Consistent histories vs. relational interpretation and Qbism

Question

I hope that my question will be suitable for this forum: I would like to understand the difference between the so called consistent history approach to QM and several other interpretations. In this discussion it is remarked that similarly to the many worlds interpretation, there is no wave function collapse in the consistent history approach: the collapse is only apparent and is caused by the interactions with the environment, in the so called decoherence effect. But there are big differences between CH and MWI: CH is fundamentally probabilistic while MWI is deterministic; there is one world in CH (but there are many ways of describing it) while MWI carries ontological baggage: all branches are no less real than our branch. So I would agree that these approches are quite different.

However, if insetad of MWI I switch to relational interpretation (by Carlo Rovelli) or to QBism, these differences disappear: both interpretations (relational and Qbism) are probabilistic and both assume unique world: in relational approach we speak about properties of the system with respect to another system, in QBism we speak about properties with respect to agents: in CH the role of the system/agent is, as far as I understood, played by a ,,set of questions which we would like to ask'' (the so called framework). I don't see where the difference lies beside slightly different philosophical flavour of way of putting it. So I would like to ask:

In which sense is consistent histories interpretation different from relational interpretation and from QBism?

Also, I believe that QBism became much more popular nowadays and CH interpretation seems a little bit forgotten:

Why was consistent histories interpretation abandoned by a physics community?

Answer 1

From a birds-eye view, all three of these are quite similar. (Consistent Histories = CH, Relational Quantum Mechanics = RQM, and QBism= QB.)

When Rovelli first published his take on RQM (1996), he explicitly compared it to CH, and didn't see much difference. QB wasn't yet around.

To read Rovelli, RQM is perfectly compatible with CH. RQM simply points out the biggest issue/problem with CH and takes it seriously rather than sweeping it under the rug. This matches my own reading, and may explain why CH doesn't have too big of a following these days; that rug-sweeping either bothers people, or is taken seriously, pushing them into RQM and/or QB.

CH points out that there are "consistent" sets of histories (events/outcomes) to which one can assign ordinary classical probabilities, so it's tempting to think of one of those sets as representing some "real" history of "real" events. But RQM then stresses the key point dodged by CH: By changing one's perspective (say, by later setting up a different experiment) one can somehow change which of those earlier histories belong in the proper "consistent" set of realistic histories. Which makes the original histories now look unrealistic (inconsistent).

(Aside: one response to this problem would be to explore the possibility that future experimental settings might help determine what really happened in the past, but that's not the response of either RQM or QB; both of those explicitly reject any future-input-dependence.)

The RQM response here is to say that different observers don't have to agree as to their consistent histories; it's all relational. What's true for one observer doesn't have to be true for another. The set of all things which are true for all observers is then what's "really" there, in the world, not merely one objectively correct history. If the reason that some people liked CH was the realistic-history part, you can see why they might jump ship once this point was clearly stressed.

QB takes a similar agent-centered perspective as RQM, but dodges the question about what is really there (depending on whose take on QB you're reading). According to QB, quantum theory just tells us how to apply and update our subjective beliefs, and does not tell us anything about reality. Evidently, if it's all about beliefs, it's then more reasonable for two observers not to agree with each other. It's all just credences, anyway. (But credences about what, exactly? That's left unanswered.) If you imagine that the credences are about each agent's slice of RQM's giant interrelational reality, I think those two perspectives probably fit together reasonably well, at the expense of some global objectivity.

That said, there are certainly also some differences between RQM and QB, as stressed by this paper -- but you'll have to get pretty far into the weeds of probability theory to see most of those differences.