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arXiv:quant-ph/0110043

On some algebraic problems arising in quantum mechanical description of biological systems

M. V. Altaĭsky

Published Oct 8, 2001• 1 citation
arXivHTMLPDF

Abstract

The biological hierarchy and the differences between living and non-living systems are considered from the standpoint of quantum mechanics. The hierarchical organization of biological systems requires hierarchical organization of quantum states. The construction of the hierarchical space of state vectors is presented. The application of similar structures to quantum information processing is considered.

DOI
10.48550/arxiv.quant-ph/0110043

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The biological hierarchy and the differences between living and non-living systems are considered from the standpoint of quantum mechanics. The hierarchical organization of biological systems requires hierarchical organization of quantum states. The construction of the hierarchical space of state vectors is presented. The application of similar structures to quantum information processing is considered.
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For years, quantum physics was seen as the physics of non-living matter. Thus, when biological living things were discussed, this sequence always came to the fore: biology > organism> organs> tissue> biochemistry> physics> classical mechanics + quantum mechanics. It can be seen that there was a reduction to the lower structures, and that at the base one reaches the level of particles such as atoms and molecules. But when the physico-chemical level is reached, it can be seen that many quantum mechanical events are taking place in living things, and that in fact these are quite normal reactions.
Founders of quantum mechanics (QM) anticipated that revisions to classical physics due to strange elements of quantum reality, would necessitate similar changes in biology. Complexity theory, systems biology and quantum biology provide possible solutions indicating that subject/object separation is a useful fiction for reductive science. Direct correlates to such QM observational/measurement issues as Complementarity and Uncertainty may justify the introduction of an analog of Heisenberg's uncertainty and the Planck constant for living systems. The phase space of "adjacent possibles" for biological systems from which one "actual" is selected resembles the collapse of the QM wave function. Since biological systems are hierarchical, this occurs across organizational scales resulting in biological coherence. The location of a quantum/classical boundary is unclear due to complexity. Whether biological systems' characteristics arise directly from QM or are of a different origin remains unsettled. To combine non-linear with quantum properties across biological scales we propose the Method of Coherent Structures (MCS), developed for quantum many-body systems. In MCS, a higher-level scale provides a classical envelope for quantum fluctuations at the lower scale. It yields a seamless transition from non-linear classical fields to quantum excitations and accounts for the emergence of complexity by incorporating metabolic energy supply.
The density matrix formalism which is widely used in the theory of measurements, quantum computing, quantum description of chemical and biological systems always implies the averaging over all states of the environment. In practice this is impossible because the environment of the system is the complement of this system to the whole Universe and contains infinitely many degrees of freedom. A novel method of construction density matrix which implies the averaging only over the direct environment is proposed. The Hilbert space of state vectors for the hierarchic quantum systems is constructed.