What happens to energy and momentum when two oppositely-moving wave pulses overlap?

Gauthier, Nicolas

doi:10.1119/1.1575765

Cited by 8 publications

(3 citation statements)

References 6 publications

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“…The following explanation of this paradox was suggested by Kislev and Vaidman [KV02]: They claim that there is another energy term missed in the above analysis, which is related to the interference of electromagnetic waves emitted by the two particles 62 and which restores the energy balance. This explanation does not look plausible, because there is actually no interaction energy associated with the interference of light waves: The interference results in a redistribution of the wave's amplitude (formation of minima and maxima) and the wave's local energy in space, while the total energy of the wave remains unchanged [Gau03]. In other words, there is no interaction between photons.…”

Section: Kislev-vaidman "Paradox"mentioning

confidence: 99%

Relativistic Quantum Dynamics

Stefanovich¹

2018

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This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds systematically from the principle of relativity and postulates of quantum measurements to the renormalization in quantum electrodynamics. In the second part of the book "Quantum theory of particles" this traditional approach is reexamined. We find that formulas of special relativity should be modified to take into account particle interactions. We also suggest reinterpreting quantum field theory in the language of physical "dressed" particles. This formulation eliminates the need for renormalization and opens up a new way for studying dynamical and bound state properties of quantum interacting systems. The developed theory is applied to realistic physical objects and processes including the energy spectrum of the hydrogen atom, the decay law of moving unstable particles, and the electric field of relativistic electron beams. These results force us to take a fresh look at some core issues of modern particle theories, in particular, the Minkowski space-time unification, the role of quantum fields and renormalization as well as the alleged impossibility of action-at-a-distance. A new perspective on these issues is suggested. It can help to solve the old problem of theoretical physics -a consistent unification of relativity and quantum mechanics.

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Section: Kislev-vaidman "Paradox"mentioning

confidence: 99%

Relativistic Quantum Dynamics

Stefanovich¹

2018

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“…In [8] the double slit interference with monochromatic waves 7 is analyzed and it is said that energy-momentum is conserved only after spatial average. On the other hand, e.g., [4] shows that Eq. (9) is the correct one for the case of two plane 5 See Figure 1 for the defintion of regions B 1 , B 2 , B 3 , B ′ 3 , C 1 ,C 2 , C ′ 1 and C ′ 2 .…”

Section: Introductionmentioning

confidence: 99%

“…See [26] and also [3]. 4 Notice that Ta = T ab θ b , where T ab are the components of the usual [15] energymomentum tensor of Maxwell theory. Discussions about the appropriateness for the use of the usual energy-momentum tensor for the description of energy-momentum propagation are given in [15,17].…”

Section: Introductionmentioning

confidence: 99%

Superposition principle and the problem of additivity of the energies and momenta of distinct electromagnetic fields

Notte-Cuello

Rodrigues

2008

Reports on Mathematical Physics

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In this paper we prove in a rigorous mathematical way (using the Clifford bundle formalism) that the energies and momenta of two distinct and arbitrary free Maxwell fields (of finite energies and momenta) that are superposed are additive and thus that there is no incompatibility between the principle of superposition of fields and the principle of energy-momentum conservation, contrary to some recent claims. Our proof depends on a noticeable formula for the energy-momentum densities, namely, Riesz formula ⋆T a = 1 2 ⋆ (F θ aF ), which is valid for any electromagnetic field configuration F satisfying Maxwell equation ∂F = 0.

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Interference-induced enhancement of intensity and energy of a quantum optical field by a subwavelength array of coherent light sources

Kukhlevsky

2008

Appl. Phys. B

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Recently, we have showed a mechanism that could provide a great transmission enhancement of the light waves passed through subwavelength aperture arrays in thin metal films not by the plasmonpolariton waves, but by the constructive interference of diffracted waves (beams generated by the apertures) at the detector placed in the far-field zone. We now present a quantum reformulation of the model. The Hamiltonian describing the interference-induced enhancement of the intensity and energy of a multimode quantum optical field is derived. Such a field can be produced, for instance, by a subwavelength array of coherent light sources.PACS numbers: 03.70.+k, 03.75.-b, 03.50.-z Since the demonstration of enhanced transmission of light through a subwavelength metal apertures in the study [1], the phenomenon attracts increasing interest of researchers working in the field of nanooptics and nanophotonics [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. It is generally accepted [25] that the excitation and interference of plasmon-polaritons play a key role in the process of enhancement in the most of experiments (see, the recent reviews [26,27]). Recently, we have showed a mechanism that could provide a great transmission enhancement of the light waves passed through subwavelength aperture arrays in thin metal films not by the plasmon-polariton waves, but by the constructive interference of diffracted waves (beams generated by the apertures) at the detector placed in the far-field zone [28]. According to the model, the beams generated by multiple, subwavelength apertures can have similar phases and can add coherently. If the spacing of the apertures is smaller than the optical wavelength, then the phases of the multiple beams are nearly the same and beams add coherently (the light power and energy scales as the number of light-sources squared, regardless of periodicity). If the spacing is larger, then the addition is not so efficient, but still leads to enhancements and resonances (versus wavelength) in the total power transmitted. The analysis [28] is based on calculation of the energy flux (intensity) of a beam array by using Maxwell's equations for classic, non-quantum electromagnetic fields. The enhancement mechanism was interpreted as a non-quantum analog of the superradiance emission of a subwavelength ensemble of atoms (the light power and energy scales as the number of light-sources squared, regardless of periodicity) predicted by the Dicke quantum model [29]. We now present a quantum reformulation of our model. The Hamiltonian describing the interference-induced enhancement of the intensity and energy of a multimode quantum optical field is derived. Such a field can be produced, for instance, by a subwavelength array of coherent light sources.With the objective of quantizing the electromagnetic (EM) field, it is convenient to begin with consideration of the Hamiltonian of a classical (non-quantum) EM field based on Maxwell's equations. The detailed description of the problem can be found i...

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What happens to energy and momentum when two oppositely-moving wave pulses overlap?

Cited by 8 publications

References 6 publications

Relativistic Quantum Dynamics

Relativistic Quantum Dynamics

Superposition principle and the problem of additivity of the energies and momenta of distinct electromagnetic fields

Interference-induced enhancement of intensity and energy of a quantum optical field by a subwavelength array of coherent light sources

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