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TobyBartels 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: TobyBartels 13 July 2011 03:27:34PM 1 point [-]

They can give different predictions. [...]

I don't understand what you're saying in these paragraphs. You're not describing how the two situations lead to different predictions; you're describing the opposite: how different set-ups might lead to the two states.

Possibly you mean something like this: In situation A, my friend intended to prepare one spin-down particle, but I predict with 50% chance that they hooked up the apparatus backward and produced a spin-up particle instead. In situation B, they intended to prepare a spin-right particle, with the same chance of accidental reversal. These are different situations, but the difference lies in the apparatus, my friend's mind, the lab book, etc, not in the particle. It would be much the same if I knew that the machine always produced a spin-up particle and the up/down/right/left dial did nothing: the situations are different, but not because of the particle produced. (However, in this case, the particle is not even entangled with the dial reading.)

A final possibility is that there never was a pure state; the universe started of in a mixed state.

I especially don't know what you mean by this. The states that most people talk about when discussing quantum physics (including Eliezer in the Sequence) are pure states, and mixed states are probabilistic mixtures of these. If you're a Bayesian when it comes to classical probability (even if you believe in the wave function when it comes to purely quantum indeterminacy), then you should never believe that the real wave function is mixed; you just don't know which pure state it is. Unless you distinguish between the map where the particle is spin-up or -down with equal odds from the map where the particle is definitely in the fullymixed state in the territory? Then you have an even greater plethora of distinctions between maps that pay no rent!

How would you analyze the Wigner's friend thought experiment?

For Schrödinger's Cat or Wigner's Friend, in any realistic situation, the cat or friend would quickly decohere and become entangled in my observations, leaving it in a mixed state: the common-sense situation where it's alive/happy/etc with 50% chance and dead/sad/etc with 50% chance. (Quantum physics should reproduce common sense in situations where that applies, and killing a cat with radioactive decay or a pseudorandom coin flip doesn't matter to the cat --ordinarily.) However, if we imagine that we keep the cat or friend isolated (where common sense doesn't apply), then it is in a superposition of these instead of a mixture --from my point of view. My friend's state of knowledge is different, of course; from that point of view, the state is completely determined (with or without decoherence). And how is it determined? I don't know, but I'll find out when I open the door and ask.

Comment author: endoself 19 July 2011 11:38:09PM 0 points [-]

I don't understand what you're saying in these paragraphs. You're not describing how the two situations lead to different predictions; you're describing the opposite: how different set-ups might lead to the two states.

I did not explain this very well. My point was that when we don't know the particle's spin, it is still a part of the simplest description that we have of reality. It should not be any more surprising that a belief about a quantum mechanical state does not have any observable consequences than that a belief about other parts of the universe that cannot be seen due to inflation does not have any observable consequences.

Unless you distinguish between the map where the particle is spin-up or -down with equal odds from the map where the particle is definitely in the fullymixed state in the territory? Then you have an even greater plethora of distinctions between maps that pay no rent!

I included this just in case a theory that implies such a thing ever turn out to be simpler than alternatives. I thought this was relevant because I mistakenly thought that you had mentioned this distinction.

And how is it determined? I don't know, but I'll find out when I open the door and ask.

What if your friend and the cat are implemented on a reversible quantum computer? The amplitudes for your friend's two possible states may both affect your observations, so both would need to be computed.

Comment author: TobyBartels 20 July 2011 04:02:36PM *  2 points [-]

My point was that when we don't know the particle's spin, it is still a part of the simplest description that we have of reality.

Sure, the spin of the particle is a feature of the simplest description that we have. Nevertheless, no specific value of the particle's spin is a feature of the simplest description that we have; this is true in both the Bayesian interpretation and in MWI.

To be fair, if reality consists only of a single particle with spin 1/2 and no other properties (or more generally if there is a spin-1/2 particle in reality whose spin is not entangled with anything else), then according to MWI, reality consists (at least in part) of a specific direction in 3-space giving the axis and orientation of the particle's spin. (If the spin is greater than 1/2, then we need something a little more complicated than a single direction, but that's probably not important.) However, if the particle is entangled with something else, or even if its spin is entangled with some another property of the particle (such as its position or momentum), then the best that you can say is that you can divide reality mathematically into various worlds, in each of which the particle has a spin in a specific direction around a specific axis.

(In the Bohmian interpretation, it is true that the particle has a specific value of spin, or rather it has a specific value about any axis. But presumably this is not what you mean.)

As for which is the simplest description of reality, the Bayesian interpretation really is simpler. To fully describe reality as best I can with the knowledge that I have, in other words to write out my map completely, I need to specify less information in the fully Bayesian interpretation (FBI) than in MWI with Bayesian classical probability on top (MWI+BCP). This is because (as in the toy example of the spin-1/2 particle) different MWI+BCP maps correspond to the same FBI map; some additional information must be necessary to distinguish which MWI+BCP map to use.

If you're an objective Bayesian in the sense that you believe that the correct prior to use is determined entirely by what information one has, then I can't even tell how one would ever distinguish between the various MWI+BCP maps that correspond to a given FBI map. (A similar problem occurs if you define probability in terms of propensity to wager, since there is no way to settle the wagers.) Even if I ask my friend who prepared the state, my friend's choice to describe it one way rather than another way only gives me information about other things (the apparatus, my friend's mind, their lab book, etc). It may be possible to always choose a most uniform MWI+BCP map (in the toy example, a uniform probability distribution over the sphere); I'll have to think about this.

For the record, I do believe in the implied invisible, if it really is implied by the simplest description of reality. In this case, it's not.

I mistakenly thought that you had mentioned this distinction.

I certainly didn't mean to; from my point of view, that makes the MWI only more ridiculous, and I don't want to attack a straw man.

What if your friend and the cat are implemented on a reversible quantum computer? The amplitudes for your friend's two possible states may both affect your observations, so both would need to be computed.

So compute both. There are theoretical problems with implementing an observer on a reversible computer (quantum or otherwise), because Bayesian updating is not reversible; but from my perspective, I'll compute my state and believe whatever that comes out to.

Probably I don't understand what your question here really is. Is there a standard description of the problem of Wigner's friend on a quantum computer, preferably together with the WMI resolution of it, that you can link to or write down? (I can't find one online with a simple search.)