(sci.physics.research; remove animal to reply) X-Mod-No.: 03   
      
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   I've come up with a couple of thought experiments that I think give   
   interesting results.  I'd like to get the reactions of knowledgable   
   physicists to these arguments:   
      
   -Consider a vertical shaft in a gravitational field mounted in bearings   
   so it is free to rotate.  At the bottom is a lever so that an   
   experimenter can  apply a torque as the shaft rotates.  At the top is a   
   generator that can convert the torque times rotation angle at the top   
   into energy.   
      
   The experimenter at the bottom applies a constant torque $t_1$ to the   
   shaft  for a rotation of a full circle, giving an input energy of $2 \pi   
   t_1$.  Assume for a moment that the same torque is transfered to the   
   generator at the top, so the same energy arrives there.  Now take that   
   energy, create a photon with it and send it down to the lower   
   experimenter.  Due to gravitational blue shift (as the photon is   
   descending the gravitational field) the energy arriving at the   
   experimenter will be greater than what he put into the shaft to begin   
   with.  Clearly this violates conservation of energy.   
      
   Since the energy is torque times rotation angle, and the rotation angle   
   is the same top and bottom, it must be that the torques are NOT the   
   same.  It appears instead that the torques must be attenuated the same   
   as photon energy is by gravitational red shift: t_2 = t_1   
   \sqrt{\frac{g_{00}(r_1)}{g){00}(r_2)}}   
      
   -Now consider a threaded shaft with two platforms supported by threaded   
   nut s on the shaft.  The nuts are free to move up and down but not to   
   rotate. On each platform is a long horizontal pole mounted in its middle   
   with a bearing so that it can be rotated about a verical axis.  That is,   
   the poles stay horizontal as rotated.  At the ends of each pole are a   
   positive and negative charge, one of each on each pole.  All charges are   
   equal in magnitude.   
      
   Initially the positive charge of the upper pole is positioned directly   
   above the negative charge of the lower pole, and so too is the negative   
   upper charge over the lower positive charge.  The geometry is such that   
   the vertical charges are much closer than the horizontal charges, so the   
   two poles are attracted to each other by the electrostatic attraction.   
      
   If we assume for the moment that the electrostatic force on each charge   
   is the same for the upper and lower charges, then per the previous   
   thought experiment the torque applied to the shaft by the upper   
   platform/nut will be greater than the toque coming up the shaft by the   
   lower platform/nut.  As a result the net torque will cause the shaft to   
   rotate and the two platforms will descend.  The generator at the top can   
   now extract some energy as the shaft rotates.   
      
   After the platforms descend some distance stop the rotation with a   
   brake. Rotate one of the poles 180 degrees so that now like charges are   
   vertical to each other.  We now have the two platforms pushed apart and   
   when the brake on the shaft is released they will start to rise due to   
   the torque imbalance. Again we can extract some energy via the generator   
   as the platforms rise. When the platforms reach their original position,   
   stop the shaft and rotate the poles to their original position again.   
   We are now back to the original configuration and yet have harvested   
   some energy via the generator.   
      
   This case is a bit more subtle to analyze.  There are several issues to   
   pay attention to: -Is the electrostatic force really the same for the   
   upper and lower charges? As I understand it, in Covariant   
   Electromagnetism the electric field is still a 1/r potential, where r is   
   the distance separating the charges along  a light cone in the tangent   
   space.  If that is the case, the electric force would have to be the   
   same top and bottom as the electric field is the gradient of the   
   potential in the tangent space (the covariant derivitive).  Is that   
   correct? -The only time the physical separation between charges changes   
   (that is, the separation along the light cone in the tangent space   
   connecting the two charges) is when the pole is rotated.  While the   
   shaft is rotating the charges are not doing any work between them. There   
   might be an issue with EM field energy and the effect of it   
   rising/falling in the gravitational field... -The energy to rotate the   
   pole has to be taken into account.  The work to rotate from the first   
   position to the second position would be the negative of the work to   
   reverse that rotation, at least if both rotations were done at the same   
   elevation.  In the experiment described one rotation is done at  the   
   lower altitude and the second at the upper altitude.  I'm thinking that   
   if the work came from and then went into a battery that rose and fell   
   with the platform, that that energy would balance out.  In anycase, the   
   amount of energy harvested by the generator would depend on how far the   
   platforms were allowed to rise and fall, and that would be independent   
   of the work to rotate the pole, so that can't balance the conservation   
   of energy equation.   
      
   If I'm thinking about this correctly (which I'm asking the group to   
   confirm or correct) the electrostatic forces must also be attenuated   
   with altitude like the gravitational red shift.   
      
   Any comments would be appreciated,   
      
   Rich L.   
      
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