scholarly journals Demonstration of time dilation using the centripetal acceleration of a clock

2020 ◽  
Author(s):  
Andrea Conte
Keyword(s):  
Equivalent Form ◽  
Lorentz Factor ◽  
Time Dilation ◽  
Centripetal Acceleration ◽  
Inverse Form ◽  
Mathematical Demonstration

A mathematical demonstration is made to derive the inverse form of the Lorentz factor using as a tool the centripetal acceleration of a clock hand. When a resistance is applied against the motion of a clock hand, the centripetal acceleration decreases. The ratio between the final centripetal acceleration of the clock hand and its initial centripetal acceleration gives a ratio between two squared velocities. By squaring root this ratio, we obtain the equivalent form of the inverted Lorentz factor.

scholarly journals Combination of time dilation and gravitational time dilation

2020 ◽  
Author(s):  
Andrea Conte
Keyword(s):  
Lorentz Factor ◽  
Time Dilation ◽  
Energy Ratio ◽  
Gravitational Attraction ◽  
Ratio Equation ◽  
Dilation Equation ◽  
Principle Of Relativity ◽  
Dilation Equations

In compliance with the principle of relativity, a time dilation equation expressed as an energy ratio is used to combine time dilation due to motion and due to gravitational attraction. To show the correlation with the time dilation equations, the Lorentz factor and the gravitational time dilation equations are derived from the equation. The equivalence between the time dilation due to motion and due to gravitational attraction emerges and a combination of both is made possible using the energy ratio equation.

scholarly journals Calculating time dilation using Euler’s formula

2020 ◽  
Author(s):  
Andrea Conte
Keyword(s):  
Imaginary Part ◽  
Complex Number ◽  
Lorentz Factor ◽  
Time Dilation ◽  
Gravitational Attraction ◽  
Speed Of Light ◽  
The Real ◽  
Euler’S Formula

This paper shows how the time dilation due to motion, calculated normally using the Lorentz factor, can be encoded in the real part of a complex number by using the Euler's formula. The imaginary part of this complex number will contain the velocity. It also shows how the time dilation due to gravitational attraction can be encoded using the same formula. A combination of time dilation and gravitational time dilation is presented using this formula. The magnitude of this complex number represents the constancy of the speed of light.

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 A reverse Hardy–Hilbert-type integral inequality involving one derivative function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Qian Chen ◽  
Bicheng Yang
Keyword(s):  
Integral Inequality ◽  
Beta Function ◽  
Equivalent Form ◽  
Constant Factor ◽  
Weight Functions ◽  
Derivative Function ◽  
The Best Possible Constant ◽  
Type Integral ◽  
Hilbert Type ◽  
Hilbert Integral

AbstractIn this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

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
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