Classically, space is a $\Bbb R^3$ manifold. According to relativity, spacetime is $4$d although I understand this is Minkowski space. The thing I was curious about, is whether the two theories agree or disagree on how many orthogonal geodesics are possible. This is the precise formulation of the question I derived which captures its essence, in both the Newtonian and Relativistic models:
From the point of view of my own reference frame, how many objects can I perceive to all be travelling at speed arbitrarily close to $\sqrt 2\cdot c$ relative to each other? Do Quantum theory, Newtonian physics and relativity agree?
This question was received very badly on Physics stack Exchange. I'm neurodivergent so I can accept that it's me, but I don't think it's a bad question - but I do apologise in advance if you don't like it. It's a maths and physics question so I thought I'd try my luck here - from a pure mathematical perspective, so I accept I can't expect an empirical answer here.
EDIT
Where I give $\sqrt2 \cdot c$ as the apparent speed from the point of view of an observer, I'l using the interpretation of superluminar speed referred to in this answer: https://physics.stackexchange.com/a/107359/122325