## Environmental decoherence or not?

23/07/2008

One of the most relevant open questions currently under study in physics is how a classical world emerges from the laws of quantum mechanics. This can be resumed in a standard philosophical question:”How does reality form?”. We have learnt from standard quantum mechanics courses that one just takes the mathematical limit $\hbar\rightarrow 0$ and the classical limit emerges from quantum mechanics. Indeed, as always, things are not that simple as in Nature $\hbar$ is never zero and this means that all objects that are seen should be in a quantum mechanical state. So, why in our everyday life we never observe weird behaviors? What is that cuts out most of the Hilbert space states to maintain a systematic classical behavior in macroscopic objects? More carefully stated the question can be put as:”Where is the classical-quantum border, if any?”. Indeed, if we are able to draw such a border we can buy all the Copenaghen interpretation and be happy.

A proposal that is going to meet increasing agreement is environmental decoherence. In this case one assumes that an external agent does the job erasing all the quantum behavior of a system and leaving only a superselected set of pointer states that grants a classical behavior. From a mathematical standpoint one can see interference terms disappear but one cannot say what is the exact state the system is left on, leaving in some way the measurement problem unsolved. It should be said that the starting point of this approach has been a pioneering work of Caldeira and Leggett that firstly studied quantum dissipation. In order to have an idea of how environmental decoherence should work, the Einstein’s question: “Do you really believe that the moon is not there when we do not look at it?” is just answered through the external effect of sun radiation and, maybe, the cosmic microwave background radiation that should act as a constant localizing agent even if I have never seen such an interpretation in the current literature. It is clear that to try to explain a physical effect by a third undefined agent is somewhat questionable and sometime happens to read in literature some applications of this idea without a real understanding of what such an agent should be. This happens typically in cosmology where emergence of classicality cannot be easily understood. As unsatisfactory may be such an approach can be seen from the relevant conclusion that it gives strong support to a multiverse interpretation of quantum mechanics. Of course, this can be a welcomed conclusion for string theorists.

Today on arxiv a preprint is appeared by Steven Weinstein of Perimeter Institute that proves a theorem showing that environmental decoherence cannot be effective in producing classical states from generic quantum states. Indeed, all applications of environmental decoherence in literature consider just well built toy models that, due to their construction, produce classicality but this behavior is not generic even if in agreement with the theorem proved by Weinstein. So, the question is still there unanswered:”Where is the classical-quantum border, if any?”. We have already seen here the thermodynamic limit, that is the border at infinity, is an answer, but the question requires a deep experimental investigation. A hint of this was seen in interference experiments with large molecules by Zeilinger’s group. This group is not producing any new result about since 2003 but their latest paper was showing some kind of blurry behavior with larger molecules. This effect has not been confirmed and one cannot say if it was just a problem of the apparatus.

The question is still there and we can state it as:”How does reality form?”.