Two methods for the description of physical phenomena, microscopic and macroscopic, are necessary to understand the physical world. We now have two examples. The first one is mechanical, whether classical or quantal, vs thermodynamic treatments, which are characterized by reversibility and irreversibility, respectively. Another one is quantal vs classical theories, which have different forms of logic and lead to various paradoxes in measurement processes. To understand these contradicting aspects, it should be noted that in both cases, chaos and measurement are involved inevitably, and averages over small regions of space and time for measurement are required. In this way, chaos mediates between the two methods of description. We have already made an attempt to treat the former example in terms of ergodicity. In this paper the latter example will be treated with the theory of quantum measurement and the EPR paradox in mind.
Two methods for the description of physical phenomena, microscopic and macroscopic, are necessary to understand the physical world. We now have two examples. The first one is mechanical, whether classical or quantal, vs thermodynamic treatments, which are characterized by reversibility and irreversibility, respectively. Another one is quantal vs classical theories, which have different forms of logic and lead to various paradoxes in measurement processes. To understand these contradicting aspects, it should be noted that in both cases, chaos and measurement are involved inevitably, and averages over small regions of space and time for measurement are required. In this way, chaos mediates between the two methods of description. We have already made an attempt to treat the former example in terms of ergodicity. In this paper the latter example will be treated with the theory of quantum measurement and the EPR paradox in mind.
The relationship between chaos and quantum mechanics has been somewhat uneasy--even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our starting point here is that a complete dynamical description requires a full understanding of the evolution of measured systems, necessary to explain actual experimental results. This is of course true, both classically and quantum mechanically. Because the evolution of the physical state is now conditioned on measurement results, the dynamics of such systems is intrinsically nonlinear even at the level of distribution functions. Due to this feature, the physically more complete treatment reveals the existence of dynamical regimes--such as chaos--that have no direct counterpart in the linear (unobserved) case. Moreover, this treatment allows for understanding how an effective classical behavior can result from the dynamics of an observed quantum system, both at the level of trajectories as well as distribution functions. Finally, we have the striking prediction that time-series from measured quantum systems can be chaotic far from the classical regime, with Lyapunov exponents differing from their classical values. These predictions can be tested in next-generation experiments.
This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description (classical in the limited sense implied by the correspondence principle of Bohr) of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from the strictly classical observables of Newtonian physics to their quasi-classical counterparts the known rules for the measurement of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics.
Introduction In this chapter I attempt to review a few somewhat loosely connected themes, which figure in recent work by physicists on decoherence and irreversibility in quantum mechanics. The looseness is forced upon us by the subject – any proper discussion inevitably drags in questions about thermodynamic reversibility and the various arrows of time, about the foundations of quantum mechanics and quantum measurement, about the nature of quantum coherence, and about the relationship between quantum and classical mechanics. There are inevitably many gaps in our understanding of these questions, both for the physicist and for the philosopher. Some philosophers may feel that the subject is too immature to be interesting to them – that it is not yet ripe for philosophical analysis. Indeed I have recently heard the opinion expressed that quantum mechanics in its entirety was still not amenable to such analysis – that if the physicists could not yet understand it, there was no point in philosophers trying! I hope this feeling is not too widespread amongst philosophers of science – I suspect that it may arise in part because the philosophical community (along with a good part of the scientific community) is unaware of some important advances that have been made in the last decade in understanding the physics of quantum processes at the macroscopic level, as well as the relation between classical and quantum mechanics. Much of the chapter is therefore unashamedly tutorial in nature; however, given the wide range of topics covered, I imagine that even physicists will find at least some of the material to be novel.
Quantum non-integrable systems have pseudochaos in the phase of the eigenfunctions. In particular, correlation function of wave functions at two different points disappears, when observation process, which requires space and/or time average over a small range, is taken into account. This gives rise to the realization of decoherence in measuring processes. By virtue of this property of quantum chaos, various problems and paradoxes are explained in the framework of conventional quantum mechanics. The subjects treated here are the duality of wave and particle, the wave function collapse in measurement, Stern–Gerlach experiments, Schrödinger's cat paradox, the Einstein–Podolsky–Rosen paradox and quantum Zeno effect.
From the preceding exposition it follows that the quantum statistical representation of an individual atomic system does not imply any renunciation regarding further knowledge about the system. On the contrary the statistical character of quantum physics directly reflects the fundamental non-causal appearance of quantal recordings, and through the discovery of the complementarity of quantal phenomena a complete but necessarily statistical description of the atom has been accomplished. Furthermore quantum physics has afforded a statistical description of macroscopic bodies through their representation as assemblies of huge numbers of identical atomic systems, and, apart from accounting in a more fundamental way for the properties already described in classical physics(the correspondence principle, p. 36), quantum statistics explains several macroscopic phenomena which cannot be understood within the conceptual frame of classical physics only. It must be maintained, however, that when observing the properties of individual atomic objects the macroscopic observational apparatus cannot be represented in terms of atomic constituents because this would destroy the unambiguity of the description. The observational apparatus fulfils its basic function of being the spacetime frame of reference for the quantal recordings precisely through its description in classical physics alone. However, when refraining from the analysis of individual quantal processes it is possible to apply quantum statistics to macroscopic phenomena, that is, the causality of classical physical phenomena can be interpreted in the quantum formalism as the statistical result of the interplay of enormous numbers of atomic processes. It is possible, then, to talk of statistical causality as a fundamental aspect of physical reality.
While physicists pursue the search for the Grand Unified Theory (GUT) and the expedition to find the Higgs that ought to solidify the Standard Model, philosophers keep inquiring as to what the nature of matter and mind might be and propose various theories. At first sight, the high energy physicist or the philosopher, both human, and the elementary particle seem to have nothing in common, however we contend and argue in this paper that we are looking at different scales of what constitutes universal behaviour and use Herman Dooyeweerd's theory of Modal Aspects to bridge the particle to the mind. To other than a physicist the dual nature of the atom or the so-called elementary particles may be difficult to comprehend and certainly appears unfathomable to intuit. This is due to the fact that the dual nature of matter finds its anchoring within the theoretical and mathematical frameworks provided by quantum mechanics, the latter tends to not be easily accessible to most individual's intuition. What would the consequences be if human nature itself had a dual character? We all know that human nature is both egoistic and altruistic, however it is not often that one considers the fact that egoism is an individual behaviour, while altruism is a collective behaviour. Likewise a particle is an individual manifestation of what we call matter, while wave nature can be considered characteristic of collective behaviour of the same matter.
Recent advances in experimental physics—the queen of reductionist science—aimed at solving the mysteries of the quantum world has led to a deepening of the mystery rather than easing it, dispelling the EPR paradox and pointing out a conceptional error in this now famous gedanken experiment, while lending some authority and validation to quantum mechanics. The strange features of the quantum world are founded on what Bohr dubbed complementarity, or the way a sub-particle entity can behave either as a wave or as a particle; and on Werner Heisenberg's uncertainty principle, which says that a quantum entity such as an electron does not avail itself to a deterministic exact measurement of both position and momentum simultaneously. Such postulates seem to contradict deeply held assumptions by the deterministic and materialistically oriented world of experimental physics where everything, including the atom, can be reduced to a single aspect. There are mounting calls for newer ways of understanding reality that are capable of handling these apparently strange incomprehensible phenomena revealed through the classical observation of the microscopic quantum world. There is also fundamental progress made in bouncing cosmology theories that bridge general relativity to quantum mechanics and provide some insight into the nature of the universe and its transition and pre-history through the big bang.
The thrust of this paper evolves around two pillars. One, is that that the apparent logical fissure emergent in reductionist thought, coming from orthodox science and the application of the scientific method that is manifest in what we know and do not understand in quantum mechanics, can be liaised to our intellectual understanding through the perspective offered by Herman Dooyeweerd's theory of Modal Aspects. The other, is the central and special role humans have in relation to the universe. Through this approach, we will argue that the dual nature of the atom or elementary particles is, rather than being a strange phenomenon, in fact an essential characteristic of what constitutes its nature