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Inverse square law resolves Olbers' paradox 
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#1
Nov612, 06:54 PM

P: 162

Treatment originally used to discard inverse square law as solution to Olbers' paradox was not set up correctly. If we include sensor (camera) in the treatment and model light as photons the result describes what we actually see.



#2
Nov812, 08:16 PM

P: 39

Not really.



#3
Nov912, 04:13 AM

P: 162

Ah well, I guess this is the point where I get banned. http://www.asterism.org/tutorials/tut091.htm Since the area of a sphere of radius r is A = 4p r2 (1) the volume of such a shell is V = 4p r2t (2) If the density of each of the luminous objects within the shell is "n", then the total number of these objects in the shell must be N = 4p r2nt (3) Now let us ask just what amount of energy such a shell will send to the Earth. Since the shell's thickness is small, it is reasonable to assume that the entire shell is at a distance "r" from the earth. The energy, E, emitted by any source at distance r, produces an intensity, "I", over a given area, A, on the Earth of (inverse square law) I = E/4p r2 (4) The total intensity received on the Earth from all the sources in the shell r units away must then be the intensity produced by each source times the total number of sources or T = IN (5) Substituting the value of N previously calculated into the above, we find that T = tnE (6) We notice at once that the total energy received from any chosen shell does not depend upon its distance from us (no r in the above equation). The total energy received from all the shells is the sum of the contributions of each shell. If there are M shells this total is S = tnEM (7) But there is an infinite number of shells and so the total intensity on the earth must be infinite. Therefore, the nighttime sky should be blindingly bright! // They completely ignored sensor surface area, that is some 2dimensional 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 is bright. They also ignored exposure time. The rate of incoming photons is proportional to distance, due to inverse square law, which is known and accepted fact, that's why very distant stars do not produce any dots on a photoplate unless we wait long enough. Just by looking at this fact makes it clear to me inverse square law explains it all. Let me explain with an example. Two stars at distance r would impact photoplate with intensity I, and four stars at double the distance will also impact photoplate with the same intensity I. That's what they are saying, and that's true. However, what they are not considering is that two closer stars will produce two dots each with brightens I/2, but four further stars will produce four dots each with brightness I/4. There is difference between two bright dots and four less bright dots of course, 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 of course 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. 


#4
Nov912, 06:57 AM

P: 740

Inverse square law resolves Olbers' paradox



#5
Nov912, 08:14 AM

P: 162




#6
Nov912, 11:29 AM

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The Inverse Square Law does not resolve Olbers' Paradox. Instead it is the state of the universe that does so. Consider the following. IF the universe was not expanding, and IF it was infinitely old we would be swamped with visible radiation, since an infinite number of stars lie at every line drawn away from the Earth, leading to an infinite number of photons coming in. However this isn't the case because both of those things are not true. It is the combination of an expanding universe that has a finite age that resolves the paradox.
But even if the inverse square law did happen to "solve" the paradox, it still wouldn't mean anything. Olbers' Paradox is about an eternal static universe. In such a universe the known laws of stellar evolution wouldn't apply, as there would need to be some sort of "recycling machine" to produce new hydrogen from old, heavier matter that stars produce. Otherwise you wouldn't get an infinite number of stars for an infinite amount of time. The fact is that a great many things resolve Olbers' Paradox, from the expansion of the universe, to the basics of nucleosynthesis and more. 


#7
Nov912, 12:03 PM

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#8
Nov912, 12:44 PM

P: 162

 You seem to ignore the key aspect, which is that the further away a star is, the faster it is moving away from us. This motion dims its light in two ways: it shifts the photons to lower frequencies where they have less energy, and it leads to longer gaps between the arrival times of successive photons than there were between the emission of the photons. So the brightness of a star decreases with distance faster than 1/r^2, while the # of stars per unit angle of the beam increases only as r^2. To which I replied:  "Thank you for your time. I don't see what you said contradicts what I said, rather just adds up to the effect of making light even dimmer than what would manifest only due to inverse square law. Can you tell me are we actually able to measure any difference in the arrival time of successive photons of certain galaxies if we compare measurements of today with measurements from say several years ago?" 


#9
Nov912, 01:10 PM

P: 162

Good point. http://en.wikipedia.org/wiki/Brightness  "Brightness" was formerly used as a synonym for the photometric term luminance and (incorrectly) for the radiometric term radiance. As defined by the US Federal Glossary of Telecommunication Terms (FS1037C), "brightness" should now be used only for nonquantitative references to physiological sensations and perceptions of light http://www.its.bldrdoc.gov/fs1037/dir005/_0719.htm  brightness: An attribute of visual perception in which a source appears to emit a given amount of light. Note 1: "Brightness" should be used only for nonquantitative references to physiological sensations and perceptions of light. Note 2: "Brightness" was formerly used as a synonym for the photometric term "luminance" and (incorrectly) for the radiometric term "radiance." http://en.wikipedia.org/wiki/Apparent_magnitude  The apparent magnitude (m) of a celestial body is a measure of its brightness as seen by an observer on Earth I'm not sure what more math there is. It's pretty simple. The original treatment does not take image resolution into account, so it can not differentiate between two stars with brightness I/2 and four starts with brightness I/4, thus it practically sums up all the intensity from any shell into an image with only one pixel resolution, ignoring all the spatial separation, and therefore the result is not complete. They get correct intensity, but that's not what we see or what camera captures, what we see is 2dimensional image where each star has its own spatial location, so we need to divide this intensity across all the "dots" to get result indicating what we actually see. 


#10
Nov912, 01:35 PM

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In astrophysics and physical cosmology, Olbers' paradox, named after the German astronomer Heinrich Wilhelm Olbers and also called the "dark night sky paradox", is the argument that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. If you are not specifically talking about Olbers' Paradox in an infinite and eternal universe, then simply ask why the night sky is dark. 


#11
Nov912, 02:45 PM

P: 162

I think it's when they found inverse square law does not answer the question when they started calling it a paradox, and since then it seem like inverse square law was completely ignored and not considered to be even a part of the solution due to conclusions of the original treatment, which I think is a mistake and should be reconsidered. 


#12
Nov912, 03:05 PM

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#13
Nov912, 03:54 PM

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Actually, the night sky should be about as bright as the surface of an average star under Olber's reasoning  since every possible line of sight falls upon the disc of a star. We are forced to conclude one or more of Olber's premises  the universe is static, spatially and temporally infinite, and infinitely populated with stars  are invalid. Modern observational evidence strongly suggest all these premises are invalid.



#14
Nov912, 04:49 PM

P: 173

You keep mentioning Olbers paradox, but you explicitly say your not arguing under the premise that the universe is eternal and static. I think what your getting at is that even IF the premises of Olbers paradox  static and eternal universe  held, the night sky would be black because the inverse square law. If thats the case then picture this. Imagine concentric shells around an observer, but not filled with stars, instead the surface area of the shell is covered with 50,000K plasma. At distance D from the observer, observer gets a total amount of energy S. At distance 2D you get still get sunlight S, even though the source is twice as far the surface area shining light at you has also doubled, so you get the same. Now picture half of the shell is at 2D and the other half at D. Still equals S light. Now imagine the shell fractured into billions of points each at different distances, but still forming a continuous shell from the point of the observer. You still get S, and this is why Olbers paradox is a paradox. Also this is independent of what size of sensor your using. So long as your pointing the sensor up at the sphere, it will receive S/(focal arc of the sensor) amount of energy. If your not arguing within the hypothetical situation of of Olber's premises, then your just saying that the night sky is black because really distant stars aren't as bright as closer stars. Which isn't much of a statement at all, akin to saying you've discovered circles are round. 


#15
Nov912, 06:27 PM

P: 162

http://en.wikipedia.org/wiki/Apparent_magnitude  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. You gonna get me banned. I don't want to argue the universe is static or infinite, I just want to say the original treatment is incomplete, and even with the result I'm suggesting it does not lead to either conclusion. 


#16
Nov912, 07:32 PM

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#17
Nov912, 08:08 PM

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#18
Nov1012, 01:33 AM

P: 39

Tris_d's original post includes someone else's mathematical breakdown of the Olber paradox, including:
I gave tris_d a subtle hint about the dangers of dividing infinity by infinity and the wisdom of using limits instead. But tris_d then wrote While perhaps not a classic troll, tris_d shows the classic signs of being a crank or crackpot. Tris_d's flawed mental picture reminds him or herself of Einstein's thought experiments and is completely unaware of the sea of math that Einstein backed his ideas up with. This person has already invested a great amount of time trying to promote this flawed notion and isn't seeing the light of day no matter how many different ways the paradox is explained. This individual will probably go to the grave thinking he or she was correct, and everybody else is wrong. It's not worth wasting any more time in this thread. 


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