Results 1 to 10 of 10

Math Help - Olbers' paradox: why is the night sky dark?

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    nz
    Posts
    5

    Olbers' paradox: why is the night sky dark?

    I believe to have found solution for Olbers' paradox. Treatment originally used to discard inverse square law as the solution was not set up correctly, and if we include sensor surface area in the treatment and model light as photons the result describes what we actually see.

    I would like to confirm this, but people on Astronomy/Cosmology forums are not receptive to even discuss it as it seems that would somehow contradict what is written in their text-books, which is what brings me here. Prove me right, prove me wrong, I don't care, just wanna know the truth.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    660
    Thanks
    133

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

    O.K. so what are you giving us to work with ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2012
    From
    AZ
    Posts
    616
    Thanks
    97

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

    How does the surface area of the sensor affect how bright the night sky is, at that sensor? (I'm not an astronomy major or anything, but I know what the paradox is).
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,964
    Thanks
    350
    Awards
    1

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

    I suspect this is "spam" of a sort. A few years ago I was looking for chat sites on special relativity. I answered a post that caused me more than a month of wasted time explaining to him that a theory did not have to be "simple" in order to be correct. That and other numerous reasons why his logic was faulty. (I'm a bit of a masochist when it comes to taking on a project. I should have ditched him almost immediately.)

    So I challenge you, abaraba, to explain yourself fully. Obler's Paradox (note where the apostrophe is!) was solved at the beginning of the last century or earlier, either by the Standard Model or the Steady State Theory of the Universe (which gives a similar result). Let's see what new ideas you have.

    By the way, please post in the correct forum. This really belongs in the Advanced Math Topics, being a Physics question.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2012
    From
    nz
    Posts
    5

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

    Quote Originally Posted by BobP View Post
    O.K. so what are you giving us to work with ?
    Great. Thank you for your time. -- So, some few hundred years ago some famous names expected inverse square law would explain why the night sky is dark despite the fact there is some star in whichever direction we look at, but when they found inverse square law is not the answer, that's when they started calling it a paradox. And since then it's like no one bothered to reconsider the problem at its starting assumptions, but everyone just concentrated to find some new solutions and there is quite a few of those today. Main one is that universe is expanding, which somehow is also supposed to explain the paradox, but I disagree. Anyway, here is how they originally came up with their conclusion in regards to inverse square law:


    Olbers' paradox - Wikipedia, the free encyclopedia
    - The paradox is that a static, infinitely old universe with an infinite number of stars distributed in an infinitely large space would be bright rather than dark. To show this, we divide the universe into a series of concentric shells, 1 light year thick (say). Thus, a certain number of stars will be in the shell 1,000,000,000 to 1,000,000,001 light years away, say. If the universe ishomogeneous at a large scale, then there would be four times as many stars in a second shell between 2,000,000,000 to 2,000,000,001 light years away. However, the second shell is twice as far away, so each star in it would appear four times dimmer than the first shell. Thus the total light received from the second shell is the same as the total light received from the first shell. Thus each shell of a given thickness will produce the same net amount of light regardless of how far away it is. That is, the light of each shell adds to the total amount. Thus the more shells, the more light. And with infinitely many shells there would be a bright night sky.


    In math language it goes like this (Olbers' Paradox):



    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!



    --//--

    What I'm saying is that they are completely ignoring sensor surface area, that is some 2-dimensional image that is 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 photo-plate unless we wait long enough, and just looking at this fact makes it clear to me that inverse square law explains it all, but people in Astronomy/Cosmology field prefer expanding universe solution and are very defensive about it. I don't even think "my" solution would contradict expanding universe theory so I have no idea why are they so much opposed to even consider it.


    Let me explain with an example. Two stars at distance r would impact photo-plate with intensity I, and four stars at double the distance will also impact photo-plate 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 a difference between two bright spots 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.

    Hope that makes sense. If not, let me know and I'll rephrase.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2012
    From
    nz
    Posts
    5

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

    Quote Originally Posted by topsquark View Post
    I suspect this is "spam" of a sort. A few years ago I was looking for chat sites on special relativity. I answered a post that caused me more than a month of wasted time explaining to him that a theory did not have to be "simple" in order to be correct. That and other numerous reasons why his logic was faulty. (I'm a bit of a masochist when it comes to taking on a project. I should have ditched him almost immediately.)

    So I challenge you, abaraba, to explain yourself fully. Obler's Paradox (note where the apostrophe is!) was solved at the beginning of the last century or earlier, either by the Standard Model or the Steady State Theory of the Universe (which gives a similar result). Let's see what new ideas you have.

    By the way, please post in the correct forum. This really belongs in the Advanced Math Topics, being a Physics question.

    -Dan
    Please move it wherever you think is more appropriate. -- It's not spam. I'm either right or wrong, and all I want is to confirm for certain, whichever is the case.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Apr 2012
    From
    Erewhon
    Posts
    188
    Thanks
    126

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

    Quote Originally Posted by abaraba View Post
    What I'm saying is that they are completely ignoring sensor surface area, that is some 2-dimensional image that is 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.
    Surface area of sensor is not ignored, Google "Light Intensity", you should find units something like Watts per steradian per sq m. That last per sq m is where the detector size would be involved if it were relevant.

    That a simplified explanation is often given for the benefit of the lay person does not mean that the knowledgeable use that particular model.

    Olbers' paradox may be summarised as: Some assumptions about the nature of the universe => a conclusion that is false.

    As the conclusion is false one or more of the assumptions must be false. A couple we know to be false are: The Universe is not infinitely old, nor is the observable Universe infinite in extent. Without knowing the detail of how expansion effects the integrated light intensity at the eye or how the space density of stars/galaxies varies with distance/look-back time ... , these are sufficient to remove the paradox.

    .
    Last edited by zzephod; November 8th 2012 at 10:07 PM.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Nov 2012
    From
    nz
    Posts
    5

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

    Quote Originally Posted by zzephod View Post
    Surface area of sensor is not ignored, Google "Light Intensity", you should find units something like Watts per steradian per sq m. That last per sq m is where the detector size would be involved if it were relevant.
    Radiance and luminance is not the same thing as brightness. And anyway watts per square meter does not differentiate between two stars of intensity I/2 and four stars with intensity I/4. The important thing about sensor surface area is resolution. Without resolution all you get is sum of intensities.


    Olbers' paradox may be summarised as: Some assumptions about the nature of the universe => a conclusion that is false.
    Olbers' paradox is a question: why is the night sky dark?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Apr 2012
    From
    Erewhon
    Posts
    188
    Thanks
    126

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

    Quote Originally Posted by abaraba View Post
    Radiance and luminance is not the same thing as brightness. And anyway watts per square meter does not differentiate between two stars of intensity I/2 and four stars with intensity I/4. The important thing about sensor surface area is resolution. Without resolution all you get is sum of intensities.
    Astrophysicists and Astronomers have a very good grasp of the performance of sensors. I doubt there is anything that you can teach us. (Also in the standard argument that goes with Olbers' paradox you cannot resolve the spaces between the stars with a finite aperture.)

    Olbers' paradox is a question: why is the night sky dark?
    A question is not a paradox, what is paradoxical is the standard proposed argument that the night sky cannot be dark. And that paradox is overturned by the observation that because the conclusion is false one or more of the premises are false.

    The plain question "Why is the night sky dark?" has the answer: "It is not dark, but it is darker than the photosphere of the Sun". Explaining why it has the brightness it does have is a question for Astrophysics, which it answers in a reasonably satisfactory manner.
    Last edited by zzephod; November 9th 2012 at 02:48 AM.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Nov 2012
    From
    nz
    Posts
    5

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

    Quote Originally Posted by zzephod View Post
    Astrophysicists and Astronomers have a very good grasp of the performance of sensors. I doubt there is anything that you can teach us.
    Your doubt in me and your blind belief in someone else is irrelevant to whether what I said is true or not.


    (Also in the standard argument that goes with Olbers' paradox you cannot resolve the spaces between the stars with a finite aperture.)
    What are you trying to say? What are you referring to?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Calculate the magnitude of dark energy?
    Posted in the Math Challenge Problems Forum
    Replies: 0
    Last Post: March 3rd 2010, 05:36 PM
  2. Help me on these all night stumpers
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: August 28th 2009, 02:34 PM
  3. having a slow night!
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 7th 2009, 01:54 PM
  4. Two More Questions For The Night.
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 12th 2009, 12:44 AM
  5. last thread for the night
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 8th 2006, 04:29 PM

Search Tags


/mathhelpforum @mathhelpforum