Electric and Magnetic Potentials of Uniformly Accelerated Charge Distributions

1997 ◽  
Vol 52 (12) ◽  
pp. 843-848
Author(s):  
Pierre Hillion
Keyword(s):  
Inertial Frame ◽  
Present Position ◽  
Charge Distributions ◽  
Stationary Charge ◽  
The Difference ◽  
Magnetic Potentials ◽  
Accelerated Charge

Jefimenko gave recently [1] new expressions for the electric and magnetic potentials of uniformly moving, time-independent charge distributions. We discuss these potentials for uniformly accelerated distributions. As Jefimenko did. we implement two procedures either converting directly retarded into present position integrals or using relativistic transformations for a stationary charge in an instantaneous comoving inertial frame (Frenet-Serret tetrad). We discuss why, at the difference of what happens for uniform motions [1], both procedures provide different expressions for potentials.

MADELUNG ENERGY AND STABILITY OF ORDERED LATTICE IN A(B′B″)O3

1991 ◽  
Vol 05 (27) ◽  
pp. 1803-1807
Author(s):  
QIANG WANG ◽  
HAN RUSHAN ◽  
Z.Z. GAN
Keyword(s):  
Charge Distribution ◽  
Structural Stability ◽  
Ionic Crystal ◽  
Ordered Structure ◽  
Charge Distributions ◽  
Madelung Energy ◽  
Calculation Results ◽  
The Difference ◽  
Good Agreement

The Madelung energies of ionic crystal A(B′B″)O3 has been calculated for various B-site charge distributions, i.e., [Formula: see text], [Formula: see text] and [Formula: see text], and ordered superlattices, i.e., 1/2(111), 1/2(110) and 1/2(001). Calculation results show that the Madelung energy increases for a certain ordered structure as the difference in charge between B-site cations increases and demonstrate the experimental observations. Furthermore, the results point out that for a certain charge distribution the sequence of the structural stability is 1/2(001)<1/2(110)<1/2(111). This is in good agreement with experimental facts.

scholarly journals Discrepancy between Power Radiated and the Power Loss Due to Radiation Reaction for an Accelerated Charge

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1833
Author(s):  
Ashok K. Singal
Keyword(s):  
Power Loss ◽  
Radiation Reaction ◽  
The Self ◽  
Constant Acceleration ◽  
Retarded Time ◽  
Poynting Flux ◽  
Radiated Power ◽  
Electromagnetic Power ◽  
The Difference ◽  
Accelerated Charge

We examine here the discrepancy between the radiated power, calculated from the Poynting flux at infinity, and the power loss due to radiation reaction for an accelerated charge. It is emphasized that one needs to maintain a clear distinction between the electromagnetic power received by distant observers and the mechanical power loss undergone by the charge. In the literature, both quantities are treated as almost synonymous; the two in general could, however, be quite different. It is shown that in the case of a periodic motion, the two formulations do yield the power loss in a time averaged sense to be the same, even though, the instantaneous rates are quite different. It is demonstrated that the discordance between the two power formulas merely reflects the difference in the power going in self-fields of the charge between the retarded and present times. In particular, in the case of a uniformly accelerated charge, power going into the self-fields at the present time is equal to the power that was going into the self-fields at the retarded time plus the power going in acceleration fields, usually called radiation. From a study of the fields in regions far off from the time retarded positions of the uniformly accelerated charge, it is shown that effectively the fields, including the acceleration fields, remain around the ‘present’ position of the charge which itself is moving toward infinity due to its continuous constant acceleration, with no other Poynting flow that could be termed as ‘radiation emitted’ by the charge.

scholarly journals Gravity, Entanglement and Spin Possible Timeless State of the Universe

2020 ◽  
Author(s):  
Ahmed Farag Ali
Keyword(s):  
Quantum Mechanics ◽  
Quantum Entanglement ◽  
Inertial Frame ◽  
Quantum Particle ◽  
Black Hole Entropy ◽  
Geometric Interpretation ◽  
Speed Of Light ◽  
Problem Of Time ◽  
The Difference ◽  
The Universe

I localize gravity to match its measurements with the local inertial frame of special relativity. I find a geometric interpretation of the speed of light and mass. I find also a relation between every mass measured and the black hole entropy which introduces information-matter equation from gravity. Through localization of gravity, a timeless state of the universe emerges and the uncertainty principle does not hold since the velocity concept is replaced by distance in this timeless state. This would resolve the problem of time because timeless state of the universe emerges naturally and mathematically consistent. This would suggest that gravity form the hidden one variable of quantum mechanics which would complete the relation between quantum mechanics and gravity. The experimental evidence of timeless state of the universe is the quantum entanglement. Since the spin measurement is the manifestation of quantum entanglement. Therefore, the spin of quantum particle can be originated from geometrical or gravitational red-shift. We introduce also a principle of least computation which is achieved when the ratio equal to the difference in the process of local gravitational measurements.

An Iterative Kalman Filter for a 3D Ultrasonic Position Estimation System

2007 ◽  
Author(s):  
Sanjeevi Chitikeshi ◽  
Ajay Mahajan ◽  
Jennifer Akers
Keyword(s):  
Kalman Filter ◽  
Inertial Frame ◽  
Position Estimation ◽  
Image Guided Surgery ◽  
Guided Surgery ◽  
Image Guided ◽  
Multiple Receivers ◽  
The Difference ◽  
Estimation System ◽  
Increase In Accuracy

This paper describes an iterative Kalman Filter to increase the accuracy of a dynamic 3D position estimation system. The novelty of the system lies in the fact that a difference in the time of arrivals is used in conjunction with an estimated speed of sound within the system formulation, and the Kalman Filter is used to further increase the accuracy and robustness of the output. The output is a 3D position of the transmitter obtained from the difference in time of arrivals of the wave burst at multiple receivers fixed within an inertial frame. Results are provided to show the increase in accuracy and robustness along with some limitations of the system. The system has many applications the most significant being image guided surgery.

The Great Ellipse Solution for Distances and Headings to Steer between Waypoints

1999 ◽  
Vol 52 (3) ◽  
pp. 421-424 ◽  
Author(s):  
P. R. Walwyn
Keyword(s):  
Circle Method ◽  
Major Axis ◽  
Great Circle ◽  
Minor Axis ◽  
Geodesic Curve ◽  
Present Position ◽  
The Earth ◽  
Shortest Distance ◽  
The Difference ◽  
A Minor

The normal Great Circle method of computing the shortest distance between two positions on the Earth – e.g. from an aircraft's present position (PP) to a waypoint (WP) – is not accurate enough to meet present-day requirements for aircraft Nav–Attack systems.On the surface of an Ellipsoid (or Spheroid), the true ‘shortest distance’ is along a geodesic curve between the two points, but the computation of this curve is complex, and as shown by R. Williams at Reference, the difference between the geodesic and Great Ellipse distances between two points is negligible (<0·01 nm).The Great Ellipse through two points on a spheroid is defined as the ellipse that passes through the two points and the centre of the spheroid; it therefore has a major axis equal to the Earth's, and a minor axis that is between the Earth's major axis (for two points on the Equator) and minor axis (for two points on the same, or diametrically opposite, longitudes). Thus the problem of deciding on which Great Ellipse the two points lie is equivalent to determining the magnitude of the minor axis β of the ellipse on which they both lie.

scholarly journals Radiation reaction from quantum electrodynamics and its implications for the Unruh effect

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
Zoltán Tulipánt
Keyword(s):  
Thermal Radiation ◽  
Quantum Electrodynamics ◽  
Inertial Frame ◽  
Radiation Reaction ◽  
Stimulated Emission ◽  
Unruh Effect ◽  
Dirac Theory ◽  
Accelerated Charge

AbstractThe Abraham–Lorentz–Dirac theory predicts vanishing radiation reaction for uniformly accelerated charges. However, since an accelerating observer should detect thermal radiation, the charge should be seen absorbing photons in the accelerated frame which, if nothing else occurs, would influence its motion. This means that either there is radiation reaction seen in an inertial frame or there should be an additional phenomenon seen in the accelerated frame countering the effect of absorption. In this paper I rederive the Abraham–Lorentz–Dirac force from quantum electrodynamics, then I study the case of a uniformly accelerated charge. I show that in the accelerated frame, in addition to the absorption of photons due to the Unruh effect there should also be stimulated emission. The net effect of these phenomena on the motion of the charge is found to be zero.

scholarly journals Gravity as the Hidden Variable of Quantum Mechanics: Information-Matter Equation from Gravity

2020 ◽  
Author(s):  
Ahmed Farag Ali
Keyword(s):  
Quantum Mechanics ◽  
Inertial Frame ◽  
Black Hole Entropy ◽  
Geometric Interpretation ◽  
Speed Of Light ◽  
Problem Of Time ◽  
Hidden Variable ◽  
Local Inertial Frame ◽  
The Difference ◽  
The Universe

I localize gravity to match its measurements with the local inertial frame of special relativity. I find a geometric interpretation of the speed of light and mass. I find also the relation between every mass measured and the black hole entropy which introduce information-matter equation from gravity. Through localization of gravity, a timeless state of the universe emerges and the uncertainty principle does not hold since the velocity concept is replaced by distance. This would resolve the problem of time because timeless state of the universe emerges naturally and mathematically consistent. This would suggest that gravity form the hidden one variable of quantum mechanics which would complete the relation between quantum mechanics and gravity. We introduce also a principle of least computation which is achieved when the ratio equal to the difference in the process of local gravitational measurements.

ENERGY OF ELECTRIC CHARGE RADIATION AND ITS EFFECTS

2021 ◽  
Vol 0 (4) ◽  
pp. 5-8
Author(s):  
V.D. PAVLOV ◽  
Keyword(s):  
Angular Momentum ◽  
Electromagnetic Radiation ◽  
Electric Charge ◽  
Electromagnetic Waves ◽  
Circular Path ◽  
Proved Theorem ◽  
Centripetal Acceleration ◽  
Starting Point ◽  
The Difference ◽  
Accelerated Charge

It is believed that an electric charge moving along a circular path, i.e. with centripetal acceleration, it is necessary to emit electromagnetic waves. This applies, inter alia, to cyclotron radiation. The purpose of the work is to establish the conditions for the radiation of an electric charge, based on the significant differences between its tangential and centripetal accelerations. The relevance of the work is determined by the widespread use of devices that generate electromagnetic radiation due to the acceleration of electric charges, including X-ray units and magnetrons. The starting point is a credible statement. A number of mathematically correct transformations are performed with it. Therefore, the result is necessarily reliable. Sad experience shows that this logic is not available for many specialists. In the event that such a necessary reliable result contradicts the existing paradigm, preference is almost always given to the paradigm, regardless of the persuasiveness of the evidence. This circumstance is an almost insurmountable obstacle to obtaining new knowledge. After all, if it does not contradict the paradigm, then it is not new and does not represent any value. Electromagnetic radiation carries away energy. It follows from this that the energy of the radiating system changes during radiation. Associated with this is the well-known rule: the change in energy is equal to the perfect work. Four theorems are proved. Theorem 1. A tangentially accelerated charge emits electromagnetic waves. Theorem 2. A normally accelerated charge does not emit electromagnetic waves. Theorem 2 formalizes a circumstance well-known in mechanics that the centripetal force does not perform work (since the scalar product of orthogonal vectors must be zero). Theorem 3. Electric charge satisfies Newton's second law. When a hydrogen-like atom passes from one stationary state to another, the orbital angular momentum changes. The difference is attributed to a photon and is called the photon's spin. Theorem 4. The spin of a photon is zero. The defect in the angular momentum of an atom during radiation can easily be attributed to the nucleus of an atom and even to an electron.

The Origin of the Moon

1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol
Keyword(s):  
Chemical Composition ◽  
Solar System ◽  
The Moon ◽  
The Earth ◽  
The Difference ◽  
Origin Of The Moon

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.

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