🚀 go-pugleaf

In article <1992Aug10.202618.1433@murdoch.acc.Virginia.EDU> crb7q@kelvin.seas.Virginia.EDU (Cameron Randale Bass) writes:
>In article <1992Aug10.184700.3204@sbcs.sunysb.edu> rscott@csws1.ic.sunysb.edu (Robert Scott) writes:

>>AS FOR YOUR COMPLAINT THAT LIGHT-SPEED DELAYS CAN NOT EXPLAIN WHY
>>TIME-DILATION OCCURS, I THINK THAT YOU GOT IT EXACTLY BACKWARDS.  THAT
>>IS, IT'S NOT THAT THE ROBOTS IN THE GAME DON'T EXHIBIT TIME-DILATION;
>>RATHER IT'S THAT THERE ISN'T EVEN ANY STANDARD AGAINST WHICH YOU CAN
>>ASK WHETHER THEIR TIME IS DILATED.  THAT IS, THE SYMMETRY GROUP
>>OPERATING HERE, WHICH IS THE INTERSECTION OF THE GROUP OF AFFINE
>>TRANSFORMATIONS (PRESERVING THE STRUCTURE RELATED TO INERTIAL MOTION
>>AND THE SPECIFICATION OF SPACE-TIME POINTS IN TERMS OF AFFINE
>>COMBINATIONS) AND THE GROUP OF "LORENTZIAN CONFORMAL" TRANSFORMATIONS
>>(PRESERVING THE STRUCTURE RELATED TO THE LIGHT-SPEED SIGNALLING
>>PROTOCOL) IS ALMOST, BUT NOT QUITE, JUST THE POINCARE GROUP OF SPECIAL
>>RELATIVITY.  
>
>     What?   If there is no relation between the time standards, there
>     is complete anarchy and you cannot describe the kinematics of the 
>     system at all.

The group Scott is referring to here, Poincare transformations plus
scaling, is sometimes called the Weyl group and is indeed a symmetry of
relativistic theories of *massless* particles.  See my forthcoming post
on symmetry for more.