Spacetime Geometry

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Coordinate System ◽  
Special Relativity ◽  
Displacement Vector ◽  
Proper Time ◽  
Plane Geometry ◽  
Spatial Displacement ◽  
Spacetime Geometry ◽  
Space And Time ◽  
Displacement Vectors

This chapter shows that the counterintuitive aspects of special relativity are due to the geometry of spacetime. We begin by showing, in the familiar context of plane geometry, how a metric equation separates frame‐dependent quantities from invariant ones. The components of a displacement vector depend on the coordinate system you choose, but its magnitude (the distance between two points, which is more physically meaningful) is invariant. Similarly, space and time components of a spacetime displacement are frame‐dependent, but the magnitude (proper time) is invariant and more physically meaningful. In plane geometry displacements in both x and y contribute positively to the distance, but in spacetime geometry the spatial displacement contributes negatively to the proper time. This is the source of counterintuitive aspects of special relativity. We develop spacetime intuition by practicing with a graphic stretching‐triangle representation of spacetime displacement vectors.

Perfecting the methods of monitoring the buildings and structures deformation

2020 ◽  
Vol 958 (4) ◽  
pp. 9-18
Author(s):  
Yu.N. Kornilov ◽  
O.S. Tsareva
Keyword(s):  
Coordinate System ◽  
Displacement Vector ◽  
Field Work ◽  
Relevant Information ◽  
Application Point ◽  
Displacement Vectors

The authors present the peculiarities of evaluating the parameters (module, direction and coordinates of the application point) of the displacement vector of the object’s deformation mark, its stabilitydegree is to be evaluated, and on this basis technologies simplifying the processes of performing field work necessary to obtain relevant information are discussed. Various options to implementpolar spatial intersection during observations from fixed stations are considered. In particular, if there aren’t any connecting marks between the instrument’s standing points, it is proposed to use a remote target or measure directional angles (magnetic azimuths) of reference directions. Methods for obtaining the coordinates and displacement vectors of deformation marks in the same coordinate system are considered, depending on the implementation of the polar spatial intersection. An example of implementing the proposed observation methodology on the example of the Hydrocorpus-1 building located at 29 Polytechnicheskaya st., St. Petersburg, Russia is presented. The results obtained indicate the correctness of the proposed methodology.

scholarly journals Testing Lorentz symmetry violation with an invariant minimum speed

2018 ◽  
Vol 33 (23) ◽  
pp. 1850148 ◽  
Author(s):  
Cláudio Nassif ◽  
A. C. Amaro de Faria ◽  
Rodrigo Francisco dos Santos
Keyword(s):  
Decay Rate ◽  
Special Relativity ◽  
Proper Time ◽  
Lorentz Invariance ◽  
Atomic Clock ◽  
Life Time ◽  
Single Atom ◽  
Symmetry Violation ◽  
Minimum Speed ◽  
Radioactive Sample

This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e.g. isotope Na[Formula: see text]) is a thermometer for an ultracold gas like the dipolar gas Na[Formula: see text]K[Formula: see text]. So, according to a Deformed Special Relativity (DSR) so-called Symmetrical Special Relativity (SSR), where there emerges an invariant minimum speed V in the subatomic world, one expects that the proper time of such a clock moving close to V in thermal equilibrium with the ultracold gas is dilated with respect to the improper time given in lab, i.e. the proper time at ultracold systems elapses faster than the improper one for an observer in the lab, thus leading to the so-called proper time dilation so that the atomic decay rate of an ultracold radioactive sample (e.g. Na[Formula: see text]) becomes larger than the decay rate of the same sample at room temperature. This means a suppression of the half-life time of a radioactive sample thermalized with an ultracold cloud of dipolar gas to be investigated by NASA in the Cold Atom Lab (CAL).

scholarly journals Ontology of a Wavefunction from the Perspective of an Invariant Proper Time

2021 ◽  
Author(s):  
Salim Yasmineh
Keyword(s):  
Quantum Mechanics ◽  
Special Relativity ◽  
Proper Time ◽  
Finite Density ◽  
Confining Potential ◽  
Standard Time ◽  
Related Matter ◽  
Local Mechanism ◽  
Non Local ◽  
The Individual

All the arguments of a wavefunction are defined at the same instant implying a notion of simultaneity. In a somewhat related matter, certain phenomena in quantum mechanics seem to have non-local causal relations. Both concepts are in contradiction with special relativity. We propose to define the wavefunction with respect to the invariant proper time of special relativity instead of standard time. Moreover, we shall adopt the original idea of Schrodinger suggesting that the wavefunction represents an ontological cloud-like object that we shall call ‘individual fabric’ that has a finite density amplitude vanishing at infinity. Consequently, measurement can be assimilated to a confining potential that triggers an inherent non-local mechanism within the individual fabric. It is formalised by multiplying the wavefunction with a localising gaussian as in the GRW theory but in a deterministic manner.

DETECTION OF MOVING OBJECT USING REMAINED BACKGROUND UNDER MOVING CAMERA

2007 ◽  
Vol 04 (03) ◽  
pp. 227-236 ◽  
Author(s):  
TAEHO KIM ◽  
KANG-HYUN JO
Keyword(s):  
Correlation Coefficient ◽  
Moving Objects ◽  
Displacement Vector ◽  
Image Sequence ◽  
Moving Object ◽  
Pixel Intensity ◽  
Current Image ◽  
Moving Camera ◽  
Lower Weight ◽  
Displacement Vectors

A background is a part that does not vary too much or change frequently in an image sequence. Using this assumption, an algorithm of reconstructing remained background and detecting moving objects for static and also moving camera is presented. For generating background, we detect regions that have high correlation coefficient compared within prior pyramid images from the current image. These detected regions are used for two process. First, we calculate the temporal displacement vector of each detected regions and classify clusters of pixel intensity based on camera movement. Second, we calculate temporally principal displacement vector using histogram of displacement vectors. Temporally principal displacement vector indicates camera movement. Finally we eliminate clusters which have lower weight than threshold, and combine remained clusters for each pixel to generate multiple background clusters. Experimental results show that remained background model and detected moving object under camera moving.

Determination of displacement vector on 180° domain boundary and polarization arrangements in lead titanate crystals

1997 ◽  
Vol 12 (2) ◽  
pp. 457-466 ◽  
Author(s):  
Chen-Chia Chou ◽  
C. Marvin Wayman
Keyword(s):  
Lead Titanate ◽  
Displacement Vector ◽  
Domain Boundary ◽  
Polarization Vector ◽  
Dynamical Theory ◽  
Fringe Contrast ◽  
Displacement Vectors ◽  
Domain Boundaries ◽  
Contrast Analysis ◽  
Diffraction Patterns

180° domain boundaries in flux-grown lead titanate single crystals show intriguing domain boundary extreme fringe contrast using transmission electron microscopy. Symmetrically distributed domain boundaries with alternate contrast have been observed, indicating that opposite displacement vectors exist one by one at boundaries. If appropriate reflection vectors were employed, an inclined domain boundary shows reversed fringe contrast. An analysis based upon the two-beam dynamical theory and a rule similar to stacking-fault contrast analysis was employed to predict the geometric configuration of a 180° domain boundary using the extreme fringe contrast (EFC) behavior. Appropriately choosing reflection vectors and utilizing the EFC reversal, a displacement vector as well as the polarization vector arrangement across a 180° domain boundary can be unambiguously identified. Employing the information derived from diffraction patterns and a tilting experiment across a nearby 90° boundary, the whole polarization configuration can be uniquely determined.

A REVIEW OF EINSTEIN'S THEORY OF SPECIAL RELATIVITY

2006 ◽  
Vol 15 (03) ◽  
pp. 755-760
Author(s):  
GERALD MOTT
Keyword(s):  
Special Relativity ◽  
Thought Experiment ◽  
Point Sources ◽  
Space And Time ◽  
Time Contraction

Using only the descriptions and the results of the 'thought experiment' contained in Einstein's seminal 1905 paper, proofs are offered which show that the transformation equations of Einstein's special relativity apply only to the joint use in his experiment of point sources of light and point reflectors. Further, it is shown that two different special relativities could have been invented by Einstein and, because they possess differing space and time contraction factors, they cannot co-exist and, therefore, both must be discarded.

Stacking faults in magnetite from the Allende meteorite

1992 ◽  
Vol 200 (3-4) ◽  
Author(s):  
Wolfgang Friedrich Müller ◽  
Gerhild Müller-Beneke
Keyword(s):  
Fault Plane ◽  
Displacement Vector ◽  
Stacking Faults ◽  
Stacking Fault ◽  
Cation Sublattice ◽  
Triple Junctions ◽  
Lattice Vector ◽  
Displacement Vectors

AbstractStacking faults of the type 1/4 〈110〉 {110} have been observed in magnetic crystals of a chondrule from the meteorite Allende. A stacking fault assemblage of all six possible orientations of the faults has been analysed in detail. The displacement vector 1/4 〈110〉 is always perpendicular to the corresponding fault plane {110}. It is shown that other orientations of fault planes would lead to unallowed short distances between closely neighboured cations. Three fault planes may meet in triple-junctions, their three displacement vectors adding up to a lattice vector. The stacking faults affect only the cation sublattice and form probably during growth of the magnetite crystals.

scholarly journals What do light clocks say to us regarding the so-called clock hypothesis?

2018 ◽  
Vol 33 (3) ◽  
pp. 435
Author(s):  
Mario Bacelar Valente
Keyword(s):  
Special Relativity ◽  
Physical System ◽  
Proper Time ◽  
Arbitrary Degree ◽  
The Status ◽  
Time Reading ◽  
Clock Hypothesis

The clock hypothesis is taken to be an assumption independent of special relativity necessary to describe accelerated clocks. This enables to equate the time read off by a clock to the proper time. Here, it is considered a physical system–the light clock–proposed by Marzke and Wheeler. Recently, Fletcher proved a theorem that shows that a sufficiently small light clock has a time reading that approximates to an arbitrary degree the proper time. The clock hypothesis is not necessary to arrive at this result. Here, one explores the consequences of this regarding the status of the clock hypothesis.

Minkowski spacetime

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Euclidean Space ◽  
Special Relativity ◽  
Three Dimensional ◽  
Minkowski Spacetime ◽  
Dimensional Euclidean Space ◽  
Fourth Dimension ◽  
Relativistic Dynamics ◽  
Newtonian Theory ◽  
Space And Time ◽  
Set Of Points

This chapter presents the main features of the Minkowski spacetime, which is the geometrical framework in which the laws of relativistic dynamics are formulated. It is a very simple mathematical extension of three-dimensional Euclidean space. In special relativity, ‘relative, apparent, and common’ (in the words of Newton) space and time are represented by a mathematical set of points called events, which constitute the Minkowski spacetime. This chapter also stresses the interpretation of the fourth dimension, which in special relativity is time. Here, time now loses the ‘universal’ and ‘absolute’ nature that it had in the Newtonian theory.

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