Dynamical Reduction Models

It would seem that the theory is exclusively concerned about `results of measurements', and has nothing to say about anything else. What exactly qualifies some physical systems to play the role of `measurer'? Was the wave function of the world waiting to jump for thousands of millions of years until a single-celled living creature appeared? Or did it have to wait a little bit longer, for some better qualified system ... with a Ph.D.? […] If the theory is to apply to anything but highly idealized laboratory operations, are we not obliged to admit that more or less `measurement-like' processes are going on more or less all the time, more or less everywhere? Do we not have jumping then all the time? J.S. Bell, Physics World, August Issue (1990)

The dynamical reduction program aims at solving the measurement problem of quantum mechanics, by assuming that the collapse of the wave function occurs spontaneously in Nature, according to a definite law which does not depend on whether measurements are performed or not. In this way it is possible to reformulate quantum theory as an objective, observer-free theory of physical phenomena.

The program has been successfully accomplished at the non relativistic level, both for systems of distinguishable particles (GRW models and its generalizations in terms of stochastic differential equations) as well as for systems of identical particles (CSL model). The problem of formulating dynamical reduction models for relativistic quantum fields theories is still open.

Solution and properties of the dynamical equations of reduction models.

At the non relativistic level several dynamical reduction models exists, which are fully satisfying in solving the measurement problem; nevertheless their mathematical and physical properties have not always been analyzed in all significant details. For example, and with reference to the QMUPL model first proposed by Diosi, the group aims at studying whether the explicit solution of the dynamical equation can be written down for the three most significant physical systems: the free particle, the harmonic oscillator and the hydrogen atom. Another relevant property to analyze is the asymptotic behavior of the solutions; it is expected that, in the large time limit, the localizing effect of the collapse mechanism and the spreading effect due to the free term in the Schroedinger Hamiltonian reach an equilibrium. In certain important cases, like the free particle and the harmonic oscillator, it should be possible to prove such as property with mathematical rigor.

Reduction models with non-markovian noises and their relativistic generalization.

In most dynamical reduction models, the stochastic process governing the collapse mechanism is chosen to be a Brownian motion, for it is a simple and very powerful mathematical tool to work with. However, there are two important reasons why one should analyze dynamical reduction models defined in terms of more general, non-markovian, noises. The first is that this noise responsible for the collapse of the wave function could be related to a real physical field (which in general does not have a Brownian character) such as the gravitational field, as suggested by R. Penrose. The second reason is that, when trying to extend dynamical reduction models to relativistic quantum field theories, one discovers that the Brownian noise causes the field to emit an infinite number of particles, per unit time and unit volume, out of the vacuum; because of such an infinite energy production, relativistic collapse models so far proposed are not physically satisfactory. The group aims at studying whether more general kinds of noise could provide a way out to this difficulty.

Further information

• List of dynamical reduction models
• Review articles on dynamical reduction models