From: nospam@de-ster.demon.nl   
      
   Luigi Fortunati  wrote:   
      
   > When Newton's bucket starts to rotate, the water slowly starts to   
   > rotate as well and accelerates outwards due to the centrifugal force.   
   >   
   > But the centrifugal force is ONLY in the rotating reference and not in   
   > the inertial one.   
   >   
   > So, how is the centrifugal acceleration of water justified EVEN in the   
   > inertial reference where the centrifugal force is not there?   
      
   This is either completely trivial,   
   or one of the great mysteries of physics,   
   depending on your philosophical inclinations.   
      
   I'll recapitulate the history:   
   1) For Newton all this was completely trivial,   
   the bucket rotates or not, wrt to his 'absolute space'.   
   2) Then Ernst Mach came along, who said that 'absolute space'   
   has no basis in empirical fact.   
   It is nothing but an unwaranted philosophical abomination   
   that has no place in physics. (by his philosophy of positivism)   
      
   All that matters, according to Mach, is relative motion.   
   So Mach said that the centrifugal and Coriolis forces   
   must be asumed to be -caused- by all those 'Ferne Sterne'   
   rotating around the stationary bucket at enormous speeds.   
   This is known as a form of "Mach's principle".   
      
   Einstein has said that Mach served as his inspiration   
   for getting started on relativity.   
   But working things out the Einsteinian way led to a great problem.   
   For Mach all was fine, because Newtonian gravity,   
   and hence also his 'Machian forces' propagated at infinite speed.   
   Finite propagation speed at c spoils it.   
      
   So now the mystery: empirically we can derive what is non-rotating   
   by observing motions in the Solar system to great accuracy.   
   (or in principle, but not in practice, also with a Foucult pendulum)   
   A frame without centrifugal and Coriolis doesn't rotate, by definition.   
      
   OTOH we can also determine what is, or isn't rotating   
   by looking at Mach's 'Ferne Sterne'.   
   (nowadays quasars at bilions of lightyears)   
      
   And indeed, those two differently defined frames local vs global,   
   do not rotate wrt each other,   
   to one of those ludicrous accuracies hat are the rule nowadays.   
   (would have to look up, think micro-arcseconds/century)   
      
   So there you are. [1]   
   You can shrug your shoulders, and say:   
   yes of course, how could it be otherwise?   
   Or you can say:   
   this is a deep mystery that needs a physical explanation.   
      
   Your choice,   
      
   Jan   
   (who hasn't kept up)   
      
   [1] This a veritable 'mer a boire'. There is a huge literature   
   on various forms of Mach's principle, weak, or strong,   
   or something else, and on how these should be understood.   
   Nevertheless, the hard empirical core of it has remained,   
   despite observable distances growing at least a millionfold.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)