This is very much a thinking-in-progress post rather than a finished argument. But I've been toying with this line of thought:
- The simultaneity relations between conscious mental states of an ordinary human (e.g., "itching while feeling cold") are not relative to reference frame.
- The simultaneity relations of spatially extended states of an object are relative to a reference frame.
- If conscious mental states are identical with or wholly constituted by brain states, then they are spatially extended states.
- So, conscious mental states of an ordinary human are neither identical with nor wholly constituted by brain states.
What makes this argument tricky—and this is the part I need think more about—is that of course the relativistic effects between different bits of the brain are practically negligible. The kind of time difference that would be involved in trying to see whether I started itching before starting to feel cold or whether it was the other way around would be so minuscule that I couldn't tell the difference as to which state started earlier or whether they started simultaneously. Nonetheless, there is some plausibility in thinking that there is a fact of the matter as to which state started earlier or whether they started simultaneously. Moreover, maybe we could imagine beings with bigger and faster brains where the effects would be real--and (1) plausibly isn't just a fact about us, but about any discursive agents with a single center of consciousness.
Here's an interesting thing. Suppose that one responds to the argument by saying that there is an absolute reference frame, despite relativity theory, much as defenders of the A-theory of time hold. That response doesn't get one completely out of the argument. We can argue: the absolute frame is insignificant for physics; yet it is significant for mind; so mind doesn't reduce to physics.
I also think the argument (though perhaps not the absolute-frame variant) may lead to some problems for supervenience theories of mind. But that's for future research.