John Schoenfeld
Apr16-04, 02:28 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>If you use the Abraham-Lorentz radiation reaction formula and Newtons\nlaw of gravity, you can model the radiating self-levitating charge as\nfollows:\n\nFg = -Frad\n\nGm1m2/r^2 = u0q^2/6pic da/dt\n\nwhere\nm1 = mass of gravitational source\nm2 = mass of charge\n\nSince da/dt is rate of change of the gravitational acceleration, da/dt\nevaluates to -Gm1/r^3.\n\nSolving for q, you get\n\nq = sqrt(m2 6 pi c r / u0 ) -------- 1.0\n\nwhere\nr = distance between gravitational source centre of gravity to\ncharge\nm2 = mass of charge\nu0 = permeability of free space\n\nThe formula at 1.0 shows that a charge q with mass m2 will levitate\nunder a newtonian gravitational field at distance r from the\ngravitational source COG.\n\nExample, the charge required to levitate a particle with electron mass\nat earth surface gravity is 1.61E-4 C, which is the charge of 1 000\n000 000 000 000 electrons precisely.\n\nJust like a magnet suspended over a superconducting loop, this charge\nseemingly levitates in a gravitational field. If you do the\ncalculations (below), it becomes clear that the energy radiated away\nby the instaneously accelerating charge is much more than the energy\nrequired to suspend it\'s levitating position. This poses an obvious\nproblem since it would violate conservation of energy laws with\nextreme prejudice (since the mass of the charge remains invariant\naccording to the laws of classical electrodynamics).\n\nHere is the solution for the net non-conserved energy:\n\nNCE = E - LEV\nwhere\nNCE = non-conserved energy radiated away\nE = energy radiated by accelerating mass (Larmor power)\nLEV = energy consumed by charge to levitate (GPE)\n\nE = Larmors formula\n= q^2 a^2 / 6 pi e0 c^3\n= q^2 g(r)^2 / 6 pi e0 c^3 (since acceleration is g(r)\n\nLEV = Is simply the GPE\n= m g(r) r\n\nNCE = q^2 g(r)^2 / 6 pi e0 c^3 - mg(r)r\n= g(r)(q^2 g(r) - 6 pi e0 c^3 m r) / 6 pi e0 c^3\n\nwhere\nm = mass of charge\nq = electric charge of charge\ng(r) = newtonian gravitational attraction at radius R\ne0 = permitivitty of free space\nc = light speed\n\nUnless there is some error here, it would seem the only way to save\nconservation of energy is to decrease the mass of the charge by NCE.\n\nJS\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>If you use the Abraham-Lorentz radiation reaction formula and Newtons
law of gravity, you can model the radiating self-levitating charge as
follows:
Fg =[/itex] -Frad
Gm1m2/r^2 = u0q^2/6pic da/dt
where
m1 = mass of gravitational source
m2 = mass of charge
Since da/dt is rate of change of the gravitational acceleration, da/dt
evaluates to -Gm1/r^3.
Solving for q, you get
q = \sqrt(m2 6 \pi c r / u0 ) -------- 1.
where
r = distance between gravitational source centre of gravity to
charge
m2 = mass of charge
u0 = permeability of free space
The formula at 1. shows that a charge q with mass m2 will levitate
under a newtonian gravitational field at distance r from the
gravitational source COG.
Example, the charge required to levitate a particle with electron mass
at earth surface gravity is 1.61E-4 C, which is the charge of 1 000
000 000 000 000 electrons precisely.
Just like a magnet suspended over a superconducting loop, this charge
seemingly levitates in a gravitational field. If you do the
calculations (below), it becomes clear that the energy radiated away
by the instaneously accelerating charge is much more than the energy
required to suspend it's levitating position. This poses an obvious
problem since it would violate conservation of energy laws with
extreme prejudice (since the mass of the charge remains invariant
according to the laws of classical electrodynamics).
Here is the solution for the net non-conserved energy:
NCE = E - LEV
where
NCE = non-conserved energy radiated away
E = energy radiated by accelerating mass (Larmor power)
LEV = energy consumed by charge to levitate (GPE)
E = Larmors formula
= q^2 a^2 / 6 \pi e0 c^3= q^2 g(r)^2 / 6 \pi e0 c^3 (since acceleration is g(r)
LEV = Is simply the GPE
[itex]= m g(r) r
NCE = q^2 g(r)^2 / 6 \pi e0 c^3 - mg(r)r= g(r)(q^2 g(r) - 6 \pi e0 c^3 m r) / 6 \pi e0 c^3
where
m = mass of charge
q = electric charge of charge
g(r) = newtonian gravitational attraction at radius R
e0 = permitivitty of free space
c = light speed
Unless there is some error here, it would seem the only way to save
conservation of energy is to decrease the mass of the charge by NCE.
JS
law of gravity, you can model the radiating self-levitating charge as
follows:
Fg =[/itex] -Frad
Gm1m2/r^2 = u0q^2/6pic da/dt
where
m1 = mass of gravitational source
m2 = mass of charge
Since da/dt is rate of change of the gravitational acceleration, da/dt
evaluates to -Gm1/r^3.
Solving for q, you get
q = \sqrt(m2 6 \pi c r / u0 ) -------- 1.
where
r = distance between gravitational source centre of gravity to
charge
m2 = mass of charge
u0 = permeability of free space
The formula at 1. shows that a charge q with mass m2 will levitate
under a newtonian gravitational field at distance r from the
gravitational source COG.
Example, the charge required to levitate a particle with electron mass
at earth surface gravity is 1.61E-4 C, which is the charge of 1 000
000 000 000 000 electrons precisely.
Just like a magnet suspended over a superconducting loop, this charge
seemingly levitates in a gravitational field. If you do the
calculations (below), it becomes clear that the energy radiated away
by the instaneously accelerating charge is much more than the energy
required to suspend it's levitating position. This poses an obvious
problem since it would violate conservation of energy laws with
extreme prejudice (since the mass of the charge remains invariant
according to the laws of classical electrodynamics).
Here is the solution for the net non-conserved energy:
NCE = E - LEV
where
NCE = non-conserved energy radiated away
E = energy radiated by accelerating mass (Larmor power)
LEV = energy consumed by charge to levitate (GPE)
E = Larmors formula
= q^2 a^2 / 6 \pi e0 c^3= q^2 g(r)^2 / 6 \pi e0 c^3 (since acceleration is g(r)
LEV = Is simply the GPE
[itex]= m g(r) r
NCE = q^2 g(r)^2 / 6 \pi e0 c^3 - mg(r)r= g(r)(q^2 g(r) - 6 \pi e0 c^3 m r) / 6 \pi e0 c^3
where
m = mass of charge
q = electric charge of charge
g(r) = newtonian gravitational attraction at radius R
e0 = permitivitty of free space
c = light speed
Unless there is some error here, it would seem the only way to save
conservation of energy is to decrease the mass of the charge by NCE.
JS