From: nicolaas.vroom@pandora.be   
      
   On Tuesday, 18 September 2018 22:11:10 UTC+2, Tom Roberts  wrote:   
   > On 9/8/18 5:43 PM, Nicolaas Vroom wrote:   
   > > The question is if the behaviour of a clock in a centrifuge can be   
   > > described by means of the equation: sqrt(1-v^2/c^2).   
      
      
   > The actual equation is:   
   > 	t' = \integral sqrt(1-v^2/c^2) dt   
      
   > > For certain clocks: Yes. For other clocks: NO.   
      
   The clock I'm simulating is described at page 12 in the book SpaceTime   
   Phyisics.   
   The clock consists of two parallel mirrors in horizontal direction.   
   The eye piece is towards the right side in horizontal direction.   
   You can also depict the eye piece at the center between the two   
   parallel mirrors.   
   There are two ways to move this clock:   
   1) in veritical direction. That is done at page 69 of the book, inside   
   a rocket. However 90 degrees rotated.   
   The equation that describe this movement is the same as above mentioned.   
   From the rocket point of view, in the direction of movement, the signal is   
   reflected against the ceiling and the floor.   
   My simulation shows exactly the same in a linear acceleration.   
   2) in horizontal direction.   
   The equation that describes this behaviour is:   
   t' = \integral (1-v^2/c^2) dt   
   From the rocket point of view, the signal is reflected against the front   
   and the back of the rocket.   
   The mathematics is the same as used to describe the Train Paradox   
   at page 63.   
   My simulation shows exactly the same in a linear acceleration.   
      
   > Nope. Somewhere you goofed. The above equation holds for all types of   
   > clocks.   
   >   
   > 	Note that t and v MUST be associated with an INERTIAL FRAME.   
   > 	That could be your mistake. etc.   
   >       Note that no rotating system is an inertial frame,   
   > 	so if you ever used rotating coordinates in any way you almost   
   > 	surely introduced an error.   
      
   I fully agree. 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)   
   My point is also that allmost all clocks in principle have this problem.   
   This is the case When for a clock in front of you on a table.   
   For a clock in circular motion around the earth, around the Sun   
   or around in our Galaxy.   
   In the simulation this is done for one revolution.   
   My point is also that accelaration is the primary influence of the behaviour   
   of a clock.   
      
   > Your simulation is wrong.   
   >   
   > Tom Roberts   
      
   Nicolaas Vroom.   
      
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