Eliezer; My suspicion is that a better representation might take its basic mathematical objects as local states of entanglement.
A local state of entanglement is a bit of an oxymoron. Though you could take one part of an entangled state and trace over all distant degrees of freedom. You’d end up with a “reduced density matrix”. If you did that for each part separately, you’d have a set of reduced density matrices. To reconstitute the whole, you need some extra information as well, about how they fit together. In any case, that would be one way to pursue this program; a potentially more sophisticated version of searching for the “elements of reality” in the tensor factors of the global quantum state, which is a bit like using entanglement to define what is local, rather than vice versa.
If I had the time myself (and maybe I’ll make the time), I would be trying to pursue this line of thought in the context of “M(atrix) theory”, which I believe is a limit of string theory that reduces to point objects (“D0-branes”) connected by a web of strings (the rows and columns of the capital-M Matrix correspond to the D0-branes, the matrix elements to the strings connecting them). There are many people who think that those are the fundamental degrees of freedom of string theory, and it has the Machian, particulate, geometry-independent feel that one might expect of the bottom level. You would then be trying to piece together the quantum state of the universe from reduced D0-brane density matrices, basically. But I think that if you could do this, you wouldn’t need the many-worlds perspective any more. These quasilocal component quantum states would not be further reduced to amplitude distributions on little configuration spaces; they would be the ultimate states of things themselves.
Eliezer; My suspicion is that a better representation might take its basic mathematical objects as local states of entanglement.
A local state of entanglement is a bit of an oxymoron. Though you could take one part of an entangled state and trace over all distant degrees of freedom. You’d end up with a “reduced density matrix”. If you did that for each part separately, you’d have a set of reduced density matrices. To reconstitute the whole, you need some extra information as well, about how they fit together. In any case, that would be one way to pursue this program; a potentially more sophisticated version of searching for the “elements of reality” in the tensor factors of the global quantum state, which is a bit like using entanglement to define what is local, rather than vice versa.
If I had the time myself (and maybe I’ll make the time), I would be trying to pursue this line of thought in the context of “M(atrix) theory”, which I believe is a limit of string theory that reduces to point objects (“D0-branes”) connected by a web of strings (the rows and columns of the capital-M Matrix correspond to the D0-branes, the matrix elements to the strings connecting them). There are many people who think that those are the fundamental degrees of freedom of string theory, and it has the Machian, particulate, geometry-independent feel that one might expect of the bottom level. You would then be trying to piece together the quantum state of the universe from reduced D0-brane density matrices, basically. But I think that if you could do this, you wouldn’t need the many-worlds perspective any more. These quasilocal component quantum states would not be further reduced to amplitude distributions on little configuration spaces; they would be the ultimate states of things themselves.