Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

TobyBartels comments on Probability is in the Mind - Less Wrong

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

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (190)

Sort By: Old

You are viewing a single comment's thread. Show more comments above.

Comment author: TobyBartels 13 July 2011 11:04:53AM *  0 points [-]

Please explain how you know this?

I wouldn't want to pretend that I know this, just that this is the Bayesian interpretation of quantum mechanics. One might as well ask how we Bayesians know that probability is in the map and not the territory. (We are all Bayesians when it comes to classical probability, right?) Ultimately, I don't think that it makes sense to know such things, since we make the same physical predictions regardless of our interpretation, and only these can be tested.

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 (which is good since the universe is really quantum). In both realms, I'm a Bayesian for the same reasons.

A half-Bayesian approach adds extra complications, like the two very different maps that lead to same predictions. (See this comment's cousin in reply to endoself.)

ETA: As for knowing what exists in the territory as an aid to explaining subjective experience, we can still say that the territory appears to consist ultimately of quark fields, lepton fields, etc, interacting according to certain laws, and that (built out of these) we appear to have rocks, people, computers, etc, acting in certain ways. We can even say that each particular rock appears to have a specific value of position and momentum, up to a certain level of precision (which fails to be infinitely precise first because the definition of any particular rock isn't infinitely precise, long before the level of quantum indeterminacy). We just can't say that each particular quark has a specific value of position and momentum beyond a certain level of precision, despite being (as far as we know) fundamental, and this is true regardless of whether we're all-Bayesian or many-worlder. (Bohmians believe that such values do exist in the territory, but these are unobservable even in principle, so this is a pointless belief).

Edit: I used ‘world’ consistently in a technical sense.

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.)