@Bracewell,
Bracewell;33671 wrote: I am told the mathematical equivalent to dyslexia is 'equalitis', a condition I am sorely afflicted with.
So am I, much to my regret. As compensation I seem to have developed a more acute spatial sense, and often visualise solutions to such questions, even if I am unable to solve them mathematically.
Have noted one or two points in this thread that I hope may be of help:
The analogy of a bag of marble is an obstacle to understanding the concept of an atom within quantum theory. Individual atoms are composed of energy. Energy, of which light is a form, has no mass. Individual atoms behave in a way consistant with the concept of solid matter because they have density of form. In other words that have a more condensed wavelength then light or pure energy. Light as a form of energy encounters less resistance in its apparent motion through the fabric of space and time, unless it encounters the influence of a more densely packed field of energy, like a star or a planet. Is this resistance that we may observe, light flowing around a dense field of energy? In the way that a finger may bend the flow of water? (As a side thought, is it possible to measure the density of space itself, separate from the matter and the light which moves through it?) The particle of an atom, as another form of energy, seem to spiral around themselves and therefore encounter greater resistance in their apparent motion within this same fabric.
I suspect, although I am not qualified to test this mathmatically, that the 'gravitational' pull on light, is the effect that a dense field of electrically charged particles (atoms, or matter) has on the lighter density of light's wavelengths. It bends into the curve created by denser forms of energy.
It also strikes me that the principle of linear anything is an abstract construct, straight lines do not exist in spacetime, nor does nature seems to create anything in straight lines of the two dimensional variety. Reality is constructed in curves and, mathematics which measure straight lines may be somewhat ill adapted a means to measure vast distances. Light as an example does not move outwards from its source in a straight line, but moves outward in a sphere surrounding its source. When we speak of the speed of light being effected by gravity, it speaks only of the effect of a specific trajectory, but that trajectory is itself an incomplete analyse of the direction or speed of travel if taken from a fixed perspective. In essence I am saying that we can take a reductionist point of view to theorise, but to truly understand the full phenomen, a holistical form of mathmatics would be required. How might one determine the mean speed of light which is moving in all directions simultaneously. Imagine you and I are perched on opposite sides of the Universe, spiraling around the center, at a distance exactly equal from the center, in other words on its circumference. A light shines from the center and, naturally, travels towards both of us. There are a series of objects spirling around the center, which will each eventually come into contact with the outward motion of the light. From certain vantage points the light will be influenced by the density of the objects within the light's outward motion. Will the light reach the entire circumference on which you and I are perched at precisely the same moment? Will the light not reach certain points along the sphere which traces that circumference due to the influence of the objects which have obstructed it? If the light has been 'bent' by the gravitational field of some of the objects within this sphere, is its trajectory readjusted to the degree that the light will arrive along the circumference at certain points, and then cause a secondary reverberation according to the readjusted trajectory caused by the gravitational influence of the objects it has encountered? Or most likely, will the light arrive simaltaneously along every point within the sphere but diminished in intensity in direct proportion to the density it has encountered along that trajectory?
Likewise, I sense troubles with your model of the atom, which already has its own 'spin' dropping in a theoretical straight line to the centre of the Earth. When objects fall to Earth they enter in an arch. Any calculation of the relative speed needs to accomodate this effect, Everything seems to move in curves, and not along a straight trajectory in order to reach its maximum velocity.
Once your theoretical atom falling to the centre of the Earth overcomes the resistance of the Earth's crust it has then to encounter the more dense consistency of the Earth's core as it falls to center. Falling to centre seems terribly paradoxical, But I suppose if we were able to drill a hole through the Earth this would be a terribly exciting experiment.
All of that said, is gravity a mechanical action or an electromagnetic field which has inward or outward influence depending on the relative position within that field.
I agree, fascinating topic to think about. Excuse my naivet? on this subject ...