From: nospam@de-ster.demon.nl   
      
   Luigi Fortunati  wrote:   
      
   > For example, if I put two clocks at the maximum distance on the floor,   
   > they remain synchronized and, therefore, horizontally there is no   
   > acceleration (there is quiet).   
   >   
   > If, on the other hand, I put a clock on the floor and one on the   
   > ceiling, they don't stay synchronized and, therefore, there is   
   > acceleration vertically (there is no quiet).   
      
   You misunderstand the situation.   
   The rate difference between the clocks, aka the gravitational red shift,   
   is given by their Newtonian potential difference \Delta\Phi.   
   (the Newtonian approximation to GTR applies, because \Delta\Phi << c^2)   
   Not quite correct first derivation by Einstein, 1907,   
   modern ones in for example MT&W and other GTR textbooks.   
      
   It is given by: \nu_1 / \nu_2 = (1 + (\Phi_1 - \Phi_2) / c^2)   
      
   Remember that the Newtonian potential is negative:   
   a clock that stands higher is at a higher (less negative) potential,   
   and it runs faster.   
      
   The acceleration that the clock would get, if released,   
   is given by the Newtonian force,   
   which is given by the gradient of the potential.   
      
   The new experimental fact that clocks with a stability of order 10^-18   
   have become available opens up a new window of experimental possibility.   
   (the rate difference is order 10^-16 per meter altitude)   
   This can be used to establish 'relativistic geodsy',   
   aka 'chronometric levelling', with centimeter accuracy.   
   Work is in progress to establish a European levelling network,   
   comparing optical clock rates over long distances (~1000 km achieved)   
   over optical fibre connections.   
      
   To see why this is important: the acceleration, the local g,   
   determined by the gradient, is a local quantity.   
   The potential otoh is global.   
   It must be obtained by solving Poisson's equation,   
   taking all masses on the whole Earth into account.   
      
   The distinction is of importance when you want for example   
   to predict the sea level rise from melting of Greenland ice.   
   (which changes the mass distribution, and hence the shape of the geoid)   
   The sea level rise will not be distributed equally over the whole Earth.   
      
   Jan   
      
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