3 ms·

I'm also a Many-Worldser, but I don't quite know how to answer the question "How does the Born Rule work?" That is, if "worlds" branch off with some amplitudes

I'm also a Many-Worldser, but I don't quite know how to answer the question "How does the Born Rule work?" That is, if "worlds" branch off with some amplitudes, and there's a "me" on this branch and another on that branch, how does it make sense to talk about the probability of "me me" being this one or that one? Empirically we know how to calculate it from the amplitude, but why is that more reasonable than any other answer (if any answer is reasonable)?

gliese1337 7y ago
Well, yeah, there is that... I suppose one could argue that lacking an a-priori explanation for the way probability is allocated over state-space is equivalent to lacking an explanation for measurement, but that seems to me like claiming that we have no answer to how thermal emission of light works because we can't explain the measurement rule in QM, which I expect most physicists would balk at. Yea, there is still work to be done at a lower level, and there are other competing explanations at this level, but that doesn't mean that we don't have an explanation at this level. "How does the Born Rule work?" is a lower-level question than "how does measurement work?"
- repsilat 7y ago
  The "measurement problem" is really a Copenhagen-specific thing -- "measurement" is the fundamental and identifying mechanism of the interpretation, and it's problematic. And In the Copenhagen interpretation the Born Rule is inextricably tied to measurement outcomes. I guess you could say that MWI removes the wishy-nastiness around what constitutes measurement, when it happens etc, and that could constitute "solving the problem", but I think - Some of "the problem" has just been moved outside those borders. (And fine -- the MWI doesn't need to solve every problem to be an improvement. And I do think it's an improvement.) - The Born Rule is weirder* in the MWI. In Copenhagen it's axiomatic: We explicitly roll the dice, a nondeterministic outcome happens, that's the mechanism. In MWI it's an afterthought: The wavefunction evolves deterministically, and oh-by-the-way you should weight the likelihood of finding yourself here or there by the squared amplitude. Maybe that's unfair though?
Strilanc 7y ago
Consider a quantum computer running a classical inference process, specified as a reversible circuit. The inference process is estimating the probability of getting a 1 insead of a 0 from some trial, with trial results provided as a series of inputs into the computation. The output of the process is then written into some specific register. This is meant to be analogous to a human embedded in a quantum world, doing experiments and thinking in classical sort of way and writing down conclusions. Now go compute what happens when, instead of feeding classical trial results into this computation, you feed in a series of qubits each in the state a|0> + b|1>. You will find that the output register ends up storing a state extremely close to the representation of the probability |b|^2, up to some precision limited by the number of samples made available to the inference process. This indicates that "almost all the branches" must be agreeing on this particular value as the probability. That's the sort of way in which quantum mechanics, minus the Born Rule, predicts that almost all agents embedded in a quantum world will conclude that it follows the Born rule.
GoblinSlayer 7y ago
According to Bayesianism probability is a subjective interpretation for the purpose of decision making, so if you think this interpretation helps you, then it's fine.
- repsilat 7y ago
  I don't think it helps, I think it just punts on the question. Let's get concrete: I fire a polarised photon at a polarised filter oriented 30° off. In Copenhagen there's a 75% chance it goes through, and a 25% chance it hits the filter. In MWI there are two branches, one with squared amplitude of 0.75 and another with squared amplitude of 0.25, and there's a "me" on each side. Now, say I can bet on what happens at even money. In Copenhagen we'd say "betting on the photon going through is positive expectation." In MWI though, one of "me" wins and the other loses, and we just say "there's less subjective chance of being the loser"? Or "the loser has less amplitude, so less moral weight"? I don't think it's super satisfying.
  - GoblinSlayer 7y ago
    Bayesianism suggests you to derive your decision from squared amplitudes, MWI provides you the same numbers 0.75 and 0.25, you can use them as usual. This doesn't look specific to quantum mechanics, how does it work with other deterministic systems, like casino? Also bayesianism predates quantum mechanics.
    - repsilat 7y ago
      Sorry, I thought your original post was meant to address my original point. I said that the Born Rule (the association between squared amplitudes and subjective probabilities) isn't intuitive in MWI, and I thought you said "It makes sense because of Bayesianism." Does it provide a deductive argument for using the squared amplitude? Or does it just make use of the same empirical evidence everyone else uses, and actually not provide any explanatory power?
vokep 7y ago
There is 100% probability that you are both. Why are you this one and not the other? Because you are not the other one. The other one wonders why it isn't you. The tautology should begin to be obvious. The answer is the same answer to why you are not me and I am not you. (The problem is the same across space within a timeline as it is across timelines)
- repsilat 7y ago
  This sounds like the most reasonable conclusion until you actually start experimenting. An example taken from another thread: Fire a laser of polarised light at a polarised filter angled at an offset of 30°. Measure the light on the other side of the filter and you'll see it's 75% as bright. Now, you could say "We have worlds splitting independently for each photon that goes through or doesn't, and we're on all of those worlds," but that isn't explanatory -- it doesn't tell us why it looks like three quarters of the photons went through, as we always measure.

gliese1337 7y ago

Well, yeah, there is that... I suppose one could argue that lacking an a-priori explanation for the way probability is allocated over state-space is equivalent to lacking an explanation for measurement, but that seems to me like claiming that we have no answer to how thermal emission of light works because we can't explain the measurement rule in QM, which I expect most physicists would balk at. Yea, there is still work to be done at a lower level, and there are other competing explanations at this level, but that doesn't mean that we don't have an explanation at this level. "How does the Born Rule work?" is a lower-level question than "how does measurement work?"

repsilat 7y ago
The "measurement problem" is really a Copenhagen-specific thing -- "measurement" is the fundamental and identifying mechanism of the interpretation, and it's problematic. And In the Copenhagen interpretation the Born Rule is inextricably tied to measurement outcomes. I guess you could say that MWI removes the wishy-nastiness around what constitutes measurement, when it happens etc, and that could constitute "solving the problem", but I think - Some of "the problem" has just been moved outside those borders. (And fine -- the MWI doesn't need to solve every problem to be an improvement. And I do think it's an improvement.) - The Born Rule is weirder* in the MWI. In Copenhagen it's axiomatic: We explicitly roll the dice, a nondeterministic outcome happens, that's the mechanism. In MWI it's an afterthought: The wavefunction evolves deterministically, and oh-by-the-way you should weight the likelihood of finding yourself here or there by the squared amplitude. Maybe that's unfair though?

Strilanc 7y ago

Consider a quantum computer running a classical inference process, specified as a reversible circuit. The inference process is estimating the probability of getting a 1 insead of a 0 from some trial, with trial results provided as a series of inputs into the computation. The output of the process is then written into some specific register. This is meant to be analogous to a human embedded in a quantum world, doing experiments and thinking in classical sort of way and writing down conclusions. Now go compute what happens when, instead of feeding classical trial results into this computation, you feed in a series of qubits each in the state a|0> + b|1>. You will find that the output register ends up storing a state extremely close to the representation of the probability |b|^2, up to some precision limited by the number of samples made available to the inference process. This indicates that "almost all the branches" must be agreeing on this particular value as the probability. That's the sort of way in which quantum mechanics, minus the Born Rule, predicts that almost all agents embedded in a quantum world will conclude that it follows the Born rule.

GoblinSlayer 7y ago

According to Bayesianism probability is a subjective interpretation for the purpose of decision making, so if you think this interpretation helps you, then it's fine.

repsilat 7y ago
I don't think it helps, I think it just punts on the question. Let's get concrete: I fire a polarised photon at a polarised filter oriented 30° off. In Copenhagen there's a 75% chance it goes through, and a 25% chance it hits the filter. In MWI there are two branches, one with squared amplitude of 0.75 and another with squared amplitude of 0.25, and there's a "me" on each side. Now, say I can bet on what happens at even money. In Copenhagen we'd say "betting on the photon going through is positive expectation." In MWI though, one of "me" wins and the other loses, and we just say "there's less subjective chance of being the loser"? Or "the loser has less amplitude, so less moral weight"? I don't think it's super satisfying.
- GoblinSlayer 7y ago
  Bayesianism suggests you to derive your decision from squared amplitudes, MWI provides you the same numbers 0.75 and 0.25, you can use them as usual. This doesn't look specific to quantum mechanics, how does it work with other deterministic systems, like casino? Also bayesianism predates quantum mechanics.
  - repsilat 7y ago
    Sorry, I thought your original post was meant to address my original point. I said that the Born Rule (the association between squared amplitudes and subjective probabilities) isn't intuitive in MWI, and I thought you said "It makes sense because of Bayesianism." Does it provide a deductive argument for using the squared amplitude? Or does it just make use of the same empirical evidence everyone else uses, and actually not provide any explanatory power?

vokep 7y ago

There is 100% probability that you are both. Why are you this one and not the other? Because you are not the other one. The other one wonders why it isn't you. The tautology should begin to be obvious. The answer is the same answer to why you are not me and I am not you. (The problem is the same across space within a timeline as it is across timelines)

repsilat 7y ago
This sounds like the most reasonable conclusion until you actually start experimenting. An example taken from another thread: Fire a laser of polarised light at a polarised filter angled at an offset of 30°. Measure the light on the other side of the filter and you'll see it's 75% as bright. Now, you could say "We have worlds splitting independently for each photon that goes through or doesn't, and we're on all of those worlds," but that isn't explanatory -- it doesn't tell us why it looks like three quarters of the photons went through, as we always measure.