I am slightly suspicious of starting with what seems to me a mostly metaphysical premise.
But surely you should not be. Leibniz defined metaphysics, or 'first' philosophy, as the task of making clear what you want to mean by words like time, space, thing, or cause before you try building them into a 'physics'. Surely that is exactly what you have to do first.
William James defined it as 'nothing but an unusually obstinate effort to think clearly'. In my experience metaphysics is only used to mean untestable or woo-woo by people who don't make that effort!
While it seems intuitively right that my experience does not merge with someone else's, I am not sure this is I impossible per se.
Yes, it is. It goes back to Aristotle and identity. You cannot change an entity because then it is a different entity. If your experience merged with someone else's it would no longer by your experience. It would have to be the experience of some combined 'me'. Leibniz realised that his all becomes self-contradictory. The very existence of a me was moot in 1676 and Leibniz worked out that Spinoza's 'me-less' cosmos was contradicted by one phenomenon - the distinctness of 'points of view'. A separate subject can only be defined as such in terms of a separate point of view. Merged points of view are a contradiction. They are just new points of view.
Or—more realistically—that my own experiences from a moment ago doesn't merge (to some degree) with my experience from now. Naively, given the messy nature of our brains, I would find this even much more likely than a clean "quantization" of experience.
Agreed. This is the one thing Leibniz never quite handles in a way that convinces. He wants temporal continuity but also temporal individuation of events. Bertrand Russell identified this problem and the Leibniz scholar Richard Arthur and I have spent happy times discussing how you resolve it and writing papers and books on that. This is a very complicated area but my current conclusion is that post-1980 QFT provides an elegant resolution that fits perfectly within the fundamental epistemic structure that quantum theory provides us with. In essence Bose modes associated with ordered condensed matter allow both for a string of events, involving shifts in the energy content quantum number, and an enduring indivisible, being the enduring ordered structure that the mode occupies.
So continuity across events of an indivisible identity probably can occur in quantum theory, even if Feynman tells us not to make that mistake for things like electrons. We still have a very robust requirement of dynamic indivisibles.
But classical physics allows building systems of discrete, indivisible state as well.
Can you give an example? My understanding is that Leibniz's 'weakness' in popularity terms at least was to focus too much on rigour. Newton just wrote equations that worked for arbitrarily divisible chunkings. Even he hated his theory of gravity and was frustrated by metaphysical implications of his optics that he could not explain, but his equations were useful.
How can a composite dynamic system have an indivisible state? Newton shows that you can cheat and treat a planet as a centre of gravity, but only accurately if you are far enough away from it. 'Systems' as now conceived are by definitions divisible into the dynamic components that form the system.
When I see an apple and smell an apple that is one experience. But it surely must involve different neurons for smelling and seeing. Why shouldn't it be separatable? Why shouldn't smelling itself be seperatable into "smelling but a bit less intense"?
Yes, different neurons mediate the input and collation of different sensory modlaities, but these are events prior to the experience. There is no 'honey smell' or 'red', of the sort we report, associated with these earlier neural events or the nose or retina. We may see 'red' simply because an area of the visual field has slightly less blue and green input. Some nerves somewhere in visual cortex infer that this area is 'redder' and tell some other nerves about this. 'Our' experience must belong to the nerves being told that it is redder.
And we know that the neural code does not work like pixels. It works like sentences such as x is red, x is round, x is left of y, y is the same as x but smaller, x is one of five, all five are the same colour. Neurons pass signals like this to each other and receiving neurons experience the totality of their meaning. Nobody has any understanding of the rules or 'reasons' for this but both Descartes and Leibniz saw clearly the need to propose this extra 'intrinsic interpreter' property. Domains of quantised fields and/or their excitations must have an intrinsic ability to support meaning.
