Observable collapse

A real collapse is an observable collapse, which happens all the time in real, open systems. Collapse is observable in open systems; it is an intrinsic part of the way these systems are commonly modeled. The equations used for the quantitatively correct modeling of open system are without exception non-unitary. An open system cannot be described by a Schroedinger equation. It is either described by a Lindblad evolution equation for the density matrix, or on a more detailed level by a stochastic Schroedinger equation (with random collapses), from which one gets the Lindblad equation by averaging.

An open system is dissipative, and dissipation is just the form an incomplete collapse takes. The equations for open systems and the equations for objective collapse are essentially of the same form. The main difference is that objective collapse theories believe that collapse happens at the most fundamental level, while the general theory of open systems takes its equations to be just as empirically validated rather than as fundamental, and often derives it under some plausibility assumptions (that are difficult to justify rigorously) from an underlying Schroedinger equation.

In fact, collapse is only approximate, but to a very good approximation. (The collapse in the Copenhagen interpretation also happens gradually, in the course of completing a measurement; it is instantaneous only in the unphysical idealization that a measurement takes no time. What happens during the measurement duration is not specified by the Copenhagen interpretation.)

On the other hand, some of the usual postulates of quantum mechanics are also only approximate. There have been many measurements of spectroscopic energy levels, but none of them produced an exact infinite decimal expansion of a discrete eigenvalue of the Hamiltonian (normalized to ground state zero) as would be required by the Born rule as typically stated in textbooks. This shows that these postulates must be regarded as approximations. Just like all claims made in physics. It is unrealistic to claim that anything in physics should be regarded as accurate to an infinite number of digits! Even for the most fundamental conservation laws there are serious ongoing efforts to detect the limits of their validity.

In the literature on open systems, unitary evolution is at best claimed for the much bigger, practically unobservable system composed of the actually observed system and its environment. What is therefore debatable is only whether collapse occurs in closed systems. But this is a moot question, as an observed system is never closed. Closed systems are not observable from the outside, hence it is both irrelevant and undecidable whether or not there is a collapse.

The interpretational problems only appear if one tries to treat an observed, hence open system as a closed system satisfying idealized postulates, and then wonders why there are apparent problems arising from taking an idealization for the real thing.

The description by von Neumann's (who introduced consciousness into the interpretational debate) applies only to observations from outside, not to observations from inside a system, as it must be when one assumes as given a closed system, described by the Schroedinger equation. Thus the usual discussions already start from an inconsistency of the descriptions.

On the other hand, nobody seems to have a useful framework for interpreting how to observe a quantum system from inside. Thus there is currently no consistent framework to discuss the question.

Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ