Hmm, no, not really. The quantum fields follow “causality” in some quantum sense (roughly speaking, operators in spacelike separations commute, and any local operator can be expressed in terms of operators localized near the intersection of its past light-cone with any spacelike hypersurface), which is different from the sense used in causal DAGsa (in fact you can define “quantum causal DAGs” which is a different mathematical object). Violation of Bell’s inequality precisely means that you can’t describe the system by a causal DAG. If you want to do the MWI, then the wavefunction doesn’t even decompose into data that can be localized.
Violation of Bell’s inequality precisely means that you can’t describe the system by a causal DAG
No, violation of Bell’s inequality means you can’t describe the system by causal interactions among particles and measurements. If we stop thinking about particles and “measurements” altogether, and just talk about fields, that’s not an issue.
As you say, under MWI, the wavefunction doesn’t even decompose into data that can be localized. So, in order to represent the system using classical causal diagrams, the “system state” has to contain the whole wavefunction. As long as we can write down an equation for the evolution of the wavefunction over time, we have a classical causal model for the system.
Quantum causal models are certainly a much cleaner representation, in this case, but classical causal models can still work—we just have to define the “DAG vertices” appropriately.
It doesn’t really have much to do with particles vs. fields. We talk about measurements because measurements are the thing we actually observe. It seems strange to say you can model the world as a causal network if the causal network doesn’t include your actual observations. If you want to choose a particular frame of reference and write down the wavefunction time evolution in that frame (while ignoring space) then you can say it’s a causal network (which is just a linear chain, and deterministic at that) but IMO that’s not very informative. It also loses the property of having things made of parts, which AFAIU was one of your objectives here.
The wavefunction does have plenty of internal structure, that structure just doesn’t line up neatly with space. It won’t just be a linear chain, and it will be made of “parts”, but those parts won’t necessarily line up neatly with macroscopic observations/objects.
And that’s fine—figuring out how to do ontology mapping between the low-level “parts” and the high-level “parts” is a central piece of the problem. Not being able to directly observe variables in the low-level causal diagram is part of that. If we want e.g. a theory of abstraction, then these issues are perfect use-cases.
Hmm, no, not really. The quantum fields follow “causality” in some quantum sense (roughly speaking, operators in spacelike separations commute, and any local operator can be expressed in terms of operators localized near the intersection of its past light-cone with any spacelike hypersurface), which is different from the sense used in causal DAGsa (in fact you can define “quantum causal DAGs” which is a different mathematical object). Violation of Bell’s inequality precisely means that you can’t describe the system by a causal DAG. If you want to do the MWI, then the wavefunction doesn’t even decompose into data that can be localized.
No, violation of Bell’s inequality means you can’t describe the system by causal interactions among particles and measurements. If we stop thinking about particles and “measurements” altogether, and just talk about fields, that’s not an issue.
As you say, under MWI, the wavefunction doesn’t even decompose into data that can be localized. So, in order to represent the system using classical causal diagrams, the “system state” has to contain the whole wavefunction. As long as we can write down an equation for the evolution of the wavefunction over time, we have a classical causal model for the system.
Quantum causal models are certainly a much cleaner representation, in this case, but classical causal models can still work—we just have to define the “DAG vertices” appropriately.
It doesn’t really have much to do with particles vs. fields. We talk about measurements because measurements are the thing we actually observe. It seems strange to say you can model the world as a causal network if the causal network doesn’t include your actual observations. If you want to choose a particular frame of reference and write down the wavefunction time evolution in that frame (while ignoring space) then you can say it’s a causal network (which is just a linear chain, and deterministic at that) but IMO that’s not very informative. It also loses the property of having things made of parts, which AFAIU was one of your objectives here.
The wavefunction does have plenty of internal structure, that structure just doesn’t line up neatly with space. It won’t just be a linear chain, and it will be made of “parts”, but those parts won’t necessarily line up neatly with macroscopic observations/objects.
And that’s fine—figuring out how to do ontology mapping between the low-level “parts” and the high-level “parts” is a central piece of the problem. Not being able to directly observe variables in the low-level causal diagram is part of that. If we want e.g. a theory of abstraction, then these issues are perfect use-cases.
I know this was 3 years ago, but was this disagreement resolved, maybe offline?
I don’t think we’ve talked about it since then.