Introduction

Eighty year ago, Schrodinger (1935) and Einstein (1935) expressed deep worries about the foundation of quantum theory. The main difficulty was a contradiction, between a universal evolution of quantum systems under the Schrodinger equation and the uniqueness of data in measurements, often expressed as the problem of “wave function collapse”.

Many answers were attempted. Some essays tried to modify in depth the interpretation of quantum mechanics (de Broglie 1956; Bohm 1952; Everett 1957) or revised its foundations (Bell 1964; Adler 2004). Attempts were made also to complete its physical content by extraneous phenomena (Ghirardi et al. 1986), or questioned its exactness (Pearle 1976; Ghirardi et al. 1990). New conceptions of

R. Omnes (is)

Laboratoire de Physique Theorique, Universite de Paris XI, Orsay, France e-mail: roomnes@wanadoo.fr © Springer International Publishing AG 2017

E. Agazzi (ed.), Varieties of Scientific Realism,

DOI 10.1007/978-3-319-51608-0_17 understanding were also proposed and the problem is now a topic of much philosophical research regarding foundations of knowledge and the nature of Reality (d’Espagnat 1995; Caves et al. 2002; Epperson and Zafiris 2013).

Many physicists are more pragmatic. They do not pay an extreme attention to questions regarding the nature of Reality. They consider often that these problems are only waiting for answer: Time will tell. The best argument for this attitude stands in the prodigious advances of quantum physics, since it carries this burden of ignorance: There is no doubt that the quantum laws are perfectly valid for all practical purposes, and this is enough for a science.

A few advances regarding parallel questions have occurred however and one can mention two of them: One knows why classical determinism is valid with high precision at macroscopic scales (Omnes 1994). The compatibility of quantum theory with standard logic has also ben shown by “consistent histories”, which discard many past paradoxes in interpretation (Griffiths 2002). One may also notice that these results required in both cases an enlargement of the standard interpre­tation of quantum mechanics, somewhat encouraging the prospect that the same procedure could apply to the collapse problem.

The research to be reviewed here is concerned with this problem. It will be convenient for a beginning to recall the status of this question, according to the “standard” interpretation of quantum mechanics. This interpretation, which can be found in most textbooks, was arrested particularly in two great books, by Dirac (1930) and by Von Neumann (1932). Von Neumann, especially, made an axiom of the condition that every statement regarding quantum physics should be expressed in terms of observables. (One recalls that, in the mathematical framework of quantum theory, an “observable” is associated with a “self-adjoint” operator in an abstract Hilbert space, which represents all the possible states of a physical system. But one will try to avoid as much as possible such technicalities).

Bohr did not accept completely this standard interpretation (Bohr 2010). He stressed that another concept, usually called “wave function collapse”, was unavoidable. One may describe it as a hidden physical phenomenon, through which a unique result emerges at macroscopic scales when an actual measurement is performed. There are variants (Laloe 2012; d’Espagnat 1995), but one may con­sider, from a philosophical standpoint, that this mysterious collapse holds the key for the place where macroscopic Reality reaches its obvious uniqueness, which is the foundation of every science.

The present work reports on recently discovered new openings in this question.

One will try to describe this conjecture in general terms, avoiding technical details as much as possible. A truly rigorous theory would need of course to go much deeper, but one acknowledges that such a level is not yet reached, which makes one speak of conjectures. The results are however so internally consistent, when suggesting from their own structure answers to the problems that they raise, that one dares to entertain the hope that they contain at least a significant part of a future right answer, which many of us are pursuing.

Even so, these ideas cannot hold into a unique brilliant vision, as some previous proposals did (like Bohm's idea of a unique reality at a macroscopic level (Bohm 1952), or Everett's of a wave function of the whole universe (Everett 1957), for instance). They show on the contrary a complex self-organization, through which the uniqueness of macroscopic Reality comes out only as a synthesis.

The basic elements of this process and their mutual relations will be introduced here in the following order: (i) Description of a notion of local entanglement between two quantum systems.

I must warn readers that several of these results, which open or seem to open new domains, encounter technical or mathematical, problems, often themselves quite new. They were discovered recently and sometimes approached only by means of simplified models. Much more work would be necessary to assert them with full confidence (or perhaps to discard them). One mentions at the present place these limitations as a preliminary warning, but without intending to come back to them. The aim of the next sections of this paper will be on the contrary to get as much clarity as its author could achieve.

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