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Juno_Watt comments on Probability is in the Mind - Less Wrong

60 Post author: Eliezer_Yudkowsky 12 March 2008 04:08AM

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Comment author: Juno_Watt 21 May 2013 05:34:27PM 0 points [-]

Nevertheless, we take a Bayesian attitude toward probability because it is fruitful; it allows us to make sense of natural questions that other philosophies can't and to keep things mathematically precise without extra complications. And we can extend this into the quantum realm as well

Where "extending" seems to mean "assuming". I find it more fruitful to come up with tests of (in)determinsm, such as Bell's Inequalitites.

Comment author: TobyBartels 22 May 2013 11:08:48PM 0 points [-]

I'm not sure what you mean by ‘assuming’. Perhaps you mean that we see what happens if we assume that the Bayesian interpretation continues to be meaningful? Then we find that it works, in the sense that we have mutually consistent degrees of belief about physically observable quantities. So the interpretation has been extended.

Comment author: Juno_Watt 23 May 2013 10:46:04AM *  2 points [-]

If the universe contains no objective probabilities, it will still contain subjective, ignorance based probabilities.

If the universe contains objective probabilities, it will also still contain subjective, ignorance based probabilities.

So the fact subjective probabilities "work" doesn't tell you anything about the universe. It isn't a test.

Aspect's experiment to test Bells theorem is a test. It tells you there isn't (local, single-universe) objective probability.

Comment author: TobyBartels 26 May 2013 07:14:15PM 1 point [-]

OK, I think that I understand you now.

Yes, Bell's inequalities, along with Aspect's experiment to test them, really tell us something. Even before the experiment, the inequalities told us something theoretical: that there can be no local, single-world objective interpretation of the standard predictions of quantum mechanics (for a certain sense of ‘objective’); then the experiment told us something empirical: that (to a high degree of tolerance) those predictions were correct where they mattered.

Like Bell's inequalities, the Bayesian interpretation of quantum mechanics tells us something theoretical: that there can be a local, single-world interpretation of the standard predictions of quantum mechanics (although it can't be objective in the sense ruled out by Bell's inequalities). So now we want the analogue of Aspect's experiment, to confirm these predictions where it matters and tell us something empirical.

Bell's inequalities are basically a no-go theorem: an interpretation with desired features (local, single-world, objective true value of all potentially observable quantities) does not exist. There's a specific reason why it cannot exist, and Aspect's experiment tests that this reason applies in the real world. But Fuchs et al's development of the Bayesian interpretation is a go theorem: an interpretation with some desired features (local, single-world) does exist. So there's no point of failure to probe with an experiment.

We still learn something about the universe, specifically about the possible forms of maps of it. But it's a purely theoretical result. I agree that Bell's inequalities and Aspect's experiment are a more interesting result, since we get something empirical. But it wasn't a surprising result (which might be hindsight bias on my part). There seem to be a lot of people here (although that might be my bad impression) who think that there is no local, single-world interpretation of the standard predictions of quantum mechanics (or even no single-world interpretation at all, but I'm not here to push Bohmianism), so the existence of the Bayesian interpretation may be the more surprising result; it may actually tell us more. (At any rate, it was surprising once upon a time for me.)