2016 International Workshop on Quantum Observers

[editor]

According to Maudlin’s (1995) formulation, the measurement problem originates from the incompatibility of the following three claims:

(C1). the wave function of a physical system is a complete description of the system;
(C2). the wave function always evolves in accord with a linear dynamical equation, e.g. the Schrodinger equation;
(C3). each measurement has a definite result (which is one of the possible measurement results whose probability distribution satisfies the Born rule).

Correspondingly, there are in general three approaches to solving the measurement problem. The first approach is to deny the claim (C1), and add some additional variables and corresponding dynamics to explain the appearance of definite measurement results. Two well-known examples are Bohm’s theory and modal interpretations. The second approach is to deny the claim (C2), and revise the Schrodinger equation by including some nonlinear and stochastic evolution terms to explain the appearance of definite measurement results. Such theories are usually called dynamical collapse theories. The third approach is to deny the claim (C3), and assume the existence of many equally real worlds to accommodate all possible results of measurements. This approach is called Everett’s approach.

It has been realized that the measurement problem in fact has two levels: the physical level and the mental level, and it is essentially the determinate-experience problem (Barrett, 1999). The problem is not only to explain how the linear dynamics can be compatible with the appearance of definite measurement results obtained by physical devices, but also to explain how the linear dynamics can be compatible with the existence of definite experiences of conscious observers like us. This requires that the physical state representing the measurement result is also the physical state on which the mental state of an observer supervenes. However, the mental aspect of the measurement problem is ignored in Maudlin’s (1995) formulation.

Here I will give a new formulation of the measurement problem which gives prominence to the psychophysical connection. In this formulation, the measurement problem originates from the incompatibility of the following three claims:

(P1). the mental state of an observer supervenes on her wave function;
(P2). the wave function always evolves in accord with a linear dynamical equation, e.g. the Schrodinger equation;
(P3). an observer obtains a definite record after each measurement (which is one of the possible measurement records whose probability distribution satisfies the Born rule).

By this new formulation of the measurement problem, we can look at the three main approaches to solving the problem from a new angle. First of all, the claim (P3) in this formulation is always correct. In particular, it is correct even in Everett’s approach. In fact, the claim (P3) is an empirical fact. As a result, the solution to the measurement problem must deny either the claim (P1) or the claim (P2). If (P1) is correct (as usually thought), then (P2) must be wrong. In other words, if the mental state of an observer supervenes on her wave function, then the Schrodinger equation must be revised and the solution to the measurement problem will be along the direction of dynamical collapse theories.
On the other hand, if (P2) is correct, then (P1) must be wrong. This means that if the wave function always evolves in accord with the Schrodinger equation, then the mental state of an observer cannot (always) supervene on her wave function. There are two other options for the psychophysical supervenience.
One is that the mental state of an observer supervenes on certain branches of her wave function, and the other is that the mental state of an observer supervenes on other additional variables. The first option corresponds to Everett’s approach, and the second option Bohm’s approach.

To sum up, the three main approaches to solving the measurement problem just corresponds to three different ways of psychophysical supervenience. In fact, there are only three possible physical states on which the mental state of an observer supervenes, which are (1) the wave function, (2) certain branches of the wave function, and (3) other additional variables.

The question is: what physical state does the mental state of an observer supervenes on? It can be expected that an analysis of this question will have implications for solving the measurement problem. For further analysis see What does it feel like to be in a quantum superposition?

[Jiri Soucek]

Dear Shan,

I have a comment and a critical remark to your argumentation.

I shall consider the property (C1) in the more complete formulation:
(C1x) the wave function of a physical system is a complete description of the individual system.
You write “The first approach is to deny the claim (C1), and add some additional variables …”.
I think that there are two possibilities how to deny (C1):
(i) to add some additional variables (as described above)
(ii) to deny that every wave function is a description of the individual system.

The second possibility is usually overlooked but it is the bases of the modified quantum mechanics (QM). The modified QM is systematically overlooked. The main idea of modified QM (see attached paper) is that for each system there exists exactly one special orthogonal bases composed from individual states (= states of individual systems) and there are no other individual states. This can be called the psi-hybrid option.

In the paper it is proved that QM and modified QM are empirically indistinguishable so that the modified QM should be considered as equivalent to QM. It is also shown that the measurement problem can be simply solved in the modified QM.

I would like only to remark that your list of possibilities how to deny some claim from (C1)-(C3) is incomplete since one possibility is missing and this possibility may be a key to the solution of the measurement problem.

Your Jiri

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