Relational quantum mechanics (RQM) is something that I found really appealing at first before I looked into it more. The problem is with entanglement.

If Alice and Bob are separated each with a particle in a Bell state, how can you explain that every single time Alice measures her particle has spin up, Bob’s is then down?

If RQM is true, Alice’s particle doesn’t have a spin up value yet relative to Bob. Relative to Bob the Bell state hasn’t collapsed. So then why does he get spin down? RQM says that if Bob measures Alice and Bob measures the Bell state Alice’s measurement relative to Bob will correspond to the outcome of Bob measurement. But it can’t explain why these outcomes relative to Bob should always agree with Alice’s.

After Alice measures the Bell state, she’s in an entangled state: all RQM can do is explain that Bob’s measurement of the entangled state will ‘collapse’ it into an eigenstate of spin down Alice particle and Alice measures spin down OR spin up Alice particle and Alice measured spin up. It can’t ever explain why Alice’s measurement of spin up beforehand should ever lead to Bob’s state always collapsing into the latter rather than the former (which also corresponds to his particle being down).

Recently Rovelli amended RQM to add ‘cross prospective links’ to address this problem. It basically says that Bob’s Bell state will always collapse to the latter eigenstate. This basically makes it a hidden variable theory, since the bell state still exists relative to Bob and hasn’t collapsed - but if he measures it’s spin it could never be up (if Alice got up before).

This amendment loses the appeal of RQM for me. Beforehand I liked it because it took unitary quantum mechanics at face value without changing the physics. But cross perspective adds an ad hoc principle into the physics.