6 ms·

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 pr

by gmkiv 6y ago

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?

LittleTester 6y ago
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 6y ago
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 6y ago
  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 6y ago
    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.
lmm 6y ago
> 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 6y ago
  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 6y ago
    > 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 6y ago
      There's a continuous infinity of alternate basis expansions. There's no reason to think you'd experience along that particular basis.
      - lmm 6y ago
        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.
im3w1l 6y ago
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.

by gmkiv 6y ago

LittleTester 6y ago

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 6y ago

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 6y ago
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 6y ago
  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.

lmm 6y ago

> 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 6y ago
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 6y ago
  > 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 6y ago
    There's a continuous infinity of alternate basis expansions. There's no reason to think you'd experience along that particular basis.
    - lmm 6y ago
      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.

im3w1l 6y ago

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.