On Dec 10, 2011, at 11:55 PM,
Yes, the negative bare mass ADM model has the really neat feature of particle stability at a finite radius. Because the negative bare mass makes gravity effectively repulsive
understood
and the electric interaction (for like charges) effectively attractive.
not understood
Since gravity remains non-linear, when the charge distribution at the radius where the two interactions balance is disturbed, the resulting force tends to restore the undisturbed configuration. :-) No multiple shells of charge. No renormalization needed. A really cute model (as the negative bare mass also allows you to have apparently highly superluminal surface velocity for the charge, making it possible to account for the angular momentum and magnetic moment in an exceedingly small object).
Roughly, if we have a SSS situation with the Newtonian potential ignoring "spin"
V/c^2 = - /
^2 + e^2/rc^2
Note with this sign convention / > 0 gives repulsive gravity as in the usual de Sitter sign convention used in precision cosmology
Newton's g = - c^2dV/dr = 2c^2/
+ e^2/r^2
There is no way to get stability here with / > 0 de Sitter, we need / < 0 Anti-de Sitter.
/ > 0 de Sitter is a way to model negative mass - repulsive gravity.
Therefore, I disagree with what Jim says here.
Technically, a shell of electric charge is stabilized by a plasma of virtual particles in which the density of virtual fermion-antifermion pairs exceeds the density of virtual bosons.
virtual bosons make / > 0
virtual fermion-antifermion pairs make / < 0
a more accurate model will use the Kerr-Newman-Reisser-Nordstrom metric with the cosmological constant / added.
On Dec 11, 2011, at 11:26 AM,
When you change the sign of the mass, you have to do so for the active and passive gravitational masses -- and also the inertial mass.
Agreed
This is the reason why a positive and negative mass pair of objects "self-accelerate".
Agreed
The repulsive force on the negative mass produces motion in the opposite direction because the inertial mass is negative too. (Richard Price has a very nice, short paper on this in Am J Phys back in 1993.)
Can you send a pdf of that paper?
In the case of the electrical dust of the ADM model, the electrical force remains repulsive irrespective of whether the bare mass is positive or negative.
Right
But the direction in which the dust moves in response to the repulsive force depends on what the sign of the inertial mass is. If it is negative, then the dust moves in a direction opposite to the force. The result is that the repulsive electrical force, for negative bare mass dust, becomes effectively attractive. Weird but true.
Interesting. Thanks.
By the way, the negativity of the inertial mass when the gravitational masses are negative is required by the Equivalence Principle.
Of course.