Inertial inductance or relational mechanics:
Here we plug our calculated values for the Cosmos into the ideas of relational mechanics and inertial inductance. Cosmos is the term I use for our local dynamic knowable subset of the entirety of the universe. The universe is an existential term for everything. The Cosmos can be called the observable universe.
Amitabha Ghosh in "Origin of Inertia" relates in his excellent book:
The force between two masses are:
which is the gravitational force +
Ghosh tells us that the wording "inertial inductance" is due to Sciama as is the acceleration dependant term which relates to inertia.
These concepts have a long history starting with Wilhelm Weber in 1848. They are articulated and expanded by A.K.T. Assis, whose books and online papers are recommended.
Velocity dependent inertial inductance:
Any point in the cosmos has a characteristic radius and velocity.
r = ru*fr = c*age*fr, The radius equals a fraction fr of the radius of the Cosmos.
vt = vr = c*fr, where vt is the tangent velocity and vr is the radial velocity.
We need the difference between a certain point and the radius or perimeter of the Cosmos ru. This is the radius where light orbits because there is enough mass within this radius to deflect light into a circle. Light is forced to orbit the Cosmos. It cannot escape the Cosmos. From outside of the Cosmos, the Cosmos would appear black. This makes it a black hole. rd is the difference in radius and vd is the difference in velocity,
vd = c - c*fr = c*(1-fr)
rd = ru - ru*fr = ru*(1-fr) = c*age*(1-fr)
(2) G*Mc*m/r2*(v2/c2) =
c3*age *m/r2 *(v2/c2) =
m *c*age *v2/r2 =
m *c*age *vd2/rd2
m *c*age *c2*(1-fr)2/(c2*age2*(1-fr)2))
The velocity dependent inertial inductance acceleration, at every location for both radial and tangent accelerations, is always c/age. The resultant of these perpendicular accelerations is a vector quantity 21/2 *c/age. Any mass subject to these accelerations would spiral out away from the mass center. Everything spirals out as the Cosmos expands and slows in its rotation. This is the same spiral that we calculated from dynamics and inertial accelerations.
Rotating bodies in space:
Rotating bodies experience a cosmic drag due to velocity dependent inertial induction. This drag is opposite the direction of the velocity and slows the rotation. The cosmos slows in its rotation as it expands.
mass *(tangent velocity)2 /(c*age), The drag force on a ring.
c/H0 = c*age = ru, radius of the cosmos, H0 is Hubble's constant 1/age.
mass *vt2 /r ,The drag force on a ring is the same as centrifugal force.
mass *vt2 /(ru), The drag force at the radius of the cosmos.
mass *c2 /(c*age)
This has the same value that we calculated for the tangent or centrifugal force at the edge of the cosmos. The gravity probe B satellite is looking for a similar effect. It is called frame dragging in general relativity. Will frame dragging get the credit for the work done by inertial inductance? See the discussion about Lense and Thirring, the originators of frame dragging, in the unique and valuable book "Relational Mechanics" by A.K.T. Assis.
Acceleration dependent inertial inductance = inertia:
(3) G *Mc *m /r2 *(a*r/c2) =
G *Mc /r *m*a /c2 =
c3*age /(c*age) *m*a /c2 =
m*a or F = m*a
This is Newton's law, force equals mass times the acceleration. An important point is that it takes the entire mass of the cosmos to produce the effect of inertia; F = m*a. The mass of our sun or even our cluster of galaxies is a very small part of inertia. If only half of the mass of the cosmos is used then F = 1/2 *m*a.
Angular acceleration from inertial induction:
drag force *r = moment of inertia *angular acceleration
m *v2 *r /(c*age) = m*r2 *angular acceleration
v2 *r /(c*age) = r2 *angular acceleration
v2 = r2 *angular acceleration
angular acceleration = c2/(c2*age2) = 1/age2
This is the rate that cosmos slows in its rotation.
Angular acceleration from torque /moment of inertia:
angular acceleration = torque /moment of inertia =
Mc*c2 /(Mc*c2 *age2) = 1/age2
Torque from inertial induction:
drag force *r = torque
m *vt2 *r /(c*age) =
Mc *c2 *c*age /(c*age) = Mc *c2
Torque from moment of inertia * angular acceleration:
moment of inertia *angular acceleration = torque
m *r2 * angular acceleration = torque
Mc *c2*age2 *1/age2 = Mc *c2
As the moment of inertia increases with age2 the angular acceleration decreases with age2 so the moment of inertia * angular acceleration stays constant. As the cosmos expands the rate of rotation slows down and the energy stays constant.