6f692b30   
   XPost: rec.arts.tv, alt.fan.rush-limbaugh   
   From: relativity@paulba.no   
      
   Den 30.10.2025 22:42, skrev Maciej Woźniak:   
   > On 10/30/2025 10:31 PM, Paul.B.Andersen wrote:   
   >> 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!   
   >   
   > No surprise you're jealous, poor trash.   
   >   
      
   Yes, I envy you your ability to make sharp   
   logical analyses of complex problems.   
      
   Therefore I would very much like you to look at   
   Michelson's and mine calculations of the distance   
   the light has travelled through the ether along   
   the transversal arm.   
      
   Is it:    D₂ = 2D/√(1−v²/c²)   
   or is it: D₂ = 2D⋅√(1+v²/c²)   
      
   Which is correct?   
      
   --   
   Paul   
      
   https://paulba.no/   
      
   --- SoupGate-Win32 v1.05   
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