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A Speculative Ontological Interpretation of Nonlocal Context-Dependency in Electron Spin

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A Speculative Ontological Interpretation of Nonlocal Context-Dependency in Electron Spin A SPECULATIVE ONTOLOGICAL INTERPRETATION OF NONLOCAL CONTEXT-DEPENDENCY IN ELECTRON SPIN Martin L. Shough1 1st October 2002 Contents Abstract ................................................................................................................... .2 1. Spin Correlations as a Restricted Symmetry Group ............................................... 5 2. Ontological Basis of a Generalised Superspin Symmetry .....................................17 3. Epistemology & Ontology of Spin Measurement ................................................. 24 4. The Superspin Network. Symmetry-breaking and the Emergence of Local String Modes .......................................................................................... 39 5. Superspin Interpretation of the Field ................................................................... 57 6. Reflections and connections ................................................................................ 65 7. Cosmological implications .................................................................................. 74 References ........................................................................................................... 89 1 [email protected] Abstract Intrinsic spin is understood phenomenologically, as a set of symmetry principles. Inter-rotations of fermion and boson spins are similarly described by supersymmetry principles. But in terms of the standard quantum phenomenology an intuitive (ontological) understanding of spin is not to be expected, even though (or rather, because) a spinor can be described as the most elementary mathematical object in quantum theory. This essay asks if it is possible, in principle, to have an intuitive model of intrinsic spin. The conclusion reached is that it is possible, given that an intuitive ontology is not necessarily a local/classical ontology. Some implications that might follow from requiring an ontological interpretation of intrinsic spin are explored. As an heuristic device, a toy conceptual model is developed in which paired spinors label states of a rotational symmetry internal to nonlocal elementary quantum objects. The basic condition for these objects is that position becomes a locally two-valued elementary parameter. Essentially this can be seen as invoking an additional basis state for many-particle systems which would allow electron 'intrinsic spin' to be treated uniformly as a broken phase of a nonlocal doublet symmetry. It is shown that this leads to a simple and elegant way of visualising Pauli exclusion and to a dynamical view of electron 'shell' structure. A hidden 'superspin' parameter, invoked to carry this (generally broken) nonlocal symmetry, would have implications for a general ontology of quantum measurement. Although the focus here is on electrodynamics, the idea can also be described as a generalisation of 'dynamical supersymmetry' from the interacting-boson model of nuclei, applied to electrons and photons. The new (broken) symmetry would be carried as a super-rotation of a photon, implying that supersymmetry is a latent property of the already-known particles of QED and that it should therefore be possible to associate its anticommuting algebras to differently symmetrised doublet properties of their interactions. But a generally nonlocal superspin symmetry of this type could not simply be attached as an add-on to a local metric manifold. It is suggested that the breaking of a dynamical supersymmetry in QED might be identified with the emergence of the Poincaré spacetime symmetry group. According to this idea a doublet superspin state becomes non- degenerate in a pair of position states, and this lifted degeneracy is ontologically prior to translations in flat SR spacetime. Moreover the resulting network of paired states can be characterised by saying that it puts particle quanta and space quanta into correspondence with one another through a general quantisation condition the essence of which is the discreteness not of scale or of volume but of direction2 Such a radical vectorial discreteness implies no homogeneous field of scalar point functions, which fights against GR but is consistent with the fact that the Dirac 2 This indicates an obvious affinity with the spin-network programme. Later it will be suggested that in its most general form the present rough proposal could be characterised as seeking a radically scale-free 'inflationary' phase of an exhaustively-connected nonlocal superspin-network. spinor is difficult to incorporate into Riemannian techniques. The essay argues that, in principle, a heuristic model could be developed along these lines with enough triviality to survive at least the constraints imposed by SR and standard QM. Some specific heuristic advantantages are also indicated in relation to a possible future theory of gravity and large scale cosmic structure. But it is also pointed out that it should be possible to falsify the class of such models easily by (among other things) the detection of a single gravitational wave event, a single sparticle, or a single Higgs boson. Part 1 reviews the broad historical context of spin correlation in theory and experiment, and summarises why an intuitive ontology of electron spin (in particular) is unavailable in standard quantum mechanics. The meaning of spin eigenstates is also discussed from the point of view of Bohmian nonlocality arguments for comparison. Bohmian electron spin has a well-defined ontology; but it is not intrinsic. However it is argued (qualitatively) that an intuitive understanding of intrinsic spin eigenstates is possible if it is accepted that EPR spin correlations are a special case of a generally nonlocal property of quantum systems which doesn't appear explicitly either in the standard phenomenology or in a Bohmian ontology. Several of the conclusions that support such a point of view can be argued from perfectly conventional grounds, and indeed have been. However it is proposed here to recover spin correlation from a broken generalised spin symmetry as a restricted case. In Parts 2 - 5 the breaking of this generalised 'superspin' symmetry is given a physical interpretation in terms of a conceptually radical ontology. This would allow spin to be 'understood' intuitively by relating polarisation direction to an underlying quantum-spacetime structure in a novel way. This structure is a network of linear 'objects', whose first simple condition is that each end of every 'object' is connected by one object to each end of all other objects. In short the connectivity of the network is (unlike the generality of space networks considered in quantum gravity theory) exhaustive and completely scale-free at all epochs. A second condition is that each object carries local quantum labels only on its ends; and it is shown that such objects need not then conflict with SR because when a 'string' of such objects self-interacts it obeys an automatic self-consistency condition. This heuristic device is tried out qualitatively on the phenomenology and epistemology of spin measurements. However the implications seem to be quite general. Very briefly (see especially Part 4), the unbroken or 'unfolded' superspin phase of this string is an inflationary mode. When folded on itself the scale-free repulsion gives rise to an 'attractive' short- range nonlinear inflaton self-coupling from the form of the folding which suggests (in a general way) that superspin could be seen as a restoring force dual with 'curvature' in an effective field theory of gravity. It is argued that once this network structure is 'understood' then the possibility of a novel quantum ontology can be said to have been (in principle) 'understood'. Part 5 discusses the status of the field in such a scale-free network ontology. In conclusion, Parts 6 and 7 then draw out some interconnections with transactional QM, absorber theory, spin networks and loop gravity, but I try to show where the quantum ontology suggested here would have distinct implications. Of particular interest is a model of Newtonian gravity proposed by Consoli and Siringo [1] based on a phase transition in a Bose-Einstein phion condensate, whose phonon excitations would be equivalent to Higgs particles in a spontaneous-symmetry-breaking vacuum model. It is claimed that the present discussion represents a sketch of a non-perturbative non-field approach which may be dual with the underlying nonlocal field theory in their model. Some rather general predictions of the present theory are indicated, mostly negative and qualitative. 1. Spin Correlations as a Restricted Symmetry Group i.) There are several avenues of proof that nonlocal correlations exist in quantum mechanical system and they have been studied extensively in systems of small quantum number. It can be shown that nonlocal connections are generally the dominant type of connectivity in quantum systems. To say that the meaning of this fact is unclear in terms of any presently debated ontology would be an understatement. Nevertheless certain nonlocal correlations involving particle spin are well defined and well understood phenomenologically. The logical rationale for exploiting spin measurements as a test of nonlocal correlations was set out by Einstein, Podolsky and Rosen [2] in 1935 and developed by Bell [3,4], leading to the experiments of Freedman and Clauser [5] and then of Aspect et al. [6] demonstrating EPR-type correlation of photon polarisations outside the light cone. A general proof by Mermin [7], which does not rely on subtle
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