Existence of objects arising in physics

Question

If you look at the configuration space of a robot arm, its a manifold, does this manifold exist in the same sense as strings in string theory? Or do the strings in string theory exist in another sense? What objects actually exist? What are the different levels physical objects can exist? Spacetime and particles, is that all that exist? If you accept holographic principle everything can exist on a boundary? So which description is right? Or are both right, that this is a duality that violates our intuition like the wave particle duality?

Answer 1

Existence of the manifolds is existence in the mathematical (platonic) sense. Existence of a physical object usually means (on the level of theoretical physics) that the object can be modeled as a mathematical object having a (classical or quantum) state. A property of an object exists (on the same level) if it can be expressed in terms of expectation values of observables defined on the state space and determined by the state. For example, an electron has mass, charge, position, and spin in any direction, although the latter two have sharp values only under special circumstances. 

A string in string theory has a state, and a robot arm has one (in the cotangent space of the configuration manifold) , so they are physical objects (on the level of theoretical physics). But the manifold of robot arm configurations has no state hence it cannot be said to be physically existent, though it is used to describe physical objects, namely robot arms. 

Of course, existence in nature is a much more restricted matter, as in this case the model is required to match Nature suffciiently well.