Measurement Problem


The basic problem with quantum mechanics is that it defines two different dynamics, meaning two different ways in which the physical reality changes over time. And they are both very weird.

The fundamental dynamics is the kind of thing we would expect to find. It is a ‘linear dynamics’, meaning logical and predictable. This is the kind of thing we are used to. The laws of Newtonian mechanics describe the linear dynamics of the ordinary world. This is called classical physics. This is how we are able to precisely predict the path of a soccer ball, and the actions to jump on a bus. Naturally, we are deeply familiar with this dynamics. Classical physics is simply how we expect things to work.

The linear dynamics of the quantum is weird because although it is predictable, it is defined only in terms of probabilities. Throw an ordinary ball, and physics can predict the trajectory with absolute precision. But throw a quantum and it goes in every possible direction at the same time, with some more probable than others.

The Wave Function

The way this is understood is the ‘wave function’. This is the wave function of a single quantum, such as an electron.

The Wave Function
The Wave Function

This is not a wave of something physical, but a wave of probability. The bigger the wave, the greater the probability of the quantum actually being at that position, if an measurement is made with a detector.

So although it is the basis of all physical reality, the quantum is not a real thing in the same way as the objects of everyday life. This was made clear by Werner Heisenberg, who won the Nobel Prize in 1932 for the creation of quantum mechanics. The elementary particles, the quanta:

… form a world of potentialities or possibilities rather than one of things or facts. (1962, 128)

So that is the basic weirdness of the quantum, with its linear dynamics. Down at the quantum level reality is nothing like the world we are used to.

The total sum of zillions of quanta add up to produce the ordinary mechanics of Newtons laws, classical mechanics. This is how the quantum world gives rise to the ordinary word we are familiar with. Because the world operates like an ordinary classical world, but is actually made of quanta which work quite differently, it often is called a ‘quasi-classical world’, as if classical.

Collapse

This is strange enough, but the totally incomprehensible thing is the ‘collapse dynamics’. When an observation is made, the quantum wave collapses to give rise to a specific tiny particle such as a ‘real’ electron. But how can just looking at something cause the physical state to change? This is the great paradox of quantum mechanics.

We know this is what happens. One hundred years of precise experiments have given a unanimous answer. Measurement of the quantum state brings about change of the quantum state. But it makes no sense.

The Standard Formulation

As described in the textbooks, the two dynamics, linear and collapse, operate alternately in a cycle. This is the ‘von Neumann-Dirac formulation of quantum mechanics’ (1932). Philosopher Jeffrey Barrett, who specialises in the measurement problem, provides a simplified form:

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. (2008; adapted)

This is the standard formulation of the quantum theory. As he also 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)

But 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 to which he is referring is the linear dynamics, the dynamics of the wave function. This is a completely predictable, deterministic, sequential logic. But the key point is that it gives rise to all possibilities. Since, Barrett is saying, the device used to make an observation can only be made of ordinary stuff, that operates according to the linear dynamics, it must therefore give rise to all possibilities. So when a measurement is made, the device must wind up in all possible states. So, going by this logic, the device must produce every possible result of the observation. But only one single result is ever observed.

Hugh Everett resolved this paradox in 1957 with his many-worlds theory. There is no collapse. Which means that the measurement instrument does indeed wind up in all possible states. But one only ever sees one specific outcome. Everett’s solution is a relative world, which is what actually works. He named his theory The ‘Relative State’ Formulation of Quantum Mechanics. His solution is described in Schrödinger’s cat, coming up shortly.

(You might see it suggested that ‘decoherence’ solves the measurement problem. It does not, as described in Decoherence.)

The great puzzle from the point of view of philosophy is that the two dynamics are incompatible. As Barrett explains:

The measurement problem arises from the fact that the standard theory’s two dynamical laws are incompatible: one is linear and the other nonlinear. … they constitute contradictory descriptions of the time-evolution of physical states (Barrett, 2011)

The resolution presented here is that the two dynamics operate in the two different types of world. The linear dynamics is the operation of the quasi-classical world of the current worldview. The collapse dynamics is the operation of the personal world of the relational interpretations. This is the breakthrough proposed in Avant Garde Science.

You cannot change the colour of a red glass marble. But you can easily change the colour of a jarful of red marbles. You change the contents for a different class of marbles, green ones. The same logic applies to the relative world. Because the world hologram changes, the class of worlds that contain the world hologram is changed. In effect, in the reality of the world hologram, the state of the world changes on observation. This is the essence of the avant garde science.