Quantum mechanics is an extremely successful physical theory due to its accurate empirical predictions. The core of the theory is the Schrodinger equation and the Born rule. The Schrodinger equation is linear and it governs the time evolution of the wave function assigned to a physical system. The Born rule says that the result of a measurement on a physical system is definite but generally random, and the probability is given by the modulus squared of the wave function of the system. However, when assuming the wave function of a physical system is a complete description of the system, the linear Schrodinger equation is apparently incompatible with the Born rule, in particular the appearance of definite results of measurements. This leads to the measurement problem. Maudlin (1995) gave a precise formulation of the problem in terms of the incompatibility.
Correspondingly, the three approaches to avoiding the incompatibility lead to the three main solutions to the measurement problem: Everett’s theory, Bohm’s theory and collapse theories.
It is widely thought that these theories can indeed solve the measurement problem, although each of them still has some other problems. Then, which solution is the right one? Although there have been many analyses of this issue, the investigation seems still not thorough and complete.
In my view, there are still three possible ways to examine these competing solutions before experiments can finally test them.
The first way is to analyze the link between the physical state and the measurement result, and in particular, whether the link satisfies certain principles or restrictions.
In Everett’s theory, Bohm’s theory and collapse theories, the measurement results are represented by different physical states. Then, which physical state represents the measurement result? There are at least two restrictions. The first one is the Born rule; the measurement result represented by a certain physical state should be consistent with the Born rule. This is not so obvious as usually think, and as I have argued, Bohm’s theory seems to be problematic (a more recent version) in this aspect.
The second restriction concerns the psychophysical connection. It has been realized that the measurement problem is essentially the determinate-experience problem (Barrett, 1999). In the final analysis, the problem is to explain how the linear dynamics can be compatible with the existence of definite experiences of conscious observers. This requires that the physical state representing the measurement result should be also the physical state on which the mental state of an observer supervenes. The restriction is then the form of psychophysical connection required by a quantum theory should satisfy the principle of psychophysical supervenience. As I have argued, it seems that Everett’s theory fails to satisfy this restriction.
The second way to examine the solutions to the measurement problem is to analyze whether they are consistent with the meaning of the wave function. The conventional research program is to first find a solution to the measurement problem, such as Bohm’s theory or Everett’s theory or collapse theories, and then try to make sense of the wave function in the solution. By such an approach, the meaning of the wave function will have no implications for solving the measurement problem. However, this approach is arguably problematic.
The reason is that the meaning of the wave function (in the Schrodinger equation) is independent of how to solve the measurement problem, while the solution to the measurement problem relies on the meaning of the wave function. For example, if assuming the operationalist psi-epistemic view, then the measurement problem will be dissolved.
There are two issues here. The first one concerns the nature of the wave function, and the second one concerns
the ontology behind the wave function. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? As I have argued in Gao (2017), even when assuming the psi-ontic view, the ontological meaning of the wave function also has implications for solving the measurement problem. In particular, it seems that Bohm’s and Everett’s theories can hardly be consistent with the suggested ontological interpretation of the wave function, while the suggested ontology behind the wave function may not only support the reality of the collapse of the wave function, but also provide more resources for formulating a collapse theory.
In my view, the underlying ontology and the psychophysical connection are the two extremes that should be understood fully in the first place when trying to solve the measurement problem; the underlying ontology is at the lowest quantum level, and the psychophysical connection is at the highest classical level. It is very likely that once we have found the underlying ontology and the psychophysical connection, we will know which solution of the measurement problem is in the right direction. Certainly, we still need to understand the dynamics bridging the quantum and classical worlds.
Finally, the third way to examine the solutions to the measurement problem is to analyze whether they are consistent with the principles in other fields of fundamental physics. A very speculative analysis is here.