You are fighting the hypothetical. It is a common pitfall when faced with a counterintuitive issue like that. Don’t do it, unless you can prove a contradiction in the problem statement. Omega is defined as a perfect predictor of your actions no matter what you do. That includes any quantum tricks. Also see the recent introduction to Newcomblike problems for a detailed analysis.
How does my objection fit into this: that it may not be possible for Omega to predict you in principle, since such an Omega would have to be able to solve the halting problem?
You are fighting the hypothetical. It is a common pitfall when faced with a counterintuitive issue like that. Don’t do it, unless you can prove a contradiction in the problem statement. Omega is defined as a perfect predictor of your actions no matter what you do. That includes any quantum tricks. Also see the recent introduction to Newcomblike problems for a detailed analysis.
How does my objection fit into this: that it may not be possible for Omega to predict you in principle, since such an Omega would have to be able to solve the halting problem?