By "hard problem" do you mean harder than "If a tree falls in a forest does it make a sound?" or as hard as the hard problem of consciousness?

Would a Star Trek style teleporter teleport you or result in a new person (in a universe where you can be made of different atoms)? What if it creates the duplicate without destroying the original? Is there any action you can take that preserves identity?

Trolley problem. For that matter, utilitarianism vs. deontological ethics.

Copenhagen vs. Many Worlds. Many Worlds vs. Timeless. Those require an understanding of quantum physics, though.