[gmkiv]

I happen to agree with you, the observer is a quantum system must get entangled with the quantum system, but that still doesn't explain probabilities. If you prepare a system - say sqrt(1/3) spin-down + sqrt(2/3) spin-up, and then observe it, repeatedly, your subjective experience is that you saw spin-down 1/3 of the time, and spin-up 2/3 of the time. I don't understand how purely unitary evolution can explain this. Does it?

[lmm]

> I don't understand how purely unitary evolution can explain this. Does it?

What's the alternative? Assuming unitary evolution and some fairly common-sense axioms about how we'd expect subjective experience to behave (things like: we never experience being in a branch that has amplitude zero; if we experience being in a given branch then we continue to be in that branch), the Born probabilities are the only model anyone's ever come up with for how our subjective experience should go. So what's there to explain?

[millstone]

The alternative is non-MWI theories, which typically introduce the Born rule via new axioms.

Regarding what's to explain, it's quantum randomness (which distills the Born rule objection). Our subjective experience is that we see spin-down 1/3rd of the time, and our theories say the result is otherwise impossible to predict, even in principle. But a deterministic theory cannot produce a random outcome, even a subjective one.

[lmm]

> Our subjective experience is that we see spin-down 1/3rd of the time, and our theories say the result is otherwise impossible to predict, even in principle. But a deterministic theory cannot produce a random outcome, even a subjective one.

Whyever not? What else would you expect the subjective experience of being in a state like 1/sqrt(3)|x> + 2/sqrt(3)|y> to be like?

[Orlanthai]

There's a continuous infinity of alternate basis expansions. There's no reason to think you'd experience along that particular basis.

[lmm]

What would you expect "experiencing along those other bases" to look like? If you expand along a different basis you just get something like: half a chance of experiencing (1/sqrt(3)|x> + 2/sqrt(3)|y>), and half a chance of experiencing (1/sqrt(3)|x> + 2/sqrt(3)|y>), so it amounts to the same thing.

[Orlanthai]

Going from your last post.

> the structure of the wavefunction is that it divides cleanly into those two branches, and that's true in any basis.

It's not. It only has this Schmidt decomposition in one basis. In other bases there will be cross terms among the basis elements. What you're doing is privileging Schmidt bases as ones that give experiences. In another basis with states w,z say the state will be: |w>|w> + |z>|z> + |w>|z> + |z>|w>

So you won't be able to give this clean "experience" reading unless you posit we can't experience in things like the w,z basis here and only in Schmidt bases, but then you run into the problem that for real macroscopic systems they won't admit a Schmidt basis.

This seems like the kind of a "vague" Many Worlds where one doesn't look any deeper than pretending a macro-device is a qubit (e.g. no thermal states etc) and looking at one basis. There's a reason properly developed MWI is nothing like this such as the Spacetime State realism of Wallace and Timpson.

Why one would believe in quantum state realism at all is a separate question.

>Of course you can

No you can't, it's a direct consequence of the Kochen-Specker theorem. If the device is treated quantum mechanically and it enters an entangled state of the form you gave then you cannot perform conditioning as the Kochen-Specker theorem, via the non-uniqueness of Hilbert space orthogonal decompositions, prevents an unambiguous formulation of Bayes's law. I can link to papers proving this if you wish.

The fact that we do experiments where we can condition is, in light of this theorem, a demonstration that our measurement devices do not enter into the kind of CHSH states you're giving.

[Orlanthai]

Those are the same states so I'm not sure what you mean.

The point is that there is no reason to select out any particular basis over another. You can't just retreat into "well this is the only basis I can experience" because the human sensory apparatus would be able to select out a range of bases in a full unitary account and also the ambiguity of basis decomposition means you can't perform conditioning which we do all the time in experiments.

[Orlanthai]

Derivations like that don't work, you've just declared it by fiat but there's no such proof that is known to work.

[lmm]

There's no proof that it's the only possible way - but no-one's ever been able to come up with a concrete alternative.

[Orlanthai]

There are other alternatives such as the derivation of quantum theory within the GPT framework and many other axiomatic derivations.

I've never seen the Born rule derived from unitary evolution and axioms for how subjective experience should work, so I don't even see this as one of the ways.

[im3w1l]

To paraphrase you, how do we get from probability amplitude to observed frequencies if there is no collapse?

This is were we have to invoke philosophy. Specifically how does consciousness interact with time? The common-sense thinking is that our soul is tied to our body and is traveling forward through time with it. Another way of thinking is that the soul is tied to a given position of the space-time-probability. It does not travel. You today is not the same as you tomorrow or yesterday. The you that observes spin up is not the same you as the one that observes spin down. Your soul is perceiving reality from a randomly chosen vantage point among all the possibilities with which have a compatible body. If we condition on those bodies belonging to experimenters who have observed frequencies, then we get the distribution.

This is one possibility anyway.

[LittleTester]

No it can't. There have been many attempts and they don't work. The Born rule is independent of unitary evolution. The closest one can get is to declare that the quantum state is fundamentally a statistical object (i.e. the only information in it is observation probabilities) and then with certain assumptions about the size of the state space you can show that the Born rule is the only possible rule for connecting the state to statistics consistent with the unitary dynamics.

So under the assumption that the state encodes probabilities, state space assumptions and consistency with unitary evolution you get the Born rule. However this is not the same as the Born rule arising dynamically from unitary evolution alone.

[Enginerrrd]

Isn't your subjective experience just one probabilistic eigenvalue of a particular combination of operators corresponding to your observation? How does unitary evolution break down here?

[LittleTester]

It's not unitary evolution breaking down, just that the Born rule isn't a consequence of unitary evolution. They're separate independent hypotheses. In most derivations of QM from an axiomatic basis they're consequences of separate combinations of axioms.

[Enginerrrd]

Thanks. Do you by chance have a good source for a gentle introduction into axiomatic QM? Like undergrad level is fine, I've taken basic QM and worked through Griffith's intro book on my own, and I've had a lot of math.

I'd love to read more but my google results aren't turning up a good definitive introduction.