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I just finished teaching a Jr/Sr undergrad Quantum Mechanics course last semester, so I'll take a stab at answering this. There are two approaches to answering

I just finished teaching a Jr/Sr undergrad Quantum Mechanics course last semester, so I'll take a stab at answering this. There are two approaches to answering this question. One of them invokes the concept of "the collapse of the wavefunction" at the moment of measurement: when an observer actually measures the outcome of such an experiment, the universe probabilistically selects one of the possible outcomes as "true" and proceeds from there. This "collapse" process is explicitly non-unitary. You may ask, "What entities qualify as 'observers' to trigger collapse?", and the answer is basically "It's not well-defined." As you might gather from that, it's not clear to me that you can include an "observer" in this sense as part of the overall wavefunction of the universe at all, though perhaps people who have studied the foundations of quantum mechanics in more detail could give a better answer. The other option is pretty much exactly what you've described in your final paragraph: you don't invoke "collapse of the wavefunction" at all, and the final quantum state of the universe after measurement is indeed a superposition of "|0> and observer who saw '0'" and "|1> and observer who saw '1'". Because anything we'd call an "observer" will be a large, complex system, there will very rapidly be a vast number of tiny, "pseudo-random" differences between the two branches of the wavefunction, ensuring that there won't be opportunities for the two branches to experience significant constructive or destructive interference in the future: they'll evolve pretty much completely independently from then on. (This concept is called "decoherence", which you've made reference to, and I'm definitely not an expert on it, but I'm told it's become quite important in research on quantum computing.) There's still a probabilistic question of which branch of the wavefunction a given observer might experience (and understanding why that happens is an enormously subtle question; I've seen some work by Sean Carroll among others trying to make progress on it), but once a given observer has measured a particular outcome to the experiment, the math of quantum mechanics guarantees that they'll continue to measure consistent results after that. This is more or less the Everett "many worlds" interpretation of quantum mechanics. As you might gather, I'm partial to the latter interpretation, in part because it's where the math seems to most naturally lead (the first time I felt like I really understood quantum mechanics was after a very math-heavy graduate course taught by Robert Geroch), and in part because I've never been able to make sense of what wavefunction collapse might mean (and never been happy about its violation of unitarity).

n4r9 8y ago
There's a third option, which historically arose out of the issues you describe with your first approach. This is to deny that quantum theory is a description of an objective, observer-independent reality. Rather it is a kind of "personal rule book" which informs an agent's beliefs about future interactions with the world. https://en.wikipedia.org/wiki/Quantum_Bayesianism https://en.wikipedia.org/wiki/Quantum_Bayesianism https://arxiv.org/pdf/1003.5209.pdf https://arxiv.org/pdf/1003.5209.pdf
danbruc 8y ago
As you might gather from that, it's not clear to me that you can include an "observer" in this sense as part of the overall wavefunction of the universe at all, though perhaps people who have studied the foundations of quantum mechanics in more detail could give a better answer. I did some more reading and it seems that at least some try to do what I also considered, try to attribute the randomness in the outcome to the randomness and uncertainty in the initial state of the measuring device, observer, and environment. This then raises the question why all kinds of measuring devices produce the same distribution of measurement results if the concrete outcome essentially only depends on the initial state of the measuring device. And this also has the smell of a hidden variable theory where the hidden variables are in the measurement device, would this be compatible with EPR? I also took away some things to follow up on from your comments on Everett but unlike you I don't really like multiverses and so this will have to wait for some time. I however agree that Everett makes the most sense with regard to completeness and consistency.

n4r9 8y ago

There's a third option, which historically arose out of the issues you describe with your first approach. This is to deny that quantum theory is a description of an objective, observer-independent reality. Rather it is a kind of "personal rule book" which informs an agent's beliefs about future interactions with the world. https://en.wikipedia.org/wiki/Quantum_Bayesianism https://en.wikipedia.org/wiki/Quantum_Bayesianism https://arxiv.org/pdf/1003.5209.pdf https://arxiv.org/pdf/1003.5209.pdf

danbruc 8y ago

As you might gather from that, it's not clear to me that you can include an "observer" in this sense as part of the overall wavefunction of the universe at all, though perhaps people who have studied the foundations of quantum mechanics in more detail could give a better answer. I did some more reading and it seems that at least some try to do what I also considered, try to attribute the randomness in the outcome to the randomness and uncertainty in the initial state of the measuring device, observer, and environment. This then raises the question why all kinds of measuring devices produce the same distribution of measurement results if the concrete outcome essentially only depends on the initial state of the measuring device. And this also has the smell of a hidden variable theory where the hidden variables are in the measurement device, would this be compatible with EPR? I also took away some things to follow up on from your comments on Everett but unlike you I don't really like multiverses and so this will have to wait for some time. I however agree that Everett makes the most sense with regard to completeness and consistency.