Notices
Results 1 to 5 of 5

Thread: Inverse square law resolves Olbers' paradox

  1. #1 Inverse square law resolves Olbers' paradox 
    New Member
    Join Date
    Nov 2012
    Posts
    3
    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.


    Reply With Quote  
     

  2.  
     

  3. #2  
    Moderator Moderator Markus Hanke's Avatar
    Join Date
    Nov 2011
    Location
    Ireland
    Posts
    7,302
    Quote Originally Posted by tris_d View Post
    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.
    What treatment would that be ? Do you have a reference ?


    Reply With Quote  
     

  4. #3  
    New Member
    Join Date
    Nov 2012
    Posts
    3
    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by tris_d View Post
    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.
    What treatment would that be ? Do you have a reference ?
    Sure. I'd prefer to give you some more "official" reference, like Wikipedia, but they don't even mention it. There are papers about it of course, but overall I found the subject is quite overlooked, which is what inspired my curiosity in the first place. It seems as if conclusion was made few hundred years ago by some famous names and since then it's like no one bothered to seriously reconsider it. In any case this how it goes:

    http://www.asterism.org/tutorials/tut09-1.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!
    Reply With Quote  
     

  5. #4  
    New Member
    Join Date
    Nov 2012
    Posts
    3
    Pardon me, Wikipedia actually does mention it. It seems that's what this paradox is all about. I suppose it was natural to expect inverse square law is the solution, but when they found that it is not, that's when they started calling it a paradox.

    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.
    Reply With Quote  
     

  6. #5  
    Moderator Moderator Markus Hanke's Avatar
    Join Date
    Nov 2011
    Location
    Ireland
    Posts
    7,302
    Well, these classical treatments are all based on the assumption that the universe is static - we know now that it isn't.
    Reply With Quote  
     

Similar Threads

  1. Olbers paradox, a possible solution.
    By in forum Astronomy & Cosmology
    Replies: 33
    Last Post: April 30th, 2013, 04:32 PM
  2. The lever paradox and the elevator paradox
    By Xinwei Huang in forum Personal Theories & Alternative Ideas
    Replies: 13
    Last Post: April 27th, 2010, 12:30 AM
  3. Replies: 8
    Last Post: December 5th, 2009, 10:24 AM
  4. Olbers paradox
    By thyristor in forum Physics
    Replies: 3
    Last Post: February 14th, 2008, 01:01 PM
Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •