Composition of Physical Systems

Krystyna Bugajska, Slawomir Bugajski

Pieter E. Vermaas

In quantum mechanics the properties of a composite system can be divided into properties which are reducible to the properties of the subsystems of the composite and properties which are irreducible to those subsystem properties. The irreducible properties are called holistic and emerge when one describes the system as a whole. In this chapter I show that the bi and spectral modal interpretations can ascribe the holistic properties to composites but, in general, fail to reproduce the relations between the reducible properties of a composite and the properties of the subsystems. The atomic modal interpretation, on the other hand, fails to ascribe the holistic properties but is much more successful in reproducing the relations between the reducible properties and the subsystem properties. I discuss whether these failures harm the empirical adequacy and the metaphysical tenability of modal interpretations. Holistic properties of composite systems The basic principle of reductionism, that all the properties of composite systems are amalgamates of the properties of the subsystems of these composites, has triumphed so much in classical physics that I find it difficult to come up with a clear example of a classical property that cannot be taken as a complex of the subsystem properties. So, in order to make a case for the idea that composites can also possess, in addition to reducible properties, so-called holistic properties which cannot be reduced to the properties of the subsystems, one has to move outside physics or to draw upon some counterfactual development of physics.

Hermann Haken

Marco Erba, Paolo Perinotti

Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A striking consequence of this facet is the violation of Bell inequalities, which has been experimentally demonstrated via Bell tests. The prediction of this phenomenon originates as quantum systems are prescribed to combine according to the composition postulate, i.e. the tensor-product rule. This rule has also an operationally salient formulation given in terms of discriminability of composite states via local measurements. However, both the theoretical and the empirical status of such a postulate have been repeatedly challenged, questioning its independence from other physical principles -- most notably from quantum postulates pertaining solely to single systems. Is the composition postulate the only viable way to combine quantum systems into a consistent physical theory? Here, this long-standing problem is resolved by answering in the negative. This is achieved by adopting an operational approach to physical theories and exhibiting a family of theories that differ from standard quantum theory in their system-composition rule. These theories have the same predictions as standard quantum theory as far as Bell-like correlation scenarios are concerned. Quantum theory is thus established to embody genuinely more than quantum correlations. As a result, foundational programmes based on single-system principles only, or on mere Bell-like correlations, are operationally incomplete. On the experimental side, ascertaining the independence of postulates is a fundamental step to adjudicate between quantum theory and alternative physical theories: hence, the composition postulate calls for experimental scrutiny independently of the other features of quantum theory.

Hermann Haken

Wesley E. Brittin, A.Y. Sakakura

A new fundamental theory of composite particles in nonrelativistic many-body systems is developed. The theory is constructed making use solely of the physical Fock space for the basic elementary particles which comprise the many-body system. In this manner exchange symmetry in the elementary particles is exact. Physical composite particle creation and annihilation operators are introduced and these operators satisfy exact Bose (Fermi) commutation (anticommutati$\stackrel{\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}{\mathrm{o}}$n) relations depending on whether the composites correspond to bosons or to fermions. Commuting physical occupation number operators for composite particles are then constructed in the usual manner from the composite creation and annihilation operators. These number operators are highly dressed in terms of the basic elementary particle operators. Finally, the foundations of statistical mechanics for bound composite particles are formulated in terms of the appropriate occupation number operators.