Notes
Chris Clarke, "Construction and reality: reflections on philosophy and spiritual/psychotic experience" in Psychosis and Spirituality: exploring the New Frontier ed Isabel Clarke, pub Whurr, 2000 Maurice Merleau-Ponty, Phenomenology of perception, trans Colin Smith, London: Routledge, 1962, p. 2123 John Heron and Peter Reason "A participatory inquiry paradigm", Qualitative inquiry, 3, 1997, pp 274-294
For the reader who has not encountered this: Schrödinger imagined a hypothetical closed box containing a radioactive atom, whose decay triggered a lethal device that killed a cat also in the box. According to quantum mechanics, the entire combined system should involve into a state which involved the absurd superposition of a live cat and a dead cat. Does the observer collapse the sate into one or the other when she opens the box and sees only one of these possibilities? Why doesn't the cat collapse the state in the same way? (There is a need for a more humane version of this paradox.) For a discussion of quantum logic see Enrico G Beltrametti & Gianni Cassinelli The Logic of Quantum Mechanics, Addison Wesley, Reading, Mass., 1981; their formalism coincides with mine, though their use of the word "logic" is slightly different. John von Neumann Mathematical Foundations of Quantum Mechanics, Addison Wesley Quoted in: Michael Lockwood, "Many-minds interpretation of quantum mechanics" Brit. J. Phil. Sci. 47, 159-88, 1996 G C Ghirardi, A Rimini and T Weber, "Unified dynamics for microscopic and macroscopic systems" Phys. Rev. D34, 470, 1986 Roger Penrose, Shadows of the Mind, Oxford UP, 1994 It should be noted, however, that this division is not without question since Kent (Adrian Kent, "Quantum Histories", Physica Scripta 76 (1998): 78-84) has argued that Ghirardi's interpretation, here classed as type 1, could be reinterpreted as a version of a histories formalism, which I am here regarding as type 2. Fay Dowker and Andrew Kent, "On the consistent histories approach to quantum mechanics" J. Stat. Phys. 82 1575, 1996; Roland Omnès, Understanding Quantum Mechanics Princeton University Press, Princeton NJ 1999. Christopher J Isham, "Quantum logic and the histories approach to quantum theory" J. Math. Phys 35 2157-85, 1994; Christopher J Isham, N Linden, K Savvida and S Schreckenberg, "Continuous time and consistent histories", J.M.P. 39, 1818-34, 1999Matthew J Donald "A mathematical characterisation of the physical structure of observers, Foundations of Physics, 25, 529-571, 1995 Quantum mechanically, this probability is given in the Heisenberg picture by
P
(ρ, H) = Tr( Pn , Pn-1 , ... , P1 ρ P1 , ... , Pn-1 , Pn ) , where P1 , P 2 , ... are the quantum projection operators corresponding to the history H = ( P1 , P2 , ... , Pn ) D Albert and B Loewer "Interpreting the Many-Worlds Interpretation", Synthese 77, 195-213, 1988 Michael Lockwood "Many-minds interpretation of quantum mechanics" Brit. J. Phil. Sci. 47, 159-88, 1996 Angelo Bassi and GianCarlo Ghirardi, , "Decoherent histories and realism", to appear in Statistical Physics, The reader is reminded that, in the quantum area, the logic becomes slightly generalised (technically, it is no longer distributive). This demands caution in handling conditions such as this: for instance, classically, A and B are exclusive is there is no third proposition which implies both A and B; but this is not true in the quantum case. The condition explicitly is that (in the notation of note )Tr(
Pn(in) , ... , P1(i1) ρ P1(j1) , ... , Pn(jn) ) = δi1j1 ... δinjn P(ρ, ( P1 , P2 , ... , Pn )) See the Chapter by George Ellis in this volume, and Nancy Murphy, "Supervenience" in Evolutionary and Molecular Biology (Ed Robert J Russell et al), 466, Vatican Observatory, 1998 Note also that we cannot test for the fact of there being a superposition: the sentence "the state is a superposition of some live and dead states" does not convert into a valid quantum proposition. Note that the combination of a past history with an initial state is equivalent to giving the present state, so that we have essentially a state-dependent interpretative principle. Chris J S Clarke, "The histories interpretation: stability instead of consistency?", Found. Phys. Lett. 14 (2001): 179-186 Some may object to this view, which I have held in some form for many years. See Chris J S Clarke "Reply to Stanley Kerr". Philosophy of Science, 43, 583-4, 1976, and references therein. Omnès, it should be noted, regards logic in a fundamental sense as a basic principle of the world, and not as a contingent matter: we are dealing here with two senses of the word. See Roland Omnès, Quantum Philosophy, Princeton U P, 1999 Mae-Wan Ho, The Rainbow and the Worm (2nd Edition) London: World Scientific, 1998 Fritz A Popp, and K H Li, "Hyperbolic relaxation as a sufficient condition of a fully coherent ergodic field" Int. J. Theoret. Phys. 32 1573-1583, 1993 Rodney Loudon, The quantum theory of light (2nd Edition) Oxford: Oxford University Press, 1983 Chris J S Clarke, "Distributed pumped dipole systems do not admit true Bose condensations", J Phys A, 27 5495--5500, 1994 This refers to the behaviour of a system as the number of degrees of freedom tends to infinity. A Bose condensation occurs if, in this limit, a finite proportion of the energy remains in the ground state. A pseudo-condensation resembles this for practical purposes, but while, in the limit, the relative energy per mode tends to infinity as the ground-state is approached, the proportion of energy in the ground state tends to zero in the limit Mark Tegmark, "The importance of quantum decoherence in brain processes", Phys. Rev. 61, 4194, 2000 S Hagen, Stuart Hameroff and J A Tuszynski (2002) “Quantum computation in brain microtubules: decoherence and biological feasibility” Physical Review E65, 061901-1 – 061901-11. Emmanuel Levinas, Totality and Infinity, Pittsburgh: Duquesne University Press, 1969. See also the discussion of Levinas' work in Arthur Still, "Immanence and Transcendence in Psychotherapy" Changes, 18 (3) 215-225, 2000 Chris J S Clarke Is Psychology Possible, http://www.scispirit.com/Psych-laws.htm I am here using a chronology relation ® between sets defined byA ® B iff (" x Î A, y Î B )( x Î I -(y) )
The second-person perspective, Buber's "I-thou", is even more important, and relates to the discussions by Ho of the extent to which coherence can extend between organisms, thus enlarging the boundaries of the self. This would, however, take us beyond the scope of this paper. See also the next footnote. Thus I am not inductively imputing autonomous being to other organisms, but following Heidegger's definition of the phenomenological approach as that which "let[s] that which shows itself be seen from itself in the very way in which it shows itself from itself."(Martin Heidegger, Sein und Zeit, English Translation Being and Time by John Macquarrie and Edward Robinson, Oxford: Blackwell, 1962. See note and the discussion in section 1 for the phenomenological background here Storrs McCall, A model of the universe Clarendon Press, Oxford, 1994 Julian Jaynes, The origin of consciousness in the breakdown of the bicameral mind, Penguin, 1993 Max Velmans, Understanding Consciousness, Routledge, 2000; pp 211-213 B Libet "Are the metal experiences of will and self-control significant for the performance of a voluntary act?" Behavioural and brain sciences, 10, 783-786, 1987 It is of course true that a subconscious decision is still "my" decision, in the sense that it is arrived at within the total organism that I refer to as "me". But the issue here is whether or not it belongs to that particular subsystem endowed with the interesting property of subjectivity. Farhad Delal, Taking the Group Seriously: Towards a Post-Foulkesian Group Analytic Theory. :London: Jessica Kingsley, 1998 Chris J S Clarke, "Consciousness and non-hierarchical physics," to appear in The physical nature of consciousness, Ed Philip van Looke, pub. Jon Benjamins Publishing, 2000 (http://www.scispirit.com/consc2.htm) The ability to choose which set of projections is to be measured, and to do it repeatedly, can be used actually to alter a state. Suppose, for example, that we have an particle with spin initially in an eigenstate of the z-angular momentum component, and that we then measure its spin n times in directions in the (z, x) plane making angles of p /n, 2p /n, ... with the z-axis. Then for n>2, at the end the particle is more likely to have its spin reversed, and this probability tends to 1 as n increases. Thus the ability to choose projections implies that ability to modify quantum states at will. Donald M Mackay, Science Chance and Providence Oxford U P, 1978 Donald M Mackay, Information, mechanism and meaning MIT Press, 1969 I am assuming in this, despite the fact that "a thousand ages in Thy sight are like an evening gone", that the characteristic timescale relevant to the action of god in the universe is short enough to allow this possibility within the stability condition. Ayam atman Brahamasti. See Bede Griffiths, "The vision of non-duality in world religions" in The Spirit of Science: from Experiment to Experience Edinburgh: Floris Books, 1998