From: heathjohn2@gmail.com   
      
   On Monday, October 2, 2017 at 9:36:49 PM UTC-4, John Heath wrote:   
   > On Monday, October 2, 2017 at 4:26:22 AM UTC-4, Lawrence Crowell wrote:   
   > > On Friday, September 29, 2017 at 8:21:02 AM UTC-5, John Heath wrote:   
   > > > A car is moving at .1 c. The tire on the road at 6:00 o'clock , bottom ,   
   > > > is moving at 0 c as it is touching the road but at 12:00 o'clock , top ,   
   > > > the tire is moving at .2 c twice as fast as the car. Does this mean the   
   > > > car is limited to speed .5 c as at this speed the top of the tire will   
   > > > be moving at c twice as fast as the car ?   
   > >   
   > > Tom Roberts has the right idea. The Lorentz transformations of dx   
   > > and dt are   
   > >   
   > > dt' = gamma(dt - vdx/c^2)   
   > >   
   > > dx' = gamma(dx - vdt) --- gamma = 1/sqrt{1 - (v/c)^2}.   
   > >   
   > > Now for dx/dt = u compute dx'/dt' to get the velocity addition   
   > > formula. You can see that you can't add up velocities so they are   
   > > greater than c.   
   >   
   > Yes but in this case it is a rigid wheel that is being mechanically   
   > forced to move twice the speed of the car.   
   >   
   > [[Mod. note -- The author is mistaken.  It's actually a rigid wheel   
   > 	[we're assuming a gedanken wheel which is indeed   
   > 	rigid, and we're ignoring the Ehrenfest paradox]   
   > whose top is being mechanically forced to move at a speed-of-car   
   > speed *with respect to the car*.  As a number of people in this   
   > thread have pointed out, velocities don't add the same way in special   
   > relativity that they do in Galilean relativity, so the top-of-wheel   
   > point is NOT moving at twice the speed-of-car with respect to the   
   > road.   
   > -- jt]]   
      
   [Moderator's note: rigid bodies are an idealization in Newtonian   
   mechanics. There are no rigid bodies in the usual sense in relativistic   
   physics. The "Born rigid body" cannot rotate!]   
      
   You may have a rigid wheel or you may have " Velocities don't add the   
   same way in special relativity that they do in Galilean relativity".   
      
   You may have one or the other but you may not have both. It is one or   
   the other. Our experience as self aware matter says rigid wheel is just   
   that "a rigid wheel". I have a open mind to a counter argument.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)