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Thread: Question on GR : Bending of light - Einstein's calculations

  1. #1 Question on GR : Bending of light - Einstein's calculations 
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    *In this link you find the pdf document by Einstein : Chapter 4 > pages 8-9 :

    http://www.relativitycalculator.com/pdfs/On_the_influence_of_Gravitation_on_the_Propagation _of_Light_English.pdf

    I
    mage from this :




    *He refers to Huygens Principle : Link :

    Huygens
    Image from this :



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    I have several questions, trying to understand this, but also trying to find out how this speed of light is influencing the bending angle.

    -Does fig 6 above refer to the Huygens image below it ?

    -In fig 6 : where do i place the massive body around which deflection takes place ?
    In this image to wich direction deflects the light ? It seems contrary to Huygens image.

    -"The principle of constant velocity of light holds good..." above in line 4 and further.
    What is meant here, given the changing propagation value of c ?

    -line 8 : "The velocity of light in the graviational field is a function of the place..."

    >These places in the fig 6 are then P1 and P2 with each a different gravitational potential ?
    Which ione with highest and wich one with lowest ?


    Can anyone give the total line of reasoning using the Huygens principle and the radii c1dt and c2dt etc ?


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    Quote Originally Posted by Noa Drake View Post
    I have several questions, trying to understand this, but also trying to find out how this speed of light is influencing the bending angle.

    -Does fig 6 above refer to the Huygens image below it ?

    -In fig 6 : where do i place the massive body around which deflection takes place ?
    In this image to wich direction deflects the light ? It seems contrary to Huygens image.

    -"The principle of constant velocity of light holds good..." above in line 4 and further.
    What is meant here, given the changing propagation value of c ?

    -line 8 : "The velocity of light in the graviational field is a function of the place..."

    >These places in the fig 6 are then P1 and P2 with each a different gravitational potential ?
    Which ione with highest and wich one with lowest ?


    Can anyone give the total line of reasoning using the Huygens principle and the radii c1dt and c2dt etc ?
    Unfortunately, the 1911 paper by Einstein is incorrect, his answer is only 50% of the correct value. This is due to the fact that by 1911 there was no general theory of gravitation (no GR), so Einstein had to wait until 1916 to produce the correct answer. The paper from 1911 you are examining has only historical interest.
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    I read indeed that the value on the angle is times 4 instead of times 2 as he corrected later.
    But the questions stay the same.
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  6. #5  
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    Quote Originally Posted by Noa Drake View Post
    I read indeed that the value on the angle is times 4 instead of times 2 as he corrected later.
    But the questions stay the same.
    Your questions no longer make sense since Einstein's approach in 1911 was not correct.
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    I found an interesting and very clear explanation comparing the 1911 and 1915 version of Einstein's calculations on the subject. :

    Doubling the Deflection


    One thing still puzzles me though : The Huygens image above shows deflection in the opposite direction as does the deflection in image 6,
    judging by the position of the 'large and small circle'. But i'm guessing that is my incorrect interpretation of the comparison.
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  9. #8  
    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by Noa Drake View Post
    I found an interesting and very clear explanation comparing the 1911 and 1915 version of Einstein's calculations on the subject. :

    Doubling the Deflection


    One thing still puzzles me though : The Huygens image above shows deflection in the opposite direction as does the deflection in image 6,
    judging by the position of the 'large and small circle'. But i'm guessing that is my incorrect interpretation of the comparison.
    In case you are interested, here is the explicit calculation in modern notation, from solving the field equations right through to the derivation of the deflection angle :

    https://dl.dropboxusercontent.com/u/...ction%20SM.pdf

    I did that as an exercise a long time ago; perhaps you find it useful.
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