kcdodd wrote:I think if you ever encountered a situation where momentum was not conserved, like an object which could be pushed on without changing its momentum, you would find that space itself is breaking symmetry.
There is no contest to the conservation of momentum. But momentum is only transferred if there is a displacement during the application of the force. That's the very heart of the point I am making. If something is 'fully stationary' (in the universe's CoM frame), then you cannot transfer momentum to it by a static force in the universe's CoM frame because the origin of that force must also come from something fixed in the CoM - yet both are stationary to each other!
I take your point that if you can push yourself away from a thing that doesn't move then you've created momentum spontaneously, which is not possible. But that's not my point. What I'm saying is that if you find something 'stationary' then it is not so much that you can push yourself away from it, so to speak, but that you just can't find a way to apply a force at all! It won't have any 'handles' to push or pull on!
And, indeed, a photon appears to be such an object. A thing with a 'force-less momentum'. Which implies we are moving at the speed of light with respect to the CoM of the universe, and the photons are stationary. Let me now re-phrase something relativity says, and make it trivial; "nothing can move slower than the speed of a photon". It is an utterly trivial statement because nothing can go slower than 'stopped'!!!
So I've now covered the origin of gravity, and that things don't appear to be able to go 'faster' than light speed. D'you want some more deductions, arising from my description of forces, or is that too much already?...