What if quantum gravity makes probabilities themselves uncertain?

Using a mathematical structure called SU_q(2) — a 'quantum deformation' of ordinary rotational symmetry thought to emerge near the Planck scale — the authors show that probabilities for spin measurements no longer commute with each other. This creates a Heisenberg-like uncertainty relation between probabilities themselves: knowing the odds of one spin outcome forces the odds of another to be indefinite. Two observers using such a framework can never precisely agree on their relative orientation.