Approaches to relativistic positioning around Earth and error estimations

A relativistic deep space positioning system has been proposed using four or\nmore pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed\nrepetition period in its rest frame.) The positioning system uses the fact that\nan event in spacetime can be fully described by emission coordinates: the\nproper emission time of each pulse measured at the event. The proper emission\ntime of each pulse from four different pulsars---interpolated as\nnecessary---provides the four spacetime coordinates of the reception event in\nthe emission coordinate system. If more than four pulsars are available, the\nredundancy can improve the accuracy of the determination and/or resolve\ndegeneracies resulting from special geometrical arrangements of the sources and\nthe event.\n We introduce a robust numerical approach to measure the emission coordinates\nof an event in any arbitrary spacetime geometry. Our approach uses a continuous\nsolution of the eikonal equation describing the backward null cone from the\nevent. The pulsar proper time at the instant the null cone intersects the\npulsar world line is one of the four required coordinates. The process is\ncomplete (modulo degeneracies) when four pulsar world lines have been crossed\nby the light cone.\n The numerical method is applied in two different examples: measuring emission\ncoordinates of an event in Minkowski spacetime using pulses from four pulsars\nstationary in the spacetime; and measuring emission coordinates of an event in\nSchwarzschild spacetime using pulses from four pulsars freely falling toward a\nstatic black hole.\n These numerical simulations are merely exploratory, but with improved\nresolution and computational resources the method can be applied to more\npertinent problems. For instance one could measure the emission coordinates,\nand therefore the trajectory, of the Earth.\n

New version of FDTD with GFM program in Schwarzschild space–time

Consistency conditions for the local existence of massless spin-3/2 fields have been explored to find the facts that the field equations for massless helicity-3/2 particles are consistent if the space–time is Ricci-flat, and that in Minkowski space–time the space of conserved charges for the fields is its twistor space itself. After considering the twistorial methods to study such massless helicity-3/2 fields, we show in flat space–time that the charges of spin-3/2 fields, defined topologically by the first Chern number of their spin-lowered self-dual Maxwell fields, are given by their twistor space, and in curved space–time that the (anti-)self-duality of the space–time is the necessary condition. Since in N=1 supergravity torsions are the essential ingredients, we generalize our space–time to that with torsion (Einstein–Cartan theory), and investigate the consistency of existence of spin-3/2 fields in this theory. A simple solution to this consistency problem is found: The space–time has to be conformally (anti-)self-dual, left-(or right-) torsion-free. The integrability condition on α-surface shows that the (anti-)self-dual Weyl spinor can be described only by the covariant derivative of the right-(left-)handed torsion.

The one-loop vacuum polarization is calculated for scalar electrodynamics in a flat space-time with the topology S^1×R^3,The effect of vacuum polarization upon photon propagation is considered.It is found that thoton propagation becomes anisotropic with some photon modes acquring a positive topological mass and thus travelling at a subluminal speed.

In modern physics, the constant “c” plays a twofold role. On the one hand, “c” is the well known velocity of light in an empty Minkowskian space–time, on the other hand “c” is a characteristic number of Special Relativity that governs the Lorentz transformation and its consequences for the measurements of space–time intervals. We ask for the interrelations between these two, at first sight different meanings of “c”. The conjecture that the value of “c” has any influence on the structure of space–time is based on the operational interpretation of Special Relativity, which uses light rays for measurements of space–time intervals. We do not follow this way of reasoning but replace it by a more realistic approach that allows to show that the structure of the Minkowskian space–time can be reconstructed already on the basis of a restricted classical ontology (Mittelstaedt, Philosophie der Physik und der Raum-Zeit, Mannheim: BI-Wissenschaftsverlag, 1988 and Mittelstaedt, Kaltblutig: Philosophie von einem rationalen Standpunkt, Stuttgart: S. Hirzel Verlag, pp. 221–240, 2003), and that without any reference to the propagation of light. However, the space–time obtained in this way contains still an unknown constant. We show that this constant agrees numerically with “c” but that it must conceptually clearly be distinguished from the velocity of light. Hence, we argue for a clear distinction between the two faces of “c” and for a dualism of space–time and matter.

Closed time-like curves in flat Lorentz space–times

There is a well-known short list of asymptotic conserved quantities for a physical system at spatial infinity. We search for new ones. This is carried out within the asymptotic framework of Ashtekar and Romano, in which spatial infinity is represented as a smooth boundary of space–time. We first introduce, for physical fields on space–time, a characterization of their asymptotic behavior as certain fields on this boundary. Conserved quantities at spatial infinity, in turn, are constructed from these fields. We find, in Minkowski space–time, that each of a Klein–Gordon field, a Maxwell field, and a linearized gravitational field yields an entire hierarchy of conserved quantities. Only certain quantities in this hierarchy survive into curved space–time.

We calculate the post-Newtonian limit in the teleparallel equivalent of General Relativity (TEGR) with a scalar eld which non-minimally couples to gravity. The background is set up at Minkowski spacetime, and both the tetrad eld and energy momentum tensor are perturbed in the parametrized post-Newtonian formalism. The comparisons of the post- Newtonian result with general relativity and solar system experiments are discussed.

The world is composed by events. We can sense the changes of events directly by our five senses or indirectly by using the measurement equipment and tools. If in a closed system including the observer no changes are sensed, no time passes and if even a very small change is sensed, time passes. It means that the time is not a real degree of freedom and can be only understood through the concept of changes in events. The events can be considered as relata and their mutual or multiple interactions can be considered as relation. Causality can be sensed if one relata creates a change in the other relata and in consequence the passage of time can be sensed. These two relates are connected to each other by a causal world line. If two relates are connected by a timelike curve theoretically, but they cannot make change in each other, one relata has only a priority in occurrence respect to other (time precedence), and in consequence, one can omit the past non-casual events from the casual world line. In addition, in causality relation, we should consider more than one causal world line due to the uncertainty principle of quantum mechanics and its probabilistic nature (superposition principle). Therefore, at Planck scale, more than one casual world line should be assigned to the relation between two casual events when we want to study the dynamic of spacetime. It means that no kinematic state can be considered at Planck scale and a quantum spacetime manifold (QSTM) should be only assigned to the casual world line, from beginning. The quantum field operators and the particles are assigned to the point of the QSTM in Planck scale and in consequence, the physical theories are background dependent at the scale.

MINKOWSKI defined the four-dimensional spacetime model (x, y, z, t) used to represent world-point and world in [1]. The spacetime light cone is an intuitive diagram, compacted one space component and replaced it by time axis, thus the spacetime light cone was based on (x, y, t). In such a way, although it made the visual expression is possible, but also the spacetime light cone exposed shortages as follows • The spacetime light cone has limited expressive ability • The relationship between two or more world lines or events cannot be expressed • Can't express different world lines correctly • Most images of spacetime light cones are wrong and no use • The image of spacetime light cone is not intuitive and is obscure in application. Because of this, we designed the 4-dimensional Spacetime World Line image representation. This new 4-dimensional Spacetime diagram presents the complete 3 space dimensions and 1 time dimension. It overcomes the weakness of spacetime light cone, gives clear and precise visual expression of the world line, is able to display multi-world lines in one figure, can clearly present the interface and development process of each of the world line, and display the interaction among them. From the 4-dimensional spacetime diagram, we deducted and proved the Law of Existence of Object, which is as such: From its birth, through its past, to the present, and into the future, an object only exists at the "present" moment.

It is well known that observers will be accelerated when they approach the planets. Thus, discussing the properties of accelerating observers in the Schwarzschild space is meaningful. For the sake of simplicity, we can construct these observers' world lines by comparing with the observers in the Hawking effect and Unruh effect, whose world lines are both hyperbolic curves in the appropriate coordinates. We do it after defining a certain special null hypersurface in the Kruskal coordinates. Our result shows that these accelerating observers defined in our paper can also detect the radiation with the analogy of the Unruh effect, though locally. Furthermore, we conjecture that, for any null hypersurface in any spacetime, the corresponding observers who can at least locally detect the radiation from it can be found.

Local and global error estimations in linear structural dynamics

Mean field approximation of IIB matrix model and emergence of four-dimensional space–time

Motivated by string-theoretic swampland conjectures, the existence of a dark fifth dimension, whose size is roughly 1–10 microns, has been proposed. A great deal of supporting evidence has been presented, and definitive experimental tests are likely to be carried out. The basic idea is that the four-dimensional space–time that we observe is confined to a brane that is localized in the dark dimension. This short note points out that there are two distinct ways to realize such a scenario in string theory/M-theory. In the one considered previously, the dark dimension is topologically a circle and our observable 4d space–time is confined to a brane that is localized in a GUT-scale region of the circle. An alternative possibility is that the dark dimension is a line interval with “end-of-the-world-branes” at each end. The latter option would imply the existence of a parallel 4d space–time, with the same gravitational forces as ours, but otherwise its own physical laws, microns away from us!

Gazetteers, i.e., lists of place-names, enable having a global vision of places of interest through the assignment of a point, or a region, to a place name. However, such identification of the location corresponding to a place name is often a difficult task. There is no one-to-one correspondence between the two sets, places and names, because of name variants, different names for the same place and homonymy; the location corresponding to a place name may vary in time, changing its extension or even the position; and, in general, there is the imprecision deriving from the association of a concept belonging to language (the place name) to a precise concept (the spatial location). Also for named time periods, e.g., early Bronze Age, which are of current use in archaeology, the situation is similar: they depend on the location to which they refer as the same period may have different time-spans in different locations. The present paper avails of a recent extension of the CIDOC CRM called CRMgeo, which embeds events in a spatio-temporal 4-dimensional framework. The paper uses concepts from CRMgeo and introduces extensions to model gazetteers and period thesauri. This approach enables dealing with time-varying location appellations as well as with space-varying period appellations on a robust basis. For this purpose a refinement/extension of CRMgeo is proposed and a discretization of space and time is used to approximate real space---time extents occupied by events. Such an approach solves the problem and suggests further investigations in various directions.