The universe is naturally defined as a Hilbert space, and the evolution of the wavefunction has a basic L^2 conservation
law. If you’re going to ask “how big” a chunk of the wavefunction is (which is the right way to compute the relative
probabilities of being an observer that sees such-and-such)
I believe the question is not “What are the sane probabilistic interpretations of the wave function?” but “why are we even asking the question “What are the sane probabilistic interpretations of the wave function” ?”. Are there no other questions we might be asking whose answer might relate to the experiences of the inhabitants of a quantum universe?
1) Look, we have this fancy differential equation describing the time-evolution of a function called the wave function. We believe this equation describes, without additional baggage, the universe.
2) This wave function has a unique sane probabilistic interpretation
3) Therefore, the inhabitants of the universe described by this equation experience a seemingly non-deterministic reality with probabilities given by said interpretation.
It is not at all clear to me how (or even if) (3) follows from (1) and (2).
One of the whole points of MW is that the universe isn’t inherently probabilistic. But there’s apparent probability (which also shows up in everyday things like coin flips, which we can assign a probability to even while they’re in the air and their course is determined). This is odd because probability is born of incomplete information (even if it’s determined, we still don’t know how the coin will land, so we use probability), and it seems like there is none here. If the hard drive is about to record 100 quantum coin flips, the computer can print out exactly what state the hard drive will be in afterwards.
But it’s tricky—because once it’s flipped the coins, when the computer does the “read the hard drive and print out the results operation,” the computer doesn’t get to look at the exact quantum state and print that out. Instead, each “1s and 0s” state gets entangled with the computer, and so the computer prints out a superposition of different messages. An external observer with a good interferometer could figure out what was going on, but no classical operation of the computer itself will figure it out or rely on it. According to the computer, it’s getting random results—in fact, the computer can run a program called “detect randomness,” which will likewise access the 1s and 0s and print out “yep, this looks random” in almost all cases. The randomness-detector can only access sequences of 1s and 0s, not quantum states.
From here, the interesting question is “how is ‘apparent probability’ different from the probability we assign to coin flips?” If the computer were ignorant about the future like it was about a coin flip, they were be exactly the same and all confusion would go away. But it’s not—it can know exactly what state its in, it’s merely that any operations it takes can only depend on sequences of 1s and 0s, which screen off any computational access to the actual quantum state. A very odd sort of “ignorance.”
I believe the question is not “What are the sane probabilistic interpretations of the wave function?” but “why are we even asking the question “What are the sane probabilistic interpretations of the wave function” ?”. Are there no other questions we might be asking whose answer might relate to the experiences of the inhabitants of a quantum universe?
If you have incomplete information, probability is how you quantify it. There are probably other questions, yes. But that’s not very relevant.
An interesing question is “if what has incomplete information?” Because then you get to think about computers and hard drives.
I failed to properly explain myself.
1) Look, we have this fancy differential equation describing the time-evolution of a function called the wave function. We believe this equation describes, without additional baggage, the universe.
2) This wave function has a unique sane probabilistic interpretation
3) Therefore, the inhabitants of the universe described by this equation experience a seemingly non-deterministic reality with probabilities given by said interpretation.
It is not at all clear to me how (or even if) (3) follows from (1) and (2).
That’s why hard drives are neat :)
One of the whole points of MW is that the universe isn’t inherently probabilistic. But there’s apparent probability (which also shows up in everyday things like coin flips, which we can assign a probability to even while they’re in the air and their course is determined). This is odd because probability is born of incomplete information (even if it’s determined, we still don’t know how the coin will land, so we use probability), and it seems like there is none here. If the hard drive is about to record 100 quantum coin flips, the computer can print out exactly what state the hard drive will be in afterwards.
But it’s tricky—because once it’s flipped the coins, when the computer does the “read the hard drive and print out the results operation,” the computer doesn’t get to look at the exact quantum state and print that out. Instead, each “1s and 0s” state gets entangled with the computer, and so the computer prints out a superposition of different messages. An external observer with a good interferometer could figure out what was going on, but no classical operation of the computer itself will figure it out or rely on it. According to the computer, it’s getting random results—in fact, the computer can run a program called “detect randomness,” which will likewise access the 1s and 0s and print out “yep, this looks random” in almost all cases. The randomness-detector can only access sequences of 1s and 0s, not quantum states.
From here, the interesting question is “how is ‘apparent probability’ different from the probability we assign to coin flips?” If the computer were ignorant about the future like it was about a coin flip, they were be exactly the same and all confusion would go away. But it’s not—it can know exactly what state its in, it’s merely that any operations it takes can only depend on sequences of 1s and 0s, which screen off any computational access to the actual quantum state. A very odd sort of “ignorance.”