On Nov 15, 3:43 pm, "Neil Bates" wrote:
Moving streams of matter should produce a "Gravitomagnetic field" analogous to the magnetic field from moving charges. This is orthodox GR, even if some details are in contention. (See for example,http://en.wikipedia.org/wiki/Gravitomagnetism.)
I played around with equivalent matter streams moving in opposite directions. That should cancel out their gravitomagnetic fields B* (usually just called "B" after context given), but I found an inconsistency. The problem was, superposition of B* from two sources as if a vector field did not work. (Sure, gravity is more complicated, but that part should approximate vector fields and emulate EM at low mass levels - ? - and I expect even non-linear superpositions to cancel out opposite fields.) For example, let's have adjacent streams going 0.5c in opposite directions, very low mass density to provide high expected linearity (albeit at relativistic speeds.) The proper value of g seen in our frame K is gamma squared times the value g_s at rest relative to either single stream (hence g = 2gamma^2(0.5c)g_s = (2*4/3)g_s = (8/3)g_s), due to the multiplied effects of Lorentz contraction and greater relativistic mass-energy density (thus field-producing power) per proper length unit in the mass flow.
We will send a unit mass M moving at 0.5c, frame K', along the streams' path, in either direction. We, expecting to see only "g" since the B* has ostensibly been canceled, expect M to experience gamma squared the value of proper acceleration towards the stream that we find in K (lateral acceleration transformation, from shorter proper time to fall.) Since effective mass-energy of M is gamma*M_0 (one of the cases where "relativistic mass" is still relevant), that is equivalent to a force in K increased to gamma times rest value and thus in K', gamma squared times the force in K (due to force transformation.) Hence by that consistent-seeming reckoning, the acceleration of M in K' should be gamma^2(0.5c)g = 2gamma^4(0.5c)g_s = (32/9)g_s.
However, in M's frame, one stream is at rest and the other one goes at 0.8c. The combined effect is therefore [1 + gamma^2(0.8c)]g_s = (34/9)g_s =(17/16)*(32/9)g_s. It is easy to verify (using the additive gamma factor being gamma(v1 + v2) = gamma1*gamma2*(1 + v1*v2/c^2)) that the ratio in general of the second prediction to the first is (1 + v^4/c^4).
That is an odd contradiction, and I just don't know what to make of it. Sure, gravitation is not like EM and with curved space etc., but would anyone expect low-gravity fields of any kind not to cancel out if apparently of opposite sign? Has anyone found good rules for B*? Has this issue been talked about before, and where? Thanks.
For simplicity, Maxwell's equations assume a axis of
symmetry that may not always exist. That is why inertial
coupling is through mass/energy equivalence in GR.
The ewald method allows the consideration of
induction components aren't symetrical
http://www.research.ibm.com/grape/grape_ewald.htm
Einstein published his theory of
gravitation, or general theory of relativity,
in 1916. And so a new paradigm, or set of
beliefs, was established. It was not until
1930 that Fritz London explained the weak,
attractive dipolar electric bonding force
(known as Van der Waals' dispersion force
or the 'London force') that causes gas
molecules to condense and form liquids
and solids. Like gravity, the London force
is always attractive and operates between
electrically neutral molecules
What a different story might have been told
if London's insight had come a few decades
earlier? Physics could, by now, have advanced
by a century instead of being bogged in a
mire of metaphysics.
http://www.holoscience.com/news.php?article=r4k29syp
GP-B
http://einstein.stanford.edu/
Tajmar / de Matos
http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html
Sue...