Delay equations and radiation damping

Chicone, Carmen; Kopeikin, Sergei M.; Mashhoon, Bahram; Retzloff, David G.

doi:10.1016/s0375-9601(01)00327-9

Cited by 28 publications

(29 citation statements)

References 27 publications

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“…It is important to stand out that what we will carry out in the following section is not a post-Newtonian approach in which τ is small. This is what has been made up to now and in the mentioned works [3,4,5,6]. In this work, we will accept that the laws governing the movement have a delay (a delay that does not need to be small) and we will find a solution of the functional differential equation in a very simple case.…”

Section: Discussionmentioning

confidence: 73%

On the origin of the gravitational quantization: The Titius–Bode law

Giné

2007

Chaos, Solitons & Fractals

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Abstract. Action at distance in Newtonian physics is replaced by finite propagation speeds in classical post-Newtonian physics. As a result, the differential equations of motion in Newtonian physics are replaced by functional differential equations, where the delay associated with the finite propagation speed is taken into account. Newtonian equations of motion, with post-Newtonian corrections, are often used to approximate the functional differential equations. In [8] a simple atomic model based on a functional differential equation which reproduces the quantized Bohr atomic model was presented. The unique assumption was that the electrodynamic interaction has finite propagation speed. Are the finite propagation speeds also the origin of the gravitational quantization? In this work a simple gravitational model based on a functional differential equation gives an explanation of the modified Titius-Bode law.

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Section: Discussionmentioning

confidence: 73%

On the origin of the gravitational quantization: The Titius–Bode law

Giné

2007

Chaos, Solitons & Fractals

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“…It is important to stand out that what we will carry out in the following section is not a postNewtonian approach in which τ is small. This is what has been made up to now and in the mentioned works [3,4,5,6]. From now on, we will accept that the laws governing the movement have a delay (a delay that does not need to be small) and we will find a solution of the functional differential equation in a very simple case.…”

mentioning

confidence: 70%

“…In 1913 Bohr [1] introduced the quantization of the angular momentum of the form L = nh/(2π) where h is the Planck constant. If we accurately study equation (5) we see that the analytic function sin(ωτ ) has a numerable number of zeros given by (6) ωτ = kπ , with k ∈ Z, which are stationary orbits of the system of equations (3) and (4). When ωτ = kπ we have a torque which conduces the electron to the stationary orbits without torque, that is, with ωτ = kπ.…”

Section: The Retarded Electrodynamic 2-body Problemmentioning

confidence: 99%

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On the origin of quantum mechanics

Giné

2006

Chaos, Solitons & Fractals

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Abstract. Action at distance in Newtonian physics is replaced by finite propagation speeds in classical post-Newtonian physics. As a result, the differential equations of motion in Newtonian physics are replaced by functional differential equations, where the delay associated with the finite propagation speed is taken into account. Newtonian equations of motion, with post-Newtonian corrections, are often used to approximate the functional differential equations. Are the finite propagation speeds the origin of the quantum mechanics? In this work a simple atomic model based on a functional differential equation which reproduces the quantized Bohr atomic model is presented. As straightforward application of the result the fine structure of the hydrogen atom is approached.

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“…While there are many proposals for the removal of runaway solutions, recent work [2][3][4][5]20] shows that, at a fundamental level, runaways are spurious artifacts of the expansion and truncation of power series; they have no physical meaning. Moreover, the correct method for the removal of runaways is reduction to a slow manifold via geometric singular perturbation theory.…”

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confidence: 99%

The field theory two-body problem in acoustics

Chicone

Heitzman

2008

Gen Relativ Gravit

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We address the problem of determining effective equations of motion for sources in field theories, where finite propagation speeds lead to radiation reaction and runaway solutions. Acoustics is used to illustrate a solution of this problem: The effective equation of motion is obtained by reduction to an inertial manifold. This equation can be approximated to any desired accuracy by expansion (and truncation) in powers of the reciprocal of the wave propagation speed and reduction to a slow manifold of a singular perturbation problem.

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Delay equations and radiation damping

Cited by 28 publications

References 27 publications

On the origin of the gravitational quantization: The Titius–Bode law

On the origin of the gravitational quantization: The Titius–Bode law

On the origin of quantum mechanics

The field theory two-body problem in acoustics

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