From: tjroberts137@sbcglobal.net   
      
   On 9/23/18 4:57 PM, Nicolaas Vroom wrote:   
   > Any clock in a centrifuge is not in an inertial frame. My point is to   
   > simulate the behaviour of a clock undergoing acceleration. What the   
   > simulation shows is that the behaviour is very complex using the clock as   
   > described on page 12 (as a function of v)   
      
   IIRC that is a light clock with a light pulse bouncing between two mirrors.   
   Remember that the mirrors are accelerated but the light is not -- the light   
   pulse moves in straight lines between bounces (relative to any INERTIAL frame).   
      
   	For instance, while they are being accelerated you must tilt the   
   	mirrors so the light pulse continues to bounce between them.   
   	Parallel mirrors work only when they are moving inertially.   
      
   Let me assume a light clock in a centrifuge, and [#]:   
      a) the center of the centrifuge is at rest in the lab   
      b) the lab is at rest in an inertial frame   
      c) we can ignore the size of the light pulse   
      d) the light clock is constructed so at every bounce its mirrors'   
         centers are at rest in the same instantaneously co-moving inertial   
         frame, and the distance between their centers remains fixed in   
         each of those frames (i.e. the mirrors adjust themselves to make   
         this so, independent of any strains in their support structures)   
      e) the light clock is constructed so the light pulse always bounces   
         from the exact center of each mirror (i.e. the mirrors adjust   
         themselves to make this so)   
      f) all bounces are perfect, with no light loss   
   Then it is straightforward to see that the trajectory of the light pulse   
   relative to the lab is a series of straight lines with corners at the   
   successive   
   locations of the mirrors' centers when it bounces. It is quite clear that the   
   rate of bouncing measured in the lab depends ONLY on the size of the clock and   
   how fast the mirrors move relative to the lab (i.e. how far apart the   
   corners/bounces are); the mirrors' acceleration DOES NOT MATTER (i.e. it does   
   not matter how they get to successive positions of the bounces/corners). This   
   is   
   just basic geometry, and if your simulation does not show this then it is   
   wrong.   
      
   	Independence of acceleration is obvious, but it is not so   
   	obvious that for a given clock speed relative to the lab that   
   	the bounce rate is independent of the orientation of the   
   	clock -- a detailed calculation MUST show that it is (because   
   	we are using SR as the basis of the calculation, and SR   
   	clearly predicts independence of clock orientation).   
      
   	[#] This is a gedanken; I know of no way to actually implement   
   	it; I do not think these assumptions are unreasonable.   
      
   > My point is also that allmost all clocks in principle have this problem.   
      
   I doubt it: SR predicts that NO clock has this "problem", and I see no reason   
   to   
   doubt that prediction. For instance, muons in a "relativistic centrifuge" (aka   
   storage ring), undergoing the enormous proper acceleration of 10^18 g, are   
   observed to decay at the rate SR predicts; that prediction depends on only   
   their   
   speed relative to the lab and their proper lifetime (see equation given earlier   
   in this thread); in particular it is completely independent of their   
   acceleration.   
      
   	Bailey et al., “Measurements of relativistic time dilation for   
   	positive and negative muons in a circular orbit,” Nature 268   
   	(July 28, 1977) pg 301.   
   	Bailey et al., Nuclear Physics B 150 pg 1–79 (1979).   
      
   > My point is also that accelaration is the primary influence of the behaviour   
   > of a clock.   
      
   Not in SR. (Also not in GR.) And apparently not in the world we inhabit.   
      
   As I said before: your simulation is wrong.   
      
   Tom Roberts   
      
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