# Best Textbook on Electromagnetics

1. Nov 20, 2017

### vanhees71

Purcell is very confusing. If you want the relativity-first approach, better read Schwartz, Principle of Electrodynamics.

2. Nov 27, 2017

### wirefree

"They say: 'Look, these differential equations—the Maxwell equations—are all there is to electrodynamics; it is admitted by the physicists that there is nothing which is not contained in the equations. The equations are complicated, but after all they are only mathematical equations and if I understand them mathematically inside out, I will understand the physics inside out.' Only it doesn’t work that way. Mathematicians who study physics with that point of view—and there have been many of them—usually make little contribution to physics and, in fact, little to mathematics."

~The Man Himself

3. Nov 28, 2017

### Demystifier

I would like to see what mathematical physicists, such as @Urs Schreiber , have to say about that Feynman's quote.

4. Nov 28, 2017

### Urs Schreiber

I like to caution against this habit of dividing people studying field theory into camps (such as theoretic physicists, mathematical physicists, mathematicans studying physics) and then declaring what people in the camps do or do not understand; this seems misguided and alien to the nature of scientific investigation. There is the unique subject of quantum field theory, and we need all the tools and all the heuristics that we can get hold of to understand it. The implicit suggestion of many of these arguments that a theoretical physicists is somebody who should not be bothered with trying to understand what they are doing is not helping the field.

5. Nov 28, 2017

### Demystifier

I agree, but I would add also philosophers of physics to your camp list. They also contribute to full understanding of "what theoretical physicists do".

6. Nov 28, 2017

### Urs Schreiber

For what it's worth, I argued for not considering any such list of camps. Maybe academic bureaucracy forces researchers to pretend being part of a camp, but for the sake of science, one should try to transcend this. Certainly one should try to not further amplify it.

7. Nov 28, 2017

### Demystifier

Well, even if we do not call them "camps", it is certainly true that there are different styles of reasoning in physics. Some are more phenomenological than others, some are more mathematical than others, some are more philosophical than others, etc. Since each style has its advantages and disadvantages, it is wise to foster them all.

8. Nov 28, 2017

### vanhees71

Well, here I object. All that philosophers do is to confuse the physics. One should have a clear no-nonsense approach, which forbids philosophical gibberish to enter the scientific debate. Urs is of course right. From the more angles you study QFT (and as a prerequesite also classical FT, i.e., classical electrodynamics and General Relativity) the better you can understand it. I've still to learn all these methods of the axiomatic QFT community yet. So I'm very sure to not have understood QFT as well as it's possible to understand it, but for sure there's nothing philosophy can add to understanding any physics, and mathematics is not philosophy but according to a newer classification of the sciences belongs, together with informatics, to what's called a "structural science".

9. Nov 29, 2017

### Demystifier

I am not talking of philosophers as such. I am talking of physicists who attack physics problems from a philosophical point of view. A great example is Bell (who in the particle-physics community is best known for ABJ anomaly), whose philosophical point of view led him to Bell inequalities and Bell theorem.

10. Nov 29, 2017

### wirefree

In the few months I had the opportunity to spend at M.I.T. undertaking undergrad courses, I saw engineers-to-be of great caliber having to undertake a philosophy course on 'Minds & Machines'.

It confused & frustrated the Jesus out of some of them, with the class witnessing great talents giving up exasperated at all the twin-Earth nonsense.

But I recognised the brightest kid in class to possess the malleability of mind to straddle laughingly through the brick-meets-mortar world of Newtonian mechanics as well as he did through the world of thought experiments that that course in philosophy of minds & machines entailed.

This was way back in 2006, but I've held on to the image of that brilliant kid who sat, always smiling, on the front row seat.

11. Nov 29, 2017

### wirefree

The Classical Theory of Fields by Landau & Lifshitz (3rd ed.)

View attachment 215809

This book was reviewed on Smodak's suggestion. And his opinion stands tall - it speaks at a slightly higher level than other suggestions I've reviewed so far. At the very least, the wave equations he derives have little semblance to the more elementary representation I've come to recognise.

Even so, the author engages the reader in a conversation, and it's not one with a didactic tone. In so far as that goes, Landau out-does my initial concern of a text that is the raison d'etre of this thread.

Last edited: Nov 29, 2017
12. Nov 29, 2017

### vanhees71

Well, for me Bell's greatest achievement in this part of his work was to clearly formulate a scientific question to be answered by an experiment which is to some extent related to the gibberish philosophers (including some philospher physicists like Bohr and Heisenberg) made concerning the apparent "problems of quantum theory", which in fact are no problems but features. To be sure about the latter Bell's theoretical work paved the way to the experimental confirmation in the following decades, including experimental results of an amazing statistical significance. I'd say, today QT is the physical theory with the highest significance of its empirical confirmation.

13. Nov 29, 2017

### vanhees71

Hm, why should one give up to study engineering only because of some stupid philosophy course? You listen to it, pass the exam and forget about it as soon as possible ;-). That's it.

14. Nov 30, 2017

### Demystifier

If we accept the Kuhn's difference between normal science and paradigm-shift science, I would say that philosophy is quite useless in normal science, but very important in paradigm-shift science. So you are right, normal scientists don't need philosophy.
On the other hand, Bohr, Heisenberg, and to some extent Bell, were paradigm-shift scientists. (If you are not sure about Bell, I can explain.)

15. Nov 30, 2017

### vanhees71

Well, Kuhn's ideas in my opinion are valid for the rare exceptions, where really a big breakthrough is reached or necessary by empirical facts. In the young history of modern physics this happened 3 times: The step from Aristotelian physics to Galilei-Newtonian mechanics; the discovery of the relativistic spacetime structure (special and general relativity); the discovery of quantum theory. The bulk work of physicists in pure research is the application of well-established models and theories to describe concrete cases, e.g., using QT in solid-state physics to understand, from first principles or via effective models, the properties of the matter around us (reaching from transport coefficients like viscosity or electric conductivity to phase transitions and so on).

The physical theories on a fundamental level are amazingly stable, and paradigm shifts happen very rarely (perhaps at most once in a century). What phillosophers describe is often far from reality, and that's also the case in their analysis of how research works. Another example is Popper. Of course, he is right in saying that you can never empirical prove anything but falsify predictions of theories. However, practice shows that one rather very often a model or theory gets "empirically confirmed", even when physicists are struggling to find a contradiction (e.g., with the Standard Model of elementary particle physics, which is too successful at the moment to bring the long-expected breakthrough in physics beyond the Standard Model, motivated by finding the way to cure some of its intrinsic shortcomings like the fine-tuning/hierarchy problems; the nature of dark matter, if there is any after all, etc. etc.).

16. 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
17. 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.

18. 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
19. 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 ;-)).

20. Dec 4, 2017

### 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.

21. Dec 4, 2017

### vanhees71

???

22. Dec 4, 2017

### Buffu

Ray Kurzweil ?

23. Dec 7, 2017

### 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.

24. Dec 8, 2017

### 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 ;-)).