This question is connected to the old post:
But 1. was explained more in the string language, and 2. did bring up some additional interesting arguments without the need of the string language.
The space time was said to have 1 time dimension and 3 spacial dimension. I wonder if there's any connection, just from purely lagrangian perspective, which means the argument could be applied to both relativity and quantum, to the fact of the number of fundamental forces. The fundamental forces have 1 weakly interacting force, gravity, which connected to the the time itself, and 3 strong interaction forces, constrained the movement in space, strong, weak and electromagnetic, though the later was explained in the electroweak unification.
Historically after the standard model, the number of the fundamental forces were not quite interesting, as explained in 1., and it's not so obvious in Gravity as explained by John Rennie in 2 (https://physics.stackexchange.com/a/129868/209383), but I'm thinking that, just from a purely lagrangian perspective, is there some sort of hidden constraints that might have overlooked that actually stated that the number of fundamental forces had to be 4? For example, Peter Wills in 2 (https://physics.stackexchange.com/a/181095/209383 ) quoted Max Tegmark's little article(though the language was explained in strange terminology again), that, just from the property of the possible PDE solutions, the solution which was intended for the current perspective of physics meant the number of space time out to be 1 for time and 3 for space. But is there any connection between the way of the allowed fundamental interactions and the dimension of the spacetime, just from the lagrangian alone?
Is there any connection between the number of spacetime dimensions and the number of fundamental forces?
