Abstract To reach the point I want to discuss, I must begin with a sketchy review of quantum mechanics. I apologise to those of you who know this material already, perhaps better than I do. But it will be an opinionated review: some of my opinions are eccentric. So there may be something in it even for those who are already expert. Quantum mechanics is, in a nutshell, the theory of suprpostons. To introduce this concept, I begin with the standard account of the benzene ring-an account so well entrenched in organic chemistry that it would probably survive even if its quantum-mechanical foundation crumbled away beneath it. The benzene ring is a hexagon of carbon atoms, each with a hydrogen atom attached. Replace two adjacent hydrogens with two different substituents, so that we can unambiguously number the sides of the hexagon. Two structures conform to the rules of valence: one with double bonds on the odd-numbered sides, another with double bonds on the even-numbered sides (see Figure 1).The molecule reacts sometimes as if it had one structure, sometimes as if it had the other. Yet we do not think that a population of molecules is a mixture of the two structures. Neither do we think that each molecule oscillates rapidly between one structure and the other. Neither do we think that the molecule has a betwixt-and-between structure- there is no such thing as a bond midway between double and single. Rather, we think that each molecule is in a superposition: a state objectively indeterminate between the two structures. Objective indeterminacy is multiplicity: a cloud of indeterminate extent, for instance, is really many clouds, almost but not quite identical to one another [Unger 1980; Lewis 1999b]. Likewise a molecule with an objectively indeterminate structure is really two coexisting molecules, one with one structure and one with the other. (Or at any rate, two things that are molecule-like except for from their coexistence with one another.)
Abstract To reach the point I want to discuss, I must begin with a sketchy review of quantum mechanics. I apologise to those of you who know this material already, perhaps better than I do. But it will be an opinionated review: some of my opinions are eccentric. So there may be something in it even for those who are already expert. Quantum mechanics is, in a nutshell, the theory of suprpostons. To introduce this concept, I begin with the standard account of the benzene ring-an account so well entrenched in organic chemistry that it would probably survive even if its quantum-mechanical foundation crumbled away beneath it. The benzene ring is a hexagon of carbon atoms, each with a hydrogen atom attached. Replace two adjacent hydrogens with two different substituents, so that we can unambiguously number the sides of the hexagon. Two structures conform to the rules of valence: one with double bonds on the odd-numbered sides, another with double bonds on the even-numbered sides (see Figure 1).The molecule reacts sometimes as if it had one structure, sometimes as if it had the other. Yet we do not think that a population of molecules is a mixture of the two structures. Neither do we think that each molecule oscillates rapidly between one structure and the other. Neither do we think that the molecule has a betwixt-and-between structure- there is no such thing as a bond midway between double and single. Rather, we think that each molecule is in a superposition: a state objectively indeterminate between the two structures. Objective indeterminacy is multiplicity: a cloud of indeterminate extent, for instance, is really many clouds, almost but not quite identical to one another [Unger 1980; Lewis 1999b]. Likewise a molecule with an objectively indeterminate structure is really two coexisting molecules, one with one structure and one with the other. (Or at any rate, two things that are molecule-like except for from their coexistence with one another.)
When the revolutionary conceptual structure for the description of the physical world which we know as quantum mechanics was first formulated nearly 90 years ago, and its predictions tested in the laboratory, most of the experiments in question were on systems which were both very well characterized and reasonably well isolated from their environments, such as single electrons and atoms, small molecules and near-perfect crystalline solids. While from the very start most physicists have taken it for granted that the formalism of quantum mechanics, when combined with appropriate system-specific information, can “in principle” account for all phenomena occurring in the physical world, including those usually regarded as the subject-matter of biology, until quite recently the overwhelmingly majority opinion has been that in a biological context the role of quantum theory is confined to elucidating the equilibrium structures of the relevant molecules and their reaction processes, and that subtle phenomena such as superposition and entanglement, of which we can now routinely exhibit spectacular effects at the level of a few well-isolated photons or atoms, play at most a very indirect role in any phenomena of biological interest. A major reason conventionally given for this view has been that biological systems, at least working ones, are by their very nature “warm and wet” – a phrase which in the physicist's lexicon translates to “prone to massive decoherence”; it looks as though any interesting superposition, say of different energy eigenstates of one's system, would be rapidly decohered by the ever-present, and usually microscopically very complex, environment.
Those defile the purity of mathematical and philosophical truthy who confound real quantities with their relations and sensible measures. —ISAAC NEWTON, Principia Before we say anything about quantum mechanics, let us take a quick look at the Newtonian (or ‘classical’) view of the physical universe. According to that view, nature consists of an enormous number of particles. When Newtonian physics is combined with the theory of the electromagnetic field, it becomes convenient to think of these particles as dimensionless (even if there is a kind of conceptual strain involved in trying to think of something as having a mass but not any size ), and as possessing electrical properties – negative charge, or positive charge, or neutrality. This leads to the well-known ‘solar system’ view of the atom – with the electrons whirling around the nucleons (neutrons and protons) just as the planets whirl around the sun. Out of atoms are built molecules; out of molecules, macroscopic objects, scaling from dust motes to whole planets and stars. These latter also fall into larger groupings – solar systems and galaxies – but these larger structures differ from the ones previously mentioned in being held together exclusively by gravitational forces. At every level, however, one has trajectories (ultimately that means the possibility of continuously tracing the movements of the elementary particles) and one has causality (ultimately that means the possibility of extrapolating from the history of the universe up to a given time to its whole sequence of future states).
Abstract In ‘How Many Lives Has Schro dinger’s Cat?’ David Lewis argues that the Everettian no-collapse interpretation of quantum mechanics is in a tangle when it comes to probabilities. This paper aims to show that the difficulties that Lewis raises are insubstantial. The Everettian metaphysics contains a coherent account of probability. Indeed it accounts for probability rather better than orthodox metaphysics does. On 27 June 2001, not four months before his untimely death, David Lewis delivered the third Jack Smart Lecture at the Australian National University. His title was ‘How Many Lives has Schro dinger’s Cat?’ > and he spoke on a topic which is absent from his published writings, the interpretation of quantum mechanics. More specifically, he discussed the ‘no-collapse’ interpretation of quantum mechanics pioneered by Hugh Everett III [1957]. Lewis allowed that this interpretation offers initial theoretical attractions, but also argued that it suffers from irremediable flaws. If you have heard of Everett because of his association with the ‘many-worlds’ interpretation of quantum mechanics popularised by Bryce Dewitt [1970; 1973], you might suppose that there is some affinity between the no-collapse interpretation and Lewis’s philosophical realism about possible worlds. But this would be a mistake. While Everett’s interpretation does add extra ‘branches’ to the reality recognized by common sense, these additions fall far short of Lewis’s multiplication of worlds. For a start, the extra ‘branches’ that Everett adds to reality all lie within the actual world that evolves from the actual initial conditions in line with the actual laws of physics-these branches by no means include all possibilities. Moreover, Everett’s branches are best conceived, not as sundering’s of the whole universe, but rather as entities that spread out causally at finite speeds, ‘like ripples on a pond’, as Lewis puts it. For example, in the Schro dinger’s Cat experiment, firstthe photon branches into a deflected and undeflected version when it passes through the half-silvered mirror; thenthe detector branches into a triggered and untriggered state when it interacts with the photon; thenthe poison bottle branches into a smashed bottle and an unsmashed bottle under the influence of the detector; and so on, culminating in the cat branching into a live and dead cat, and the human observer branching into a self who sees a live cat and a self who sees a dead cat. >
Philosophical introduction The following seemingly trivial story raises important questions which lead to the philosophical issues essential for our discussion. My cat is alive and well. I can describe her by size, color, behavior, etc. I can watch her, touch her, play with her, and feed her. I know this animal is really there. But my biologist friend came to visit and informed me that my cat is really nothing but a very complicated collection of different kinds of cells in mutual interaction, and he can prove it to me by having me look through his microscope, and, if I would only let him, by dissecting my cat. But the biochemist next door has a quite different opinion: he claims that my cat is really just a very complex assemblage of organic compounds, proteins, nucleic acids, etc., etc., all in mutual interaction. He, too, can prove his claim. Of course, physicists know better: a cat, like all matter living or dead, is in last analysis really nothing but atoms bonded together to form the complicated molecules my biochemist friend is talking about. And they can prove that too. But, finally, one cannot ignore the elementary particle people who tell us that atoms are just composed of quarks, gluons, and electrons, so that a cat is really, really just a very complicated assembly of those few types of elementary particles in mutual interaction.
02 June 1999, “Please Do” You know what I'm really trying to get at here: I want the structure of quantum mechanics to be extremal for some kind of more abstract (i.e., QM-independent) information-disturbance problem. But the first thing that needs to be done is to pin down what quantum mechanics itself has to say. Another thing that keeps coming to mind is that the assumptions behind Gleason's theorem might have something to do with the allegory I presented you with at Charlie and Theo's house. God said, “Ok I will make information gathering invasive, but not so invasive that you will be forever science-less.” The connection is this. I think one can split the assumption behind Gleason up into at least two parts: (1) The questions that can be asked of a quantum system only correspond to orthonormal bases over some vector space, with there being no good notion of measuring two distinct questions simultaneously (there being no good notion of an AND operation). And (2) It is the task of physical theory to give probabilities for the outcomes of those questions, but we can say at least this much about the probabilities. They are context-independent in the sense that, for a given outcome, it does not matter which physical question (which basis) we've associated it with. I.e., the probabilities can be assumed to be of the form of a frame function.