Best Textbook on Electromagnetics

1. Nov 30, 2017

Demystifier

Yes, those were 3 big paradigm shifts that required big philosophy. But there are also many small paradigm shifts (or changes in perspective, if you like that term more) which require a small amount of philosophy.

Can you tell one great idea in theoretical physics that didn't involve any philosophy at all?
Take, for instance, the idea of renormalization in otherwise divergent QFT. How it does not contain philosophy?

Last edited: Nov 30, 2017
2. Nov 30, 2017

vanhees71

I don't know any great idea in theoretical physics that involved any philosophy. The great breakthroughs were all triggered by empirical evidence or intrinsic inconsistencies of models: The lack of Galilei invariance of Maxwell electrodynamics, which has resulted from a theoretical analysis of the collected experimental work on electromagnetic phenomena, either implied the existence of a preferred reference frame (usually attributed to the rest frame of a fictitious "aether") or, as has been clearly seen finally by Einstein, made a revision of the spacetime model necessary. The latter solution prevailed all empirical tests so far and thus is considered the valid theory today. The same holds for quantum mechanics: A plethora of findings involving matter and radiation (and their mutual interaction) indicated that classical physics cannot be right (black-body radiation, low-temperature phenomenology in thermodynamics like the specific heat of solids, atomic structure and the stability of matter,...), and a about 25-year long struggle finally lead to modern quantum theory. Of course, unfortunately, after the theory had been discovered, a lot of philosophical "thinking" has been produced, but that was hindering the involved scientists (Schrödinger and Einstein, for example) partially rather than bringing progress in their research. Those physicists who were not too much concerned about the new worldview, which of course indeed has been emerged from quantum theory (particularly the stochastic nature of the fundamental physical laws in an "irreducible" way and the consequence of indeterministic laws), pushed the new theory forward to a plethora of successful applications to physics rather than getting trapped in useless philosophical quibbles.

3. Nov 30, 2017

Demystifier

I think we are using different definitions of "philosophy".

Let me give an example. The mathematical proof that
1) The Einstein's 1905 non-covariant 3-dimensional view of relativity
is equivalent to
2) Minkowski covariant 4-dimensional view of relativity
is not philosophy. However, the decision to choose one approach or the other in teaching introductory special relativity is, in my dictionary, a matter of philosophy. I anticipate that you wouldn't call it "philosophy", but how do you choose which approach to use? I don't think that you make the choice by scientific method.

Last edited: Nov 30, 2017
4. Dec 1, 2017

vanhees71

Well, I'm a bit more down to earth :-)). Einstein's paper of 1905 is Einstein at his best, i.e., before getting involved (and in my opinion for the disadvantage of physics lost) in philosophy. His emphasis is as physical as it can be, and it's not so much the math of relativity, which has been known for about 10-20 years before (starting with Voigt's symmetry transformations of the Maxwell equations, which already were very close to Lorentz's and Poincare's discovery of the Lorentz group), but the essential physical features of electromagnetism, which (a) was the lack of symmetry not present in the Maxwell equations but in the contemporary interpretation of them (which I read as a clearly abandoning unjustified "philsophical prejudices"!) and (b) the possibility of the "coexistence" of the special principle of relativity and the invariance of the phase-velocity of free electromagnetic waves using a different spacetime model. The latter point is particularly important, because it enabled Einstein to immediately identify the solution of the invariance problem of the Maxwell equations in the sense of the special principle of relativity as affecting all physics, including mechanics.

Minkowski's merit is to make the mathematical structure of the theory explicit and to develop the adequate mathematical formulation in terms of four-vectors/tensors in a pseudo-Euclidean (Lorentzian) affine space. Of course, when teaching relativity I use this much simpler formulation to introduce the theory and explain the (1+3)-split introducing an inertial reference frame using the covariant formalism. This helps a lot in understanding relativity. At least, for me Minkowski's famous talk, written down as a paper that is a masterpiece in both mathematical style and pedagogics, was a revelation, when I first read it when I was still at highschool.

So also the choice of how to teach relativity is not a philsophical issue but simple an issue of convenience (I hope not only for me as a teacher but also for the students listening to my lectures ;-)).

5. Dec 4, 2017 at 8:54 AM

wirefree

Let's find a new norm, shall we...?

If it's true when he says, and I won't name who, that the law of accelerating returns affords humanity not 100 but 20,000 years of progress in the 21st century, then I propose we strap in for that.

6. Dec 4, 2017 at 9:04 AM

vanhees71

???

7. Dec 4, 2017 at 3:07 PM

Buffu

Ray Kurzweil ?

8. Dec 7, 2017 at 1:16 AM

wirefree

The economy of this statement attracted me to it.

And so the face-off continues...

Electromagnetic Fields by Roald K. Wangsness (2nd ed.)

NOTE: This book is available on Scribd as part of their university students subscription.

1) Wave equations

Modulo my limited exposure, the level of instruction in this text resonates incredibly with my undergraduate course.

Once again, like previous authors reviewed, there is a degree of engagement with the reader; for example, when the authors says "We can eliminate one of the fields in the following way...", he furnishes a reason for proceeding in the manner in which he does, as opposed to the banal & unengaging "Taking the dot product" route.

Wangsness might end up being a good find. I like how the chapters are several many, with each key topic deserving one.

There's an element of quirkiness as well, as when how a chapter 23 titled 'System of Units - A Guide for the Perplexed' pops out of nowhere.

2. Poynting Theorem

This portion is covered is the same level of detail as Sadiku, but the brevity of the solution stands out to some extent.

9. Dec 8, 2017 at 2:58 AM

vanhees71

Well, units indeed leave me perplexed, and it's good to have a chapter on it. I was just preparing a review for the Theory 3 lecture. I was a bit surprised that it's hard to find a clear instruction how to convert from Gaussian to SI units. So I had to figure it out for myself, which took me an entire morning ;-). This experience the more solidified my opinion that the best units to be used are Heaviside-Lorentz units. Unfortunately the SI units have been inspired by the unrationalized Gaussian (or some other of the zillions of different CGS units around in the history of the subject), so that you get convenient simple powers of 10 (sometimes with appropriate powers of the speed of light) between the SI and CGS units only when using the unrationalized CGS units. That's the origin of the somewhat artificial sounding definition of the Ampere in the SI with the force between two infinite infinitesimally thin wires carrying 1 A when a force per unit length of $2 \cdot 10^{-7} \text{N}/\text{m}$ acts between them. This makes $1 \, \text{statA} \hat{=} \frac{1}{10 c} \text{A} \, \text{m}/\text{s}$, where the $\text{statA}=\sqrt{\text{dyn}} \text{m}/\text{s}$ is the unit of currents in Gaussian CGS units ;-).

The reason for the additional factor $1/c$ is that obviously the SI Ampere has been defined in view of the magnetic unit abA=Bi (Bi for Biot) from the EMU CGS units, for which $1 \, \text{abA} = 100 c \text{statA}=10 \text{A}$.

It's rather confusing, and one must admit for practical purposes the SI is much simpler, but it's ugly from a theoretical point of view.

The best system at the end are of course "natural units", which you get from the SI by setting $\mu_0=\epsilon_0$ and consequently $c=1/\sqrt{\mu_0 \epsilon_0}=1$. Then in natural units the SI becomes the same as Heaviside-Lorentz units. In HEP one sets $\hbar=c=1$, and then charges are dimensionless, which makes it all very transparent and easy, but the numbers for household currents and voltages become a bit unhandy (express, e.g., 1 A in terms of natural units ;-)).