You assume that the conscious part of the brain consists of interacting but independent subunits, whose only property of significance is how they interact with their neighbors.
This is not the only ontological option. For example, there is the quantum notion of entanglement. There may exist a situation in which there are nominally two entities, but the overall quantum state cannot be reduced to one entity being in one state, and the other entity in a second state.
Consider a state of two qubits. If the overall state is |01>, that can be decomposed into |0>|1>. But a superposition like |01>+|10> cannot.
There is a further issue of whether one ascribes reality to quantum states. In the (original, true) Copenhagen interpretation, quantum states are not real things, that role is reserved only for observables and only when they take definite values.
However, if one’s ontology says quantum states are things that exist, and if the conscious part of the brain is one big entangled state, then you can’t just replace the parts independently. There may be other operations you can perform, like quantum teleportation, but what they signify or allow, in the way of identity transfer, is unclear (at least, in the absence of a definite quantum theory of consciousness).
You assume that the conscious part of the brain consists of interacting but independent subunits, whose only property of significance is how they interact with their neighbors.
This is not the only ontological option. For example, there is the quantum notion of entanglement. There may exist a situation in which there are nominally two entities, but the overall quantum state cannot be reduced to one entity being in one state, and the other entity in a second state.
Consider a state of two qubits. If the overall state is |01>, that can be decomposed into |0>|1>. But a superposition like |01>+|10> cannot.
There is a further issue of whether one ascribes reality to quantum states. In the (original, true) Copenhagen interpretation, quantum states are not real things, that role is reserved only for observables and only when they take definite values.
However, if one’s ontology says quantum states are things that exist, and if the conscious part of the brain is one big entangled state, then you can’t just replace the parts independently. There may be other operations you can perform, like quantum teleportation, but what they signify or allow, in the way of identity transfer, is unclear (at least, in the absence of a definite quantum theory of consciousness).