Dynamic properties of almost monochromatic standing waves

Elbaz, C

doi:10.3233/asy-2010-0985

Cited by 4 publications

(3 citation statements)

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“…We restrict to summarize some equations for the properties of the c-scalar field, according to Einstein's program, previously published, (Elbaz, 2010(Elbaz, , 2012(Elbaz, , 2013(Elbaz, , 2014, in order to show how they are related to some main equations of classical and quantum mechanics, otherwise widely documented.…”

Section: Properties Of the C-scalar Fieldmentioning

confidence: 99%

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Incompleteness of General Relativity Regarding Einstein's Program

Elbaz¹

2018

APR

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The detection of gravitational waves substantiates the undeniable achievement of general relativity theory by increasing its theoretical and experimental accuracy. One century after predicting it has set again Einstein's works at the front of research. Absence of quantum particle associated to gravitation emphasizes that general relativity theory remains not included in the standard model of physics. Then Einstein’s disagreement about it incompleteness regarding wave-particle and matter-field becomes actualized. In order to circumvent these difficulties he privileged field, rather than matter for universe description in his program. In consequence a scalar field e(r0,t0) propagating at speed of light c yields matter from standing waves moving at speed strictly inferior to c, and interactions from progressive waves. Electromagnetic interactions derive from local variations of frequencies, and gravitation from local variations of speed of light. A space-like amplitude functions u0(k0r0) supplements fundamental time-like functions of classical and quantum mechanics. It tends toward Dirac’s distribution Delta (r0) in geometrical optics approximation conditions, when frequencies are infinitely high, and then hidden. More generally, it allows theoretical economies by deriving energy-momentum conservation laws, and least action law. Quantum domain corresponds to wave optics approximation conditions. Variations of frequencies give rise to an adiabatic constant, formally identical with Planck's constant, leading to first quantification for electromagnetic interactions and to second quantification for matter.

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Section: Properties Of the C-scalar Fieldmentioning

confidence: 99%

“…They lead to dynamical properties for energy-momentum conservation, and to least action, principles, for standing fields and for almost standing fields (Elbaz, 1984(Elbaz, , 2010(Elbaz, , 2014.…”

Section: Dynamical Properties Of Standing Fieldsmentioning

confidence: 99%

Incompleteness of General Relativity Regarding Einstein's Program

Elbaz¹

2018

APR

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“…полученной на основе u(x, ct) с помощью преобразований Лоренца. Де Бройль в работе[2] рассматривал волны типа U в связи с выяснением природы введенной им ранее фазовой волны exp [ikγ(ct − βx)].…”

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Illustration of the Relativity Principle Using a Double Breather

Goncharov¹

2021

Известия АлтГУ

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The purpose of this article is to give more clarity to some relativistic laws, primarily the principle of relativity.These laws have been illustrated using linear waves in several of our previous articles. In this work, solutions of the nonlinear sine-Gordon equation in the form of double breathers are used for the same purposes. The exact two-breather solution and the approximate one that is convenient for analysis are presented. Moving breathers are derived from standing breathers through the active Lorenz transformations. Oscillations in a moving breather become out of phase. For each system, the distance between the amplitude maxima is taken as a unit length, and the oscillation period is taken as a time interval unit. It is shown that the observer associated with a moving breather and an observer associated with a standing breather see the same picture; an observer cannot distinguish the state of movement of his breather from rest. Therefore, in a frame of reference based on a moving breather, its oscillations are considered in-phase. In this case, time is determined as if the clocks were synchronized according to the Einstein method.Space-time coordinates of the same event in different frames of reference turn out to be related by the passive Lorentz transformations.

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