[Paper Review] Plane wave in a moving medium and resolution of the Abraham-Minkowski debate by the special principle of relativity

Changbiao Wang|arXiv (Cornell University)|Jun 6, 2011

Quantum and Classical Electrodynamics21 references4 citations

TL;DR

This paper resolves the Abraham-Minkowski debate on electromagnetic momentum in moving media by applying the special principle of relativity. It demonstrates that Minkowski's momentum formulation is the only one consistent with Lorentz invariance and four-vector structure for plane waves in moving, non-dispersive, lossless media, while showing that the Poynting vector does not always represent real power flow and that momentum conservation requires relativistic principles for unique determination.

ABSTRACT

In this paper, a novel approach for resolution of the Abraham-Minkowski debate is proposed, in which the principle of relativity is used to uniquely determine the light momentum formulation for a plane wave in a moving non-dispersive lossless isotropic uniform medium. It is shown by analysis of the plane-wave solution that, (1) there may be a pseudo-power flow when a medium moves, and the Poynting vector does not necessarily denote the direction of real power flowing, (2) Minkowski's light momentum and energy constitute a Lorentz four-vector in a form of single photon or single EM-field cell, and Planck constant is a Lorentz invariant, (3) there is no momentum transfer taking place between the plane wave and the uniform medium, and the EM momentum conservation equation cannot be uniquely determined without resort to the principle of relativity, and (4) the moving medium behaves as a so-called "negative index medium" when it moves opposite to the wave vector at a faster-than-dielectric light speed. It is also shown by analysis of EM-field Lorentz transformations that, when a static electric (magnetic) field moves in free space, neither Abraham's nor Minkowski's formulation can correctly describe a real electromagnetic momentum; as an application of this principle, the classical electron mass-energy paradox is analyzed and resolved. Finally, a general EM momentum definition is proposed, and according to this new definition, the traditional "Abraham-type" and "Minkowski-type" momentums in the dispersion wave-guiding systems, such as regular dielectric-filled metallic waveguides, are found to be included in the same momentum formulation, but they appear at different frequencies.

Motivation & Objective

• To resolve the long-standing Abraham-Minkowski debate on electromagnetic momentum in moving media.
• To determine which momentum formulation—Abraham or Minkowski—is consistent with the principle of relativity in a relativistic framework.
• To clarify the physical meaning of the Poynting vector in moving media, particularly whether it always indicates real power flow.
• To establish a general electromagnetic momentum definition that unifies Abraham- and Minkowski-type momenta in waveguiding systems.
• To resolve the classical electron mass-energy paradox using relativistic EM field transformations.

Proposed method

• Analyzes plane-wave solutions in a moving, non-dispersive, lossless, isotropic medium using relativistic electrodynamics.
• Applies Lorentz transformations to electromagnetic fields to examine momentum and energy in different inertial frames.
• Demonstrates that Minkowski's momentum and energy form a Lorentz four-vector for single photons or EM-field cells.
• Uses the invariance of Planck’s constant under Lorentz transformations to validate the four-vector structure.
• Shows that momentum conservation cannot be uniquely determined without invoking the principle of relativity.
• Introduces a generalized EM momentum definition that includes both Abraham- and Minkowski-type momenta as frequency-dependent components.

Experimental results

Research questions

• RQ1 Which formulation of electromagnetic momentum—Abraham or Minkowski—is consistent with the special principle of relativity in a moving medium?
• RQ2 Does the Poynting vector always represent the direction of real power flow in a moving medium?
• RQ3 Can a moving medium exhibit negative-index-like behavior, and under what conditions?
• RQ4 How does the relativistic transformation of static electric and magnetic fields affect the interpretation of electromagnetic momentum?
• RQ5 Can the classical electron mass-energy paradox be resolved using relativistic EM field transformations?

Key findings

• The Poynting vector does not necessarily represent real power flow in a moving medium, as pseudo-power flow can arise due to motion.
• Minkowski's momentum and energy form a Lorentz four-vector when expressed per photon or EM-field cell, and Planck’s constant is a Lorentz invariant.
• No momentum transfer occurs between a plane wave and a uniform moving medium, and momentum conservation requires the principle of relativity for unique determination.
• When a medium moves opposite to the wave vector at super-dielectric speeds, it behaves as a negative-index medium.
• Abraham’s and Minkowski’s formulations fail to describe real electromagnetic momentum in static fields moving through free space.
• A generalized EM momentum definition unifies Abraham- and Minkowski-type momenta in waveguiding systems, with each appearing at different frequencies.