# 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.

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)

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.

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 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.

Linear

This is here illustrated using the worldline of the observer. The first picture below shows a worldline threading through time going up the page. Each of the blobs sits at a moment in time where an observation is made: each horizontal plane symbolises one moment in time. But the further we look into the future, the more the wave function spreads out, like ripples on a pond. This is illustrated by the picture in Quantum Reality; that is the linear dynamics visualised. To symbolise this spread the second picture shows the blobs become more and more vague going into the future: what will be observed becomes more and more indeterminate.

These pictures symbolise a process that is all contained within the world defined by a specific quantum state, defining a specific wave function of the world. Within this context, the frame of reference of consciousness moves along the worldline, up the diagram as shown by the white arrow. This gives rise to the appearance of the passage of time as described Universe Consciousness. In effect the linear dynamics enacted.

The Appearance of Collapse

When the progression comes to the point in time where an observation is made, something quite different takes place. As a specific version of this observation is made, the world hologram is redefined; and as a result the frame of reference of this individual is defined as existing in a different version of the world, defined by a different quantum state. For the sake of illustration one can say the frame of reference moves ‘sideways’, to a different, parallel version of the world, a different snapshot, as represented by the black arrow. As Lockwood states, this is a: “… dimension running, so to speak, perpendicular to time and space.” (1989, 232).

Each of these parallel physical realities is a specific version of the world, a specific snapshot, defined by a specific quantum state. The experience of making an observation is the experience of the transition as the frame of reference passes to a new snapshot.

In the next snapshot over, the frame of reference continues to crawl up the worldline, through time, until the next observation is made; and then there is another jump ‘sideways’ to the next snapshot. Thus the dynamics cycle as described in the standard textbook formulation. These are the the dynamics of the two different types of time, as described in Time & Quantum Time.