In the years from 1986 to 1989, I had the great privilege of becoming acquainted with the late J. S. Bell, and this gave me the opportunity of fully appreciating his deep views on the basic formal, conceptual, and epistemological problems that affect our best theory, i.e., quantum mechanics. This lucid thinker had absolutely clear that the so-called macro-objectification problem—and the related issue of establishing an acceptable psychophysical correspondence for such a theory—represented crucial challenges that had to be faced by all those who are truly concerned with the significance and the conceptual relevance of the scientific enterprise. In particular, he maintained firmly that what was needed to overcome the problems was “mathematical work by theoretical physicists rather than vague, imprecise verbal assertions.” I shared, and I still share, this precise opinion.

The problems met by standard quantum mechanics that I have just mentioned are well known and can be summarized in quite simple terms: the very linear structure of the theory implies the unavoidable occurrence of linear superpositions of states corresponding to macroscopically different physical situations. Such superpositions cannot be interpreted, as it has been done by less thoughtful physicists, as describing a statistical mixture of systems that actually have the properties corresponding to the different terms of the superposition—those properties that are directly connected with our definite perceptions. All proposed ways out of this embarrassing situation, even the most serious and popular, like those that make appeal to the unavoidable decoherence induced by the environment, have been proven to be logically and epistemologically untenable.

Stephen Adler (2004) has made this point absolutely clear (see also Adler Reference Adler2003); what is of particular interest for us here is that he lucidly and convincingly leads the reader to reach this conclusion in the introduction and overview of his stimulating book, Quantum Theory as an Emergent Phenomenon. This is the starting point of his work, and it puts into full evidence the real and deep motivations that have led the author to become involved in a fascinating intellectual and scientific project, the one that is described in the rest of the book. Adler's work represents an extremely interesting attempt going precisely in the direction indicated by J. S. Bell, i.e., to work out a quite general formal and conceptual scheme (a serious work by a theoretical physicist) that might lead, when fully developed, to really overcoming the difficulties of the standard formalism, and to a fully satisfactory account of physical phenomena at all levels, from the microscopic to the macroscopic.

The general formal outline of the new approach, denoted as the trace dynamics, is presented in Chapter 1, in which the basic mathematical entities of his approach, i.e., phase-space noncommutative variables, are introduced and their dynamics are discussed. Such a dynamics is not the quantum one; its formulation is obtained by resorting to the trace Lagrangian and Hamiltonian, which represent generalizations of their classical analogues. At this stage the reader is confronted with the real innovative nature of the approach: the quantum behavior emerges only when one considers the statistical mechanics ensuing from the ‘classical’ matrix dynamics of the noncommutative variables. The two subsequent chapters discuss the general problem of the conserved quantities within the considered framework when one imposes appropriate restrictions to the formalism, and they show how the approach can be naturally extended to cover the case of globally supersymmetric theories. An extremely significant analysis and comparison with the Wess Zumino and Yang Mills models is also presented. Obviously this is not the place to even make an attempt to be specific about the formalism: the reader has surely grasped that the treatment is quite subtle and highly technical.

Accordingly, let me leave aside the more technical aspects and come to describe the really interesting (from the point of view of the foundational problems of quantum mechanics) part of the book. After having shown how the quantum formalism emerges when one considers thermodynamical averages of functions of the ‘classical’ noncommutative variables, Adler makes a further fundamental step forward and analyzes in great detail the fluctuations around their average values. This procedure leads to the emergence of the richest and most interesting aspects of the formalism, i.e., it leads to stochastic modifications of the quantum dynamics that have close connections with the line of thought at the very basis of the so-called dynamical reduction program. It seems appropriate to recall the lively interest of J. S. Bell for such a program and to mention its most fascinating features for the foundations of quantum mechanics. The crucial point of dynamical reduction models derives from the fact that they imply—on the basis of a unique, universal evolution law governing all natural processes—that linear superpositions of macroscopically distinguishable states are forbidden just by the stochastic terms of the dynamical equations. Consequently, in measurement-like situations the reduction of the wave packet has not to be postulated and does not conflict with the basic dynamical equations: the measurement problem finds a natural and consistent solution, and macroscopic objects are governed by classical mechanics. The two embarrassing points of the standard formulation of quantum mechanics—the conflict between the linear and the deterministic evolution of the state vector and the stochastic and the nonlinear nature of the reduction processes, as well as the nonoccurrence of linear superpositions of macroscopically different states—find a perfectly consistent solution that allows one to work out a perfectly acceptable ‘quantum worldview’.

However, it has to be noted that the dynamical reduction program, as developed before Adler's investigations, has been based on fundamentally phenomenological modifications of the standard quantum dynamics. Accordingly, its interest derives entirely from its being a clear example that a coherent way out of the puzzling problems of our best theory is possible, and from having identified some consistent way out. Adler, in his fascinating and deep book has taken the challenge quite seriously, by presenting a lucid attempt to build, starting from new basic principles and assumptions, a quite general theoretical scheme that provides an explanation of the origin of the phenomenological stochastic modifications of the Schrödinger equation that were plainly postulated within the dynamical reduction models.

The remarkable interest of this fascinating book can then be expressed simply: the author has succeeded in showing that a modification of the standard quantum dynamics that makes it logically consistent emerges as a consequence of a coarse graining of an underlying deeper dynamical level. Obviously, many problems remain open, and the program still requires a lot of work before it can be considered as an example of a theory that fulfils all the requests that it must satisfy in order to be considered as completed. But the book, accessible to mathematicians and theoretical physicists, represents really a quite deep and serious attempt to overcome all difficulties that have plagued quantum theory since its very formulation, and it gives some extremely interesting indications of how to reach this goal. For these reasons the book is surely a fascinating and stimulating reading for all theoretical physicists, and more specifically, for researchers interested in the conceptual and epistemological problems of modern science, in particular for those—like Einstein, Schrödinger, Bell, and many others—who think that quantum mechanics has not yet seen a conceptually fully satisfactory formulation. I strongly recommend this stimulating reading, in particular to all those who are really concerned about the logical and philosophical problems of the scientific enterprise.