- #71
Jano L.
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What's the advantage?
It depends on what is it you are trying to do with the unit system. For basic lab measurements of macroscopic properties SI is great. In theoretical physics, sometimes one deals with such involved calculations that obscuring relativistic nature of the theory by using the asymmetric SI convention for units of E, B is not reasonable.I don't understand why anyone would say that SI is sub-optimal.
vanhees71 said:It is interesting that you find bad what I'd call a good thing about the traditional Gaussian units ;-). I think it's a good thing not to introduce superfluous "constants". Why should the (classical) vacuum have another permeability and permittivity than 1? The classical vacuum is really empty after all, and why should there be anything to be polarized, i.e., react to the electromagnetic field.
I agree that the unrationalized nature of the traditional Gaussian units, i.e., the appearance of (superfluous ;-)) factors of [itex]4 \pi[/itex] in the fundamental equations is not nice either, but there is no problem to use rationalized Heaviside-Lorentz units as is common in theoretical HEP.
Of course, the SI is the right choice for experimental physics and engineering, because it gives nicely handable numbers for everyday situations, i.e., 1 V and 1 A are common everyday voltages and currents, respectively. You'd also not give your height in fm or your weight in GeV ;-).
vanhees71 said:The physics of the matter is hidden in the constitutive relations, which usually are given in linear-response approximation (see Jackson's or Schwinger's books on this; I'm not aware that there is a textbook writing the relations in relativistically covariant form, which is another great sin in didactics of theoretical electromagnetism, but that's another story).
vanhees71 said:I further don't understand in which sense you do not need averaging (coarse graining) to go from the microscopic description (QED) to a macroscopic approximation (classical macroscopic electrodynamics). Also the quantities in post #46 only make sense to me in a macroscopic picture. In the microscopic formalism all these quantities are represented by operators! The book by Craig mentions the usual coarse-graining argument already on page 5!
marmoset said:I believe the microscopic magnetization in iron for example can be measured by spin-polarized neutron scattering. My reference is the article 'The microscopic magnetization: concept and application' by L.L. Hirst which begins by discussing the view that magnetization is a macroscopic quantity defined by averaging.
cabraham said:[...]
Like I said, I've used cgs in magnetics design and consistently arrived at the correct answer. But SI for me makes more sense to a widget designer who works in industry, not a theoretical research lab. To me, I like the distinction between H & B. They are both important and neither is "derived" from the other. In Halliday-Resnick elementary physics, the authors stated that the decision to treat B as the basis, and regard H as derived from B, is purely arbitrary. I concur.
[...]
Neither is the more "fundamental" at all. Our universe consists of free space as well as molecular structures and quantized atomic energy levels. Polarization, electric or magnetic, is just as "real" as a vacuum. Besides, more than one poster has attempted to propagate the crackpot heresy that B is the counterpart of E, while H is that to D. This is nonsense.
Claude
Jano L. said:Claude, in macroscopic theory I agree with you, all EBDH are equally important. However nowadays we know about atoms and molecules and have the possibility to understand the macroscopic theory on the basis of microscopic theory. In microscopic theory, 4 independent field quantities make little sense. Usually we think that there is only one EM field with two components: electric and magnetic, as vanhees71 said. These may be denoted as ##\mathbf e, \mathbf b## (microscopic) and their meaning (definition) is that they give us the force on a point-like test particle
$$
\mathbf F = q\mathbf e + q\frac{\mathbf v}{c} \times \mathbf b.
$$
So in this picture, the fields e,b are more basic, since they directly give force. The macroscopic fields E,B can then be sought as a kind of average of these microscopic fields. The fields D,H are then necessarily only auxiliary quantities that play little role in the logic of microscopic theory; there is little reason to consider microscopic fields ##\mathbf d,\mathbf h##.
If I'm generating a mag field with a current, H is medium-independent and canonical.
But the attractive force depends on μH since it depends on B. So a charge in the center of the loop will incur a force of e(vXB) = e(vXμH) = eμ(vXI/2R).
Jano L. said:I do not know what do you mean by the word "canonical". Field H depends on the conduction currents which are well controlled and can be easily calculated as their function. Field B depends also on the properties of the medium and may be harder to calculate, especially in ferromagnetic material.
This does not imply any of them as more basic.
My point exactly. I've been saying the same since day 1. I concede to your point with no argument whatsoever. The current loop was brought up by me not to establish H as a basis, but rather to illustrate the futility of trying to establish either as more basic. We agree perfectly.
The force on charge is established to be e(vXB) in vacuum, where μ = μ0. In medium, I do not think one can simply take the same formula. The microscopic field in the medium varies on atomic length scale and most probably neither H nor B is sufficient to find the force.
I would say, in macroscopic theory, both fields are equally important and neither seems more basic. But in microscopic theory, which is more detailed than the macroscopic theory and explains it in more elementary notions, there is place only for one magnetic field. It used to be denoted by ##\mathbf h## but I think it should be written as ##\mathbf b##.
Jano L. said:The main reason I consider ##\mathbf B## as basic is that microscopic theories give it as a result of (some of many kinds of) averaging of the microscopic field ##\mathbf b##. While ##\mathbf H## does not seem to be result of such direct averaging - there is no microscopic##\mathbf h##. Instead, ##\mathbf H## is defined only in macroscopic theory as the quantity that gives only part of total current density - the conduction current density due to mobile charges - via
$$
\nabla \times \mathbf H = \mathbf j_{\text{cond.}}
$$
Jano L. said:Of course, both fields are present and non-zero in the dielectric. The distinction between macro and micro is that macroscopic field is that used in basic theory when we ignore the atomic structure of the material. The microscopic field varies randomly on the scale of molecules since it reflects their presence.
vanhees71 said:Formally it's pretty simple: The fundamental microscopic description is quantum electrodynamics for many-body systems, macroscopic is a description derived from that via the one or other type of coarse graining, i.e., the derivation of tranport equations for the matter coupled to mean fields (Vlasov-Boltzmann-Uehling-Uhlenbeck -> Vlasov-Boltzmann) and some simplifications. The usual "macroscopic classical electrodynamics" we learn in introductory E+M is then linear response theory, where "matter" is reduced to the electromagnetic four-current and consititutive relations (response functions like the dielectric function, conductivity, ...).
To really establish these connections is, of course, rather complicated.
mikeph said:I just think of mu as dB/dH in nonlinear materials. Surely that works in analytic evaluations of energy etc.?
DrDu said:… L. L. Hirst,The microscopic magnetization: concept and application, Reviews of Modern Physics, Vol. 69, No. 2, April 1997 …