I have developed a theory for why space would have to appear 3-dimensional for all observers and I would welcome feedback. I think it's possible to show that any causally-consistent system in which sequences can be observed can only have 3 spacelike dimensions.
I reasoned that, while for any two observers (Me & You) in motion WRT each other there will be some possible events, A & B, for which You will perceive A happening first but Me will see B preceding A. This is not the case of causally-connected events like a sequence of falling dominoes. Then, all observers agree on sequence.
Make special dominoes which flash a light pulse when they tap each other so, in a dark room, a row of falling dominoes would look like a series of flashes moving along the row. All observers of the flashes, regardless of their frame of reference, will agree on the sequence. Spacetime can twist and stretch but the lines-of-sight (light beams) cannot pass through each other. If lines-of-sight could pass through each other, different observers could see flashes out of sequence.
Anyway, it wasn’t until I read that it’s only possible for knots to be tied in 3 dimensions that the lines-of-sight argument clicked. In fewer, you cannot wrap a string about itself, and in more space dimensions, all knots fall open. After many hours of trying to imagine this, I convinced myself that in 4 space dimensions, you’d get the same problem with lines-of-sight… it would be possible to have observers who saw a different sequence.
It’s probably testable mathematically, but I don’t know how. Anyway, that’s my theory.
Thoughts?