Abraham-Minkowski Contradiction_Part 2
Like I mentioned on previous Part 1...The Lorentz Classical (No Minkowski) would never admit a "Rotational Field" (Irrotational) and Non Divergent Field (divergenceless) either...rigid as a stick pole Theory.
So all this Lorentz Soldiers are completely stuck on the 19th Century...
However, it is great we can also look at others work who are "Non Lorentz Soldiers" and be able to draw our own conclusions:
First principles approach to the Abraham–Minkowski controversy for the momentum of light in general linear non-dispersive media
Now that is a very well written work!!...without any inclinations, as they also speak about Lorentz as well, but keeping in mind the main essence from the work of the Two principal original authors...are Abraham and Minkowski.
And then...:
Am done...for this morning...lol
Like I mentioned on previous Part 1...The Lorentz Classical (No Minkowski) would never admit a "Rotational Field" (Irrotational) and Non Divergent Field (divergenceless) either...rigid as a stick pole Theory.
So all this Lorentz Soldiers are completely stuck on the 19th Century...
However, it is great we can also look at others work who are "Non Lorentz Soldiers" and be able to draw our own conclusions:
First principles approach to the Abraham–Minkowski controversy for the momentum of light in general linear non-dispersive media
Now that is a very well written work!!...without any inclinations, as they also speak about Lorentz as well, but keeping in mind the main essence from the work of the Two principal original authors...are Abraham and Minkowski.
Abstract
We study the problem of the definition of the energy–momentum tensor of light in general moving non-dispersive media with linear constitutive law. Using the basic principles of classical field theory, we show that for the correct understanding of the problem, one needs to carefully distinguish situations when the material medium is modeled either as a background on which light propagates or as a dynamical part of the total system. In the former case, we prove that the (generalized) Belinfante–Rosenfeld (BR) tensor for the electromagnetic field coincides with the Minkowski tensor. We derive a complete set of balance equations for this open system and show that the symmetries of the background medium are directly related to the conservation of the Minkowski quantities. In particular, for isotropic media, the angular momentum of light is conserved despite of the fact that the Minkowski tensor is non-symmetric. For the closed system of light interacting with matter, we model the material medium as a relativistic non-dissipative fluid and we prove that it is always possible to express the total BR tensor of the closed system either in the Abraham or in the Minkowski separation. However, in the case of dynamical media, the balance equations have a particularly convenient form in terms of the Abraham tensor. Our results generalize previous attempts and provide a first principles basis for a unified
understanding of the long-standing Abraham–Minkowski controversy without ad hoc arguments.
We study the problem of the definition of the energy–momentum tensor of light in general moving non-dispersive media with linear constitutive law. Using the basic principles of classical field theory, we show that for the correct understanding of the problem, one needs to carefully distinguish situations when the material medium is modeled either as a background on which light propagates or as a dynamical part of the total system. In the former case, we prove that the (generalized) Belinfante–Rosenfeld (BR) tensor for the electromagnetic field coincides with the Minkowski tensor. We derive a complete set of balance equations for this open system and show that the symmetries of the background medium are directly related to the conservation of the Minkowski quantities. In particular, for isotropic media, the angular momentum of light is conserved despite of the fact that the Minkowski tensor is non-symmetric. For the closed system of light interacting with matter, we model the material medium as a relativistic non-dissipative fluid and we prove that it is always possible to express the total BR tensor of the closed system either in the Abraham or in the Minkowski separation. However, in the case of dynamical media, the balance equations have a particularly convenient form in terms of the Abraham tensor. Our results generalize previous attempts and provide a first principles basis for a unified
understanding of the long-standing Abraham–Minkowski controversy without ad hoc arguments.
3. Electromagnetic field in matter as an open system
We begin our discussion by considering the electromagnetic field in matter as an open system, in which only the electro-magnetic field is assumed to have dynamics described by the macroscopic Maxwell equations. This is the case if the influence of the electromagnetic field on the macroscopic dynamics of the medium is negligible or if an external agent keeps the medium in a predetermined state of motion, independently of the values of the electromagnetic field. The validity of this approach is the same as the usual macroscopic electromagnetic theory [66,74,79] with the continuum
hypothesis assumed; no atomic systems will be studied in this framework...
We begin our discussion by considering the electromagnetic field in matter as an open system, in which only the electro-magnetic field is assumed to have dynamics described by the macroscopic Maxwell equations. This is the case if the influence of the electromagnetic field on the macroscopic dynamics of the medium is negligible or if an external agent keeps the medium in a predetermined state of motion, independently of the values of the electromagnetic field. The validity of this approach is the same as the usual macroscopic electromagnetic theory [66,74,79] with the continuum
hypothesis assumed; no atomic systems will be studied in this framework...
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