On Quantum Theories of the Mind *

Replies are given to arguments advanced in this journal that claim to show that it is to nonlinear classical mechanics rather than quantum mechanics that one must look for the physical underpinnings of consciousness. ∗This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098. In a paper with the same title as this one Alwyn Scott (1996) has given reasons for rejecting the idea that quantum theory will play an important role in understanding the connection between brains and consciousness. He suggests that it is to nonlinear classical mechanics, not quantum mechanics, that we should look for the physical underpinnings of consciousness. I shall examine here all of his arguments, and show why each one fails. Scott contrasts, first, the linearity of quantum theory with the nonlinearity of certain classical theories, and notes the complexities induced by the latter. Thus he asks: “Is not liquid water essentially different from gaseous hydrogen and oxygen?” Of course it is! And this difference is generated, according to quantum field theory, by certain nonlinearities in that theory, namely the nonlinearities in the coupled field equations. These field equations (or, more generally, Heisenberg equations) are the direct analogs of the coupled nonlinear equations of the corresponding classical theory, and they bring into quantum theory the analogs of the classical nonlinearities: these nonlinearities are in no way obstructed by the linearity of the wave equation. To understand this point it is helpful to think of the equation of motion for a classical statistical ensemble. It is linear: the sum of two classical statistical statistical ensembles evolves into the sum of the two evolved ensembles. This linearity property is a trivial consequence of the fact that the elements of the ensembles are imaginary copies of one single physical system, in different contemplated states, and hence they do not interact with one another. Thus in classical statistical mechanics we have both the (generally) nonlinear equations for coupled fields, and also the (always) linear equation for a certain statistical quantity. Similarly, in quantum field theory we have both the (generally) nonlinear field equations for the coupled fields, and also the (always) linear wave equation for a certain statistical quantity, the wave function. The fact that a group of several atoms can behave very differently from how they would behave if each one were alone is a consequence of the nonlinearity of the field equations: this nonlinearity is not blocked by the linearity of the wave equation. This blurring of the important distinction between the completely compatible linear and nonlinear aspects of quantum theory is carried over into Scott’s