Natural Science Forum / Physics / New Theories / April 2004

Paraphrasing the Associated Press (April 13, 2004):

Next week, if all goes well, NASA will launch a rocket
that will measure how space-time is warped and dragged
along by the gravity of the spinning Earth--one of the
stranger implications of Einstein's general theory  of
relativity.

End Paraphrase.

I used to be opposed to the notion of the curvature
of space, time, or space-time. Now I realize that this
refers exclusively to space-time.

The effect to be measured is small. The experient uses
near-perfect spherical gyroscopes that, after one year
will point 1/100,000th of a degree from their initial
direction.

A much larger warping of space-time by a rotating mass
could be accomplished by ferromagnetic resonance. Instead
of simple rotation, the precession of electrons in a
voluminous iron mass mass would be employed.

Precession is the rotation of the axis about which a
body spins. A top spins; under gravity, it also precesses.
The angle between the vertical and the top is called
the precession angle.

Given a constant precession, a constant centripetal
force acts on the mass of the top. The top has a
tangential velocity in its precession about the vertical.

According to Feynman's Lectures on Physics (v1 ch19 p9) a
centripetal force is equivalent to a corioli force when the
velocity is tangential and the force is radial. Einstein
observed that the corioli force is a type of gravitational
force.

In ferromagnetic resonance, the superposition of electronic
magnetic moments is also a superpostion of electronic
angular momenta. The net angular momentum is:

J = -MV / y

where M is the saturation magnetization of iron, 1.70x10^6
A/m, V is the volume of the iron (8.66x10^3 m^3) and (y) is the
magnetogyric ratio or 1.76x10^11 C / Kg.

The precession (or resonance) frequency is:

Wp = y Bo  radians/s

Bo = Bf - delta_B  (field is not static)

Bf is the saturation induction, or 2.13 Tesla, and delta_B
is 1.13 Tesla. Therefore, Bo is 1 Tesla and Wp is 1.76x10^11
radians/s.

A funnel can be thought of as layers of circles of differing
radii. The precession of the angular momentum vector describes
a funnel. The vertex of the funnel has a radius of:

r = (J / (m Wp))^1/2

where (m) is the mass of the iron equal to the volume times
the density of iron (7.86x10^3 Kg/m^3) or 6.80x10^7 Kg.
Therefore, r is 8.36x10^-11 meters.

The expression for centripetal force is:

F(r) = m v^2 / r        or,

F(r) = m (Wp)^2  r

F(r) = (6.8x10^7) (1.76x10^11)^2 (8.36x10^-11)

F(r) = 1.76x10^20 N

For a precession angle of zero there are no torques acting
on the iron mass (the torque being proportional to sin(zero)).
This means that the iron mass will not rotate. This is similiar
to the non-rotation of the Trouton-Noble capacitor. (See
http://www.iop.org/EJ/abstract/0305-4470/32/20/308).

The precession angle would probably be small and not zero. If
sin(angle)is small enough, then the resulting torque would
be insufficient to rotate the iron mass.

Torque(Wp) = J Wp sin angle

For a voluminous iron mass the vortex of the precession funnel
will have a radius greater than one meter. The centripetal
(radial corioli) force for a radius of one meter is:

F(r) = (6.8x10^7) (1.76x10^11)^2 (1)

F(r) = 2.10x10^30 N

Apparently, either a Kerr black hole has formed with its traversable
ring singularity or a magnetic wormhole has appeared. Notably, the
volume of the iron mass compares with that of a ship like the DE-173
in the Philadelphia Experiment.

Since the energy of the system changes with a jump at resonance, the
Kerr black hole or magnetic wormhole exists only briefly.  ###