I've had an interesting discussion with Ian Durham which I'd like to re-iterate here:
[Myself]
Hi Ian, you sound like an intelligent guy who's mathematically minded so I want to put to you this quandry regarding another ancient Greek:
Newton's inability to consider a particle model for the force of gravity has left a legacy where the ideology of a spacetime continuum has been set in stone. His equation negates the possiblity of a particle for the force of gravity. If he had considered the Archimedes screw as a GRAVITON he would have included an element of ORIENTATION in his simplistic equation, wouldn't he?
[Ian Durham]
Hmmm. Why does his equation negate a particle model for gravity? Coulomb's law is similar and yet we have a very successful particle model for electrostatics.
[Myself]
His declaration of universality or put simply "every object attracts every other object equally in all directions" is a BIG assumption which is then set in stone within his gravity equation. No wonder it can't be reconciled with particle based QM! Why did no-one at the time of Newton consider the Archimedes screw as a mechanical method for explaining the force of gravity, his spooky action at a distance?? The history of science would have been very different if someone had imo!
I'd just like to re-iterate my point about a spinning helix which travels around a hypersphere being analogous to an electric circuit. Imagine you are on the inside of a battery which is connected to a simple loop of wire which makes an electric circuit. Imagine a handle rotates clockwise from the positive terminal as seen from your internal perspective. Now trace this turning handle as it travels along the wire and arrives at the negative terminal of the battery. Which way is the handle now turning from the viewpoint of the battery's interior? Is it clockwise or is it anti-clockwise?
The thought experiment illustrates the important relationship between chirality, loops and mirror images. Incidentally, I learnt from a repeat of QI on TV last night about oranges and lemons. The aroma of a lemon is the exact mirror image of an orange and vice versa. Our olfactory sense, the first one to develop via evolution I believe, is ultra sensitive to right and left handedness of airborne molecules, which I find quite interesting.
[Ian Durham]
Very interesting concept, but I still don't see why his theory of gravity is any different in that sense from electrostatics. In other words, just because he worded it in a certain way doesn't automatically make it incompatible with a particle model. It certainly could have affected the interpretation historically, but it doesn't a priori rule out a particle interpretation.
[Myself]
Okay, that's a good point about the similarity with electrostatics, which I've just thought about a bit more. The difference is that Coulombs law assumes "charged" particles, so that they come in two opposite types. Electric charge is a physical property of matter which causes it to experience a force when near other electrically charged matter. The way these two types interact hasn't been modelled by mechnical means, just like gravity itself. Why do like charges attract and opposites repell? The mechanism is an enigma.
If a 'fabric' of spacetime is visualised as the 'mechanism' of gravity, then this fabric is uniform and symmetrical. It therefore can't be the cause of the elctrostatic forces. His equation therefore negates gravity as being behind the eletrostatic force. It therefore renders the unification of all the forces an impossiblity. Therefore his equation must be wrong imo.