Antimatter- Something Rather than Nothing

Like skis and skates, stuff came in pairs. Pairs that annihilated one another, shared mass but differed in charge and spin. It's the Jekyll and Hyde personality of particles that corresponds to the existence of matter and antimatter; Dirac envisaged a sea of negative energy levels, each filled with a pair of electrons of opposing spin with the positron appearing as a 'hole' in the sea as a state with a positive charge and energy. While Feynman and Stueckelberg likened negative energy particles moving backward in time to positive energy antiparticles moving forward in time. But the ultimate question remains the origin of the asymmetry of matter, and why unlike a world filled with antiparticles or emptiness, we are made of matter anyways; why there is something rather than nothing. Let's look back at the early universe, before primordial nucleosynthesis and into baryogenesis; the making of baryons and antibaryons. Sakharov noted three conditions necessary for the production of the baryon asymmetry namely; the violation of baryon number, violation of C and CP symmetry and a withdrawal from thermal equilibrium. Electroweak theory, the synthesis of the electromagnetic and weak interactions, incorporates gauge symmetries useful to explaining the matter asymmetry and fulfilling the Sakharov prerequisites; just like a hot iron ferromagnet with a series of randomly spinning electrons exhibiting rotational symmetry which may be broken and magnetised when cooled and aligning the spins, the weak symmetry breaks giving W and Z bosons mass via the Higgs field and preserves the electroweak symmetry keeping photons massless. So during the early epochs, the universe must have cooled down to a critical temperature like the ferromagnet, causing the electroweak phase transition out of thermal equilibrium to form like bubbles in boiling water, breaking the symmetry. At first sight, the electroweak interaction also  seems to apparently conserve the baryon number but this may be violated in the current phase of broken symmetry via quantum tunneling but during the early universe, a barrier to fluctuation was not present and the baryon number was permitted to vary freely. But how can electroweak theory account for the differences between matter and antimatter? Like a roulette wheel likely to land in a spot of equal probability, a tilted wheel is biased toward a particular symmetry breaking much like the violation of charge conjugation (C) and parity (CP). Charge conjugation ensures the interchanging between particles and antiparticles while parity preserves spin but reverses direction; so here the CP symmetry can counteract particle production with antiparticles leading to annihilation, but how did a bit more matter than antimatter end up being made? The electromagnetic and strong interactions have C and P symmetries but the weak force violates it through the beta minus decay of kaons, thus the quark components of baryons should also be able to violate it through weak interactions and break the symmetry. Now that we've fulfilled the prerequisites via electroweak theory, it can be speculated that the initial early universe was full of a symmetric phase but as the phase transition broke the symmetry, bubbles formed and baryon number was violated out of thermal equilibrium; it may be further hypothesised that as the bubbles spread cross the universe via a plasma of particles  and antiparticles, quarks were sealed in the bubbles, leaving their baryon number unscathed  whereas the antiquarks were annihilated creating the asymmetry. However, the traditional Kobashi-Maskawa CP violation may prove inefficient as all quarks other than the 'top' are remarkably light compared the W boson; necessitating a new type of symmetry violation that will allow the weak interaction to manipulate the charge and flavour of all six quarks indiscriminate of their masses. A saga to be continued...

Topology- From Euler to Poincaré

Turning a sphere inside out is one easy task. Simply poke a hole in it and yank it through. Or is it? Can it be done without poking a hole? And with a material that can bend, stretch and pass through itself? Enter topology; where doughnuts meet coffee mugs and where pretzels become nontrivial trefoils. It's way of looking at space with a sense of 'sameness' and connectivity, where even gravity is reduced to curvature on a trampoline. Indeed topology is the product of the cross fertilization of graph and knot theory, in 1736 Euler established the impossibility of the circuit round the seven bridges of Königsberg; by envisaging each plot of land as a vertex connected by lines, it became clear that an even number of edges was needed to cross each bridge once and fulfill the problem. But since the vertices all had odd numbers of edges, it was out of the question. More imaginary was the discovery of the Möbius strip, a surface with a single edge and a single side. Such a surface emerges via twisting a strip so that one side is reversed and formed into a closed loop, this introduced the notion of a non-orientable plane that confuses the sense of 'inside' and 'outside'. Attaching two Möbius strips together results in a Klein bottle, a closed surface lacking a defined boundary and may also be formed abstractly by gluing the remaining edges of a cylinder in opposite directions to make a torus. But to achieve this is everyday Euclidean space, the surface would have to go through itself to situate the edges. More intriguing was the Poincaré conjecture posited in 1904 and the topology of the sphere; simply put, the simplest object which is closed in any number of given dimensions. Any closed 3D manifold where a loop may be contracted to a single point is a 3D sphere, whereas loops on a torus fail to contract to a single point. But the central issue at large remained whether a closed 3D manifold could exist independent of the sphere but by considering Thurston's geometrisation theorem, where 8 types of manifolds could be sewn to form other 3D surfaces and Ricci flow, whereby irregular and lopsided spaces can be turned into uniform ones, the concept of a non-spherical closed manifold could be ruled out. Algebraic topology also introduces the idea of a vector bundle, considering spaces and structures described above a surface as opposed to within it; by designating a vector space to each point, followed by a fibre, a vector field is produced. Suppose a series of vectors lying tangent on a sphere, at least a single point will remain with a vector value of zero is inevitable making a hairy torus easily combable whereas a hairy ball will produce a crown at each pole. Moreover, at even the simplest topologies; the concept of homeomorphism forms a continuous transformation function between the torus and the coffee mug, both objects are said to be homotopic just as the 2D sphere and the horned sphere can be converted into one another without tearing or incising. Homotopy may also be applied when fine spaces or holes cannot be accounted by via homology or by examining features of the topological space that lack a boundary and are not boundaries in themselves.

Dark Matter- A Standard Model of Cosmology

We lie off-centre in the disk that is our Milky Way. A crowd of a hundred thousand million stars, accompanied by globular clusters embedded in a galactic halo kilo-parsecs across. We are part of the local group, a community of galaxies with our closest neighbor, the Canis Major Dwarf and our twin, Andromeda. And while a GPS won't get you far in an increasingly homogeneous and isotropic universe, we are only beginning to peel back the layers of the cosmic onion. We see it's expansion via the receding of galaxies, the meandering of supernovae through standard candles and their speeds by their red-shift. But an anomaly remains on how to account for the accelerated expansion in conjunction with attractive gravity. Dark matter is the 'stuff' of the universe that pulls things together via its attractive gravity and boasts thirty percent of it. It's dark, bleak and invisible but when you consider the cluster dynamics of galaxies for instance, there seems to be more mass determined by velocity rather than what can be accounted by with observation. Gravitational lensing also hints it's existence where the curvature of space-time near a mass deflects light and distorts images of background galaxy clusters. We can rest assured that non-baryonic WIMPS, weakly interacting massive particles, are the ideal candidates for exotic dark matter species as opposed to baryonic MACHOS or massive compact halo objects. There may even be no dark matter but rather modified Newtonian mechanics on an intergalactic scale, rogue planets, black holes or even mass challenged dwarf stars. On the flip side, dark energy pushes things apart, exhibits a repulsive gravity and brags seventy percent of the cosmos. An all pervading fluid as envisioned by the Friedman-Robertson-Walker models will be a source of positive pressure at every single point and would drive deceleration of expansion, however dark energy exerts negative pressure to accelerate expansion as inferred from CMB anisotropies. Think of the Casimir effect, when two closely partitioned metallic plates in a vacuum attract each other, arising from the influence that the plates exhibit on the space between them and the effective negative pressure produced. Indeed Einstein's 'greatest blunder' may be a contender for dark energy; matter and energy under the cosmological constant will not be impaired by expansion but would remain uniform and release negative pressure. Moreover, the energy of the quantum vacuum may be another contender; given that vacuum energy is intrinsic to the vacuum, it won't be diluted by expansion and would exert the required negative pressure. Finally, cosmology is topped off with inflation; the hot big bang model presents two unique limitations: the flatness and horizon problems. Stated simply, the universe is essentially flat with a curvature parameter k of 0, the CMB is the same temperature in all directions and Grand Unified Theories predict an abundance of relic magnetic monopoles. Inflationary cosmology tells the tale 10^-36 seconds after the bang where the scale factor of the universe inflated exponentially, solving the problems by smoothing out any rough edges and separating regions with the same temperature across large distances and diluting any relic particles. The source of cosmic energy for such an initial singularity may be resolved via t=0, given that the total energy of the universe is 0 as the gravitational field has a negative quantity; thus cancelling out. And the universe is largely a 'nothing' for 'nothing' phenomenon, we are merely a speck in her finite yet unbound being.

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Morphic Resonance- The Presence of the Past

They are the organising fields of self-organising systems. The habitual blueprints of pattern and form and the inherent collective memory strung across space and time. Morphic resonance remains a hypothesis of formative causation, one where the field concept is extended upon the biological realm and presents an evolutionary account of instincts and behaviors. One where the laws of nature become manifestations of acquired habits, where developing embryos become products of an architectural, morphogenetic plan and one where flocks of birds and schools of fish orient themselves in a seamless fashion via morphic fields. Just as a bar magnet can be split into infinitely many smaller magnets, each with their respective north and south poles; the holistic rather than mechanistic nature of living systems, especially in their developmental stages is reminiscent of the field. Matter is not fundamental to such fields but rather conversely fields are fundamental to matter.Take the embryonic development of species from flat and nematode worms to dragon flies and newts; terminating the growth of one half of the embryo will allow the other half to grow independent of it as if a mechanism beyond bilateral gene expression and modulation is vested. Willow tree cuttings and amputated newts grow readily as if a morphology in the form of a field, where nested hierarchies of holons centered on lower level systems govern their self-organising behavior. Morphic resonance is the inference from similar patterns of form acting on subsequent patterns of activity, a kind of collective unconscious comparable to that proposed by Jung. If rats in San Francisco learn a new trick then rats in London should learn such a trick more readily and with ease; similarly, the synthesis of a new crystalline compound more often yields easier crystallisation rates in the future. Such phenomena may be deduced from the presence of the past, a sort of collective-rat memory, a morphic field rather than coincidence or fragments travelling on the beards of migrant chemists. Homoeotic mutations in Drosophila fruit flies produces extra wings in the place of halteres, such a tuning into the morphic field of the fly revisits the heresy of heredity whereby acquired traits may have the potential to be inherited. Indeed the anthropocentric notion of physical laws or constants are somewhat outrun by the idea of habits, verily human laws evolve and change with time and so could the laws of nature arise via habitual means of non-local reinforcement of similarity and natural selection. Similarly, the same means by which a magnetic field stretches beyond the horizon of a magnet and the gravitational field of the sun reaches out to keep the planets in orbit; the extended mind reaches out beyond the vicinity of the physical brain, a morphic field between minds and thoughts. But in the long run, the ascent of alternative hypotheses rather than merely mechanistic truisms spells a resonance of morphic proportions.