Note: The following text aims to elicit more discussions about the bare theory, which may help understand quantum observers more deeply.
Suppose that a quantum observer M is asked not with the question
Did you get a definite result to your xspin measurement?”, but with the question
Did you get some definite result to your xspin measurement, either xspin up or xspin down?” Then the same observer M will also have the disposition to answer this question with
Yes” if she recorded xspin up (if M + S ended up in the state $\ket{up}_S \ket{up}_M$) and with
Yes” if she recorded xspin down (if M + S ended up in the state $\ket{down}_S \ket{down}_M$). Then if M + S is in a superposition of these two states:
\alpha \ket{up}_S \ket{up}_M+\beta \ket{down}_S \ket{down}_M,
\label{ss}
it follows from a similar analysis that M will also answer
Yes” to the question; that is, M will report that she got a definite xspin result, either xspin up or xspin down.
However, M in fact fails to have either definite record when she is physically in the superposition (\ref{ss}). We call this puzzle the either/or puzzle.
It thus seems that the usual assumption that a qualified observer can correctly report her mental content is not always true in the quantum context.
This also raises the doubt about the correctness of M’s report that she got a definite xspin result when she is physically in the superposition (\ref{ss}).
According to the wellknown solution to this puzzle (Albert, 1992; Barrett, 1999), M will indeed report that she got a definite xspin result, either xspin up or xspin down, when she is physically in the superposition (\ref{ss}), but the report is false. This means that even a qualified observer cannot know what she is currently experiencing and what she had experienced, and she will be fundamentally mistaken concerning the basic nature of her conscious experience.
The resulting theory is called the bare theory (Albert, 1992), which has many serious problems such as the empirical incoherence problem (which is that if the theory were true, we would have no empirical evidence to confirm that it is true) (Barrett, 1996, 1999; Dickson, 1998; Magnus, 2004).
However, although the bare theory is generally rejected due to these serious problems, it seems that the origin of the either/or puzzle has not been deeply analyzed.
Let us compare the two questions
Did you get a definite result to your xspin measurement?” and
Did you get some definite result to your xspin measurement, either xspin up or xspin down?”. The difference lies in that the second question also concerns the specific result of measurement, while the first question does not. In order to answer the second question, the observer M must first know the content of her immediate conscious experience or memory about the measurement result. Moreover, only after an either/or logical analysis can she give an answer to the question. (In contrast, M needs not know her specific mental content to answer the first question.)
Therefore, the fact that M fails to have either definite record will not result in the mental illusion assumed by the bare theory; rather, it will result in the negative answer of M to the second question, and this report is true.
Concretely speaking, since the mental states corresponding to the physical states $\ket{up}_M$ and $\ket{down}_M$ differ in their mental content, the observer M being in the superposition (\ref{ss}) will have a conscious experience different from the experience of M being in each branch of the superposition by the symmetry of the two branches. In other words, the result that M is consciously aware of is neither xspin up nor xspin down when she is physically in the superposition (\ref{ss}).
Thus M will, in fact, answer
No”, not
Yes”, to the second question,
Did you get some definite result to your xspin measurement, either xspin up or xspin down?” (if she is a qualified and honest observer).
Another way to understanding this result is to notice that since the mental states corresponding to the physical states $\ket{up}_M$ and $\ket{down}_M$ are incompatible in their mental content, there is no common part of the two physical states on which the mental content of the observer M being in a superposition of them can supervene. As a result, even though the observer M being in each branch of the superposition answers
Yes” to a question concerning her mental content, she cannot give the same answer to the question when she is in the superposition.
It is worth noting that even though the observer M being in the superposition (\ref{ss})) has a (definite) disjunctive conscious experience, such as
I am consciously aware of a result, either xspin up or xspin down” (Barrett, 1999), the conscious experience is also different from the experience of M being in each branch of the superposition. If the question
Did you get some definite result to your xspin measurement, either xspin up or xspin down?” means that
Are you consciously aware of a xspin up result or a xspin down result to your xspin measurement?”, then M’s answer to the question will be still
No”, not
Yes”.
This solution to the either/or puzzle makes the invalidity of the bare theory more obvious. Moreover, the solution also helps clear the doubt about the validity of the usual assumption that a qualified observer can correctly report her mental content in the quantum context, and in particular, the correctness of M’s report that she got a definite xspin result when she is physically in the superposition (\ref{ss}). (See Section 2 of the above analysis)

This topic was modified 2 years, 3 months ago by editor.