Despite the similar terminology, people on this site usually aren’t talking about the many worlds interpretation of quantum mechanics when they say things like “in 50% of worlds the coin comes up heads”.
The overwhelmingly dominant use of probabilities on this website is the subjective Bayesian one i.e. using probabilities to report degrees of belief. You can think of your beliefs about how the coin will turn out as a distribution over possible worlds, and the result of the coin flip as giving you information about which world you inhabit. This turns out to be a nice intuitive way to think about things, especially when it comes to doing an informal version of Bayesian updating in your head.
This has nothing really to do with quantum mechanics. The worlds don’t need to have any correspondence to the worlds of the many-worlds interpretation, and I would still think and talk like this regardless of what I believed about QM.
It probably comes from modal logic, where it’s standard terminology to talk about worlds which some proposition is true. From a quick google this goes back to at least CI Lewis (1943), which predates the many-worlds interpretation of quantum mechanics, and probably further. Here’s the wikipedia page on possible worlds. Probably there’s a good resource which explains the terminology in a subjective probability context, but I can’t find one right now.
I try to answer the question that was asked, not the question I most want to answer, and I have failed at that aim here, so I’m glad someone else gave you a satisfactory answer.
(I failed because it has been so long since I thought of probabilities as anything but subjective and because I feel strongly about the misuse of the concept of Everett branches on this site.)
My apologies to you for my off-topic comments here that would’ve been better put in their own post.
I am trying to see what is the spectrum of approaches to this in the LessWrong community (obviously, people do disagree, but I am going for completeness here (so the more the various viewpoints are represented in the discussion, the better is my understanding of how people on LessWrong are thinking about all this)).
Despite the similar terminology, people on this site usually aren’t talking about the many worlds interpretation of quantum mechanics when they say things like “in 50% of worlds the coin comes up heads”.
The overwhelmingly dominant use of probabilities on this website is the subjective Bayesian one i.e. using probabilities to report degrees of belief. You can think of your beliefs about how the coin will turn out as a distribution over possible worlds, and the result of the coin flip as giving you information about which world you inhabit. This turns out to be a nice intuitive way to think about things, especially when it comes to doing an informal version of Bayesian updating in your head.
This has nothing really to do with quantum mechanics. The worlds don’t need to have any correspondence to the worlds of the many-worlds interpretation, and I would still think and talk like this regardless of what I believed about QM.
It probably comes from modal logic, where it’s standard terminology to talk about worlds which some proposition is true. From a quick google this goes back to at least CI Lewis (1943), which predates the many-worlds interpretation of quantum mechanics, and probably further. Here’s the wikipedia page on possible worlds. Probably there’s a good resource which explains the terminology in a subjective probability context, but I can’t find one right now.
Thanks!
I try to answer the question that was asked, not the question I most want to answer, and I have failed at that aim here, so I’m glad someone else gave you a satisfactory answer.
(I failed because it has been so long since I thought of probabilities as anything but subjective and because I feel strongly about the misuse of the concept of Everett branches on this site.)
My apologies to you for my off-topic comments here that would’ve been better put in their own post.
I think Everett-related views are also on topic.
I am trying to see what is the spectrum of approaches to this in the LessWrong community (obviously, people do disagree, but I am going for completeness here (so the more the various viewpoints are represented in the discussion, the better is my understanding of how people on LessWrong are thinking about all this)).