Storrs McCall offers what he thinks is a unified framework for understanding a wide variety of fundamental issues. The topics range from the nature of scientific laws, the enigma of the asymmetric flow of time, the interpretation riddles of quantum mechanics and the origin of probability, to the subtle interplay between free will and decision. An all-embracing comprehension is sought to be founded on a few general ideas about the way physical events occur in the universe. McCall succeeds in generating provocative ideas. But the physical content of his scheme and the manner in which it is applied to specific problems falls short of the rigour and clarity required for his lofty goal.

McCall's entire programme is based on what he calls the "branched" model of the universe. All sets of events in the universe, represented in this model on a Minkowski diagram, take the shape of a tree, with a single four-dimensional trunk for the past and a densely branching set of four-dimensional manifolds for the future. Each of these manifolds in turn branches, thus providing a branching set of many spacetime manifolds. Of all possible future courses of events represented by these spacetime manifolds, only one is assumed to be actualised. The model of physical events occurring in the universe is therefore analogous to a tree that "grows" by losing branches (referred to as the property of "branch attrition"). McCall motivates his scheme as an ontological approach seeking to provide an observer-independent description of quantum phenomena. This is thus put forward as a "realist'' model of quantum mechanics, alternative to the orthodox (Bohr, Heisenberg) interpretation that does not recognise the possibility of an ontological spacetime description of quantum events.

That McCall's scheme is seriously deficient is evident from his analysis of the measurement problem. This quantum riddle stems from the fact that standard quantum mechanics is unable to account for how a definite outcome is obtained in a measurement process described by the Schrodinger equation.

McCall begins by outlining a brief account of some of the approaches to this problem. But there is not here, or indeed anywhere in the book, even a cursory mention of David Bohm's ontological model. This is astonishing. Bohm's model is formulated in such a way that the measurement problem does not exist. With regard to quantum nonlocality, Bohm provides a form of "explanation'' that McCall seeks in quantum correlations between events widely separated in space. Bohm's scheme puts forward the ontological notion of particles as seats of objective properties that are influenced nonlocally, rather than proposing, as McCall does, an abstract convoluted notion of "branch attrition" whose precise ontological status is rather obscure. In fact, I suspect that the very idea of certain outcomes occurring on some selected branches relative to appropriate sets of initial ontological conditions embodies in some sense the relatively well-known concept of "hidden variables'' (added to the wave function to provide a "complete'' description of the state of a particle, McCall does not make clear to what extent he departs from assuming wave function to be a "complete'' description of the state of an individual quantum entity. An in-depth critique of the Bohmian scheme would have helped to clarify these critical aspects of his model.

Returning to the measurement problem, the "branched" model suggests a "triggering mechanism'' for wave-function collapse. (Here it differs from Bohm's because the latter does not require wave-function collapse at any stage.) But McCall's conception of the "triggering mechanism'' is logically unsatisfactory - rather than arising from his formalism it relates to "branch attrition" in a rather ad hoc way. The inadequacy of the entire procedure is clear, in that it decrees the wave function of an observed system to collapse instantaneously at the "moment of measurement'': but the key question - how is an apparatus left in one particular pointer state? - is dealt with only through vague statements.

Among the book's other chapters, those dealing with causality and free will contain a number of perceptive observations, and the chapter on probability has an admirably succinct summing-up of rival interpretations. But such positive philosophical features of the book are blown off course by persistent efforts to demonstrate the strength of the "branched" model in foundational physics. To take an example from outside the domain of quantum physics, in the chapter on flow of time, temporal directionality is implicitly assumed at the outset by building it into the branching structure. There is then no scope for a deeper comprehension of three important physical issues: why one observes time asymmetry in physical processes (for example, entropy increase) despite the fact that the underlying laws are time-symmetric; whether the arrows of time observed in branches of physics such as thermodynamics, electrodynamics and cosmology are fundamentally linked; and to what extent these arrows are related, if at all, to the flow of time perceived by human consciousness.

Finally, it is questionable whether the oft-repeated claim that if the "branched" model does succeed in explaining a broad range of physical problems, it would constitute "strong evidence that the universe is as the model portrays it". This is questionable if one recalls that it is possible to have radically different but internally consistent interpretations and ontologies corresponding equally well to only one empirically adequate formalism (the Duhem-Quine thesis of underdetermination of theory). There can be no objective way of deciding which one of them is to be preferred. It is therefore too simplistic to suggest that a particular interpretation or model represents the "true" picture of the universe.

Dipankar Home is a physicist at the Bose Insitute, Calcutta, currently on a Homi Bhabha fellowship.

## A Model of the Universe:: Space-Time, Probability and Decision

Author - Storrs McCall

ISBN - 0 19 824053 8

Publisher - Clarendon Press, Oxford

Price - £30.00

Pages - 328pp

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