I've been thinking about some issues regarding gravity, and the need for gravity to be quantised, not for reasons of unifying any current laws of physics, but due to philosophical problems with classical gravity.
For gravity to operate, the curvature of space at every point needs to be stored. Mass shines out its existence at the speed of light with a ray of communication. Some points of space are more curved than others, depending on the strength of the gravity, but in essence this 'strength' is a simple result of the density of the rays emitted from the massive object. Let's assume these rays are streams of particles, the so-called graviton.
In classical gravity, this curvature of space can vary smoothly; sometimes shallow, sometimes steep. I presume that in a place without mass, space would be flat.
Space must be divided into tiny cells, grids, which store information like this. If not, there would be no sense of scale, no root, things would slide to infinity. Classical gravity has this problem, quantum mechanics does not; and the quantum must be correct. There are no infinities in the universe. One infinity would create another, and quickly and infinite number of infinite everything. If we find or need infinities, we, I submit, are wrong.
So, space is divided into cells which store information on the curvature of space into time. What sort of value is this? We may imagine it's a variable quantity, a 'steep' curve, a 'shallow' curve, no curve, an 'infinitely steep' curve. If this were the case then what value is the curvature of space on the boundaries between cells?
Thinking of this reminded me of the problem of dithering a sound wave into a low-bit resolution. I've written another piece here about audio dithering and quantum mechanics but I'll recapitulate. When digitising a smooth wave, we can assign a value to the nearest number that the wave amplitude corresponds with, sort of like fitting the wave into a series of boxes and choosing the nearest box to the current amplitude. See here:
Were are converting our nice smooth wave into 8 bits of digital, the 8 boxes on the right. Value 1 is exactly in the centre of the box, so that's perfect for the top box. Value 2 is not in the middle of a box, but it has a nearest box, so we put it there. Value 3 is on a boundary though... which box do we put it into?
We can choose top or bottom consistently, but there's something not quite right about it, because the reality we are trying to represent is that the sound is half way between, not in one box or the other.
The solution to the problem is dithering. We choose a random value, roll a dice so to speak, and 50% of the time we choose the top box and 50% of the time we choose the lower. For Value 2 we choose the upper box most of the time, but sometimes choose the lower box. This random value doesn't add 'noise', it makes the results more accurate; and quantum mechanics does the same thing. Dithering in this way is how and why quantum mechanics can be both accurate and random, and how it can avoid infinities by using random values in a digital arena.
Gravity must do the same, because without it any storage of analogue information on a cell-by-cell level would create inaccuracies across the cell boundaries. So, the curvature of space must not be a variable quantity, but a binary one. At each cell of space, space is flat or infinitely curved; that is all. What do we mean by the curvature of space, and flat and infinitely curved when we have already railed against infinities? General relatively shows that spatial dimensions are curved into the time dimension. Objects move fully in space, and the faster they move, the slower they move in time. At the speed of light, an object is moving fully in space and not at all in time. Stationary objects are not moving in space but moving fully in time. As an object accelerates, its movement through time decelerates.
This seems like a smooth, analogue process, but I postulate that it is not, that it is merely two extremes. At every point we either move fully though space at the speed of light, or move fully though time and are stationary. These are the only two values for the curvature of space: zero and one. Thus the map of the spatial curvature of our solar system is not smooth, analogue, and 'greyscale', but black and speckled with white. Compare these two photographs:
The latter is a binary image of the former, it uses only black and white dots, yet from a distance, the level of grey can be inferred due to random scattering. It is in this way, I postulate, that the curvature of space is stored. Objects which move though this space move, on a per-particle basis, fully through space or fully through time, but on average, it appears that the whole object is gliding through space-time in the correct proportions.
Problems regarding infinite spatial curvature in the centre of black holes vanish; objects are either stationary or moving at the speed of light. Everything on a quantum level is only doing either of these, and in our macroscopic experience changing rapidly between the two to produce the illusion of something in between.
