Sunday, July 29, 2012

Newton's Black Hole

Yes, it may surprise many, that the concept of "Black Hole" goes back, not to Hawking, Schwartzchild, Einstein, or even Maxwell, but Newton.

Newton's attempt to put the intuitive and useful gravity equation on a secure footing, required many unusual concepts, the most remarkable being the Uniform Hollow Sphere of negligible thickness.  This indeed, was the first "Black Hole", once Newton decided to assign it the most remarkable property: it is the only Newtonian object that can create a space inside itself which exerts zero gravitational force upon any massive test-object, and vise versa, regardless of the size/mass of either the sphere or the object, and irregardless of the test-object's shape.

Newton had decided (probably through clever self-deception,) that the gravitational pull would be perfectly balanced inside such a sphere, and the net force would be zero.

Outside its surface however, the sphere would exert the same force as a point-mass of the same mass, located at its Geometrical Center (GC).

Hollow Sphere Exerts Gravity Outside its surface only.
We are justified then, in portraying Newton's Hollow Sphere as a kind of "Black Hole", in which the forces are represented as light colors of increasing strength approaching the surface, but having no color inside (representing zero gravitational force).

Newton's Gravitational "Black Hole" (shading indicates field strength)

Outside its surface, objects flying by would travel in elliptical orbits, or follow the same path just as if they were circling a point-mass of the same mass, according to Newton.  Below we trace the orbit of an approaching test-mass as if it were trapped in an orbit and otherwise 'unpowered' and simply free-floating in space.  It is assumed to have had an already existing (constant) velocity before becoming entrapped:

Orbital Path of a Body trapped in gravitational Pull of Hollow Sphere

We mark the path around the Center of Mass and Geometrical Center, just as the test-mass would travel if the sphere were very small, but of the same mass.   Here the CM/GC is marked as a small dot.

Note however, that once the object pierces the surface of the sphere, it would no longer feel the pull, and would continue in a straight line (in Euclidean Space) due to inertia, and without any friction or force, would maintain the same velocity (speed and direction). It would continue coasting straight, until it exited the sphere at the opposite side.

At that time, the test-mass would again take up an elliptical orbit, although offset, and starting up rather sooner than expected (after a short time inside).

This new elliptical orbit would not have had the benefit of acceleration (and balancing deceleration) while inside.  Thus, it exits at the same speed it would have exited, but at a different than expected point, and at a different time.

One can see that depending upon the angle of entry, one can have almost any pattern of precession of the orbit, with accompanying arbitrary changes in phase or timing.

Orbit Displacement of a particle Passing through Sphere
Given that we could also be talking about electrical charges as easily as gravity, one can see the potential for all kinds of phenomena in regard to orbital patterns, including quantized and stable orbitals with synchronizing 'beats'. 

It doesn't take much to picture molecular arrangements which would stabilize or enhance synchronization in interesting and unusual ways.

Newtonian theory then, has plenty of potential for mechanisms of quantization without resort to "unknown" causes.

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