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We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of 1 2 —these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of 1 2 , or it remains a boson and precedes without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, Q8, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion causes the observed violation of Bell's Inequalities and resolves the EPR paradox. [ABSTRACT FROM AUTHOR]

We present a statistical simulation replicating the correlation observed in EPR coincidence experiments without needing non-local connectivity. We define spin coherence as a spin attribute that complements polarization by being anti-symmetric and generating helicity. Point particle spin becomes structured with two orthogonal magnetic moments, each with a spin of 12—these moments couple in free flight to create a spin-1 boson. Depending on its orientation in the field, when it encounters a filter, it either decouples into two independent fermion spins of 12, or it remains a boson and precedes without decoupling. The only variable in this study is the angle that orients a spin on the Bloch sphere, first identified in the 1920s. There are no hidden variables. The new features introduced in this work result from changing the spin symmetry from SU(2) to the quaternion group, Q8, which complexifies the Dirac field. The transition from a free-flight boson to a measured fermion causes the observed violation of Bell’s Inequalities and resolves the EPR paradox.

We find all hyper-Kähler 4-manifolds admitting conformal Kähler structures with respect to either orientation, and we show that these structures can be expressed as a combination of twistor elementary states (and possibly a self-dual dyon) in locally flat spaces. The complex structures of different flat pieces are not compatible however, reflecting that the global geometry is not a linear superposition. For either orientation, the space must be Gibbons–Hawking (thus excluding the Atiyah–Hitchin metric), and, if the orientations are opposite, it must also be toric and have an irreducible Killing tensor. We also show that the only hyper-Kähler 4-metric with a non-constant Killing–Yano tensor is the half-flat Taub–NUT instanton. [ABSTRACT FROM AUTHOR]

This paper describes conservation laws in general relativity (GR) dating back to the mass-energy conservation of Bondi and Sachs in the early 1960s but using 2-spinor techniques. The notion of conformal infinity is employed, and the highly original ideas of E. T. Newman are discussed in relation to twistor theory. The controversial NP constants are introduced, and their meaning is considered in a new light related to the problem of equations of motion in GR. This article is part of a discussion meeting issue 'At the interface of asymptotics, conformal methods and analysis in general relativity'. [ABSTRACT FROM AUTHOR]

The study of physical theories in various signatures has been important for uncovering structures not easily visible or definable in Lorentz signature. In split signature, global twistor constructions for conformally self-dual (SD) gravity and Yang–Mills construct solutions from twistor data that can be expressed in terms of free data without gauge freedom. This is developed for asymptotically flat SD gravity to give a fully nonlinear encoding of the asymptotic gravitational data in terms of a real homogeneous generating function h on the real twistor space. The recently discovered L w 1 + ∞ celestial symmetries, when real, act locally as passive Poisson diffeomorphisms on the real twistor space. The twistor data, h, generates an imaginary such Poisson transformation that then generates the gravitational field by shifting the real slice of the twistor space. The twistor chiral sigma models, whose correlators yield the Einstein gravity tree-level S-matrix, are reformulated as theories of holomorphic discs in twistor space whose boundaries lie on the deformed real slice determined by h. The real L w 1 + ∞ symmetries act on the corresponding formula for the S-matrix geometrically with vanishing Noether currents, but imaginary generators yield graviton vertex operators that generate gravitons in the perturbative expansion. A generating function for the all plus 1-loop amplitude, the analogous framework for Yang–Mills, possible interpretations in Lorentz signature and similar open string formulations of twistor and ambitwistor strings in 4d in split signature, are briefly discussed. [ABSTRACT FROM AUTHOR]

We consider holomorphic Poisson-BF theory on twistor space. Classically, this describes self-dual Einstein gravity on space-time, but at the quantum level it is plagued by an anomaly. The anomaly corresponds to the fact that integrability of the self-dual vacuum Einstein equations does not survive in self-dual quantum gravity. We compute the anomaly polynomials in the Poisson-BF theory, as well as in this theory coupled to a holomorphic BF theory on twistor space describing self-dual Yang–Mills. We show that all anomalies may be cancelled by further coupling to a twistor field representing a type of axion on space-time. When the twistor anomalies are cancelled, all n ≥ 4 -pt amplitudes vanish and integrability is restored. [ABSTRACT FROM AUTHOR]

For integrated pose control of six-degree-of-freedom (6-DOF) leader–following spacecraft formations, the coupled relative pose between two spacecraft is described by a unified model in the framework of twistors, based on which a finite-time control law is devised for the 6-DOF dynamic system. Firstly, some necessary coordinate frames are defined, and then, relative 6-DOF dynamics of the follower spacecraft with respect to the desired frame are modeled by using twistors. Secondly, an integrated pose controller is designed for the 6-DOF formation that takes full advantage of homogeneous theory to guarantee finite-time stability. Finally, numerical simulations are carried out to validate the effectiveness of the proposed controller. Developing integrated 6-DOF formation control law based on twistors is more straightforward than conventional methods, and the finite-time algorithm achieves stronger robustness than asymptotic ones. [ABSTRACT FROM AUTHOR]

In this paper, I discuss the impact of the positive cosmological constant on the interplay between the equivalence principle in general relativity, and the rules of quantum mechanics. At the nonrelativistic level, there is an ambiguity in the definition of a phase of a wave function measured by inertial and accelerating observes. This is the cosmological analogue of the Penrose effect, which can also be seen as a nonrelativistic limit of the Unruh effect. The symmetries of the associated Schrödinger equation are generated by the Newton–Hooke algebra, which arises from a nonrelativistic limit of a cosmological twistor space. [ABSTRACT FROM AUTHOR]

The existence of interacting higher-spin theories is tightly constrained by many no-go theorems. In this paper, we construct a chiral, higher-spin generalization of Yang–Mills theory in flat space which avoids these no-go theorems and has non-trivial tree-level scattering amplitudes with some higher-spin external legs. The fields and action are complex, so the theory is non-unitary and parity-violating, yet we find surprisingly compact formulae for all-multiplicity tree-level scattering amplitudes in the maximal helicity violating (MHV) sector, where the two negative helicity particles have identical but arbitrary spin. This is possible because the theory admits a perturbative expansion around its self-dual sector. Using twistor theory, we prove the classical integrability of this self-dual sector and show that it can be described on spacetime by an infinite tower of interacting massless scalar fields. We also give a twistor construction of the full theory and use it to derive the formula for the MHV amplitude. [ABSTRACT FROM AUTHOR]

The construction of amplitudes on curved space-times is a major challenge, particularly when the background has non-constant curvature. We give formulae for all tree-level graviton scattering amplitudes in curved self-dual (SD) radiative space-times; these are chiral, source-free, asymptotically flat spaces determined by free characteristic data at null infinity. Such space-times admit an elegant description in terms of twistor theory, which provides the powerful tools required to exploit their underlying integrability. The tree-level S-matrix is written in terms of an integral over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map corresponding to the helicity configuration of the external gravitons. For the MHV sector, we derive the amplitude directly from the Einstein–Hilbert action of general relativity, while other helicity configurations arise from a natural family of generating functionals and pass several consistency checks. The amplitudes in SD radiative space-times exhibit many novel features that are absent in Minkowski space, including tail effects. There remain residual integrals due to the functional degrees of freedom in the background space-time, but our formulae have many fewer such integrals than would be expected from space-time perturbation theory. In highly symmetric special cases, such as SD plane waves, the number of residual integrals can be further reduced, resulting in much simpler expressions for the scattering amplitudes. [ABSTRACT FROM AUTHOR]

We present all-multiplicity formulae, derived from first principles in the MHV sector and motivated by twistor string theory for general helicities, for the tree-level S-matrix of gluon scattering on self-dual radiative backgrounds. These backgrounds are chiral, asymptotically flat gauge fields characterised by their free radiative data, and their underlying integrability is captured by twistor theory. Tree-level gluon scattering scattering amplitudes are expressed as integrals over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map related to the helicity configuration of the external gluons. In the MHV sector, our formula is derived from the Yang–Mills action; for general helicities the formulae are obtained using a background-coupled twistor string theory and pass several consistency tests. Unlike amplitudes on a trivial vacuum, there are residual integrals due to the functional freedom in the self-dual background, but for scattering of momentum eigenstates we are able to do many of these explicitly and even more is possible in the special case of plane wave backgrounds. In general, the number of these integrals is always less than expected from standard perturbation theory, but matches the number associated with space-time MHV rules in a self-dual background field, which we develop for self-dual plane waves. [ABSTRACT FROM AUTHOR]

On-shell kinematics for gluon scattering can be parametrized with points on the celestial sphere; in the limit where these points collide, it is known that tree-level gluon scattering amplitudes exhibit an operator product expansion (OPE)-like structure. While it is possible to obtain singular contributions to this celestial OPE, getting regular contributions from both holomorphic and anti-holomorphic sectors is more difficult. In this paper, we use twistor string theory to describe the maximal helicity violating (MHV) sector of tree-level, four-dimensional gluon scattering as an effective 2d conformal field theory on the celestial sphere. By organizing the OPE between vertex operators in this theory in terms of soft gluon descendants, we obtain all-order expressions for the celestial OPE which include all regular contributions in the collinear expansion. This gives new, all-order formulae for the collinear splitting function (in momentum space) and celestial OPE coefficients (in the conformal primary basis) of tree-level MHV gluon scattering. We obtain these results for both positive and negative helicity gluons, and for any incoming/outgoing kinematic configuration within the MHV sector. [ABSTRACT FROM AUTHOR]

The aim of this paper is to explore the conceptual and mathematical physics foundations of the work of Sir Roger Penrose. This is a transcript of an interview that took place on 15 November 2021. [ABSTRACT FROM AUTHOR]

An adaptive finite-time attitude and position coupled tracking controller for six-degree-of-freedom (6-DOF) leader-following spacecraft formation is proposed in this paper. The relative motion of the follower with respect to its desired pose is represented by twistors in a unified way without state redundancy. A fast terminal sliding surface is proposed for the twistor-based dynamic system to achieve finite-time convergence. Then an adaptive finite-time controller is developed with the unknown inertial parameters of the follower spacecraft and the upper bounds of the disturbances estimated by elaborately designed adaptive laws. The finite-time convergence of the closed-loop system is proven via Lyapunov analysis. In addition, an simple but effective strategy is proposed to eliminate the attitude unwinding phenomenon. The proposed adaptive finite-time control scheme possesses faster convergence, higher control accuracy, and more preferable control inputs. In addition, the possible numerical difficulties caused by logarithmic function of dual quaternions is avoided. Finally, simulation results demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The space of light rays N of a conformal Lorentz manifold (M , C) is, under some topological conditions, a manifold whose basic elements are unparametrized null geodesics. This manifold N , strongly inspired on R. Penrose's twistor theory, keeps all information of M and it could be used as a space complementing the spacetime model. In the present review, the geometry and related structures of N , such as the space of skies Σ and the contact structure H , are introduced. The causal structure of M is characterized as part of the geometry of N . A new causal boundary for spacetimes M prompted by R. Low, the L-boundary, is constructed in the case of 3–dimensional manifolds M and proposed as a model of its construction for general dimension. Its definition only depends on the geometry of N and not on the geometry of the spacetime M. The properties satisfied by the L–boundary ∂ M permit to characterize the obtained extension M ¯ = M ∪ ∂ M and this characterization is also proposed for general dimension. [ABSTRACT FROM AUTHOR]

The classical double copy relating exact solutions of biadjoint scalar, gauge and gravity theories continues to receive widespread attention. Recently, a derivation of the exact classical double copy was presented, using ideas from twistor theory, in which spacetime fields are mapped to Cech cohomology classes in twistor space. A puzzle remains, however, in how to interpret the twistor double copy, in that it relies on somehow picking special representatives of each cohomology class. In this paper, we provide two alternative formulations of the twistor double copy using the more widely-used language of Dolbeault cohomology. The first amounts to a rewriting of the Cech approach, whereas the second uses known techniques for discussing spacetime fields in Euclidean signature. The latter approach indeed allows us to identify special cohomology representatives, suggesting that further application of twistor methods in exploring the remit of the double copy may be fruitful. [ABSTRACT FROM AUTHOR]

In the framework of twistors, a saturated adaptive six-degree-of-freedom (6-DOF) control law for asteroid landing, which avoids the collision between the spacecraft and asteroid, is proposed with both the inertial parameters of the spacecraft and the bounds of the uncertainties unknown. First, the 6-DOF dynamics of the spacecraft relative to the desired coordinate frame is represented in a unified way by the application of twistors, and the collision avoidance constraint is established via separating the spacecraft and asteroid with an elaborately designed safety surface. Then, a saturated controller for the landing is proposed with the collision avoidance constraint considered by combining the backstepping method and artificial potential field technique. Further, the inertial parameters and the upper bounds of the magnitude of the uncertainties in the controller are substituted with their estimates obtained from the designed adaptive laws. Finally, the previous design is adjusted slightly to complete the adaptive control scheme. The stability of the closed-loop system is proven via Lyapunov theory, and numerical simulations are presented to demonstrate the effectiveness of the control scheme. The proposed adaptive control law can fully consider the orbit-attitude coupling and effectively enforce the collision avoidance constraint in the presence of unknowns in asteroid landing missions. [ABSTRACT FROM AUTHOR]

We review Lie polynomials as a mathematical framework that underpins the structure of the so-called double copy relationship between gauge and gravity theories (and a network of other theories besides). We explain how Lie polynomials naturally arise in the geometry and cohomology of M 0 , n , the moduli space of n points on the Riemann sphere up to Mobiüs transformation. We introduce a twistorial correspondence between the cotangent bundle T D ∗ M 0 , n , the bundle of forms with logarithmic singularities on the divisor D as the twistor space, and K n the space of momentum invariants of n massless particles subject to momentum conservation as the analogue of space–time. This gives a natural framework for Cachazo He and Yuan (CHY) and ambitwistor-string formulae for scattering amplitudes of gauge and gravity theories as being the corresponding Penrose transform. In particular, we show that it gives a natural correspondence between CHY half-integrands and scattering forms, certain n - 3 -forms on K n , introduced by Arkani-Hamed, Bai, He and Yan (ABHY). We also give a generalization and more invariant description of the associahedral n - 3 -planes in K n introduced by ABHY. [ABSTRACT FROM AUTHOR]

The search for a geometrical understanding of dualities in string theory, in particular T-duality, has led to the development of modern T-duality covariant frameworks such as Double Field Theory, whose mathematical structure can be understood in terms of generalized geometry and, more recently, para-Hermitian geometry. In this work we apply techniques associated to this doubled geometry to four-dimensional manifolds, and we show that they are particularly well-suited to the analysis of integrability in special spacetimes, especially in connection with Penrose's twistor theory and its applications to general relativity. This shows a close relationship between some of the geometrical structures in the para-Hermitian approach to double field theory and those in algebraically special solutions to the Einstein equations. Particular results include the classification of four-dimensional, possibly complex-valued, (para-)Hermitian structures in different signatures, the Lie and Courant algebroid structures of special spacetimes, and the analysis of deformations of (para-)complex structures. We also discuss a notion of "weighted algebroids" in relation to a natural gauge freedom in the framework. Finally, we analyze the connection with two- and three-dimensional (real and complex) twistor spaces, and how the former can be understood in terms of the latter, in particular in terms of twistor families. [ABSTRACT FROM AUTHOR]

We discuss the equivalence principle in quantum mechanics in the context of Newton–Cartan geometry, and non-relativistic twistor theory. [ABSTRACT FROM AUTHOR]

We introduce the notion of tame ρ -quaternionic manifold that permits the construction of a finite family of ρ -connections, significant for the geometry involved. This provides, for example, the following: • A new simple global characterisation of flat (complex-)quaternionic manifolds. • A new simple construction of the metric and the corresponding Levi-Civita connection of a quaternionic-Kähler manifold by starting from its twistor space; moreover, our method provides a natural generalization of this correspondence. Also, a new construction of quaternionic manifolds is obtained, and the properties of twistorial harmonic morphisms with one-dimensional fibres from quaternionic-Kähler manifolds are studied. [ABSTRACT FROM AUTHOR]