2016 International Workshop on Quantum Observers

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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 x-spin measurement?”, but with the question Did you get some definite result to your x-spin measurement, either x-spin up or x-spin down?” Then the same observer M will also have the disposition to answer this question with Yes” if she recorded x-spin up (if M + S ended up in the state $\ket{up}_S \ket{up}_M$) and with Yes” if she recorded x-spin 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 x-spin result, either x-spin up or x-spin 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 x-spin result when she is physically in the superposition (\ref{ss}).

According to the well-known solution to this puzzle (Albert, 1992; Barrett, 1999), M will indeed report that she got a definite x-spin result, either x-spin up or x-spin 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 x-spin measurement?” and Did you get some definite result to your x-spin measurement, either x-spin up or x-spin 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 x-spin up nor x-spin 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 x-spin measurement, either x-spin up or x-spin 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 x-spin up or x-spin 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 x-spin measurement, either x-spin up or x-spin down?” means that Are you consciously aware of a x-spin up result or a x-spin down result to your x-spin 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 x-spin result when she is physically in the superposition (\ref{ss}). (See Section 2 of the above analysis)

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