Abstract Even though physicists often claim that their theories can, in principle, be reduced to the supposedly most fundamental theory, which is quantum physics, a look at how physics is practiced reveals that this reduction is almost never performed. Instead, effective models are built that include various types of contextual information and that are often incompatible with the supposedly fundamental theory. The phenomena described by these models can be characterized as contextually emergent. This chapter illustrates contextual emergence by means of examples from different fields of physics. In quantum physics, explanations of the measurement process require the assumption of a classical context that specifies the observable being measured and that induces the measurement event. In condensed matter theory, we find many types of quasiparticles that can only exist due to the solid that embeds them and the structure of which determines the properties of the quasiparticles. In thermodynamics, state variables such as the pressure and temperature of a system are given by its environment, and its phase transitions are triggered by changes in the environment. In the early universe, the degrees of freedom and the density and temperature determine the types of particles that are found in the universe. Later, the overall properties of the universe determine whether matter can condense to form stars. From all this it follows that processes and descriptions at different scales are equally important in physics. There are even contextual influences from outside physics. The chapter will thus conclude that physics is not causally closed.
Abstract Even though physicists often claim that their theories can, in principle, be reduced to the supposedly most fundamental theory, which is quantum physics, a look at how physics is practiced reveals that this reduction is almost never performed. Instead, effective models are built that include various types of contextual information and that are often incompatible with the supposedly fundamental theory. The phenomena described by these models can be characterized as contextually emergent. This chapter illustrates contextual emergence by means of examples from different fields of physics. In quantum physics, explanations of the measurement process require the assumption of a classical context that specifies the observable being measured and that induces the measurement event. In condensed matter theory, we find many types of quasiparticles that can only exist due to the solid that embeds them and the structure of which determines the properties of the quasiparticles. In thermodynamics, state variables such as the pressure and temperature of a system are given by its environment, and its phase transitions are triggered by changes in the environment. In the early universe, the degrees of freedom and the density and temperature determine the types of particles that are found in the universe. Later, the overall properties of the universe determine whether matter can condense to form stars. From all this it follows that processes and descriptions at different scales are equally important in physics. There are even contextual influences from outside physics. The chapter will thus conclude that physics is not causally closed.
This paper argues that the physics of condensed matter cannot be fully reduced to the supposedly fundamental quantum mechanical theory for all the atoms of which the system consists. In fact, there are many reasons to reject the idea that the world of physics is causally closed with everything being determined bottom-up by fundamental microscopic laws. This is illustrated by considering how condensed-matter theory is done in practice. It is never done by starting with a microscopic theory for the interaction of all the atoms of the system. Instead, approximations, plausible assumptions, intuitive models, and phenomenological theories are used to mathematically describe and explain the properties of systems that consist of a macroscopic number of particles. I argue that this is not merely a matter of convenience, but that there are fundamental and qualitative differences or even contradictions between the microscopic theory and the theory that is used in practice. The paper includes a list of arguments in favor of strong emergence and top-down causation within the realm of physics, and a response to several widespread objections against this view.
The context of an operational description is given by the distinction between what we consider as relevant and what as irrelevant for a particular experiment or observation. A rigorous description of a context in terms of a mathematically formulated context-independent fundamental theory is possible by the restriction of the domain of the basic theory and the introduction of a new coarser topology. Such a new topology is never given by first principles, but depends in a crucial way on the abstractions made by the cognitive apparatus or the pattern recognition devices used by the experimentalist. A consistent mathematical formulation of a higher-level theory requires the closure of the restriction of the basic theory in the new contextual topology. The validity domain of the so constructed higher-level theory intersects nontrivially with the validity domain of the basic theory: neither domain is contained in the other. Therefore, higher-level theories cannot be totally ordered and theory reduction is not transitive. The emergence of qualitatively new properties is a necessary consequence of such a formulation of theory reduction (which does not correspond to the traditional one). Emergent properties are not manifest on the level of the basic theory, but they can be derived rigorously by imposing new, contextually selected topologies upon context-independent first principles. Most intertheoretical relations are mathematically describable as singular asymptotic expansions which do not converge in the topology of the primary theory, or by choosing one of the infinitely many possible, physically inequivalent representations of the primary theory (Gelfand Naimark Segal-construction of algebraic quantum mechanics). As examples we discuss the emergence of shadows, inductors, capacitors and resistors from Maxwell's electrodynamics, the emergence of order parameters in statistical mechanics, the emergence of mass as a classical observable in Galilei-relativistic theories, the emergence of the shape of molecules in quantum mechanics, the emergence of temperature and other classical observables in algebraic quantum mechanics.
Within condensed matter physics, there are many extremely interesting physical systems which are strongly coupled. Although various approaches have been developed within condensed matter physics to deal with strongly coupled systems, there are many important physically relevant examples where a description in terms of theoretical models has not been successful. It thus appears natural to make use of gauge/gravity duality, which is very effective for describing systems at strong coupling, in this context as well. Of course, the microscopic degrees of freedom in a condensed matter system are very different from those described by a non-Abelian gauge theory at large N . For instance, these systems are non-relativistic in general. Nevertheless, the idea is to make use of universality again and to consider systems at second order phase transitions or renormalisation group fixed points, where the microscopic details may not be important. A prototype example of this scenario is given by quantum phase transitions , i.e. phase transitions at zero temperature which are induced by quantum rather than thermal fluctuations. These transitions appear generically when varying a parameter or coupling, which does not have to be small, such that the use of perturbative methods may not be possible. In many cases, the study of models relevant to condensed matter physics involves the introduction of a finite charge density in addition to finite temperature. This applies for instance to Fermi surfaces or condensation processes. In the gauge/gravity duality context, this is obtained in a natural way by considering charged black holes of Reissner–Nordström type. Their gravity action involves additional gauge fields. Within this approach, standard thermodynamical quantities such as the free energy and the entropy may be calculated. A further important observable characterising the properties of condensed matter systems is the frequency-dependent conductivity. This is calculated in a straightforward way using gauge/gravity duality techniques. A very instructive example of a quantum phase transition within gauge/gravity duality is obtained by using a magnetic field as the control parameter.
At each level of hierarchy, especially in the relevant energies for the phenomena under study, various concepts and entities of physics emerge. While reducible to other levels that are smaller in size or higher in energy, many of those degrees of freedom are frozen and do not come into play, so that it is the emergent entities that are relevant. With examples such as temperature and phases of matter, this approach to complexity is seen as fundamental, with lessons also for emergent concepts in other sciences. In blurring over the coherences of quantum wave functions, classical mechanics,with its familiar concepts of position, momentum etc., is itself emergent from quantum physics. Much of the mystery of quantum physics lies in this distinction between the underlying reality, which is out of reach directly, but accessible only through these emergent concepts, however natural they may appear.
This short review paper is devoted to 90th anniversary of S.T. Belyaev birthday. Belyaev’s ideas associated with the condensate state in Bose interacting systems have stimulated intensive studies of the possible manifestation of such a condensation in Fermi systems. In many Fermi systems and compounds at zero temperature a phase transition happens that leads to a quite specific state called fermion condensation. As a signal of such a fermion condensation quantum phase transition (FCQPT) serves unlimited increase of the effective mass of quasiparticles that determines the excitation spectrum and creates flat bands. We show that the class of Fermi liquids with the fermion condensate forms a new state of matter. We discuss the phase diagrams and the physical properties of systems located near that phase transition. A common and essential feature of such systems is quasiparticles different from those suggested by L.D. Landau by crucial dependence of their effective mass on temperature, external magnetic field, pressure, etc. It is demonstrated that a huge amount of experimental data collected on different compounds suggest that they, starting from some temperature and down, form the new state of matter, and are governed by the fermion condensation. Our discussion shows that the theory of fermion condensation develops completely good description of the NFL behavior of strongly correlated Fermi systems. Moreover, the fermion condensation can be considered as the universal reason for the NFL behavior observed in various HF metals, liquids, compounds with quantum spin liquids, and quasicrystals. We show that these systems exhibit universal scaling behavior of their thermodynamic properties. Therefore, the quantum critical physics of different strongly correlated compounds is universal, and emerges regardless of the underlying microscopic details of the compounds. This uniform behavior, governed by the universal quantum critical physics, allows us to view it as the main characteristic of the new state of matter.
The nature of emergence of complexity out of the underlying physics is a key issue in understanding the world around us (1). Genuine emergence can be claimed (2⇓–4) to depend on top-down causation, which enables higher emergent levels to direct the outcomes of causation at lower levels to fulfill higher-level causal requirements; for example, the needs of heart physiology at the systems level determine gene expression at the cellular level via gene regulatory networks (5) (Fig. 1). However, the idea of top-down causation has been denied by a number of commentators (e.g., refs. 6 and 7). The paper by Aharonov et al. (8) makes a strong contribution to this debate by giving quantum physics examples where top-down causation manifestly occurs. This physics result has strong implications for the philosophical debate about whether strong emergence is possible. Indeed, it gives specific examples where it occurs in a remarkably strong form.
Fig. 1.
Bottom-up and top-down causation from the quantum level up to the organism level and down again. Adapted with permission of Royal Society, from ref. 5; permission conveyed through Copyright Clearance Center, Inc.
Now, the word “causation” is regarded with suspicion by many philosophers of science, so to characterize what is happening one can perhaps rather use a number of different descriptions such as “whole–part constraint” or “top-down realization.” The key point remains the same, that higher levels can influence lower-level outcomes in many ways, and hence explain how strong emergence is possible. This occurs across science in general, and in physics in particular (3, 4). The latter point …
[↵][1]1Email: george.ellis{at}uct.ac.za.
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