XPost: rec.arts.tv, alt.fan.rush-limbaugh   
   From: relativity@paulba.no   
      
   Den 30.10.2025 22:09, skrev Maciej Woźniak:   
   > On 10/30/2025 10:01 PM, Paul.B.Andersen wrote:   
   >> Den 29.10.2025 05:09, skrev The Starmaker:   
   >>>   
   >>> Michelson’s analysis of errors in his 1881/87   
   >>> experiments of the two swimmers contest;   
   >>   
   >> You obviously meant Reinhard A. Schumacher's analysis of errors in   
   >> Michelson's 1887 MMX experiment.   
   >>   
   >> Michelson never made an experiment with two swimmers.   
   >>   
   >>>   
   >>> https://iopscience.iop.org/article/10.1088/1742-6596/2197/1/012012/pdf   
   >>   
   >> The idea of using two swimmers to analyse the MMX is quite stupid.   
   >>   
   >> Schumacher claims that he with this analogy can prove that   
   >> if light were a wave in the ether as assumed by Michelson,   
   >> then a Michelson interferometer would not be able to measure   
   >> the speed of the ether relative to the interferometer.   
   >>   
   >> This is a ridiculous claim, and I will not bother to explain why.   
   >>   
   >> However, Schumacher is correct when he claims that there is   
   >> an error in Michelson's derivations, so let's go through them.   
   >>   
   >> (I am sure that this error is well known.)   
   >>   
   >> https://paulba.no/paper/Michelson_1887.pdf   
   >>   
   >> In the following is "c" the speed of light relative to the ether,   
   >> and "v" is the speed of the ether relative to the interferometer.   
   >> "D" is length of the interferometer arms.   
   >>   
   >> Analysis of the interferometer arm which is parallel to   
   >> the velocity of the ether:   
   >> =======================================================   
   >>   
   >> In the rest frame of the interferometer, the speed of the light   
   >> going with the speed of the ether is (c+v) while the speed   
   >> of the light going in the opposite direction is (c-v).   
   >>   
   >> So the time for the light to go forth and back the arm is:   
   >>   t₁ = D/(c+v) + D/(c+v) = 2D⋅c/(c²−v²)   
   >> The distance the light have travelled through the ether is:   
   >>   D₁ =  t₁⋅c = 2D/(1-v²/c²) ≈ 2D⋅(1+v²/c²)    (v/c << 1)   
   >>   
   >> This is in  accordance with Michelson's calculation.   
   >>   
   >> Analysis of the interferometer arm which is transverse to   
   >> the velocity of the ether:   
   >> =======================================================   
   >>   
   >> The correct calculation:   
   >> -----------------------   
   >>          .   
   >>         / \   
   >>        /θ|θ\   
   >>       /  |  \   
   >>    ct/   |   \ct   
   >>     /    |D   \   
   >>    /     |     \   
   >>   /______| _____\   
   >>      vt     vt   
   >>   
   >>   (vt)² + D² = (ct)² => t = D/√(c²−v²)   
   >>   
   >> So the time for the light to go forth and back the arm is:   
   >>    t₂ = 2D/√(c²−v²)   
   >> The distance the light has travelled through the ether is:   
   >>   D₂ = t₂⋅c = 2D/√(1−v²/c²) ≈ 2D/(1-v²/2c²) ≈   
   2D⋅(1+v²/2c²)   
   >>   
   >> Note: sin θ = v/c   
   >>   
   >> Michelson's calculation:   
   >> ------------------------   
   >>          .   
   >>         / \   
   >>        /θ|θ\   
   >>       /  |  \   
   >>    D'/   |   \D'   
   >>     /    |D   \   
   >>    /     |     \   
   >>   /______| _____\   
   >>      vt     vt   
   >>   
   >> Michelson (wrongly) consider it as evident that   
   >> the angle θ is the classical aberration.   
   >> (Aberration according to the Galilean transform.)   
   >> That is, tan θ = v/c   
   >>   
   >> So vt/D = v/c  => vt = D⋅v/c   
   >>   
   >> D'² = D² + (vt)² = D² + D²⋅v²/c² = D²(1+v²/c²)   
   >> D' = D⋅√(1+v²/c²)   
   >>   
   >> The distance the light has travelled through the ether is:   
   >>   D₂ = 2D' =  2D⋅√(1+v²/c²) ≈ 2D⋅(1+v²/2c²)   
   >>   
   >> Note that this approximation of the wrong D₂ is equal   
   >> to the approximation of the correct D₂.   
   >>   
   >> So Michelson's calculation that (D₁-D₂) ≈ D⋅v²/c²   
   >> remains correct.   
   >>   
   >> Michelson's error has no consequence for the validity of the MMX.   
   >   
   > But in the meantime in the real world - forbidden   
   > by your insane church improper clocks keep measuring   
   > improper t'=t in improper seconds.   
   >   
      
   It is evident from your very wise response that you   
   have read and have understood my post.   
      
   So you can actually read!   
      
   Well done!   
      
   --   
   Paul   
      
   https://paulba.no/   
      
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