Measurement Problem

Measurement Problem

The fundamental definition of reality is the wave function as described in Quantum Reality. This defines all possible states of a quantum as real, existing in superposition. But when an observation is made of a quantum, a specific result is always observed. Thus it seems that the wave function ‘collapses’ to a specific actuality when an observation is made. The question of how this happens, why this happens, and even whether or not it does in fact happen, has been the subject of heated debate ever since the discovery of quantum theory nearly a hundred years ago. This is the measurement problem.

The dynamics of the wave function is called the linear dynamics: the wave function evolves deterministically as a linear superposition of different states, as defined by the Schrödinger wave equation. The process of collapse, the abrupt change of the wave function, is called the collapse dynamics. The textbook relationship between them was defined in the von Neumann-Dirac formulation of quantum mechanics (1932). Barrett provides a simplified form of this definition:

Linear: If no observation is made, then the quantum system evolves continuously according to the linear, deterministic dynamics.
Collapse: If an observation is made, then the quantum system instantaneously and randomly jumps to a state where it either determinately has or determinately does not have the property being observed. (1998; adapted)

As he states, this is a superb theory:

The standard theory … is in one sense the most successful physical theory ever … it successfully predicts the behaviour of the basic constituents of all physical things (1999, 1)

However, as he goes on to explain, the theory seems inherently flawed:

… if one supposes that measuring devices are ordinary physical systems just like any other, constructed of fundamental particles interacting in their usual determinate way (and why wouldn’t they be?), then the standard theory is logically inconsistent since no system can obey both the deterministic and stochastic dynamics simultaneously. This is the measurement problem. (1999, 15)

The usual determinate way he is referring to is the linear dynamics, the dynamics of the wave function. The time evolution of the wave function gives rise to all possibilities; so, he is saying, since the device used to make a measurement, an observation, can only be made of ordinary stuff, that operates according to the linear dynamics, it can hardly represent only one specific version of reality, and give just one specific outcome to the observation. Hence the measurement problem.

Clearly, the two dynamics are quite different kinds of phenomena. The wave function is the physical reality defined  by a specific quantum state. The linear dynamics is what happens within the context of that quantum state, while the collapse dynamics is the change of the quantum state. The linear dynamics is completely predictable; it has a precise mathematical definition of what will happen over time, although this is always probabilistic. The collapse dynamics is random; there is no way to predict exactly what will happen. The linear dynamics is like going down a long straight road; you can see what is coming up next and what is in the distance, though this is always fuzzy, meaning in terms of probabilities. The collapse dynamics is like jumping sideways to a parallel road. And, exactly which parallel road you get to, and what is coming up next on that road, is random. That is what it means.

The measurement problem exists because one single system cannot do both these things. The resolution is that these two dynamics are operating in two different kinds of frame of reference. The experience of the linear dynamics happens as the moving frame of reference passes along the world-line, within the context of the world of a specific quantum state. This is the experience of the dynamics defined by the physical world. The collapse dynamics is a jump from one version of the physical world, defined by a specific quantum state, to another, defined by a different quantum state. They are processes operating at different levels of logical type. The linear dynamics is a property of the physical, of the first, primitive logical type. The sequence of states, brought about by the sequence of observations, a process of information, is a completely different kind of thing, a second logical type phenomenon. This is the resolution of the measurement problem.

It has been suggested that quantum decoherence solves the measurement problem. This is an interference phenomenon that induces the appearance of collapse. However, as stated by Guido Bacciagaluppi, “Unfortunately, naive claims of the kind that decoherence gives a complete answer to the measurement problem are still somewhat part of the ‘folklore’ of decoherence, and deservedly attract the wrath of physicists (e.g. Pearle 1997) and philosophers (e.g. Bub 1997, Chap. 8) alike.” (2012)