The Work of Gravity

I have no intuition about the ultra-small – apart from a yet-unanswered question about how transparent objects slow light in a profound and perfect interaction (refraction), I will leave alone quanta and nuclear physics. My interest is gravity, and in developing a model understandable to our 3-dimensional conciousness.

To rehash a previous post, the balls of lead shot on the surface of a rubber balloon do well up to a point. Looking for a model that demonstrates the characteristics of gravity, using a trick of removing one of the four dimensions of space-time to enable us to envisage it (as a 2-D photograph or painting represents a 3-D scene). A rubber balloon is elastic. Although the balloon exists in three dimensions, it is the macro dimension inclding the whole balloon which represents the real-world 4th dimension, and of the local space dimensions, only north-south and east-west are present, up-down is missing hence the locally "flat" membrane.

In our gravity-free laboratory, lead balls rest at the outside surface. As the balloon is inflated, the balls resist, and cause indentations. Adjacent balls find themselves sharing an indentation, and roll down the slope towards each other. The model is a simplification through removal of the radial dimension (the direction of inflation), so we have to imagine that although elastic and having no thickness, the membrane is perfectly strong ie cannot be punctured. (Its “puncturability” is where the models for black holes will come in.) The main conundrum with this model is that work is needed to inflate the balloon, which gets thinner. Before assuming this, I am searching for a shape and motion of membrane which can cause the lead shot to move and therefore resist against and distort the membrane, without requiring the membrane itself to absorb energy or become increasingly stretched. In particular, the model needs the elastic medium to exert a continuous and constant force on the masses without doing work on them.

The answer is a continuous belt-shaped rubber membrane. If it is spinning like the tyre of a bicycle wheel, with the lead balls on the inside, the rotation and their inertia will force them to resist and cause them to indent the membrane, with pairs in the same “well” apparently attracting each other. The attractive force originates not with the pair of balls which are completely passive, but the fact that both are being pulled away from the straight line by the rotating rubber membrane, as they are forced into orbit around the centre of the ring’s rotation.

This is an elegant model because the size of the ring can remain constant, or it may expand or contract according to other influences. (Astronomers report that the universe is expanding, though it could reverse in the future.) And the driving force of the active or shining universe is in angular momentum. Once a bicycle wheel is turning, every part of the tyre experiences centripetal force away from the centre, determined by its mass and the speed of rotation, yet with no air and frictionless bearing will do so indefinitely and with no further input of energy.

Interesting though that rotation is around an axis (a line); the orbit exists in a plane which is two-dimensional. The dimension we have stripped off to simplify the model is the radial one (the dimension containing the spokes of the ‘wheel), not the dimension above and below the plane. Is the universe flat? I find it difficult to imagine the reinsertion of all dimensions to show how the model represents the real universe, especially when dimensions invent themselves. I think the rubber belt model is extremely elegant but it throws up a bunch of new conundrums. Of course we need two of them counter-rotating in the same plane to sum to zero angular momentum. Or could the belt be a Mobius shape? Wow! A two-sided belt with only one surface – relevance not clear, just a thought.