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This article explores the search for a theory of everything in physics, which aims to explain all aspects of reality. Traditional approaches have not been successful, but new ideas from abstract geometry, such as the amplituhedron and twistor theory, offer alternative ways to understand the fundamental laws of nature. The article also discusses the evolving understanding of atoms as the fundamental units of reality, highlighting recent discoveries of subatomic particles like quarks that challenge the notion of atoms as the smallest building blocks. It emphasizes the importance of ongoing research and the ever-changing nature of scientific knowledge. [Extracted from the article]

The article in New Scientist explores the life of physicist Roger Penrose, highlighting his achievements and the personal costs associated with his genius. The biography delves into Penrose's professional collaborations, famous connections, and the impact on his family and friends. It also discusses his contributions to physics, including his work on black holes, twistor theory, and the big bang theory, while also shedding light on his limited approach to relationships and isolation in later years. The article presents a nuanced view of Penrose's life, showcasing his intellectual brilliance alongside his personal struggles. [Extracted from the article]

The article focuses on the integration of twistor theory and string theory. In twistor theory, the location and time of events fluctuate but causal sequences do not. The idea was imprecise until string theorists realized an event with ambiguous location and time is a string. At first, string theory could only produce a single dimension of highly warped space. Twistor theory allows string theorists to show how all the dimensions of ordinary space and time can emerge.

We develop the basics of twistor theory in de Sitter space, up to the Penrose transform for free massless fields. We treat de Sitter space as fundamental, as one does for Minkowski space in conventional introductions to twistor theory. This involves viewing twistors as spinors of the de Sitter group S0(4,1). When attached to a spacetime point, such a twistor can be reinterpreted as a local SO (3,1) Dirac spinor. Our approach highlights the antipodal map in de Sitter space, which gives rise to doublings in the standard relations between twistors and spacetime. In particular, one can generate a field with both handedness signs from a single twistor function. Such fields naturally live on antipodally identified de Sitter space dS4/Z2, which has been put forward as the ideal laboratory for quantum gravity with a positive cosmological constant. [ABSTRACT FROM AUTHOR]

Maximally helicity-violating (MHV) diagrams give an efficient Feynman diagramlike formalism for calculating gauge theory scattering amplitudes on momentum space. Although they arise as the Feynman diagrams from an action on twistor space in an axial gauge, the main ingredients were previously expressed only in momentum space and momentum twistor space. Here we show how the formalism can be elegantly derived and expressed entirely in twistor space. This brings out the underlying super-conformal invariance of the framework (up to the choice of a reference twistor used to define the axial gauge) and makes the twistor support transparent. Our treatment is largely independent of signature, although we focus on Lorentz signature. Starting from the N = 4 super-Yang-Mills twistor action, we obtain the propagator for the antiholomorphic Dolbeault operator as a delta function imposing collinear support with the reference twistor defining the axial gauge. The MHV vertices are also expressed in terms of similar delta functions. We obtain concrete formulas for tree-level NkMHV diagrams as a product of MHV amplitudes with an R invariant for each propagator; here the R invariant manifests superconformai as opposed to dual-superconformal invariance. This gives the expected explicit support on k + 1 lines linked by k further lines associated to the propagators. The R invariants arising correspond to those obtained in the dual conformai invariant momentum twistor version of the formalism, but differences arise in the specification of the boundary terms. Surprisingly, in this framework, some finite loop integrals can be performed as simply as those for tree diagrams. [ABSTRACT FROM AUTHOR]

We discuss various formulations of null polygons in full, nonchiral J\T = 4 superspace in terms of spacetime, spinor, and twistor variables. We also note that null polygons are necessarily fat along fermionic directions, a curious fact which is compensated by suitable equivalence relations in physical theories on this superspace. [ABSTRACT FROM AUTHOR]

We study the symplectic reduction of the phase space of two twistors to the cotangent bundle of the Lorentz group. We provide expressions for the Lorentz generators and group elements in terms of the spinors defining the twistors. We use this to define twistor networks as a graph carrying the phase space of two twistors on each edge. We also introduce simple twistor networks, which provide a classical version of the simple projected spin networks living on the boundary Hilbert space of Engle, Pereira, Rovelli, Livine and Freidel, Krasnov spin foam models. Finally, we give an expression for the Haar measure in terms of spinors. [ABSTRACT FROM AUTHOR]

Abstract: A unified physical theory called U theory, that is different from M theory, is defined and characterized. U theory, which includes spinor and twistor theory, loop quantum gravity, causal dynamical triangulations, E-infinity unification theory, and Clifford-Finslerian unifications, is based on physical tradition and experimental foundations. In contrast, M theory pays more attention to mathematical forms. While M theory is characterized by supersymmetry string theory, U theory is characterized by non-supersymmetry unified field theory. [Copyright &y& Elsevier]

A complexification of the twisted theory allows one to determine the Yang–Mills theory in its third twist formulation. The imaginary part of the gauge symmetry is used to eliminate two scalars fields and create gauge covariant longitudinal components for the imaginary part of the gauge field. The latter becomes the vector field of the thirdly twisted theory. Eventually, one gets a one to one correspondence between the fields of both theories. Analogous complexifications can be done for topological 2d-gravity and topological sigma models. [Copyright &y& Elsevier]

Abstract: In this study, dual unitary matrices SU D(2) were obtained. We correspond to one to one elements of the unit dual sphere with the dual unitary matrices SU D(2). Thus, we express spherical concepts such as meridians of longitude and parallels of latitude on SU D(2). The equality SO(R 3)≅ S 3/{±1}= RP 3 known as the real projective spaces was generalized to the dual projective space and then, the equality was acquired. In particular, 2-sphere S 2 was obtained by considering dual parts as zero of . Hence, it was found that Hop fibriation map of S 2 can be used for Twistors in quantum mechanics applications. [Copyright &y& Elsevier]

We describe a novel twistorial construction of the asymptotic Bondi-Metzner-Sachs (BMS) symmetries at null infinity for asymptotically flat spacetimes. We define BMS twistors as spinor solutions to some set of components of the usual spacetime twistor equation restricted to null infinity. The space of BMS twistors is infinite dimensional. We show that given two BMS twistors, their symmetric tensor product can be used to generate (complex) vector fields which are the infinitesimal BMS symmetries of null infinity. In this sense, BMS twistors are "square roots" of BMS symmetries. We also show that these BMS twistor equations can be written a pair of covariant spinor-valued equations which are completely determined by the intrinsic universal structure of null infinity. [ABSTRACT FROM AUTHOR]

Twistors appear to provide a satisfactory treatment of angular momentum for gravitationally radiating systems. The approach is manifestly Bondi-Metzner-Sachs (BMS) invariant, and there are no supertranslation ambiguities. The resulting definitions of center of mass and spin are appealing: unphysical contributions from bad cuts are canceled off from the center of mass, and the spin appears formally as a displacement of the center of mass into the complex. For transitions between asymptotically Minkowskian regimes (nonradiative regimes with purely electric Bondi shear), when there is no supertranslation offset (equivalently, radation memory) between the regimes, the results are in agreement with those deducible from other approaches. However, when there is an offset, the results are different. The twistor-derived change-of-origin formula is closely parallel to the special-relativistic one, with an algebraic cross-product between the energy-momentum and a direction-dependent translation derived from the supertranslation. (No supermomenta appear.) There is also a "longitudinal" contribution to the emitted angular momentum (one sensitive to the total energy-momentum and not just the emitted energy-momentum), and terms which are both linear and cubic in the gravitational radiation (whereas BMS-based definitions give purely quadratic contributions). The first-order terms mean that the supertranslation offsets can contribute to the exchange of angular momentum with gravitational radiation, even in weak-field limits. This is illustrated with a simple almost-special-relativistic model. [ABSTRACT FROM AUTHOR]

We elaborate the two-fold simplexlike structures of tree amplitudes in planar maximally supersymmetric Yang-Mills (N=4 SYM), through its connection to a mathematical structure known as the positive Grassmannian. Exploiting the reduced Grassmannian geometry and the matrix form of on-shell recursion relation in terms of super momentum twistors, we manifest that tree amplitudes can be remarkably refined via the essential building blocks named as fully spanning cells. For a fixed number of negative helicities, an amplitude can be entirely captured by finite, compact information of the relevant fully spanning cells up to an arbitrarily large number of external particles. [ABSTRACT FROM AUTHOR]

We consider massless fields of arbitrary spin in de Sitter space. We introduce a spinor-helicity formalism, which encodes the field data on a cosmological horizon. These variables reduce the free S-matrix in an observer's causal patch, i.e., the evolution of free fields from one horizon to another, to a simple Fourier transform. We show how this result arises via twistor theory, by decomposing the horizon↔horizon problem into a pair of (more symmetric) horizon↔twistor problems. [ABSTRACT FROM AUTHOR]

A finite geometric model of space-time (which we call the bulk) is shown to emerge as a set of error correcting codes. The bulk is encoding a set of messages located in a blow up of the Gibbons-Hoffman-Wootters (GHW) discrete phase space for n-qubits (which we call the boundary). Our error correcting code is a geometric subspace code known from network coding, and the correspondence map is the finite geometric analogue of the Plücker map well-known from twistor theory. The n=2 case of the bulk-boundary correspondence is precisely the twistor correspondence where the boundary is playing the role of the twistor space and the bulk is a finite geometric version of compactified Minkowski space-time. For n≥3 the bulk is identified with the finite geometric version of the Brody-Hughston quantum space-time. For special regions on both sides of the correspondence we associate certain collections of qubit observables. On the boundary side this association gives rise to the well-known GHW quantum net structure. In this picture the messages are complete sets of commuting observables associated to Lagrangian subspaces giving a partition of the boundary. Incomplete subsets of observables corresponding to subspaces of the Lagrangian ones are regarded as corrupted messages. Such a partition of the boundary is represented on the bulk side as a special collection of space-time points. For a particular message residing in the boundary, the set of possible errors is described by the fine details of the light-cone structure of its representative space-time point in the bulk. The geometric arrangement of representative space-time points, playing the role of the variety of codewords, encapsulates an algebraic algorithm for recovery from errors on the boundary side. [ABSTRACT FROM AUTHOR]

Twistor string models have been known for more than a decade now but have come back under the spotlight recently with the advent of the scattering equation formalism which has greatly generalized the scope of these models. A striking ubiquitous feature of these models has always been that, contrary to usual string theory, they do not admit vibrational modes and thus describe only conventional field theory. In this paper we report on the surprising discovery of a whole new sector of one of these theories which we call "twisted strings," when spacetime has compact directions. We find that the spectrum is enhanced from a finite number of states to an infinite number of interacting higher spin massive states. We describe both bosonic and world sheet supersymmetric models, their spectra and scattering amplitudes. These models have distinctive features of both string and field theory, for example they are invariant under stringy T-duality but have the high energy behavior typical of field theory. Therefore they describe a new kind of field theories in target space, sitting on their own halfway between string and field theory. [ABSTRACT FROM AUTHOR]

An interview with Roger Penrose, Emeritus Rouse Ball Professor of Mathematics at Oxford University. Penrose regards his "twistor theory" as the most important idea in his career, saying it has helped provide a better understanding of the universe and holds important applications in the high-energy community. His most controversial idea, he says, is his proposition that non-computational activity can come about through processes acting in accordance with physical laws.

Discusses a branch of higher mathematics called `twistor theory'. Conference at the University of Plymouth on the subject; Applications in solving equations.