What exactly do [the authors] mean by a quantum state being “statistically interpretable”?... Basically, [the authors] call something “statistical” if two people, who live in the same universe but have different information, could rationally disagree about it.... As for what “rational” means, all we’ll need to know is that a rational person can never assign a probability of 0 to something that will actually happen.
To illustrate, suppose a coin is flipped, and you (but not I) get a tip from a reliable source that the coin probably landed heads. Then you and I will describe the coin using different probability distributions, but neither of us will be “wrong” or “irrational”, given the information we have.
That's Scott Aaronson discussing a paper about the nature of quantum states. Googling "define statistical," I see, unsurprisingly, "of or relating to the use of statistics," and then googling "define statistics," I see "the practice or science of collecting and analyzing numerical data in large quantities."
To me, the large quantities bit emphasizes that the role of statistics is to parse signal from noise, which is only possible with more than two data points (or, to be fair, some assumptions). So, I'd consider the authors' use of the word statistical to be sort of non-standard, because it seems to be able to be used for interpreting just one quantum state.
Quite possibly this is actually standard use of the word statistical among certain physicists, which would make this yet another example of why you shouldn't assume that terminology is at all consistent across disciplines.
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Aaronson himself makes a similar point at the bottom of that entry:
"I expect the rebuttal to prove a contrary theorem, using a definition of the word “statistical” that subtly differs from PBRs. I expect the difference between the two definitions to get buried somewhere in the body of the paper.
I expect the rebuttal to get blogged and Slashdotted. I expect the Slashdot entry to get hundreds of comments taking strong sides, not one of which will acknowledge that the entire dispute hinges on the two camps’ differing definitions.
There’s an important lesson here for mathematicians, theoretical computer scientists, and analytic philosophers. You want the kind of public interest in your work that the physicists enjoy? Then stop being so goddamned precise with words! The taxpayers who fund us—those who pay attention at all, that is—want a riveting show, a grand Einsteinian dispute about what is or isn’t real. Who wants some mathematical spoilsport telling them: “Look, it all depends what you mean by ‘real.’ If you mean, uniquely determined by the complete state of the universe, and if you’re only talking about pure states, then…”"
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