From: nicolaas.vroom@pandora.be   
      
   Copied from the tread "in making a new theory cannot be postulated what is   
   patentely false"  in sci.physics.relativity   
      
   On Thursday, 14 May 2020 00:55:50 UTC+2, tjrob137  wrote:   
      
   **** Start of posting.   
   On 5/13/20 11:00 AM, Nicolaas Vroom wrote:   
   > On Friday, 17 April 2020 02:49:37 UTC+2, tjrob137  wrote:   
   >> Indeed, the second postulate is not needed in a modern derivation of SR.   
   >   
   > However, I also have a problem with this sentence.   
   > Do you mean that the second postulate is not needed at all in relation to SR?   
   > or only in relation to a modern derivation of SR?   
      
   First remember that Einstein's 1905 paper was about ELECTRODYNAMICS.   
   Since then we have found it convenient to split his subject into two   
   separate theories:   
     1. SR, which models the (local) geometry of spacetime.   
     2. Electrodynamics, which models electromagnetic interactions.   
      
   Einstein's second postulate involves light, putting it FIRMLY in theory   
   #2. So it cannot be used in theory #1.   
      
   Today we understand group theory (which Einstein did not in 1905). We   
   can use group theory to show that there can be only three transformation   
   groups among inertial frames, and that just one of them, the Lorentz   
   group [#], agrees with all the experiments.   
      
   So Einstein's second postulate is not needed at all in theory #1 above,   
   SR as understood today by physicists.   
      
           Not all popular articles and elementary textbooks adhere   
           to the separation above. But that separation is necessary   
           to go from SR to GR -- that relies on the invariant speed   
           of SR, and has nothing to do with light.   
      
           [#] Well, the Poincare' group. Which is the same as the   
           inhomogeneous Lorentz group.   
      
   > The second postulate discusses the speed of light and that seems very   
   > important in relation to SR, specific in relation to the invariant:   
   >     ds^2 = dx^2 + dy^2 + dz^2 - c^2dt^2   
      
   Do not be deceived into thinking that "c" there is the speed of light.   
   IT ISN'T. It represents the invariant speed of the Lorentz group.   
      
   Historically, "c" was used to represent the vacuum speed of light, and   
   "c" was also used to represent the invariant speed of the Lorentz group.   
   This has caused countless confusion, but it is only a confusion about   
   history and nomenclature -- the two theories above are distinct and   
   quite clear about the meanings of their symbols.   
      
   The remarkable thing is that the two meanings of "c" in those two   
   theories have the same numerical value, established experimentally to   
   high precision (yes, separate sets of experiments).   
      
           So in a very real sense, Einstein "lucked out" in 1905.   
           Had it happened that those two meanings of "c" were   
           significantly different, the history of physics would   
           have been VERY different.   
      
   > Should this link: https://en.wikipedia.org/wiki/Special_relativity   
   > not be updated?   
      
   Perhaps. Even probably. I have not looked at it.   
      
   Tom Roberts   
   ******  End of posting   
      
   Any comments   
      
   Nicolaas Vroom   
      
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