For the reader who is unfamiliar: This refers to a position I have previously taken with respect to ontology of mind. I will put a version of it here in quotes, for future reference. I apologize in advance for the length and complexity of my discussion below.
I have said: Qualia exist objectively, but functional states are inherently vague when it comes to microphysical details. There are edge cases, there is a sorites problem, which prevent the definition of a functional state from being made microphysically exact for all physical states, in a non-arbitrary way. But it needs to be exact, if it is to be part of a psychophysical bridge law that specifies for each possible physical world, what qualia that world contains.
In a dilemma between computation-based and substrate-based theories of consciousness, I have therefore preferred the latter, in the sense that I prefer a theory of qualia which is based on states and properties whose existence is just as objective.
At the same time, I have also said: Conscious states are complex unities in which numerous qualia are united in some way; perhaps they correspond to entangled states, these being complex in various ways, while also not being tensor products (tensor products being the standard way to construct a mereological sum in quantum mechanics).
But @green_leaf is asking, how are entangled states any more objective than functional states?
This is a valid question because, if you look at things from the perspective of a wavefunction of the universe, everything is entangled with everything else! There is a risk that constructing exact states for subsystems of the universe will once again require arbitrary choices.
But first a few words on distinctness of states and exactness of properties in quantum theory.
First of all, let me emphasize that according to the Copenhagen interpretation of quantum theory, wavefunctions are not “elements of physical reality”, they simply codify the knowledge of an observer. The elements of physical reality are the “observables”. Schrodinger and Einstein criticized this framework as necessarily an incomplete description of reality.
The most elegant heir to the Copenhagen interpretation is what I’ll call the Hartle multiverse model (though Gell-Mann and Omnes worked on it too). This has a wavefunction of the universe, then a set of observables (e.g. field values and/or field momenta at particular space-time locations) whose possible values define a set of possible histories. If these histories all satisfy the technical property of being mutually decoherent, then each history inherits an apriori probability from the universal wavefunction, and you can derive ordinary quantum mechanics from conditional probabilities within this ensemble of possible histories.
This formalism in itself is not yet a full-fledged ontological interpretation of quantum theory. For that, I add the further postulate that these decoherent histories are maximally fine-grained—you can’t add any more observables while retaining the decoherence condition. This does not yet single out a unique ensemble—Dowker and Kent pointed out that there’s a vast number of choices for the maximally fine-grained observables.
But a few extra postulates might suffice to single out a unique ensemble. Maybe a rule, similar to a cellular automaton rule, that determines the observables. Maybe a principle that the apriori probabilities must all be equal. At this point you’d have a multiverse theory with no ambiguity about what is posited to exist, and no problem of some worlds having a larger probability measure than others.
That’s all a digression but I’ll return to it later.
Strictly speaking, according to the Copenhagen interpretation, wavefunctions are not fundamental physical entities, they are just epistemic states. However, most quantum physicists talk like defacto wavefunction realists, and any choice of definite values for the observables can be encoded in a wavefunction, the corresponding eigenstate. So I’ll talk as a wavefunction realist from now on.
Returning finally to distinctness and exactness… An eigenfunction of an observable is definitely exact. If the observable also has a discrete spectrum of possible values, such as the energies of an electron bound to an atomic nucleus, the eigenfunctions will also be inarguably distinct: the different orbitals in an atom are separated from each other by a quantum jump in the energy.
However, it’s the exactness of the state that I was after. I have no problem with a continuum of quantum states being mapped onto a continuum of qualic states. I have a problem with psychophysical mappings which get microphysically vague on the physical side, because if we ask about an edge case, what qualia are present, there’s no definite answer. At worst, you could even end up with no definite answer about whether or not a given possible physical world contains a person, a conscious being.
Now let us consider entangled wavefunctions. They give us a whole new set of properties which, in principle, could be part of a psychophysical correspondence between quantum and quale. There are not only the various measures of entanglement, which quantify how much entanglement is present; there are the different forms of multipartite entanglement (e.g. Borromean states, a form of tripartite entanglement analogous to the Borromean rings, no two of which are linked, but which as a trio cannot be separated). I’m not really sure how rich these possibilities are, but they are a novel kind of physical property on which conscious states might supervene.
However, I already mentioned the issue that validates @green_leaf’s question: if the universal wavefunction is the ultimate objective description of the physical world, then everything is entangled with everything else. For example, all occurrences of any given species of fermion, such as all electrons, are antisymmetrically entangled with each other. This is implied by the spin-statistics theorem, and this is what implements the Pauli exclusion principle, that keeps the electrons (in atoms and molecules) in their separate orbitals. Wavefunctions describing just a few entangled entities, such as show up in quantum chemistry and quantum computing, are truncations of this universal entanglement, and have no particular claim to objective significance. There is a psychophysical sorites problem, not just for functionalism, but for “wavefunctionalism”.
It is possible that dynamics within the universal wavefunction does produce localized temporary examples of complete disentanglement. Maybe a natural mereology could be built on this. But otherwise, my only counter-proposal would be a version of the maximally fine-grained Hartle multiverse which, to my knowledge, has never been investigated: one in which the observables, the elements of physical reality, are “multipartite” in some way. Since in fundamental physics we deal with quantum fields, I think the logical candidates are observables associated with extended objects, like “Wilson loops” and “surface operators”. Interestingly, Lee Smolin worked both on a version of loop quantum gravity in which the physical states are eigenfunctions of gravitational WIlson loops, and on a version of “quantum causal histories” which might be sufficiently general to allow for a Hartle multiverse with multipartite observables. It would be interesting to implement something like these in a well-explored modern framework like AdS/CFT.
If something like this turns out to be viable, not just as physics but as psychophysics, then functionalism’s emphasis on causality and representation will still be relevant! It’s just that to produce specific conscious states, casual structure alone would not be enough, the substrate would need to be these fundamental extended observables, and not virtual state machines running at a more coarse-grained level of description.
For the reader who is unfamiliar: This refers to a position I have previously taken with respect to ontology of mind. I will put a version of it here in quotes, for future reference. I apologize in advance for the length and complexity of my discussion below.
This is a valid question because, if you look at things from the perspective of a wavefunction of the universe, everything is entangled with everything else! There is a risk that constructing exact states for subsystems of the universe will once again require arbitrary choices.
But first a few words on distinctness of states and exactness of properties in quantum theory.
First of all, let me emphasize that according to the Copenhagen interpretation of quantum theory, wavefunctions are not “elements of physical reality”, they simply codify the knowledge of an observer. The elements of physical reality are the “observables”. Schrodinger and Einstein criticized this framework as necessarily an incomplete description of reality.
The most elegant heir to the Copenhagen interpretation is what I’ll call the Hartle multiverse model (though Gell-Mann and Omnes worked on it too). This has a wavefunction of the universe, then a set of observables (e.g. field values and/or field momenta at particular space-time locations) whose possible values define a set of possible histories. If these histories all satisfy the technical property of being mutually decoherent, then each history inherits an apriori probability from the universal wavefunction, and you can derive ordinary quantum mechanics from conditional probabilities within this ensemble of possible histories.
This formalism in itself is not yet a full-fledged ontological interpretation of quantum theory. For that, I add the further postulate that these decoherent histories are maximally fine-grained—you can’t add any more observables while retaining the decoherence condition. This does not yet single out a unique ensemble—Dowker and Kent pointed out that there’s a vast number of choices for the maximally fine-grained observables.
But a few extra postulates might suffice to single out a unique ensemble. Maybe a rule, similar to a cellular automaton rule, that determines the observables. Maybe a principle that the apriori probabilities must all be equal. At this point you’d have a multiverse theory with no ambiguity about what is posited to exist, and no problem of some worlds having a larger probability measure than others.
That’s all a digression but I’ll return to it later.
Strictly speaking, according to the Copenhagen interpretation, wavefunctions are not fundamental physical entities, they are just epistemic states. However, most quantum physicists talk like defacto wavefunction realists, and any choice of definite values for the observables can be encoded in a wavefunction, the corresponding eigenstate. So I’ll talk as a wavefunction realist from now on.
Returning finally to distinctness and exactness… An eigenfunction of an observable is definitely exact. If the observable also has a discrete spectrum of possible values, such as the energies of an electron bound to an atomic nucleus, the eigenfunctions will also be inarguably distinct: the different orbitals in an atom are separated from each other by a quantum jump in the energy.
However, it’s the exactness of the state that I was after. I have no problem with a continuum of quantum states being mapped onto a continuum of qualic states. I have a problem with psychophysical mappings which get microphysically vague on the physical side, because if we ask about an edge case, what qualia are present, there’s no definite answer. At worst, you could even end up with no definite answer about whether or not a given possible physical world contains a person, a conscious being.
Now let us consider entangled wavefunctions. They give us a whole new set of properties which, in principle, could be part of a psychophysical correspondence between quantum and quale. There are not only the various measures of entanglement, which quantify how much entanglement is present; there are the different forms of multipartite entanglement (e.g. Borromean states, a form of tripartite entanglement analogous to the Borromean rings, no two of which are linked, but which as a trio cannot be separated). I’m not really sure how rich these possibilities are, but they are a novel kind of physical property on which conscious states might supervene.
However, I already mentioned the issue that validates @green_leaf’s question: if the universal wavefunction is the ultimate objective description of the physical world, then everything is entangled with everything else. For example, all occurrences of any given species of fermion, such as all electrons, are antisymmetrically entangled with each other. This is implied by the spin-statistics theorem, and this is what implements the Pauli exclusion principle, that keeps the electrons (in atoms and molecules) in their separate orbitals. Wavefunctions describing just a few entangled entities, such as show up in quantum chemistry and quantum computing, are truncations of this universal entanglement, and have no particular claim to objective significance. There is a psychophysical sorites problem, not just for functionalism, but for “wavefunctionalism”.
It is possible that dynamics within the universal wavefunction does produce localized temporary examples of complete disentanglement. Maybe a natural mereology could be built on this. But otherwise, my only counter-proposal would be a version of the maximally fine-grained Hartle multiverse which, to my knowledge, has never been investigated: one in which the observables, the elements of physical reality, are “multipartite” in some way. Since in fundamental physics we deal with quantum fields, I think the logical candidates are observables associated with extended objects, like “Wilson loops” and “surface operators”. Interestingly, Lee Smolin worked both on a version of loop quantum gravity in which the physical states are eigenfunctions of gravitational WIlson loops, and on a version of “quantum causal histories” which might be sufficiently general to allow for a Hartle multiverse with multipartite observables. It would be interesting to implement something like these in a well-explored modern framework like AdS/CFT.
If something like this turns out to be viable, not just as physics but as psychophysics, then functionalism’s emphasis on causality and representation will still be relevant! It’s just that to produce specific conscious states, casual structure alone would not be enough, the substrate would need to be these fundamental extended observables, and not virtual state machines running at a more coarse-grained level of description.
Thanks—I’ll get back to this as soon as I have time.