The Measurement Problem

The Measurement Problem

The fundamental definition of reality is the wave function as described in Quantum Reality. The wave function is a wave of probability, which means that it defines the probabilities of all the possible positions of where the quantum might found to exist, if it were observed. 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 a hundred years ago. This is the measurement problem. It has been suggested that quantum decoherence solves the measurement problem but this is false, as described at the end of this page.

The Standard Formulation

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). Jeffrey 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. And everything is defined by the wave function of the universe. So, Barrett 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 cannot randomly jump into some other state, and give just one specific outcome to the observation. Hence the measurement problem. What is going on?

Logical Types

The resolution is that these are the dynamics of different types of frame of reference. Naturally, physical measuring devices can follow only the linear dynamics of the absolute state. However, as Everett demonstrates, it is not the measuring device that is the protagonist of the collapse dynamics but its product, the record of observations, here the world hologram. As described in Quantum Theory, the world of the world hologram is a superworld, a second-logical-type phenomenon.

It means that the two dynamics operate in the two different types of world. The linear dynamics is the time evolution of the ordinary world, the quasi-classical world. The collapse dynamics is the time evolution of the superworld. A dualism of ontologies is defined. The assumption of a single type of world, and a single ontology, is the category error that gives rise to the measurement problem.

Schrödinger’s cat

Schrödinger’s cat is an ideal example of the two different processes. This is a thought experiment by the great physicist Erwin Schrödinger. The put-upon cat is in a box with a quantum device, essentially a quantum toss of a coin, and heads means it dies instantly and tails means it lives. But according to quantum theory, our best and most thoroughly researched scientific understanding of all time, the cat is then both alive and dead at the same time. This is described in Schrödinger’s Cat. Here the dynamics are illustrated in the diagram below.

The moment Schrödinger observes inside the box, this observation defines him as existing only in one specific version of the world or the other. But what state is it in before it is observed? The answer is it is both states, in parallel realities.

The whole thing is explained by parallel worldlines, as illustrated in this diagram by Lockwood (1989, 231; adapted).

 

Diagram of worldlines of Schrödinger's cat - from Lockwood 1989

The cylinder represents all the possible versions of Schrödinger’s worldline in his superworld. Each one exists in a specific quasi-classical world. The worldlines in which the cat dies are on the left, and those in which it survives on the right.
In the lower section, before the observation is made, Schrödinger sees only the outside of the box, so at this point his world hologram is the same on both sides. Thus his class-of-worlds-as-a-world contains both versions of physical reality, dead cat and alive cat. So in the physical reality of his superworld, his holographic universe, the cat really is alive and dead at the same time.

The Meaning

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 operates going up the diagram. The collapse dynamics is a redefinition of the class of worldliness.

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. This is the change of the definition of the superworld, caused by the change in definition of the world hologram, resulting in the change of the definition of the quantum state of the physical reality. The cycle of these two dynamics is explained with illustrations in Time & Quantum Time.

Exactly which parallel road you get to, and what is coming up next on that road, is random. That is what it means. And of course in this domain interactive destiny operates.

Decoherence

Quantum decoherence is an interference phenomenon that induces the appearance of collapse. This gives rise to the quasi-classical worlds of the many-worlds universe. But this does not resolve the measurement problem. As stated by Guido Bacciagaluppi in The Role of Decoherence in Quantum Mechanics:

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)

Furthermore, the basis on which decoherence operates, how exactly the world is defined, remains unresolved. This is the preferred basis problem:

… this is the problem, we do not really know what basis would make our most immediately accessible physical records, those records that determine our experiences and beliefs, determinate in every world. The problem of choosing which observable to make determinate is known as the preferred-basis problem. (Barrett, 2008)

Naturally, taking the records of experiences themselves as the basis in operation resolves this problem. This is Lockwood’s solution. This: “… in a sense is the primary observable” (1996, p. 185; emphasis in original).

As Everett states, it is only in experience: “Judged by the state of the memory”, that one single, specific version of the world exists.