Metaphorical cones? Do you object to the possibility of geometrical representation of speed of influence-propagation in Hilbert space or what? Because (relativistic) quantum mechanics is local by both “you can’t spread influence faster than light” and “it uses only local derivatives” definitions of locality.
You can argue that QM doesn’t allow nonlocal influences or signalling, but that isn’t the result of the existence of anything analogous to a Hilbert space light cone, it’s the result of the fact that you cant control a nonlocal correlation,.so you cant signal with it. But nonlocal correlations are still there.
First, to be clear, there are direct analogs of lightcones in relativistic QM that disallows just moving faster than light. But even when talking about entanglement specifically, it depends how analogous you want it to be? It’s still “the space/equations prevent FTL signaling”—why it matters that it’s lightcone in pieces of paper case and “you can only move nearby blobs of amplitude in some dimensions”? I mean, from that perspective it’s kinda weird you can’t signal through entanglement. Is it just that it fits the “you can only affect stuff that is associated with your classical spatial location” definition of locality? But sticking to that definition is not motivated by the reasons we initially cared about it!
That’s not how it works. Hilbert spaces don’t even have light cones.
Metaphorical cones? Do you object to the possibility of geometrical representation of speed of influence-propagation in Hilbert space or what? Because (relativistic) quantum mechanics is local by both “you can’t spread influence faster than light” and “it uses only local derivatives” definitions of locality.
You can argue that QM doesn’t allow nonlocal influences or signalling, but that isn’t the result of the existence of anything analogous to a Hilbert space light cone, it’s the result of the fact that you cant control a nonlocal correlation,.so you cant signal with it. But nonlocal correlations are still there.
First, to be clear, there are direct analogs of lightcones in relativistic QM that disallows just moving faster than light. But even when talking about entanglement specifically, it depends how analogous you want it to be? It’s still “the space/equations prevent FTL signaling”—why it matters that it’s lightcone in pieces of paper case and “you can only move nearby blobs of amplitude in some dimensions”? I mean, from that perspective it’s kinda weird you can’t signal through entanglement. Is it just that it fits the “you can only affect stuff that is associated with your classical spatial location” definition of locality? But sticking to that definition is not motivated by the reasons we initially cared about it!