# 2016 International Workshop on Quantum Observers

## Is Everett's approach consistent with psychophysical supervenience?

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Note: The following text aims to elicit more discussions about the question of whether Everett’s approach can really solve the measurement problem when considering the status of quantum observers in the theory.

Let us analyze Everett’s approach to quantum mechanics. This approach claims that after the a quantum measurement of spin there will be two observers, each of who is consciously aware of a definite record, either x-spin up or x-spin down. There are in general two ways of understanding the notion of multiplicity in Everett’s approach.

One is the strong form which claims that there are two physical observers (in material content) after the quantum measurement (e.g. DeWitt and Graham, 1973). This view is consistent with the doctrine of psychophysical supervenience. As is well known, however, this view has serious problems such as violation of mass-energy conservation and inconsistency with the dynamical equations (Albert and Loewer, 1988). The problem of inconsistency can also be seen as follows. The existence of many worlds is only relative to decoherent observers, not relative to non-decoherent observers, who can measure the whole superposition corresponding to the many worlds (e.g. by protective measurements) and confirm that there is no increase in the total mass-energy and number of particles.

The other way of understanding the notion of multiplicity is the weak form which claims that there is one physical observer (in material content), but there are two mental observers or two mental states of the same physical observer after the quantum measurement. Wallace’s (2012) latest formulation of Everett’s approach is arguably this view in nature (see also Kent, 2010).\footnote{Note that in Wallace’s formulation it is claimed that there are also two emergent physical observers, but their existence is only in the sense of branch structure (i.e. the structure of certain parts of a whole physical state), not in the sense of material content.}

In order to derive the multiplicity prediction of Everett’s approach, the mental state of a conscious observer cannot always supervene on her whole physical state. For each of the physical states $\ket{up}_M$ and $\ket{down}_M$, the mental state directly supervenes on the whole physical state. But for a superposition of these two physical states such as (\ref{ss}), the mental state does not supervene on the whole physical state; rather, the mental state supervenes only on a part of the whole physical state, such as one of the two terms in the superposition (\ref{ss}), and as a result, a physical observer has two distinct mental states at the same time.

This obviously contradicts the common assumption of psychophysical supervenience, which states that the mental state of a conscious observer supervenes on her (whole) physical state. Note that a whole physical state is independent, while any two parts of the state are not independent; once one part is selected, the other part will be also fixed. But a mental state is usually assumed to be autonomous. Thus it is arguably that a mental state supervenes on a whole physical state, not on any part of the state.

Although one may still object that this common assumption may be invalid in the quantum domain, one must explain why the assumption applies to the physical states $\ket{up}_M$ and $\ket{down}_M$, but not to any superposition of them.
It seems that the only difference one can think is that being in the superposition the physical observer has no definite mental state which contains a definite conscious experience about the measurement result, while being in each branch of the superposition, $\ket{up}_M$ or $\ket{down}_M$, she has a definite mental state which contains a definite conscious experience about the measurement result. According to our analysis, however, this difference does not exist; a physical observer being in the superposition also has a definite mental state which contains a definite conscious experience about the measurement result.

Note that these objections also apply to the single-mind theory and many-minds theory. Moreover, it seems that these objections will be more serious for Wallace’s formulation of Everett’s approach, since in this formulation, which is arguably a weak form of Everett’s approach too, there are no definite parts of the whole physical state on which the mental states can supervene.

Finally, we give a brief comment on the relationship between Everett’s approach and decoherence. It is usually thought that the appearance or emergence of two observers after a quantum measurement with two possible results is caused by decoherence. However, even if this claim is true for the strong form of Everett’s approach, it cannot be true for the weak form of Everett’s approach.
The reason is that the generation of a superposed state of a physical observer (e.g. a superposition of two physical states $\ket{up}_M$ and $\ket{down}_M$), as well as the psychophysical supervenience, have nothing to do with decoherence. In this sense, the weak form of Everett’s approach is more like a many-minds theory than a many-worlds theory. Note again that in the weak form of Everett’s approach the observer still has a whole physical state after a quantum measurement. In our opinion, it is just the fuzzy border between a many-minds theory and a many-worlds theory that causes much confusion in understanding Everett’s approach to quantum mechanics (see also Kent, 2010).

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