### Abstract

Features of consciousness difficult to understand in terms of conventional neuroscience have evoked application of quantum theory, which describes the fundamental behavior of matter and energy. In this paper we propose that aspects of quantum theory (e.g. quantum coherence) and of a newly proposed physical phenomenon of quantum wave function "self-collapse" (objective reduction: OR - Penrose, 1994) are essential for consciousness, and occur in cytoskeletal microtubules and other structures within each of the brain's neurons. The particular characteristics of microtubules suitable for quantum effects include their crystal-like lattice structure, hollow inner core, organization of cell function and capacity for information processing. We envisage that conformational states of microtubule subunits (tubulins) are coupled to internal quantum events, and cooperatively interact (compute) with other tubulins. We further assume that macroscopic coherent superposition of quantum-coupled tubulin conformational states occurs throughout significant brain volumes and provides the global binding essential to consciousness. We equate the emergence of the microtubule quantum coherence with pre-conscious processing which grows (for up to 500 ms) until the mass-energy difference among the separated states of tubulins reaches a threshold related to quantum gravity. According to the arguments for OR put forth in Penrose (1994), superpositioned states each have their own space-time geometries. When the degree of coherent mass-energy difference leads to sufficient separation of space-time geometry, the system must choose and decay (reduce, collapse) to a single universe state. In this way, a transient superposition of slightly differing space-time geometries persists until an abrupt quantum -→ classical reduction occurs. Unlike the random, "subjective reduction" (SR, or R) of standard quantum theory caused by observation or environmental entanglement, the OR we propose in microtubules is a self-collapse and it results in particular patterns of microtubule-tubulin conformational states that regulate neuronal activities including synaptic functions. Possibilities and probabilities for post-reduction tubulin states are influenced by factors including attachments of microtubule-associated proteins (MAPs) acting as "nodes" which tune and "orchestrate" the quantum oscillations. We thus term the self-tuning OR process in microtubules "orchestrated objective reduction" ("Orch OR"), and calculate an estimate for the number of tubulins (and neurons) whose coherence for relevant time periods (e.g. 500 ms) will elicit Orch OR. In providing a connection among (1) pre-conscious to conscious transition, (2) fundamental space-time notions, (3) non-computability, and (4) binding of various (time scale and spatial) reductions into an instantaneous event ("conscious now"), we believe Orch OR in brain microtubules is the most specific and plausible model for consciousness yet proposed.

Original language | English (US) |
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Pages (from-to) | 453-480 |

Number of pages | 28 |

Journal | Mathematics and Computers in Simulation |

Volume | 40 |

Issue number | 3-4 |

DOIs | |

State | Published - Apr 1996 |

### Keywords

- Consciousness
- Cytoskeleton
- Microtubules
- Quantum gravity
- Quantum theory

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)
- Numerical Analysis
- Modeling and Simulation
- Applied Mathematics