Relativistic causality and conservation of energy in classical electromagnetic theory

Kislev, A.; Vaidman, Lev

doi:10.1119/1.1512901

Cited by 6 publications

(8 citation statements)

References 17 publications

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“…energy non-conservation [11]. 2 On the other hand, the indirect support for field-less electrodynamics is provided by numerous experiments [12,13,14,15,16,17,18,19], which can be interpreted as an evidence of instantaneous action-at-a-distance.…”

Section: Introductionmentioning

confidence: 99%

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Classical Electrodynamics without Fields and the Aharonov-Bohm effect

Stefanovich

2008

Preprint

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The Darwin-Breit Hamiltonian is applied to the Aharonov-Bohm experiment. In agreement with the standard Maxwell-Lorentz theory, the force acting on electrons from infinite solenoids or ferromagnetic rods vanishes. However, the interaction energies and phase factors of the electron wave packets are non-zero. This allows us to explain the Aharonov-Bohm effect without involvement of electromagnetic potentials, fields, and topological properties of space.

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Section: Introductionmentioning

confidence: 99%

“…The explanation of this paradox suggested in[11] is not satisfactory, because it assumes interaction of overlapping light waves, which is known to be negligibly small from QED.…”

mentioning

confidence: 99%

Classical Electrodynamics without Fields and the Aharonov-Bohm effect

Stefanovich

2008

Preprint

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“…Now let both charges accelerate at the same time and rate. Kislev and Vaidman [16] calculated their radiation:…”

Section: The Clue: the Non-radiating Accelerating Pairmentioning

confidence: 99%

“…Radiation is therefore barely noticed. A more precise account, in the spirit of [16], would invoke radiation emitted by both the main and envelope charges, but with destructive interference, leaving only little net radiation exchanged. It is only the accelerating frame's walls, whose dipoles are now polarized by the charge, that will radiate outwards.…”

Section: Radiation Of a Gravity-resisting Chargementioning

confidence: 99%

Charge Acceleration and Field-Lines Curvature: A Fundamental Symmetry and Consequent Asymmetries

Elitzur¹,

Cohen

Beniamini³

2011

AIP Conference Proceedings

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When a charge accelerates, its field-lines curve in a typical pattern. This pattern resembles the curvature induced on the field-lines by a neighboring charge. Not only does the latter case involve a similar curvature, it moreover results in attraction/repulsion. This suggests a hitherto unnoticed causal symmetry: charge acceleration  field curvature. We prove quantitatively that these two phenomena are essentially one and the same. The field stores some of the charge's mass, yet it is extended in space, hence when the charge accelerates, inertia makes the field lag behind. The resulting stress in the field stores some of the charge's kinetic energy in the form of potential energy. The electrostatic interaction is the approximate mirror image of this process: The potential energy stored within the field turns into the charge's kinetic energy. This partial symmetry offers novel insights into two debated issues in electromagnetism. The question whether a charge radiates in a gravitational field receives a new twist: If all the charge's fieldlines end with opposite charges that also resist gravity, no radiation is expected. Similarly for the famous absence of a physical manifestation of the Maxwell equations' advanced solution: Just as Einstein argued, the reason for this absence is probabilistic rather than reflecting some inherent time-asymmetry. Despite the apparent equivalence between the "ontological" and "instrumentalist" viewpoints concerning the physical reality of field-lines, there may be cases in which their experimental predictions differ.

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“…Certainly, there are some works considering the energy conservation law in the special relativity (SR). They, however, focus only on microscopic phenomena with relativistic speeds such as retardation effect on energies of particles in electromagnetic field [2][3][4]. In this paper, we carry out a thought experiment concerning the generation of the MTWMM and thereby theoretically study whether the TRE is conserved.…”

Section: Introductionmentioning

confidence: 99%

Violation of the Relativistic Energy Conservation Law and Einstein’s Principle of Relativity Caused by the Generation of Mechanical Transverse Waves in a Moving Medium

Kawashima¹

2021

Preprint

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We study the effect of the generation of the mechanical transverse wave (MTW)　travelling in the opposite direction (OD) to a moving medium (MM) on the relativistic energy conservation law (RECL). From the viewpoint of the relativity of simultaneity (RS), the time on the coordinate coinciding with the advance end of the wave (AEW) travelling toward the rear of the MM passes faster than that on the coordinate coinciding with the wave source (WS). Then the AEW in the MM travels forward compared to that in the rest frame of reference (RFR) which is stationary relative to the medium when the time on the coordinate coinciding with the WS is same for each inertial frame of reference (IFR). Hence, the coordinate interval (CI) between the AEW and WS in the MM is observed to be larger than that between them in the RFR. We show that this difference holds true for the CI of any portion having transverse velocities mutually converted by the Lorentz transformation (LT). This difference in the CI leads to that in the rest mass (RM). We demonstrate that the RM included in wave motion (WM) in the MM is larger than one included in WM in the RFR when comparing the portions having transverse velocities mutually converted by the LT. This relation holds true for all portions in WM. Therefore, the total coordinate interval of the portion (CIP) and total RM (TRM) included in WM in the MM (WMMM) are large compared to them included in WM in the RFR. Furthermore, we compare the relativistic kinetic energy (RKE) of the MTW travelling in the OD to the MM (ODMM) with that of the MTW propagating in the direction vertical to the moving direction of the medium. We prove that the CIP and RM included in the former MTW are larger than them included in the latter MTW when comparing each portion with the same transverse velocity (TV). Moreover, the total CIP and TRM included in the former MTW are also large compared to them included in the latter MTW. The reason for these is that the latter CIP and RM are equal to them in the RFR when comparing the portions having transverse velocities mutually converted by the LT. On the other hand, the energy supplied to generate each MTW is the same. From these, we demonstrate that the RKE of the MTW travelling in the ODMM can be larger than the total relativistic energy (TRE) of the MTW propagating in the direction vertical to the moving direction of the medium. Consequently, we propose a violation of the RECL and Einstein’s principle of relativity (EPR) because the TRE is not necessarily conserved in the IFR in which the medium is moving.

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Relativistic causality and conservation of energy in classical electromagnetic theory

Cited by 6 publications

References 17 publications

Classical Electrodynamics without Fields and the Aharonov-Bohm effect

Classical Electrodynamics without Fields and the Aharonov-Bohm effect

Charge Acceleration and Field-Lines Curvature: A Fundamental Symmetry and Consequent Asymmetries

Violation of the Relativistic Energy Conservation Law and Einstein’s Principle of Relativity Caused by the Generation of Mechanical Transverse Waves in a Moving Medium

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