scholarly journals On null geodesically complete spacetimes under NEC and NGC: Is the Gao‐Wald “time dilation” a topological effect?

2019 ◽  
Vol 43 (2) ◽  
pp. 747-749
Author(s):  
Kyriakos Papadopoulos
Keyword(s):  
Time Dilation ◽  
Topological Effect ◽  
Geodesically Complete

The Equivalence Principle

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Equivalence Principle ◽  
Time Dilation ◽  
Gravitational Redshift ◽  
Coordinate Systems ◽  
Spacetime Metric

The equivalence principle is an important thinking tool to bootstrap our thinking from the inertial coordinate systems of special relativity to the more complex coordinate systems that must be used in the presence of gravity (general relativity). The equivalence principle posits that at a given event gravity accelerates everything equally, so gravity is equivalent to an accelerating coordinate system.This conjecture is well supported by precise experiments, so we explore the consequences in depth: gravity curves the trajectory of light as it does other projectiles; the effects of gravity disappear in a freely falling laboratory; and gravitymakes time runmore slowly in the basement than in the attic—a gravitational form of time dilation. We show how this is observable via gravitational redshift. Subsequent chapters will build on this to show how the spacetime metric varies with location.

Energy and Momentum

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Time Dilation ◽  
Speed Of Light ◽  
Massless Particles ◽  
The Everyday ◽  
Low Speeds ◽  
Energy And Momentum ◽  
Deep Relationship ◽  
Insight Into ◽  
Momentum Relation

Tis chapter explains the famous equation E = mc2 as part of a wider relationship between energy, mass, and momentum. We start by defning energy and momentum in the everyday sense. We then build on the stretching‐triangle picture of spacetime vectors developed in Chapter 11 to see how energy, mass, and momentum have a deep relationship that is not obvious at everyday low speeds. When momentum is zero (a mass is at rest) this energy‐momentum relation simplifes to E = mc2, which implies that mass at rest quietly stores tremendous amounts of energy. Te energymomentum relation also implies that traveling near the speed of light (e.g., to take advantage of time dilation for interstellar journeys) will require tremendous amounts of energy. Finally, we look at the simplifed form of the energy‐momentum relation when the mass is zero. Tis gives us insight into the behavior of massless particles such as the photon.

scholarly journals Time Dilation and Contraction for Programmable Analog Devices with Jaunt

2018 ◽  
Vol 53 (2) ◽  
pp. 229-242
Author(s):  
Sara Achour ◽  
Martin Rinard
Keyword(s):  
Time Dilation ◽  
Programmable Analog

scholarly journals Utilizing relativistic time dilation for time-resolved studies

2021 ◽  
Vol 154 (11) ◽  
pp. 111107
Author(s):  
Hazem Daoud ◽  
R. J. Dwayne Miller
Keyword(s):  
Time Dilation ◽  
Time Resolved ◽  
Relativistic Time

scholarly journals Quantum time dilation in atomic spectra

2021 ◽  
Vol 3 (2) ◽  
Author(s):  
Piotr T. Grochowski ◽  
Alexander R. H. Smith ◽  
Andrzej Dragan ◽  
Kacper Dębski
Keyword(s):  
Time Dilation ◽  
Atomic Spectra ◽  
Quantum Time

Topological Effect on Macromonomer Polymerization

2021 ◽  
Author(s):  
Ning Ren ◽  
Chunyang Yu ◽  
Xinyuan Zhu
Keyword(s):  
Topological Effect

scholarly journals Topological Effect on MO Energies, IX. On Topologically Related 1,4-Dibora-2,3-diazarine and 1,4-Dibora-2,5-diazarine

1984 ◽  
Vol 39 (8) ◽  
pp. 1053-1057 ◽  
Author(s):  
loan Motoc ◽  
Oskar E. Polansky
Keyword(s):  
Basis Set ◽  
Complete Agreement ◽  
Mo Calculations ◽  
Symmetry Constraint ◽  
Topological Effect ◽  
Equilibrium Geometries

AbstractMinimal STO-NG (N = 3, 4 and 6 ) basis set non-empirical HF SCF MO calculations have been performed for topologically related 1,4-dibora-2,3-diazarine (S) and 1,4-dibora-2,5-diazarine (T). The equilibrium geometries of these S and T isomers have been computed by symmetry-constraint geometry optimizations using the STO-3G basis set. The calculations lead to the prediction that: i) the T isomer is about 48 kJ/mole less stable than the S isomer, and ii) the π -MO energy patterns of the S and T isomers are in complete agreement with the TEMO theorem, while the bonding σ-MO eigenvalues exhibit four inversion points.

scholarly journals Flat strips, Bowen–Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces

2015 ◽  
Vol 37 (3) ◽  
pp. 939-970 ◽  
Author(s):  
RUSSELL RICKS
Keyword(s):  
Geodesic Flow ◽  
Isometric Action ◽  
Structural Result ◽  
Curved Manifolds ◽  
Rank One ◽  
Unit Speed ◽  
Flat Strip ◽  
Geodesically Complete ◽  
Positively Curved ◽  
General Technical

Let$X$be a proper, geodesically complete CAT($0$) space under a proper, non-elementary, isometric action by a group$\unicode[STIX]{x1D6E4}$with a rank one element. We construct a generalized Bowen–Margulis measure on the space of unit-speed parametrized geodesics of$X$modulo the$\unicode[STIX]{x1D6E4}$-action. Although the construction of Bowen–Margulis measures for rank one non-positively curved manifolds and for CAT($-1$) spaces is well known, the construction for CAT($0$) spaces hinges on establishing a new structural result of independent interest: almost no geodesic, under the Bowen–Margulis measure, bounds a flat strip of any positive width. We also show that almost every point in$\unicode[STIX]{x2202}_{\infty }X$, under the Patterson–Sullivan measure, is isolated in the Tits metric. (For these results we assume the Bowen–Margulis measure is finite, as it is in the cocompact case.) Finally, we precisely characterize mixing when$X$has full limit set: a finite Bowen–Margulis measure is not mixing under the geodesic flow precisely when$X$is a tree with all edge lengths in$c\mathbb{Z}$for some$c>0$. This characterization is new, even in the setting of CAT($-1$) spaces. More general (technical) versions of these results are also stated in the paper.

scholarly journals KINKS, ENERGY CONDITIONS AND CLOSED TIMELIKE CURVES

2000 ◽  
Vol 09 (05) ◽  
pp. 531-541 ◽  
Author(s):  
PEDRO F. GONZÁLEZ-DÍAZ
Keyword(s):  
Energy Condition ◽  
Weak Energy Condition ◽  
Energy Conditions ◽  
Closed Timelike Curves ◽  
Causality Violation ◽  
Incoherent Radiation ◽  
Cylindrically Symmetric ◽  
Cylindrically Symmetric Spacetime ◽  
Geodesically Complete ◽  
Symmetric Spacetime

A link between the possibility of extending a geodesically incomplete kinked spacetime to a spacetime which is geodesically complete and the energy conditions is discussed for the case of a cylindrically-symmetric spacetime kink. It is concluded that neither the strong nor the weak energy condition can be satisfied in the four-dimensional example, though the latter condition may survive on the transversal sections of such a spacetime. It is also shown that the matter which propagates quantum-mechanically in a kinked spacetime can always be trapped by closed timelike curves, but signaling connections between that matter and any possible observer can only be made of totally incoherent radiation, so preventing observation of causality violation.

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