Chaitan's construction and Uncertainty

Question

Is there a relationship between the Uncertainty Principle and Chaitin's construction?

e.g. if momentum is known, and position is uncertain, would it be correct to say position can be considered a physical example of a halting probability?

Comments

No. The halting problem is a problem in discrete mathematics, while the uncertainty relation is a property of an infinite-dimensional representation of the Heisenberg relations