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We live in a 3D world comprised of 4 dimensions, if you include time. The unit of spacetime as we "see" it is the proton, comprising of 6 quarks, fermions. Hence since these quarks cannot occupy the same "space" and they are confined by the strong force to the lowest state , then the optimal configuration would be a 3D cartesian systems, i.e. the orbits would always average out to maintain the stable 3D configuration w.r.t the couplings.

So, if our 3D world is defined by the 3D proton, can you extrapolate this idea to dark matter and say the dark matter could be world with a different proton configuration, a higher order of quarks similarly confined.?

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Dark matter cannot be made out of quarks. Primordial nucleosynthesis is well understood, and the limits on how much matter it could have created are restricted by the relative amounts of hydronge, helium, etc that were created. For details see the question Why can't dark matter be baryonic? and Why isn't dark matter just ordinary matter?.

You are quite correct that excited states of the quarks inside a proton exist, but they are just normal matter and have been observed in accelerators. For example the $\Delta^+$ baryon is also composed of two up and one down quarks.

One last comment: you say our 3D world is defined by the 3D proton but this is the wrong way round. The bound state of the quarks that makes up a proton is defined by the dimensionality of spacetime, not the other way around.

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  • $\begingroup$ "wrong way round"? If there were no fermions, would there be any space, let alone 3D space? $\endgroup$ – A' Oaktree Aug 2 '15 at 5:07
  • $\begingroup$ @A'Oaktree: in all experimentally tested theories there is no connection between the existance of spacetime and the existance of fermions. Indeed, spacetime could exist quite happily even if no matter were present. That's what the Minkowski metric describes. In string theory the situation is a bit different since the theory implies the existance of both spacetime and matter. However this still does not mean fermions create spacetime. $\endgroup$ – John Rennie Aug 2 '15 at 5:18
  • $\begingroup$ Minkowski metric is the best fit mathematical but not be considered final, nothing is final. I guess the question is one of definitions, what is the accepted definition of spacetime and as you pointed out the Minkowski space is definitely on the leading edge. But the Pauli exclusion principle states that fermions cannot occupy the same space. By Pauli we can also see why bosons can indeed occupy the same space and hence would converge to the same quantum state. So without fermions to stretch the spacetime continuum by Pauli, space would also collapse. Fermionic fields stretch space = Gravity? $\endgroup$ – A' Oaktree Aug 2 '15 at 13:20

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