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 statistical arguments to demonstrate violation of the Bell inequalities, extends Bell's theorem to systems of three spatially separated particles by showing that the eigenvalues of the individual spin operators are not independent of one another, in a way that is not consistent with the assumption of local hidden variables.
ii.) The ontological interpretation of quantum mechanics proposed by Bohm & Hiley [8] offers a useful summary of the theoretical status of spin for our purposes. Their discussion of the above issues leads them to conclude that the wave functions of systems of particles must in general be considered to be strongly, i.e. nonlocally, context-dependent. They draw attention to the fact that the antisymmetric wavefunction for a pair of fermions subject to the Pauli exclusion principle is a special case of an EPR-type wave function, and argue that even in the simplest cases spin cannot be regarded as an intrinsic particle property but emerges in an essentially participatory 'measurement' process. This conclusion is consistent with experimental evidence that if an electron were a spinning particle it would have to have a radius of <10-16 cm, which would imply superluminal peripheral velocity to obtain angular momentum h/4p. With regard to larger systems Bohm & Hiley further point out that the number of independent spin parameters of the wavefunction for n particles increases as 2(n+1) whereas individual particle properties can only increase as n. In many-particle systems, therefore, spin determinations depend on a huge number of terms which have nowhere to live if they are regarded as having physical correlates attached to particles. 'There is no way,' they conclude, 'to give a physical meaning to all the parameters . . . . One might consider properties belonging to sets of 2, 3 or 4 particles etc., but it is difficult to see what this could mean physically. Such properties would be nonlocal and might be significant even when the particles are far apart. In any case the simple model of a set of spinning particles would no longer apply.' [9]
iii.) Since their ontology requires a discrete particle with a deterministic (if unobservable) trajectory Bohm & Hiley are driven to conclude that an electron is a point particle whose only intrinsic property is its position, deriving spin angular momentum from an additional circulatory component of orbital motion. This interpretation requires the concept of 'active information' to supply the guidance condition for a neo-classical mass point according to the form (but not the amplitude) of a new quantum potential related to the de Broglie 'pilot wave'. [10] In the form developed by Bohm this new quantum field has vanishing energy and cannot do work; hence the source of the acceleration of the particle mass is sought separately in the vacuum energy, which can be surmised to have structure hidden in the seventeen orders of magnitude between the Planck scale and the finest present measurements.
iv.) These conditions might be thought a large cost for an intuitive picture of intrinsic (or in fact, in this case, extrinsic) spin, unless there is a strong attachment to the concept of an electron as a point particle; and even then the notion of position as an 'intrinsic property' of a point remains difficult, given that position must be the canonical context-dependent parameter. Alternatively one might attempt to address the paradox that electron 'intrinsic spin' is not an intrinsic property of a particle by supposing that 'an electron' is not a particle at all - i.e., neither a classical extended particle nor an infinitesimal point. Traditionally attempts to avoid the infinities of the latter have run into the locality problems of the former; but there is a sense in which these are technical issues beside the fact that an overall lack of intelligibility accompanies any kind of elementary 'object' in a probabilistic quantum theory. A great deal of theoretical and experimental development lies behind the QM phenomenological view that, for all practical purposes, a quantum particle is a group of observables whose only commonality is an association with a narrow peak in some root mean square distribution of probabilities, and although string theories negotiate the locality and infinity difficulties of points and blobs, they nevertheless work inside standard QM and succeed in mimicking the traditional conception and function of a QM particle so well that the ontological intelligibility of a probabilistic superstring is essentially the same as that of a traditional probabilistic particle. So the 'measurement problem' is addressed in Bohmian theory by a new nonlocal quantum field but measurements are still made on unintelligible point particles; whilst string theory has intelligible particles but remains at the mercy of the measurement problem. But what about a model which is less successful than either superstring theory or Bohmian theory at preserving free particles and quantum fields? Might a radically different kind of extended elementary object more successfully interpret nonlocal spin entanglement and the meaning of QM measurement along with it?
v.) Continuing optimistically and in a heuristic spirit one can ask the question: 'Can intrinsic spin be preserved as an intuitive property by associating it to an ontological element that is not particle-like?' The answer offered here is that it can, provided that 'an electron' is incompletely defined by just one position variable, and completely defined (as regards extension) by two, and that this binary position state is generally, but covertly, shared between pairs of electrons, irrespective of scale, in the exact sense of a wave function which is symmetrical in the two coordinates. In this way it becomes possible to resolve the paradox of an 'intrinsic position' which is inherently relational. In outline, the hypothesis will be that the nonlocal symmetry describing this binary state is a universal EPR-type spin correlation which is in general broken in the emergence of Lorentz invariance, but in such a way that the hidden 'superspin' operates as a hidden variable 'internal' to the quantum electrodynamical interactions of what QM characterises as pairs of electrons, spin therefore being intimately related to a primitive conception of 'distance' underlying that of metrical space. Of course, if a Bohmian theory seems a large cost, then this approach probably threatens an even larger cost and may not in the end lead to models that prove well-defined. On the other hand QM itself is presently not well-defined and in fundamental respects - i.e., nonlocality and relativistic causality, gravity, measurement etc. - is neither lucid nor integrated. It may be that a radical shift of principle is necessary for it to become well-defined. Deotto and Ghirardhi [11] have shown that an equivalence class of Bohmian deterministic particle theories in fact contains an infinite number of empirically equivalent such theories. Whilst this complicates one's attitude to the uniqueness of Bohm's model and the falsifiability of nonlocal field theories in general, it may also prompt reflections on the true uniqueness of standard QM. Indeed Rohrlich and Popescu [12] have shown from general principles that QM is only one of the class of possible theories that combine nonlocality and relativistic causality in consistent ways and they therefore follow Shimony [13] in asking: what is the additional 'simple and fundamental principle' missing from QM which selects it from the class of such theories as the unique theory? One 'fundamental' and 'missing' principle which immediately springs to mind is the quantum gravity principle. Taking one's lead from Ghirardi, Grassi and Rimini [14], Penrose [15,16] and others who argue that gravity is needed to understand the reduction of the QM state vector, one might speculate that these were questions in search of the same answer. Then, one possible answer might be the principle that elementary 'position' is not a single-valued quantity on a metric manifold but is a two-valued quantity on a network. This can be expressed in the idea that the quantisation condition of spacetime is not one of position but of direction. Clearly there are several large claims here which need to be justified, at least in principle, before any detail need be considered.
vi.) As a probabilistic variable conjugate with momentum, position nevertheless has a precise meaning in standard QM. A narrow enough peak in the distribution of probable positions maps a point-electron's position to arbitrary accuracy in the limit of infinitely uncertain momentum. According to QM all that can be known about an electron's position is contained in the wave function. Classical assumptions about the particulate nature of elementary objects are imported, however, in that locality arguments are applied to classical blobs, reducing them to dimensionless points with the result that 'position' is held to be single-valued quantity. This assumption can be said to be justified by its success over a huge range of theoretical and experimental experience. Indeed, how can an elementary position function not be single-valued? Even string theories approximate single-valuedness of position to a high degree of accuracy on atomic length scales. (Uncertainty then introduces fuzziness, but this is not what we might mean by a radical many-valuedness of position.) Many-valuedness of position is possible, however, consistently with the locality conditions of measurements made at 'points'. For example, string theories preserve classical locality constraints without making the ultimate reduction to point-particles for reasons that in principle can be (but aren't) applied free of scale (i.e. prior to a 'background' manifold), and it is possible to imagine, in place of swarms of pseudo-particulate string loops, structures of nonlocal objects which each have more than one local position value, and which are topologically elementary, and which yet exist on arbitrarily large scales. Conditionally, this need not conflict with SR. (See 2.v.- ix. below) Then if, for example, elementary local position turned out to be double-valued it would be the case that what the wave function maps as one peak in the distribution of probable position is an abstraction, and the group of observables associated to this peak should actually always be associated to a pair of such peaks along with another group of observables. One would then say that the half-unit of quantum spin attached at one electron position is always to be complemented, via some broken general symmetry, by a half-unit attached at another - as it is sometimes found to be via a residual restricted symmetry. In this way what QED would call a two-electron wave function becomes a special case of the fundamental entity, because a particle is in general only one end of a nonlocal elementary 'string'. (Note that a more detailed justification for the idea introduced here is given beginning in Part 2.)
vii.) The connection to standard QM here is easy to make. Linden and Popescu [17], Popescu and Rohrlich [18] and others have shown that the quantum state of any typical ensemble of large n is overwhelmingly characterised by the entangled relationships. QM requires that any many-particle system be represented by a single wave function which contains all the possible position states interdependently - to the degree that a 'many-particle' system becomes a self-contradiction - and the primitive connectivity of any system of particles naturally resolves into some number of pairs of states. It is also a commonplace that a quantum particle may be in a linear superposition of different position states and so may be 'in two places at once' when solutions of such functions are projected onto a Lorentzian manifold, with 'measurement' then reducing the state vector so that one alternative state vanishes to yield a unique position. It can be the case that the alternative was one of an infinite number of unoccupied position states in classical Cartesian coordinates and its vanishing, an infinite distance away, leaves that position state empty of any observable, with no trace of mass, charge or spin. But the distinction from standard QM introduced here is the proposal that such binary states are at the deepest level robust and that they live on nonlocal objects which, networked, would replace the classical manifold. In this case an alternative position state does not vanish, because a position which is not located at a vertex of the network has no meaning and all vertices are by definition paired. There is no notion of position which does not correspond to some implicit state of the network, meaning that a boundary condition analogous to that of a central field at infinity need not occur. Then, all quantum labels must be attached at vertices and the same conservative principle applies. Indeed, the general question of the origin of conservative forces and the peculiar aptness of Hamiltonian/Lagrangian functions in such a wide range of areas is arguably addressed more naturally in such a context than by assuming that an homogeneous central space-field approximation is valid everywhere.
viii.) This last issue, of the weight that nature seems to attach to such functions (most generally, the action function analogous to the classical Lagrangian), is of acknowledged fundamental interest but remains not wholly understood [19]. A connection between quantum mechanics and spacetime, via the relativistic invariance of the action functional as embodied in Noether's theorem [20], was achieved in Feynman's spacetime representation [21], but the deeper extension to quantum gravity has not been made. And one sees that this relates to the fact that the origin of the Planck constant itself is not really understood in present theory and remains a mysterious expedient with no underlying physicality. The ontology outlined here does address this issue directly (see 4.iii below). Briefly, the locality condition of our construction (see 2.vii. below) is embodied in the network rule that each end, exclusively, of every 'object' is connected by one object to each end of all other objects, so that the network only self-interacts via these fermionic ends of its object-elements. This means that the self-interaction associated with a conserved fermion number remains linear, or alternatively that the fermion number may be considered to change, but only subject to self-consistency requirements of a conserved total energy, in which case the self-interaction rate also remains linear. This linearity can therefore be said to underlie not only the linear non-interactivity of Bose-Einstein photon statistics but also the fundamental quantum condition itself, which becomes that of a network of scale-free Planck oscillators. This will be easiest to exhibit by showing how it fits with the canonical early history of quantum theory.
ix.) As is well known Planck applied his own quantised radiation law [22] to an internal atomic oscillator, preserving a radiation field with continuous energy density variations through an arbitrary volume. Einstein [23] applied the same law directly to the radiation field, again in an arbitrary volume. The classical Lorentz law for the incoherent statistical mixture of harmonic waves in some volume gave the mean square fluctuation of energy per wavelength as equal to the Rayleigh-Jeans case, but the empirical black-body curve required the Wien distribution for short wavelengths. So Einstein rewrote the Lorentz law as a relation of a mean square fluctuation of a number of photons to the mean number of photons in some volume to account for the Wien part of the statistics, which leads to the Bose-Einstein distribution for an ideal quantum gas. But all these treatments assume a classical volume containing an infinite number of possible position states, either filled with waves or peppered with quanta. If the only actual approach to such a smooth volume is the linear network connecting some set of pairs of position states on its surface then the interior of the volume does not contain a continuous infinity of degrees of freedom. Thus a continuous wave theory will fail for the thermodynamic behaviour of enclosed monochromatic radiation of low energy density, whilst a particle (fermion gas) theory will fail as radiation density increases, because the interaction rate remains linear as the number of independent quanta passing through some region of the volume rises without limit. The entropy of this situation will evidently be the same as for non-interacting 'particles' reflected back and forth in the cavity, but the mean square fluctuation law given by Einstein as a statistic for an ideal photon gas can then be taken right back to the empirical black-body radiation law from which the Planck constant arose - i.e., it is a statistical law for radiation that is always in equilibrium in the sense that it is always 'enclosed' between pairs of fermionic observables (of which the radiation cavity is just a schematised case for large n), and each part of the total energy 'emitted and absorbed' satisfies the statistical independence of the elements of the Einstein fluctuation formula because of a linear self-interaction condition of the network. The photons 'in the cavity' are independent of one another because of a condition demanded for the locality of the network, which (we will argue) contains the Pauli exclusion principle as a special case and so demonstrates supersymmetry in the radiation cavity (see 2.v. et seq.). This linear containment supplies the Einstein photon condition as a case of the Planck quantum condition by replacing both the continuous radiation field and its continuous space volume with a network of complex oscillators. The atomic Planck oscillator therefore does remain as a scale-specific case of this scale-free network, inasmuch as long-scale electromagnetic transitions between pairs of fermionic states of the network, mediated by its photon modes, are always associated with equivalent short-scale electric dipole transitions between pairs of electron orbitals. In all cases the notion of measurable position always coincides with a self-interaction involving a self-consistent state of the entire network manifest as some relative displacement or excitation of one of a pair of fermions. (See section 7.xx. et seq. for a development of this argument. There it is shown that there should be observable cosmological consequences of this model of black body equilibrium.)
x.) Evidently, saying that there is no notion of position which does not correspond to some implicit state of the network is equivalent to saying that a 'measurement' is just a particular case of the general quantum transition process, as for example in a Bohmian ontology. But in the latter the Schrödinger wave function represents a continuously varying field acting on point-particles, where empty wave packets corresponding to alternative states that are unrealised in a particular measurement carry parts of the wave function away (as it were) until the 'inactive information' they contain is entirely degraded in the generality of other 'measurement' transitions [24]. The situation described in vi. - viii. above is constructively the same in the sense of its implication for the 'null measurement' paradox and the cat problem etc., but the wave function would not describe a nonlocally-varying potential of a continuous field in which (say) a photon wave packet might in principle spread to infinity without ever encountering an atom in a suitable condition to absorb it. The perennial problem with having concentric disturbances that spread though this stack of quantum fields pegged out over a metric manifold is: If the packet should eventually encounter such an atom, how does the indefinitely spread-out wave then get absorbed as a single quantum? (Note that this is every bit as problematic for gravitational radiation on the metric manifold as for light on the em field, so the stack isn't even soundly underpinned.) Standard QM has itself struggled with ontological implications of Eddington's [25] 'ray of luck' conundrum for decades, of course, and has conceded failure, by and large retreating to the default 'Copenhagen' epistemology of Bohr, Heisenberg et al rationalised by the probability-amplitude formalism introduced by Born [26]. But a Bohmian ontology brings this problem back into focus. The Bohmian answer to the criticism of Renninger [27] in relation to this point is to allow the atom to 'sweep in' the energy of the entire wave packet thanks to a nonlinear and nonlocal 'super-quantum potential'. Bohm's nonlocal quantum field thus immitates the existence of discrete bosonic quanta of a local field and effectively reifies the standard phenomenology. But in either model it remains the case that 'inactive' information states or uncollapsed quantum amplitudes can be imagined to disperse asymptotically at infinity. On the other hand, if all quantum labels must be attached to paired vertices in a network of nonlocal objects then there is a simple scale-free boundary condition: The only valid solutions of the wave function would live on this network of objects (of which there may be an indefinite number). It then makes no sense to think of a photon going nowhere, since a photon is constrained always to be a relation between two vertices. This principle of course contains the quantum condition of electromagnetic radiation deduced by Einstein [28], according to which the energy of one quantum of light goes directly to one electron so as to explain the photoelectric effect observed by Lenard [29], and it provides an ontological basis which imposes the Wheeler-Feynman [30] 'absorber theory' boundary condition (otherwise asserted by an extraneous prescription) and thereby illuminates the Cramer [31] transactional QM interpretation (see Part 6). In standard QM, and I believe in Cramer's transactional theory, it remains true despite field quantisation that radiation can be described as concentric spherical waves some of whose energy can remain unintercepted at infinity; but in our new ontology the correct (local) generalisation of the Einstein condition would be that the energies of all bosonic quanta go directly from one fermionic vertex to another. Two-valuedness of elementary local position means not merely that a fermion or a boson can be in two places once; it evidently carries the much stronger and more pregnant stipulation that no supersymmetric combination of boson and fermion can ever be in less than two (vertical) 'places' at once.
xi.) If this sounds strange, consider that a single-valuedness of the variable 'position' is demanded by a classical local vector field or manifold with a continuous infinity of degrees of freedom attached to a continuous infinity of coordinates in space. Such position states on a classical manifold have proved problematic for a traditional perturbative quantisation of gravity (neither standard QM nor any of the interpretations mentioned include gravity at all). Traditionally, attempts to quantise this manifold assume a discrete structure near the Planck scale and hope to recover GR as an approximation valid in a large scale classical limit so that an effective single-valuedness of spatial 'position' becomes available (even if not occupied with certainty) on length scales comparable to those of measurements in QED. Given this programme one can defend the received wisdom mentioned in 1.vi. above - that the wave function tells us all that can be known about the system - from the objection that it doesn't include 'gravity', by saying that gravitational effects are either confined to fluctuations at the Planck scale or are small GR curvatures on very large scales - either way, a vanishingly small correction for all practical purposes. But this is circular: It is vanishing only in terms of a quantum field theory of gravitation where position becomes single-valued on a manifold with an effective continuous infinity of degrees of freedom, because then the force constant reflects a ratio of coupling strengths of fields which can be mapped onto one another with a point-to-point equivalence. The 'vanishing correction' argument assumes that departures from positional single-valuedness (i.e., as some radically altered topology) can only occur on length scales so small that they are smoothed away for any possible measurement. If this is fundamentally wrong because position is generically not single-valued (i.e. if the boundaries of scalar volume elements of quantised spacetime are not inevitably some approximation to single-valued point positions) then what is left out of account in the quantisation procedure might be a 'correction' so radical as to transform the procedure. Then one might conclude that the wave function gives an extremely accurate half-answer to a half-question, whereas the 'missing' context would transform the answer by addressing the whole question. If local position were only ever half of the total position specification of an elementary object, then it would never be possible for the wave function to give a complete prescription of any ensemble of point-electrons without also including all other possible point-electrons with which those in the ensemble might form nonlocal doublets. This is of course held to be true in a general way in standard QM, where a many-particle wave function involves the many position observables jointly, but the assumption there is that a function with the identical number of eigenstates can be extended to the set of all such systems (quantum cosmology) in a highly conservative linear extrapolation based on the hope that a quantised geometrical theory of gravity at large scales can remain a 'vanishing correction' somewhat aloof from a quantised theory of states at particle scales. On the other hand, the principle of two-valuedness of elementary position is a priori a scale-free principle, and leads to the idea that 'intrinsic spin' devolves from a generalised nonlocal spin symmetry which (this paper will argue) gets locally broken and for which the wave function requires an additional hidden momentum eigenstate. Therefore this very speculative possibility cannot be ruled out: That the breaking of a generalised nonlocal 'intrinsic spin' symmetry, or superspin, which respects a fundamental two-valuedness of 'particle' position, is equivalent to the introduction of a gravitational symmetry, so that a spectrum of (imaginary) angular momentum eigenvalues is hidden, in a manner without regard to scale, in the relativistic symmetries of spacetime.
xii.) The idea that a spin symmetry might be ontologically prior to the continuous coordinates of the metric manifold is not new, of course, and the view that the manifold in some sense 'hides' a superspin symmetry is perfectly conventional in the sense that the space of quantum spin supersymmetry is already taken as a superadded coordinate space attached to a point particle in 4-space. Physics has become at ease with augmented Cartesian coordinates. But the implication of recovering an intuitive ontology for intrinsic superspin might be more radical, as indicated above. As suggested, instead of augmenting the spacetime metric we might wish to allow the constraints of superspin symmetry to alter the radical function of 'a particle in 4-space', which would be equivalent to putting all possible spacetime position measurements into correspondence with elements of the quantum spinor field by identifying 'an electron' as a super-spacetime element defined by a pair of spinors. This would be moving so far from the notion of a quantum field theory formulated over a classical metric manifold that a system of electrons would start to look like an analogue of a loop quantum gravity weave [32] stretched to macro scales, with echoes of the Penrose spin-network programme [33] in which loop quantum gravity has its origins. But these likenesses are merely suggestive. It is at this stage entirely unclear how a field description of localisable, unitary 'elementary objects' passes in some appropriate limit to a combinatorial description in terms of nonlocal, binary 'elementary objects' whilst preserving most (but hopefully not all: vide the unrenormalised electron self-energy) of the results of integrating over a continuous manifold. Nevertheless it can be argued that the evidence for long-range nonlocal correlations in fermion and boson spin suggests some rapprochement along these lines in at least a restricted class of cases, and a little conjecture about the possibility of generalising from these correlations to other cases may at least do no harm. (Let me acknowledge again here that I am fully aware of how very speculative these suggestions are, but since speculation is the point of this essay I stop short of apology!)
xiii.) In broad principle this is a much more conservative position than might at first appear. The Copenhagen epistemology [34] declares the relation between observables to be unanalysable, a position which has sometimes been construed as positivistic, sometimes as epistemological. The correlated spin operators of a long-distance pair of EPR measurements, or an atomic wave function which is symmetrical in the two position coordinates of a spin-balanced pair of electron states, can be described as examples of scale-free elementary quantum systems 'without parts'. Once it is pointed out that the limit of the unanalysability in these cases occurs as two complementary or reciprocal states whose essence is a space- or time-like separation of two measurements, and when it is realised that the extreme case of a symmetrical two-electron wave function at the lower limit of scale finds epistemological equivalence going over into ontological identity (Leibnitzian indiscernibility), then a deep connection can be discerned between spin and displacement. It is then not such a difficult leap to derive this unanalysability of a pair of spinors from that of an underlying, non-local, object-like substrate rather than from the superposition of a quantum spinor field and a metrical field (classical or quantised). There is indeed a certain economy in this point of view. And if the Copenhagen interpretation of QM can be described as a scale-free epistemological relation of observables which does not include gravity, we could describe a successful formulation of the present point of view - should one ever emerge - as cousin to a Copenhagen interpretation which (implicitly) 'includes gravity'.
xiv.) The suggestion is that the partless element discovered in these correlations is an element not just of a restricted class of wavefunctions but can be generalised to a binary element of all pairs of electron states, of which certain classes are selected out by the spin correlations we have discussed as belonging to a restricted symmetry group. Now in the ordinary way a very limited loss of unanalysability due to parsing the general set of all spin-pairs into two classes (the correlated and the not) may not be thought too onerous - as long as the correlation can be treated as a rare and generally unnatural deviation from the randomised norm, to be dealt with separately. This assumes that the 'randomised norm' is effectively a flat background to the special cases of interest. But if each non-correlated pair breaks a general symmetry in a different way then this assumption fails and it is the background which contains a great deal of information, notwithstanding that the few rare 'deviations' in which that symmetry remains preserved exemplify unanalysability. This 'figure/ground reversal' illuminates the fact that the unanalysability criterion of the Bohr system is a defining criterion of a non-relativistic model which doesn't give an account of intrinsic spin. It is as a result of 'simply' seeking to linearize [Note 1] the relativistic relation Spr2 + m20 c2 = E2, that Dirac [35] introduces new momentum components and four new 4-by-4 matrix operators in place of the 2-by-2 Pauli matrix for the fermion wave equation, giving rise to spin angular momentum and magnetic moment variables in the context of a properly Lorentz- invariant wave equation. Why does this procedure generate spin states 'like a rabbit out of a hat', as it has been described? We can express what happens by saying that imposing a local spacetime symmetry lifts a degeneracy in a basis state which takes on eigenvalues characterised as 'intrinsic spin'. In one sense this is 'obvious'. Spin angular momentum cannot have meaning in the absence of mass and space relations, and a magnetic moment has no meaning in the absence of magnetic field; spin is therefore co-emergent with the magnetic field relations which are space according to SR, and with the mass relations which generalise that space according to GR. Classically, therefore, one could ignore the idea of a degenerate spin eigenstate as simply unphysical. But this is not strictly permissible in QM. Although electron spin is never seen except as a positive non-zero eigenvalue, the formalism accords to it a zero value at which the eigenfunction does not vanish. (See 3.v. et seq.) The issue of this paper then focuses down to the question: 'What is this quantum basis state that is prior to spacetime rotational symmetry but only expresses non-degenerately in terms of it?' And the interpretation suggested is that each electron spin as measured arbitrarily in relation to any given other electron spin is a non-degenerate state of an eigenfunction properly intrinsic to doublets. A degenerate 'superspin' eigenfunction would identify an EPR-correlated spin-singlet. The degeneracy is lifted generally in the spontaneous symmetry-breaking that gives rise to the Lorentzian spacetime relations embodied in the 'field' of electrodynamics, and so it is the absence of spin-degeneracy in the randomised background which hides what can thought of as a torque or restoring potential in the spacetime relations of electron pairs.
Note 1. The Klein-Gordon equation being second order in t led to negative probabilities.
xv.) It was suggested that an ontological interpretation of a generalised superspin symmetry might even lead to an improved intelligibility for QM as a whole. At this point one anticipates the objection a priori that the edifice of QM is too tightly interlocked either to be substantially reinterpreted or extended without disturbing the extraordinary coexistence of local and nonlocal connections that it permits. An inherent randomisation accurately cancels out all opportunities for nonlocal signalling to preserve relativistic self-consistency. The interesting question of whether the present formulation of QM is the only form of the theory that could protect locality in this way was addressed by Popescu and Rohrlich [36] who proved that nonlocality and a no-signalling condition could indeed coexist even in a theory which assumed very strong entanglements. 'Supercorrelations' between the spin measurements of entangled particles in their model universe might be a weak version of the superspin correlation posited here as the unbroken condition of a generalised spin symmetry. Of course it remains to be seen if, and exactly how, such a generalisation might be achieved. It is obvious that the most general symmetry group to which the spin-correlation group belongs, as a restricted set of a general spin symmetry (s), will also include the mass-energy (m) and the electroweak symmetries (e). These groups ideally will all imply one another in terms of the space-like nonlocal object substrate mentioned in ix.) and x.) above. Thus (e) will include the electromagnetic gauge which transforms the scalar (s) to vector potentials by bringing in a real time, such that {(s) Û (m) Û (e)} µ (g), where (g) is a gradient of vector potentials equivalent to the Einstein gravitational tensor. But it is evidently not possible that our generalisation could lead to a tensor field with potentials at all points of a continuous real space since we are attempting to include the symmetry (g) in the specification of our elementary object(s) without recourse to a classical metric manifold.
xvi.) The effect of demanding a metasymmetry in this way is to restrict dramatically the spacetime degrees of freedom to those made available by the substrate, in such a way that an approximation to a concentric wavefront of radiation in phase can generally occur only at short scales (or with induced coherence, or at horizons), becoming increasingly an imaginary wavefront of separate diverging elements at longer scales. 'Radiation from a source' becomes some set of definite radius vectors corresponding to a set of linear objects coordinate at the 'source' and so each quantum is constrained to correspond to a discrete 'history'. Visualised as a construction in geometrical optics it now becomes possible to trace quanta 'backwards' from their absorbers as smooth fronts converging on their foci. This construction is potentially helpful in understanding the logical structure of quantum theory. In particular it elucidates wave/particle complementarity and allows implications analogous to those of Feynman-Wheeler absorber theory and Cramer's transactional interpretation of QM to be discussed without reference to the degree of openness/closure of any cosmic spacetime geometry (Part 6). It is also the inverse of the large-scale averaging of small-scale divergences that is characteristic of the usual quantum formalism. Insofar as (g) and (e) in 1.xiv. above stand for the symmetries of, respectively, general and special relativity, this inversion has interesting implications for a quantum theory of gravity. In particular, the dramatic restriction of the degrees of spacetime freedom to those paths actually congruent (in terms of some map correspondence to be discovered) with the nonlocal object-like substrate suggests the possibility that the constraints imposed on a necessary reformulation of the QED quantum condition may produce automatically the quantum condition of a future non-perturbative, non-field theory of gravity. Interestingly, the discrete form of the substrate seems to suggest that, if it should prove possible to recover some duality with GR, this duality would not extend to gravitational wave radiation as predicted by GR. But leaving these remote speculations to one side for the time being, let us return to the question of electron spin.