc, so let's not say EXACTLY constant) until the sun got smaller than the pixel size, at which point that one single pixel's value would start to drop, until it hit zero.


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## tris_d (Nov 12, 2012)

Buckster said:


> Or a physics forum.



Would you mind snapping a photo of two light bulbs where one is at double the distance than the other? Anyone? -- It is important pixels do not get overexposed, that is photo should not contain any pixel with brightness higher than 99, where 100 is maximum brightness (complete white).


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## christop (Nov 12, 2012)

Buckster said:


> Or a physics forum.



True.

Astronomy combines a few different scientific disciplines like physics and geometry. I'm kind of a physics nerd, which is probably what attracts me to astronomy and photography.



amolitor said:


> We don't need even to look at a picture. The correct exposure for any sunlit object is (roughly) given by the sunny-16 rule. This applies to an apple six inches from the lens, as well as to the moon.


That would really suck for us if we had to take subject distance into account when calculating the proper exposure. We'd have to increase the exposure for the moon (356700 km) by 57 stops compared to a sun-lit subject at 1 meter away!


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## TCampbell (Nov 12, 2012)

tris_d said:


> The light bulbs are the same, further one is at double the distance. And so I take it you confirm my image representing such two light bulbs is correct and the further light bulb would indeed appear dark gray. Ok? -- Now, before I get into argument about stars and the universe, I would like to clear this conclusion a bit more. Consider the photo below, those lights do not seem to shift their brightens to more darker shades with the distance like on my picture, they actually seem to keep their brightness and only shrink in size. Is this because the pixels get over exposed, and if we change exposure time we would actually see those lights do indeed become dimmer (darker shades) as my image would suggets?



There are more rules involved.  The nearest light does appear brighter than the next light.  The next light appears to be much smaller even though we know they're really the same size.  

Also, stars are so distant that they all resolve to a pinpoint even in the largest scopes (well.. they resolve to an "Airy disk" due to the wave nature of light.  We would have to magnify a point of light considerably to see it that way and it really only works on stars because they're the point sources of light that are so far away that they really do appear to be a "point" and not a larger surface area.)  That means that if we use actual stars instead of street lights, they'll basically appear to be the same size... but different brightnesses.  They wont appear to be both bigger AND bright as you've depicted in your diagram.   They're all far enough away that none of them appear to have a large physical diameter as you have in this photo of streetlights.  

However... if we use a light meter to measure the light, we could report the distance to each of these street lights with a fair degree of accuracy as long as we know the baseline distance to at least one light and if the lights are all equally bright.

What exactly is your question?  

Are you asking if the inverse-square law works?  Yes.  

Are you asking why Olbers' paradox breaks down?  It breaks down because it is based on several incorrect assumptions, over-simplifies rules, and then ignores a few other realities of the physical universe.


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## tris_d (Nov 12, 2012)

amolitor said:


> tris_d said:
> 
> 
> > Are you saying as long as they are bigger than one pixel they will keep the brightness and shrink in apparent size, but when they get smaller than one pixel they will start turning to darker shades with the distance?
> ...



Ok. That sounds reasonable enough, but again, that's not what this picture below would suggest, is it?


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## amolitor (Nov 12, 2012)

tris_d said:


> Ok. That sounds reasonable enough, but again, that's not what this picture below would suggest, is it?




The picture is actually pretty miserable, since it suggests a "focused" light that's NOT falling off as the inverse square. Lasers do not follow the inverse square law, and I think to a less extent spotlights do not either, and this picture looks a little spotlight-ish.

Still, the numerical values give for falloff are fine, I think.

The total amount of light does fall off as indicated. In our "flying away from the sun" scenario, when you get 8x as far from the sun as when you started, there will only be 1/64 as many pixels inside the image circle of the sun on the sensor, so there's 1/64 as much total light falling on the sensor. In fact, since we KNOW the circle of pixels is 1/8th the diameter (this is simple geometry), we then KNOW that there are only 1/64 as many pixels in it (again, simple geometry). Since we also know, from the inverse square law, that the total light is down by 1/64, we KNOW that each pixel MUST be just as bright as it was originally. Otherwise there would be missing light.


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## tris_d (Nov 12, 2012)

TCampbell said:


> tris_d said:
> 
> 
> > What exactly is your question?
> ...


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## tris_d (Nov 12, 2012)

christop said:


> Buckster said:
> 
> 
> > Or a physics forum.
> ...



I think you guys know this stuff better than people on physics forums. In any case I'd rather trust experience and actual photos than theory and bare numbers. -- Would you mind taking a photo of two light bulbs for us, where one is at double the distance than the other, please?


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## tris_d (Nov 12, 2012)

amolitor said:


> The total amount of light does fall off as indicated. In our "flying away from the sun" scenario, when you get 8x as far from the sun as when you started, there will only be 1/64 as many pixels inside the image circle of the sun on the sensor, so there's 1/64 as much total light falling on the sensor. In fact, since we KNOW the circle of pixels is 1/8th the diameter (this is simple geometry), we then KNOW that there are only 1/64 as many pixels in it (again, simple geometry). Since we also know, from the inverse square law, that the total light is down by 1/64, we KNOW that each pixel MUST be just as bright as it was originally. Otherwise there would be missing light.



This is too important to me, so I'm afraid I can not settle without seeing an actual photo. I'll take two diodes to some photographer and ask them to take a photo. Would diodes be appropriate light source for this experiment?


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## christop (Nov 12, 2012)

By "diodes" do you mean LED's? Those should be fine, as long as both LED's are the same style (LED's come in a variety of brightnesses and light coverage, as well as color) and the current through both is the same (use current-limiting resistors!). EDIT: also make sure you take a picture of both LED's at the same angle. Some LED's change in apparent brightness depending on the angle at which you view them (ie, they're usually brighter straight-on than from the side).

You can come back here to let us know that they have the same brightness in the photo.


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## pgriz (Nov 12, 2012)

Olber's paradox (see: http://en.wikipedia.org/wiki/Olbers'_paradox) was formulated before we were aware that space itself is not static and the concept of the "big bang" was not known. IF you assume that space IS static AND the universe existed for an infinite length of time, then Olber's paradox makes sense. It essentially says if space is infinite (and static), that looking at any point in the sky will allow you to see a star (however far), and therefore you should see blazing light from all directions.

However, in an expanding universe, with a definite starting point, this is not what happens. According to current cosmological theory, the light that was present at the "big bang" has been red-shifted by the universe's expansion to the microwave wavelengths. Light emitted AFTER the big bang, say by the first stars, has also been red-shifted, but not as much as the light of the big bang. However, THAT light was most probably absorbed by the interstellar gas that exists between us and the source body. As the stars get closer to us, there is a higher probability that their light will be seen, partly due to less obscuration by interstellar gas, and partly due to less space that the light photon had to traverse. Astronomers use the position of known wavelengths of light to determine the degree of red-shift that an emitting object has at cosmological distances, and the amount of optical extinction due to scatter or absorption by interstellar medium, to arrive at an estimate of the distance of the light source from us at the time that it was emitted.
&#12288;
The other side of the issue that you're dealing with is the wave/particle duality of light. As a starting point, if the intensity of light never changes, moving a light further away causes less light to be seen because the apparent size becomes smaller. The intensity per unit area is constant, but there is less and less area. Keep moving the light away, and its size diminishes, following the inverse square rule. The torrent of photons diminishes to a stream, to a trickle, and eventually, to a few per minute or even days.Which is why for very distant objects, astronomers use as big a mirror as they can, and expose for as long as possible to accumulate enough photons to make an image. 

It is interesting to note that while the absolute speed limit of the speed of light applies to particles travelling through space, the rulebook is thrown out when it comes to space itself. Apparently, space can expand at speeds much higher than the speed of light, and it continues to expand at an accelerating rate after slowing down around 6 billion years or so. The consequence of this appears to be that object at the "edge" of the visible universe will become invisible to us as the expansion of space over a long enough distance exceeds the speed of light (the ability of a photon to travers that distance). Billions of year in the future (I know, like we care...) the universe that we can see will be much less populated than what we see now, because the expansion of space will have carried those galaxies and other objects past our "horizon". The energy powering the expansion of space is known as "dark energy" (see http://en.wikipedia.org/wiki/Dark_energy) .


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## tris_d (Nov 12, 2012)

christop said:


> By "diodes" do you mean LED's? Those should be fine, as long as both LED's are the same style (LED's come in a variety of brightnesses and light coverage, as well as color) and the current through both is the same (use current-limiting resistors!). EDIT: also make sure you take a picture of both LED's at the same angle. Some LED's change in apparent brightness depending on the angle at which you view them (ie, they're usually brighter straight-on than from the side).
> 
> You can come back here to let us know that they have the same brightness in the photo.



Yes, I meant LED. Thank you. Can you think of anything better, more convenient? -- Yes, I will post the photo when I get back. I don't really care what the result will be, I think I can make my argument either way.


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## tris_d (Nov 12, 2012)

pgriz said:


> Olber's paradox (see: http://en.wikipedia.org/wiki/Olbers'_paradox) was formulated before we were aware that space itself is not static and the concept of the "big bang" was not known. IF you assume that space IS static AND the universe existed for an infinite length of time, then Olber's paradox makes sense. It essentially says if space is infinite (and static), that looking at any point in the sky will allow you to see a star (however far), and therefore you should see blazing light from all directions.



I'm surprised, but glad to see people here are in the mood to discuss more than photography. At least I will not get banned for saying stuff that is not in the text-books, I hope, like they banned me on every physics/astronomy forum. So if you don't mind let me tell you that in my theory the universe (space) existed forever and is infinite in size. Matter gets created in the centers of galaxies, so each galaxy is a little Big Bang on its own. 




> However, in an expanding universe, with a definite starting point, this is not what happens. According to current cosmological theory, the light that was present at the "big bang" has been red-shifted by the universe's expansion to the microwave wavelengths. Light emitted AFTER the big bang, say by the first stars, has also been red-shifted, but not as much as the light of the big bang. However, THAT light was most probably absorbed by the interstellar gas that exists between us and the source body. As the stars get closer to us, there is a higher probability that their light will be seen, partly due to less obscuration by interstellar gas, and partly due to less space that the light photon had to traverse. Astronomers use the position of known wavelengths of light to determine the degree of red-shift that an emitting object has at cosmological distances, and the amount of optical extinction due to scatter or absorption by interstellar medium, to arrive at an estimate of the distance of the light source from us at the time that it was emitted.



It's interesting that we can measure red shift just due to slower rate of incoming photons, that is just due to distance, even if there is no any relative velocity between an observer and the light source, or so some papers say.



> The other side of the issue that you're dealing with is the wave/particle duality of light. As a starting point, if the intensity of light never changes, moving a light further away causes less light to be seen because the apparent size becomes smaller. The intensity per unit area is constant, but there is less and less area. Keep moving the light away, and its size diminishes, following the inverse square rule. The torrent of photons diminishes to a stream, to a trickle, and eventually, to a few per minute or even days.Which is why for very distant objects, astronomers use as big a mirror as they can, and expose for as long as possible to accumulate enough photons to make an image.



I simulated positron-electron interaction and it looks just like they draw diagrams of photons in text-books. 










Photon - Wikipedia, the free encyclopedia






When positron and electron interact initially they will try to stick  together, orbit each other, but due to magnetic force acting  perpendicularly to both velocity vector and magnetic field vector they will  twist around and produce spiral trajectory, or more precisely said  their paths will describe double-helix, which is transverse wave and  *particle-wave duality in the most literal sense*. Interesting, isn't it? 

This is based on actual equations, Lorentz force  and Biot-Savart law. I did not fiddle with any parameters or invent any new equations, it just came up like that by itself. Try it in Matlab and you should get the same thing. Text-books will tell ya when positron and electron collide they annihilate and emit a photon, but I'm pretty sure they simply just combine into a photon, and that's what photon is. Does that not make more sense than some "annihilation"? And if you consider it some more you can see then that light polarization is simply geometrical plane of charge oscillation, while EM superposition principle would explain why photons do not have net electric charge despite their evident electromagnetism.




> It is interesting to note that while the absolute speed limit of the speed of light applies to particles travelling through space, the rulebook is thrown out when it comes to space itself. Apparently, space can expand at speeds much higher than the speed of light, and it continues to expand at an accelerating rate after slowing down around 6 billion years or so. The consequence of this appears to be that object at the "edge" of the visible universe will become invisible to us as the expansion of space over a long enough distance exceeds the speed of light (the ability of a photon to travers that distance). Billions of year in the future (I know, like we care...) the universe that we can see will be much less populated than what we see now, because the expansion of space will have carried those galaxies and other objects past our "horizon". The energy powering the expansion of space is known as "dark energy" (see http://en.wikipedia.org/wiki/Dark_energy) .



Speed of light in my theory is terminal velocity  of EM fields. Just like free-falling object reaches terminal  velocity due to air drag, so does the photon or any EM radiation have  its terminal velocity due to resistance of Aether. And gravity, it's due to density gradients or pressure differences of the aether. These density gradients define propagation speed of EM waves, so everything is relative to gravity and it's what defines reference frames for electromagnetic interaction, kind of like in General Relativity, only more true. Heh! 

Of course I'm crazy, but unlike other crackpots that only have lots of assumptions and abstract mathematics, I can actually simulate the things I'm talking about and those simulations resemble what we see in reality, so I guess I can't be that far away from the true mechanics of how the things work. Anyhow, I just told you guys this stuff for the purpose of entertainment, something to muse about, but I don't mean to argue any of this as we have plenty to talk about as it is, unless someone would insist, of course, then it will be my pleasure.


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## fjrabon (Nov 12, 2012)

tris_d said:


> TCampbell said:
> 
> 
> > tris_d said:
> ...


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## amolitor (Nov 12, 2012)

Sorry, tris, I didn't realize that you're a kook.

If you've got a theory about.. something or other to do with EM theory, but can't figure out how the inverse square law works, you're just a kook. Of course they booted you out of the science forums. They get kooks all the time, gumming up the works. You're no Archimedes Plutonium, but you're in the same clan, aren't ya?


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## fjrabon (Nov 12, 2012)

how did we go from a misunderstanding of the inverse square law to a theory where matter is created in the center of galaxies?


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## pgriz (Nov 12, 2012)

> in my theory the universe (space) existed forever and is infinite in size



There have been many theorists who have had these ideas, but the theories have to have some kind of predictive value which can then be tested.  If a theory cannot be tested, then its value as a means to better understanding is doubtful.  When tests have been devised, they seem to point to definite beginning that is known colloquially as the "big bang", and there are discussions of an infinite universe in the thory of multiverses, but it is difficult to formulate a test that sense a space outside of our current horizon.



> Matter gets created in the centers of galaxies, so each galaxy is a little Big Bang on its own.


  That was a key component of the steady-state universe model (see: Steady State theory - Wikipedia, the free encyclopedia) but the predictions of that model failed observational tests and alternate models were felt to be better fits for the data.



> It's interesting that we can measure red shift just due to slower rate of incoming photons, that is just due to distance, even if there is no any relative velocity between an observer and the light source, or so some papers say.


  I don't understand what "slower rate of incoming photons" actually means.  Red shifts have been linked to the relative motions of emitters from the observers, the stretching out of space due to expansion, and I think gravity effects such as at the black hole horizon, although the latter is still speculative.  It has been proven time and again that the speed of a photon through empty space is always constant, and the relative motions of emitter and receiver influence the energy (frequency) of the received photon but not the speed.  There was a discussion that reddening could be due to "tired light" (see:Tired light - Wikipedia, the free encyclopedia), but this hypothesus has been disproved.



> Speed of light in my theory is terminal velocity  of EM fields. Just like free-falling object reaches terminal  velocity due to air drag, so does the photon or any EM radiation have  its terminal velocity due to resistance of Aether. And gravity, it's due to density gradients or pressure differences of the aether. These density gradients define propagation speed of EM waves, so everything is relative to gravity and it's what defines reference frames for electromagnetic interaction, kind of like in General Relativity, only more true.


  Prior hypothesis of "ether" as a medium for transmitting light waves were disproved by the Michaelson-Morley experiments.  There are a number of people who still believe that "Aether" is a useful concept, but so far we have not seem much in terms of testable predictions.  And until there is a set of predictions that can be tested and verified, the theory is just that - a theory.  The linkage of gravity and quantum physics remains an unsolved problem, although the recent probable observation of the Higgs boson (the theorized particle that carries the gravitational force) could start to unravel that problem.

I'm sorry, Tris_D, I cannot intelligently debate the merits of your theories as my math skills are not adequate to the task, nor am I current in terms of the discussions in this field.  I do enjoy reading about the various directions being pursued in cosmology, observational astronomy and particle physics, but that is pretty much at the level of semi-intelligent observer in the peanut gallery.  

And as for your earlier question, if you do the tests, you'll find that the picture on the right is more correct.


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## tris_d (Nov 12, 2012)

amolitor said:


> Sorry, tris, I didn't realize that you're a kook.
> 
> If you've got a theory about.. something or other to do with EM theory, but can't figure out how the inverse square law works, you're just a kook. Of course they booted you out of the science forums. They get kooks all the time, gumming up the works. You're no Archimedes Plutonium, but you're in the same clan, aren't ya?



Don't hate me just because I'm crazy. I could be arrogant and assume that I know, repeat like a parrot things other people came up with as if it was my own understanding, but instead I prefer to work things out myself and I am not ashamed about the things that I do not know. That's why I'm here, I just hope that you know, so can you point some reference that confirms what you said about inverse square law? Where is it I could have learned about it? -- By the way, I have a storm going on here, ice-cubes falling from the sky, I will not be going to see a photographer today. Why don't you take a minute and snap that photo of two bulbs for us, please?




			
				fjrabon said:
			
		

> how did we go from a misunderstanding of the inverse square law to a theory where matter is created in the center of galaxies?



I was bored waiting to see if the storm here will stop. Just ignore it if you don't care. But let me say positron-electron stuff is serious thing, everything just fits. And perhaps I'm lousy physicist, terrible astronomer and stupid photographer, but when it comes to programming I know my stuff. You will not see anywhere else in the world n-body simulation of EM fields. I challenge anyone to try and find anything like that in the whole world. And since you guys seem to be into astronomy and physic I thought I would share some of my craziness with you, it was kind of way to introduce myself, so you know I'm crazy. That's my gift, my curse. Who am I? I'm your friendly neighborhood Driver-Man!


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## tris_d (Nov 12, 2012)

pgriz said:


> There have been many theorists who have had these ideas, but the theories have to have some kind of predictive value which can then be tested.  If a theory cannot be tested, then its value as a means to better understanding is doubtful.  When tests have been devised, they seem to point to definite beginning that is known colloquially as the "big bang", and there are discussions of an infinite universe in the thory of multiverses, but it is difficult to formulate a test that sense a space outside of our current horizon.



I'm not sure if it is appropriate for me to talk about it here. But while we are waiting for the photo to continue original discussion and if no one has any objections then great. So let me ask this straight, is it ok if we go on and blabber about this stuff unrelated to original topic?


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## christop (Nov 12, 2012)

Ok, here's a lightbulb at about 1 foot and about 2 feet, both taken at 1/4000s f/8 ISO 100 (the only variable is the camera-subject distance).

The filament in the center is slightly overexposed, but you can take a sample from any of the rest of the bulb.

If you sample them properly you'll find the brightnesses to be close enough to each other. Any variations will be due to noise, inexact shutter speed, power fluctuations, etc (but still within 1% or so).


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## tris_d (Nov 12, 2012)

Ok, since I had no way to control exposure time and aperture size I had to come up with some way to not over-expose. What you are looking at here is my LCD monitor turned off and reflection of a cigarette lighter. On the left photo the lighter is about 20 cm away, and on the right one about 40cm away from the screen. After I burned my fingers I converted the image to gray-scale in Photoshop and picked the brightest pixel in the middle. Left one has brightness 83 and the right one 57. I'm now 75% confident if this experiment is performed accurately we would get the result I was suggesting in my opening post.


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## tris_d (Nov 12, 2012)

christop said:


> Ok, here's a lightbulb at about 1 foot and about 2 feet, both taken at 1/4000s f/8 ISO 100 (the only variable is the camera-subject distance).
> View attachment 25553View attachment 25552
> The filament in the center is slightly overexposed, but you can take a sample from any of the rest of the bulb.
> 
> If you sample them properly you'll find the brightnesses to be close enough to each other. Any variations will be due to noise, inexact shutter speed, power fluctuations, etc (but still within 1% or so).



Awww. You'd have me convinced if I didn't do my experiment in the mean time. I surely appreciate that photo, thank you, but I'm not sure what to think now. Let me examine your photo more closely and think about it some more.


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## jake337 (Nov 13, 2012)

It's dark here in Minnesota right now.


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## enzodm (Nov 13, 2012)

tris_d said:


> christop said:
> 
> 
> > Ok, here's a lightbulb at about 1 foot and about 2 feet, both taken at 1/4000s f/8 ISO 100 (the only variable is the camera-subject distance).
> ...



in the scientific method, christop contribution is called "falsification". You have a theory, someone does an empirical experiment and demonstrates that is not true. It was nice, but did not survive. This is also how other theories grew and died, letting survive one that until now has been able to explain phenomena and produce real devices that function.
Anyway, ask you old uncle how he used a lightmeter to calculate exposure for his photographs  .


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## amolitor (Nov 13, 2012)

tris_d said:


> Don't hate me just because I'm crazy. !



i don't hate you at all! I'm just not going to spend any more time teaching. I've given you a complete and accurate thought experiment which shows clearly that your picture is wrong, and the other one is right. You are not interested in learning, you are interested, really, in expounding your incoherent mass of words which you call your theory.

there's nothing really wrong with that, it does't hurt anyone except, perhaps, you. This probably isn't the right forum for it, and to be honest I don't know if there is a forum for it. I wish you well.


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## Dao (Nov 13, 2012)

I believe the expand universe from the big band theory can explain the dark sky.

- Light were able to move freely after the big bang at one point.
- Light were able to move freely was part of the result of the big bang. (Expanding universe)
- At this point, those light that is far far away from earth are not arrive to earth as visible light.  Due to the expanding universe, the wavelength of the light are stretch.  We cannot see them with our eyes anymore.
- Instead of light, we see a lot of Cosmic Background Radiation.  So I think if you treat the Cosmic Background Radiation as visible light, then the sky is bright.


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## tris_d (Nov 13, 2012)

amolitor said:


> tris_d said:
> 
> 
> > Don't hate me just because I'm crazy. !
> ...



Aha. I note you failed to provide any reference to support your assumptions. And while those insults are cute, the topic here is not about me, but inverse square law.

Inverse-square law - Wikipedia, the free encyclopedia












Cosmology | Stephen's Website






Cosmic distance ladder - Wikipedia, the free encyclopedia
_- By comparing the known luminosity of the latter to its observed brightness, the distance to the object can be computed using the inverse square law._

Apparent magnitude - Wikipedia, the free encyclopedia
_- Note that brightness varies with distance; an extremely bright object  may appear quite dim, if it is far away. Brightness varies inversely with the square of the distance._


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## tris_d (Nov 13, 2012)

enzodm said:


> in the scientific method, christop contribution is called "falsification". You have a theory, someone does an empirical experiment and demonstrates that is not true. It was nice, but did not survive. This is also how other theories grew and died, letting survive one that until now has been able to explain phenomena and produce real devices that function.
> Anyway, ask you old uncle how he used a lightmeter to calculate exposure for his photographs  .



I'm afraid those photos were overexposed, and I said several times it is very important they must not be, so I'm afraid I can not accept that. Instead of me asking my uncle, why can you not simply point some reference that confirms what you guys are saying? Why is it every single article on the internet only confirms what I said? How is it easier to write all these posts over two days and four pages than simply take a camera and snap a few photos?


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## amolitor (Nov 13, 2012)

Ok, what the heck, one more try!

----

Let's set the camera up for a good exposure of the sun, at such a distance from the sun that the camera will render the sun as a circle on the sensor 1000 pixels wide. Let us suppose that the sensor reads the pixels inside that circle at a value of something intermediate, say 2048 on a 12 bit sensor (an exactly middle value). We have about 78,500 pixels in the on-sensor image, each giving a reading of 2048 out of a range of values from 0 to 4095.

Now leave the camera settings exactly alone. Move away from the sun, double your distance from the sun.

How large is the image circle on the sensor? 500 pixels, one half of the original value.
How many pixels are included in this circle? 19,600 more or less, one quarter the original value.

You claim that the values read out by the pixels are much less than 2048 (less than in the first case), I claim that the are 2048 (same as the first case).

Since the intensity of the sun seen from the new position is 1/4 as much as it was originally, and there are 1/4 as many pixels available, how can the value at each pixel be less? Your model has missing light? Where is it?

----

And now a prediction. Tris will respond with something that has the general shape and tenor of a rebuttal, but which nobody except Tris can quite make sense of. Tris will dismiss my discussion above, and go back to demanding that someone take a picture.


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## christop (Nov 13, 2012)

I just opened both of my lightbulb pictures in Gimp. After desaturating both images (using luminosity) I used the color picker to find the brightness of each image.

Averaged sample near the filament (4px radius):
far: 57% (pixel value 145)
near: 57% (pixel value 145)

Both bulbs are the same brightness.

Averaged sample for almost the whole bulb (300px radius):
far: 8% (pixel value 20)
near: 37% (pixel value 94)

The far bulb has about 21% of the total light as the near bulb. The far bulb was in reality slightly more than twice as far from the camera than the near bulb (roughly 250% as far), so it should have only about 16% of the total light as the near bulb, but note that these pixel values have unknown in-camera curves applied, which scales pixel values non-linearly. If I cared more about the actual values I would have captured the pictures in RAW format and processed them with linear response curves. Regardless, these results agree with what I've been saying all this time.

EDIT: you (tris_d) said my pictures were overexposed. Only the filaments were (barely) overexposed. I should have stopped down some more to ensure that they were not overexposed. Either way, I sampled pixels near the filament which clearly were not overexposed (yes, my "whole bulb" average values are slightly affected by the overexposure, but the conclusion is the same).


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## tris_d (Nov 13, 2012)

fjrabon said:


> The problem with your logic is that when you have infinite light sources, you will still have an infinite steam of a very small number of photons hitting the sensor.
> 
> the problem is that if ANY number of photons are reaching the viewer  from the source, the fact that there are infinite source stars would  equal pure brightness.



If every line of sight ends at some star, well that's where that line of  sight ENDS, and if every line of sight ends at some point then there is  nothing infinite about it.




> But, when you have an infinite number of point light surfaces, the  inverse square law no longer holds, because then you no longer have a  point surface of light, but a flat plane.
> 
> The fact that every star is  immediately adjacent to another in the visual plane means that the sky  should act like a complete plane of light that completely envelops the  universe.



There is no plane, stars are not adjacent. Distribution of stars is 3-dimensional, you are forgetting about the "depth". They might appear to be one next to another, but when you see two stars are close you can be sure their distance from us is different.


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## tris_d (Nov 13, 2012)

christop said:


> I just opened both of my lightbulb pictures in Gimp. After desaturating both images (using luminosity) I used the color picker to find the brightness of each image.
> 
> Averaged sample near the filament (4px radius):
> far: 57% (pixel value 145)
> ...



How do you explain my experiment then? You can confirm that in few seconds. How do you explain all the articles on the internet are saying intensity is supposed to drop with the square of the distance? No one is mentioning any apparent size when talking about inverse square law, everyone just says intensity falls off. -- Look, I really do not know, I just hate to assume. I think there is something fishy about this whole thing because I searched internet for days and I could not find any conclusive answer to my satisfaction. Theory says one thing but photos show something different. So please take some more faint source of light, like a candle or LED, and take two more photos, ok? Please?


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## tris_d (Nov 13, 2012)

amolitor said:


> Let's set the camera...



Then take a camera and snap a photo, I don't care about assumptions.

Do you have any reference that can confirm any of what you are saying?


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## KmH (Nov 13, 2012)

The horse is dead.
Continue on a physics forum.


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