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NeuroQuantology

Reply to ‘Mathematical Error in “Incompatibility between Quantum theory and Consciousness”’

Daegene Song

Published May 22, 2008• 0 citations

Abstract

1 In (Georgiev, 2008), Georgiev claims to have spotted a critical mathematical error in the paper (Song, 2008) showing the incompatibility between quantum theory and consciousness. This note's goal is to show that Georgiev's claim comes from a simple misunderstanding of the paper. The whole point of (Song, 2008) was to show that quantum theory's existing standard axioms cannot consistently describe the phenomenon presented as (N2), which describes a case where an observer in the mental reference frame e is observing his own reference frame's unitary evolution. This phenomenon can be pictured as follows: consider a closed system with an observer and a qubit. The observer can choose or change the measurement basis for the given qubit. Moreover, the observer can still have or change this basis choice e even when the closed system contains no qubit. Philosophy literature widely discusses self-observation, i.e., the observer observing his own mental state, which is also known as reflexive selfconsciousness or simply reflexive consciousness (for example, see (Halliday, 1989; Velmans, 2008)). (N2) considers a case when subject and the object being observed are identical, i.e., both correspond to a single vector, e , rather than two vectors pointing in the same direction. Let us now discuss the fallacy in Georgiev's argument (Georgiev, 2008).

DOI: 10.14704/nq.2008.6.2.176

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1 In (Georgiev, 2008), Georgiev claims to have spotted a critical mathematical error in the paper (Song, 2008) showing the incompatibility between quantum theory and consciousness. This note's goal is to show that Georgiev's claim comes from a simple misunderstanding of the paper. The whole point of (Song, 2008) was to show that quantum theory's existing standard axioms cannot consistently describe the phenomenon presented as (N2), which describes a case where an observer in the mental reference frame e is observing his own reference frame's unitary evolution. This phenomenon can be pictured as follows: consider a closed system with an observer and a qubit. The observer can choose or change the measurement basis for the given qubit. Moreover, the observer can still have or change this basis choice e even when the closed system contains no qubit. Philosophy literature widely discusses self-observation, i.e., the observer observing his own mental state, which is also known as reflexive selfconsciousness or simply reflexive consciousness (for example, see (Halliday, 1989; Velmans, 2008)). (N2) considers a case when subject and the object being observed are identical, i.e., both correspond to a single vector, e , rather than two vectors pointing in the same direction. Let us now discuss the fallacy in Georgiev's argument (Georgiev, 2008).

In the paper “Incompatibility between quantum theory and consciousness” by Daegene Song is presented mathematical argument according to which quantum theory and self-observing consciousness are incompatible. Here we spot a critical mathematical error in Song’s equations, showing that Song’s argument is mathematically messed and is quite irrelevant for solving issues concerning consciousness. Moreover, Song’s error does not apply specifically for quantum mechanics but for any unitary transformation in configuration space.

Based on the standard axioms of quantum theory, we provide a counter-example which invalidates the full compatibility between consciousness and quantum theory. In particular, we present an example of a natural phenomenon in which an observer's the mental state can be fully described in mathematical terms analogous to the state vector that is being observed. This mathematical description of the observer's mental state enables us to examine consciousness within the standard axioms of quantum theory. The separation between the observing party and the physical system being observed, imposed by the axiom of quantum theory, poses a problem when the observer is observing his own mental state, i.e., self-observing consciousness.

Based on the standard axioms of quantum theory, we provide a counter-example which invalidates the full compatibility between consciousness and quantum theory. In particular, we present an example of a natural phenomenon in which an observer's the mental state can be fully described in mathematical terms analogous to the state vector that is being observed. This mathematical description of the observer's mental state enables us to examine consciousness within the standard axioms of quantum theory. The separation between the observing party and the physical system being observed, imposed by the axiom of quantum theory, poses a problem when the observer is observing his own mental state, i.e., self-observing consciousness.

In [NeuroQuantology 6, 46 (2008): arXiv:0706.4180], a certain natural phenomenon of self-observing consciousness was shown to be incompatible with the standard axioms of quantum theory. In order to consider a possibility of removing this inconsistency, which arises due to the separation between an observing party and a state vector being observed stated in the quantum theory axioms, we provide a conjecture where ‘being’, or existence, is identified with the experience of observing the state vector. That is, the observer is not observing the state vector in terms of the relative difference between reference frames, instead, the experience of observing the state vector should define the observer, or being. It is shown that the Heisenberg picture provides a natural description of this conjecture. 1

In [arXiv:0706.4180], a certain natural phenomenon of self-observing consciousness was shown to be incompatible with the standard axioms of quantum theory. In order to consider a possibility of removing this inconsistency, which arises due to the separation between an observing party and a state vector being observed stated in the quantum theory axioms, we provide a conjecture where ‘being ’ is identified with the conscious experience of observing the state vector. That is, the observer is not observing the state vector in terms of the relative difference between reference frames, instead, the conscious experience of observing the state vector should define the observer, or being. It is shown that the Heisenberg picture provides a natural description of this conjecture. 1

The original Copenhagen interpretation of quantum mechanics was offered as a pragmatic methodology for making predictions about future experiences on the basis of knowledge gleaned from past experiences. It was, therefore, fundamentally about mental realities, and refrained from speaking about a more inclusive reality. Von Neumann created, later, what is called the orthodox formulation of quantum mechanics. It incorporates all of the Copenhagen-based predictions about connections between experiences into a rationally coherent conception of a dynamically integrated psychophysical reality. Von Neumann’s formulation allows the same laws and concepts that are used to make predictions about atomic phenomena to account for the capacity of our mental intentions to influence our bodily actions. Danko Georgiev claims to have found logical flaws in my use of von Neumann’s theory to explain this causal effectiveness of our mental intentions. The bulk of Georgiev’s paper gives a detailed discussion of a system with just two base states, up and down. This is not an adequate model of the pertinent physical system, a human brain. Georgiev’s attempt to relate his two-state work to the case at hand is flawed by statements such as “…in von Neumann’s formulation there are no such things as minds, spirits, ghosts, or souls, …” Von Neumann’s formulation certainly does involve minds. Georgiev’s choice of words seems designed to suggest that I am introducing mental qualities and assumptions that go beyond what are already parts of von Neumann’s theory. I explain here why these allegations, and all his other allegations of errors, are incorrect. NeuroQuantology | December 2012 | Volume 10 | Issue 4| Page 601-605